BROAD STREET SCIENTIFIC
VOLUME 6 | 2016-2017
The North Carolina School of Science and Mathematics Journal of Student STEM Research
KRYPTON, above and on front cover, is a colorless and odorless noble gas used in fluorescent lighting and photography flash lamps.
BROAD STREET SCIENTIFIC The North Carolina School of Science and Mathematics Journal of Student STEM Research ncssm.edu/bss VOLUME 6 | 2016-2017
TABLE of CONTENTS
Letter from the Chancellor
Words from the Editors
Broad Street Scientific Staff
Essay: Gene Therapy: The Medical Frontier or Time to Curb our Enthusiasm?
SAMUEL LI, 2018
Determining the Geometries of Methyltransferase Reactions in DENV Using Model
TESIA BOBROWSKI, 2017 ONLINE
Analysis of Electrocyclic Reactions Using Woodward-Hoffman Rules and Frontier Molecular
KATHERINE MUELLER AND NEIL PALKAR, 2017 ONLINE
Fascin Expression and Purification and Formation of Fascin-Actin Paracrystal as a Scaffold for
Future Plasmonic Nanofibers
TEJAS PRUTHI, 2018 ONLINE
Targeting Cancer Through Altering Hyaluronan Synthesis and Degradation
EMMA GARVAL, 2017
Drastic Conditions Call for Drastic Measures: the Viability of Terrestrial Extremophiles
in Simulated Martian UV Radiation
ANA SOFIA UZSOY, 2017
Physics and Engineering 44
Variation of Maximum Levitation Distance in Type-II Superconductors Due to Changing
Magnetic Dipole Moments
OMKAR APTE, 2017
The Effects of Shape and Mass of a Particle on its Stability in a Standing Wave Acoustic
RENZO BENAVIDES AND BRENDAN KANE, 2017
Mathematics and Computer Science 54
Using Differential Equations to Determine the Effects of Bt Corn on Monarch Butterfly
(Danaus plexippus) Populations
AMBER DETWILER, 2018 ONLINE
3-tone k-colorings of Graphs
CARY SHINDELL, 2017
Feature Article 65
An Interview with Dr. Rachel Levy â€˜85
LETTER from the CHANCELLOR The most exciting phrase to hear in science, the one that heralds the most discoveries, is not ‘Eureka!’ (I’ve found it!), but ‘That’s funny…’ ~ Isaac Asimov I am proud to introduce the sixth edition of the North Carolina School of Science and Mathematics’ (NCSSM) scientific journal, Broad Street Scientific. Each year students at NCSSM conduct significant scientific research, and Broad Street Scientific is a student-led and student-produced showcase of some of the outstanding research being done by students at NCSSM. The importance of scientific research and the understanding of its impact on innovation and economic development are clear, as exampled by a record $499 billion investment in research and development in the U.S. in 2015 (NSF, 2016). Providing students at NCSSM with opportunities to apply their learning through research is not only vitally important in preparing and inspiring students to pursue STEM degrees and careers after high school, but also essential to encouraging innovative thinking that will allow them to scientifically address the major challenges and problems we face in the world today and will face in the future. Opened in 1980, NCSSM was the nation’s first public residential high school where students study a specialized curriculum emphasizing science and mathematics. Teaching students to do research and providing them with opportunities to conduct high-level research in biology, chemistry, physics, computational science, engineering and computer science, math, humanities, and the social sciences
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is a critical component of NCSSM’s mission to educate academically talented students to become state, national and global leaders in science, technology, engineering and mathematics. I am thrilled that each year we continue to increase the outstanding opportunities NCSSM students have to participate in research. The works showcased in this publication are examples of the research that students conduct each year at NCSSM under the direction of the outstanding faculty at our school and in collaboration with researchers at major universities. For thirtytwo years, NCSSM has showcased student research through our annual Research Symposium each spring and at major research competitions such as the Siemens Competition in Math, Science and Technology, the Regeneron Science Talent Search, and the International Science and Engineering Fair to name a few. The publication of Broad Street Scientific provides another opportunity to highlight the outstanding research being conducted by students each year at the North Carolina School of Science and Mathematics. I would like to thank all of the students and faculty involved in producing Broad Street Scientific, particularly faculty sponsor Dr. Jonathan Bennett and senior editors Dory Li, Sreeram Venkat, Avra Janz, and Miguel de los Reyes. Explore and enjoy! Dr. Todd Roberts, Chancellor
WORDS from the EDITORS Welcome to Broad Street Scientific, NCSSM’s journal of student research in science, technology, engineering, and mathematics. In this sixth edition of Broad Street Scientific, we aim to showcase student research and highlight the importance of active participation and engagement in the STEM fields by demonstrating the scientific virtuosity of NCSSM students to the global scientific community. We hope you enjoy this year’s issue! This year’s theme is based on atomic spectra, the emission of discrete wavelengths of light by hot gases. Studied since the late 1700s, the emission spectra of atoms continue to fascinate scientists today. In 1913, Niels Bohr solved the mystery of the hydrogen spectrum using his theory of quantized electron orbits, bolstering the theory of quantum mechanics that would later evolve into one of the most widely accepted and experimentally sound theories known. Bohr’s discoveries, along with those of Gustav Kirchhoff, Robert Bunsen, and other scientists, rapidly expanded the field of spectroscopy. The ability to identify matter by its emitted light led to revolutionary discoveries in astronomy, physics, and chemistry. Today, scientists are examining the spectra of antimatter to gain insight on its properties. We would like to thank the following photographers for their images: Jurii (Krypton; License: Creative Commons Attribution 3.0) and Heinrich Pniok (Hafnium, iridium, copper, osmium, neon; License: Creative
Commons Attribution 3.0). We would also like to thank the administration, faculty, and staff of NCSSM for giving us the opportunity to pursue our research goals in the fields of science, technology, engineering, and mathematics. The support for student research at this school is unparalleled, and the student body would like to recognize the significance of this investment in our, and the state’s, future. We would like to thank our faculty advisor, Dr. Jonathan Bennett, for his advice and guidance through the sixth issue of Broad Street Scientific. We would also like to thank Mr. Ormand Moore, copy editor at the North Carolina Medical Journal, for his guidance in developing a style guide for the journal. We appreciate the active support of Chancellor Dr. Todd Roberts, Dean of Science Dr. Amy Sheck, and Research/Mentorship Coordinator Dr. Sarah Shoemaker. Lastly, we are extremely grateful to NCSSM alumnus Dr. Rachel Levy ‘85, Professor of Mathematics at Harvey Mudd College and Vice President for Education at the Society for Industrial and Applied Mathematics (SIAM), for her participation in this year’s interview and her insights about the myriad applications of mathematics in our daily lives. Dory Li, Sreeram Venkat, Miguel de los Reyes and Avra Janz, Editors
Broad Street Scientific | 2016-2017 |
BROAD STREET SCIENTIFIC STAFF Chief Editors
Avra Janz, 2017 Elizabeth Beyer, 2018 Lindsey Green, 2018 Vanessa Lin, 2018 Sofia Sanchez-Zarate, 2018
Sarah Grade, 2017 Evan Jiang, 2017 Isabella Li, 2018
Ahmad Askar, 2017 Alexander Allen, 2017
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Dory Li, 2017 Sreeram Venkat, 2017
Sreekar Mantena, 2018 Gandhar Mahadeshwar, 2018 Karl Westendorff, 2017
Sophia Luo, 2018
Nolan Miranda, 2017 Nikhil Reddy, 2017
Miguel de los Reyes, 2017 Deven Jahnke, 2018
Dr. Jonathan Bennett
GENE THERAPY: THE MEDICAL FRONTIER OR TIME TO CURB OUR ENTHUSIASM? Samuel Li Samuel Li was selected as the winner of the 2016-2017 Broad Street Scientific Essay Contest. His award included the opportunity to interview Dr. Rachel Levy, Professor of Mathematics at Harvey Mudd College, as part of the Featured Scientist section of the journal. More than a quarter million papers and a hundred thousand review papers over half a century have been published on gene therapy in the United States National Library of Medicine database. But what exactly is gene therapy? In pursuing treatments for hereditary diseases, gene therapy has been hailed by some as the holy grail, and by others as a dangerous double-edged sword. The use of humans in gene therapy trials is even more recent, with the first trials dating only 28 years ago to 1989 (Rosenberg et al., 1990). A team led by Dr. Steven Rosenberg, Chief of Surgery at the National Cancer Institute, sought to discover new treatments for patients with advanced melanoma. By introducing marker genes into five patients, they established that retroviral-mediated gene insertion was a safe and feasible method for gene therapy. Since then, nearly 2000 clinical trials have been conducted worldwide (Ginn et al., 2013). However, despite the apparent success of the technique, gene therapy is still far from being routinely used safely and effectively. What is Gene Therapy? To understand the current challenges posed by gene therapy, we first need to understand how gene therapy works. According to the National Institute of Health, “Gene therapy is an experimental technique that uses genes to treat or prevent disease.” In other terms, it replaces or deactivates mutated DNA, and introduces functioning DNA to reverse the effects of a mutation. There are two broad categories of vehicles or vectors used to deliver genes: viral delivery systems and non-viral delivery systems (Nouri et al., 2012). The viral delivery system, also known as retroviral delivery, is the most commonly used method. Non-viral delivery encompasses all physical and chemical delivery mechanisms, including nanotechnology-based delivery. Both of these methods pose their own unique advantages and challenges. Challenges and Solutions Retroviral vectors work by inserting transgenes (genes that have been transferred from one organism to another) permanently into the host genome to treat patients with genetic disorders. However, as with anything permanent, inserting a gene into an unexpected location could lead to tragic consequences, known as insertional mutagenesis. For ESSAY
example, the occurrence of leukemia in 3 out of 11 children with x-linked SCID, a severe form of immunodeficiency, was determined to be caused by the insertion of transgenes into pre-oncogenes (genes that cause various cancers), inducing the activation of an oncogene (Hacein-Bey-Abina et al., 2003). Currently, the completion of the human genome sequence and extensive research in animal modeling allow for increased accuracy in pinpointing optimal gene insertion locations. However, until the success of more effective gene delivery systems are developed, the cures for many diseases will remain beyond reach. When new genes are inserted, they are often marked as “foreign” by the patient’s body. Compared to viral vectors, non-viral gene delivery systems have an advantage in the form of low preexisting immunogenicity, which is critical in preventing a severe immune response (Nouri et al., 2012). However, in this case, a challenge arises from maintaining the inserted gene in cells, since they are quickly removed by the host body. In order to keep newly introduced genes from functioning, native cells equip various mechanisms to silence or deactivate certain gene functions. For example, de novo methylation, which adds methyl groups to the DNA molecule to change its behavior without changing its sequence, assists in transgene silencing by blocking gene expression of unwanted genes. Great progress has been made in creating a much safer and more efficient system to use in clinical trial patients. However, gene therapy still faces numerous challenges and risks inherent in new methods. No matter what mechanism is used in conventional gene therapy, a full copy of a functioning gene is introduced into a patient genome. This process could potentially cause unforeseen consequences and further deteriorate a patient’s health. The fact that humans are complex biological systems capable of having many different responses to a treatment further indicates that gene therapy still has a long way to go before it is deemed safe for widespread use in the medical field. However, a much faster, simpler, and precise way to introduce changes in the genome is raising a storm in the scientific world. This method, which only changes the nucleotides of an endogenous gene instead of replacing the entire mutated gene, is called CRISPR-Cas9.
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CRISPR-Cas9: The Brightest Star in Gene Therapy Clustered Regularly Interspaced Short Palindromic Repeats(CRISPR)-CRISPR Associated 9 (Cas9) proteins function to edit genomes by removing, adding, or altering specifically targeted DNA sequences. Specifically, it is an RNA-mediated adaptive immune system, composed of two components (Singh et al., 2017): Guide RNA: A small RNA sequence with bases designed to complement those of the target DNA sequence in the genome. This RNA directs Cas9 to the genome location where changes are to be made. Cas9: A nuclease that follows the guide RNA to the target location. The nuclease property of Cas9 acts as a pair of molecular â€œscissorsâ€? that can cut DNA double strands at precise locations.
Figure 1. Cas9 cutting the target sequence based on the guide RNA (CRISPR/Cas9 Genome Editing, n.d.). Although this technique was discovered nearly 30 years ago, it was only recently popularized (Lander, 2016). CRISPR has become one of the most powerful tools in the current gene therapy toolbox, managing to avoid the pitfalls caused by other methods. It employs an extremely accurate method of introducing precise genetic changes in a variety of organisms (Lander, 2016). Advances have been made to optimize Cas9 for improved flexibility, fidelity, and precision. As a result, CRISPR-Cas9 remains one of the most popular techniques used in modern biology research. Even still, there are limitations to CRISPR. Though the guide RNA sequence can be designed to specifically target a region, other regions in the genome might share the same sequences, and cause an injection into the wrong location. Hope vs. Hype Many people are excited by all the recent achievements in gene therapy; however, gene therapy inherently carries its fair share of risks and consequences. Accompanying advances in gene therapy are complex debates centering around its medical, technical, financial, and social aspects. The first clinical human gene therapy trial was performed by Dr. Rosenberg et al (Rosenberg et al., 1990) in 1989. 8 | 2016-2017 | Broad Street Scientific
This pioneering study sparked interest in the use of gene therapy as a medical treatment technique, and served as a guide for subsequent trials. However, several major setbacks, such as patient deaths, provide sobering reminders of failure (Hacein-Bey-Abina et al., 2003). Unpredictable consequences and long term toxicity have also hampered the progress of gene therapy. To date, the Food and Drug Administration has only approved gene therapy for clinical trials, and has not approved any products for sale. However, gene therapy still harbors the potential to revolutionize the way we approach treatment for diseases where one is nonexistent. The first clinical human gene therapy trial was performed by Dr. Rosenberg et al (Rosenberg et al., 1990) in 1989. This pioneering study sparked interest in the use of gene therapy as a medical treatment technique, and served as a guide for subsequent trials. However, several major setbacks, such as patient deaths, provide sobering reminders of failure (Hacein-Bey-Abina et al., 2003). Unpredictable consequences and long term toxicity have also hampered the progress of gene therapy. To date, the Food and Drug Administration has only approved gene therapy for clinical trials, and has not approved any products for sale. However, gene therapy still harbors the potential to revolutionize the way we approach treatment for diseases where one is nonexistent. Research in gene therapy has also been highly controversial from an ethically standpoint. Critics have loudly questioned its ethics due to the possibility of causing unforeseen safety issues. There are two different types of gene therapy: germline gene therapy and somatic gene therapy. Germline cells contain one set of chromosomes and are able to produce and reproduce. Somatic cells, on the other hand, are differentiated and have a diploid number of chromosomes. With germline gene therapy, the changes made are permanent and passed down to future generations, and as a result, is prohibited worldwide. Current gene therapy trials rely on somatic cells, where genetic changes are limited to only the individual patient. There is an astounding number of publications on the social and environmental impacts of gene therapy, some of which raise the aforementioned issue of interfering permanently with genes, possibly leading to dramatic changes after several generations. Gene therapy has brought hope to the eyes of many patients with diseases incurable with traditional methods. Nonetheless, progress has been slow. Often, the only way to seek treatment is through FDA approved clinical trials. Adding to the technical challenges, the expense of treatment remains an obstacle to widespread adaptation. The massive time investment from discovering, testing, and eventual marketing are long, and capital investments are enormous. The heterogeneity and genetic complexity of many diseases have made gene therapy suitable for only a small cohort of patients, whereas pharmaceutical companies are more eager to produce medicines that work for a larger proportion of the population.
Conclusion Ultimately, the history of gene therapy is very short and is still in its infant stage. The exploding amount of research done in this field provides a positive outlook for the future, and the possibility of tackling diseases previously thought of as incurable are within closer reach. Collaboration among research scientists around the world will pave the way for rapid progress, but only after the legitimate questions about gene therapyâ€™s social and ethical concerns are answered. This practice raises further questions that must be addressed. Where do we draw the line between curing mutations and unnecessary alterations? How will effects compound after several generations? Before taking gene therapy as a possible cure-all, we must curb our enthusiasm and take steady, prudent steps towards the long journey ahead. References Ginn, S. (2013). Gene therapy clinical trials worldwide to 2012 â€“ an update. The Journal of Gene Medicine, 15, 65-77. Hacein-Bey-Abina, S. (2003). A Serious Adverse Event after Successful Gene Therapy for X-Linked Severe Combined Immunodeficiency. New England Journal of Medicine, 348, 255-256. Lander, E. (2016). The Heroes of CRISPR. Cell, 164, 18-28 Nouri, N. (2012). Viral and nonviral delivery systems for gene delivery. Advanced Biomedical Research, 1, 27. Rosenberg, S. (1990). Gene transfer into humansImmunotherapy of patients with advanced melanoma, using tumor-infiltrating lymphocytes modified by retroviral gene transduction. The New England Journal of Medicine, 323(9), 570-578. Singh, V. (2017). Exploring the potential of genome editing CRISPR-Cas9 Technology. Gene, 599, 1-18.
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DETERMINING THE GEOMETRIES OF METHYLTRANSFERASE REACTIONS IN DENV USING MODEL MOLECULAR SYSTEMS Tesia Bobrowski Abstract In this study, the geometries of model systems for two principal methyltransferase reactions in DENV — the N-7 and 2’-O methylation reactions — were determined computationally using MOPAC PM3 and compared to geometries determined using DFT methods in order to locate possible places in each model system where an antiviral drug could be introduced to inhibit the reaction. On the NCSSM Computational Chemistry server, geometry and transition state optimization calculations were run using MOPAC PM3 for each of the reaction stages (reactants, transition state, products) of the two methylation reactions. IRC calculations were then performed on the TS optimized state after determining that there was one imaginary frequency value via a vibrational frequency calculation. The most stable measurements were d2 for the N-7 reaction and d2, d3, and α2 for the 2’-O reaction. The most variable measurements were α1 for the N-7 reaction and d4 for the 2’-O reaction. Considering the geometries in the methyltransferase reactions, it is posited that the more variable distances/angles in DENV methyltransferase identified here be investigated as possible sites where a chemical could be introduced to inhibit the reactions, effectively serving as an antiviral therapy for DENV infections. Key words: dengue virus methyltransferase, computational chemistry, geometry optimization, semiempirical v. DFT, antiviral therapy 1. Introduction Dengue virus (DENV) is endemic in many tropical and subtropical countries and infects approximately 390 million people each year, 50-100 million of whom develop clinical dengue and 24,000 of whom die (Dong et al., 2013). Infection with DENV results in dengue fever, which can turn into hemorrhagic fever or dengue shock syndrome. There is no vaccine or antiviral treatment currently available for dengue infections (Potisopon et al., 2014). DENV belongs to the genus Flavivirus, which includes about 50 virus species (Potisopon et al., 2014). Other clinically significant viruses in the same genus are West Nile virus (WNV), yellow fever virus (YFV), and Japanese encephalitis virus (JEV) (Dong et al., 2013). The genomes of flaviviruses are composed of single stranded RNA 11kb long. These are made of three principal regions: (1) a 5’ untranslated region (UTR); (2) a long open reading frame (ORF); and (3) a 3’ UTR (Dong et al., 2013). The 5’ end of the RNA genetic material has a type 1 cap structure, which is critical in the replication of the virus inside its host cell, ensuring mRNA stability and efficient translation. Four enzyme-driven reactions are needed in order to form the RNA cap: (1) RNA guanylyltransferase hydrolyzes the 5’-triphosphate end of nascent RNA transcript to 5’-diphosphate, (2) RNA guanylyltransferase caps the 5’-diphosphate RNA with GMP, (3) RNA guaninemethyltransferase (N-7 MTase) methylates the N-7 position of the guanine cap, and (4) nucleoside 2’-O MTase methylates first and second nucleotides of viral mRNAs at the ribose 2’-OH position (Dong et al., 2013). 10 | 2016-2017 | Broad Street Scientific
Figure 1. The methyl donor (SAM) is converted to SAH, resulting in a methylated nucleophile (Nu-CH3).
Figure 2. Reaction mechanism where R1 and R2 represent the adenosyl and aminobutryl moieties. The reactions involving N-7 and 2’-O MTase activity are of special clinical interest and are being researched as possible antiviral targets for DENV. Several studies have demonstrated the importance of these reactions in DENV and other flavivirus replication cycles, and suggest that the N-7 reaction may be more important than the 2’- O reacCHEMISTRY RESEARCH
tion in DENV replication and proliferation for currently unknown reasons (Zhou et al., 2007). The methyl donor for both MTases is S-adenosyl-L-methionine (SAM), which is converted into an S-adenosyl-L-homocysteine (SAH) byproduct over the course of the two reactions (Zhou et al., 2007). The DENV methyltransferase cap reactions are also interesting not only for their possible clinical merit, but for the fact that the two methylation reactions are catalyzed by the same enzyme. It is hypothesized that the N-7 methylation reaction happens due to the close proximity and geometry of its two substrates, as it involves no direct contact between the MTase or the attacking nucleophile N-7 atom of guanine, the methyl carbon of SAM, or the leaving group sulfur of SAH (Zhou et al., 2007). However, the 2’-O reaction is hypothesized to involve an SN2 method of methyl transfer in which a conserved amino acid sequence in the MTase drives the deprotonation of the target 2’OH, which nucleophilically attacks the methyl portion of a SAM molecule, resulting in the transfer of a methyl group (Zhou et al., 2007). Figures 1 and 2 depict the mechanisms by which the methylation reactions are achieved for the N-7 and 2’-O reactions (adopted from Schmidt et al., 2014). A computational approach to discerning the inner workings of the MTase reactions in DENV replication is helpful, as it involves no wet lab experimentation yet can reasonably approximate the true reaction mechanisms or geometries of the molecules involved. Large systems like those involving entire enzymes are usually not very practical to run quantum computational calculations on, as there are a myriad of atoms and therefore a myriad of possible interactions between said atoms, which makes the mathematics inextricably complicated. However, some reactions can be easily modeled using smaller chemical model systems. A computational determination of the nature or properties of the reaction is especially useful in this context, as the reactions are simple enough to be modeled using smaller molecules whose properties can be approximated easily using the mathematics of quantum computational chemistry. In this paper, a computational approach was taken to solving the geometries and relative energies of the different stages of the N-7 and 2’-O methylation reactions using smaller molecular model systems, and to compare the two reactions with the goal of determining possible sites at which an antiviral drug could be introduced into these chemical systems to inhibit DENV proliferation. 2. Computational Approach The computational chemistry server located at the North Carolina School of Science and Mathematics (NCSSM) and the web interface WebMO (version 17.0.008e, Schmidt et al., 2017), uploaded on the server, were used to perform the calculations in this paper. The two main methyltransferase reactions important in CHEMISTRY RESEARCH
DENV replication are the 2’-O reaction and the N-7 reaction. These two reactions both involve the interaction of molecules containing methyl groups with the DENV methyltransferase, a relatively large enzyme, which in humans contains 476 amino acids (UniProt, 2017). Performing quantum computations on a compound of this size interacting with another molecule would not be feasible given the sophistication of today’s computational chemistry calculations. Given this, the 2’-O and N-7 methyltransferase reactions were simulated using smaller model systems (Fig. 3). In the model system for the N-7 reaction, thereactants are: a SAM-mimicking methyl donor and a guanosine-mimicking methyl acceptor (an N-methylimidazole). The products formed are the original methyl donor with two remaining methyl groups and 1,3-dimethylimidazole. In the model system for the 2’-O reaction, the reactants are: a SAM-mimicking methyl donor; a methyl acceptor ribose moiety; and part of the side chain of lysine (Lys181 in DENV MTase) acting as a proton acceptor. The products formed are the methyl acceptor with an accepted methyl group, the methyl donor with two remaining methyl groups, and the SAM methyl donor with an additional hydrogen atom.
Figure 3. Schema for the model systems of the N-7 and 2’-O reactions. Italic labels are used for all distances and bond angles. Figure taken from Schmidt et al. (2014). These systems were based off those created by Schmidt et al. (2014). Several distances and angles were measured within these molecular systems over the course of the reactions: • d1 — distance between methyl group and donor atom • d2 — distance between acceptor and donor atom • d3 — distance between acceptor atom and transferring methyl group • d4 — distance between proton donor and transferred proton • d5 — distance between proton donor and acceptor • d6 — distance between transferred proton of 2’-O hydroxy group and nitrogen atom of lysine model moiety • α1 — angle between donor atom, carbon atom in methyl group, and hydrogen atom in methyl group (S-C-H) • α2 — angle between proton donor, proton, and proton acceptor (O-H-N) Broad Street Scientific | 2016-2017 | 11
All distances are measured in angstroms and all angles are measured in degrees. Due to the complexity of the systems involved, relatively simplistic computational methodologies (MOPAC PM3) were used in order to reduce the amount of CPU usage. The payoff for CPU usage versus accuracy was weighed. It was determined that using simpler calculations (i.e., semi-empirical vs. DFT) with some loss in accuracy would be most advantageous. In addition, any quantum computational calculations designed for smaller systems are bound to be at least slightly inaccurate when applied to larger systems, no matter how much CPU time they use or how complex their mathematics are. MOPAC PM3 was used to perform all calculations. Geometry optimizations were performed on the model systems for the reactants and products, and transition state optimizations were performed on the optimized structures of the reactants. To determine if these were the true transition structures of the reactions, vibrational frequency calculations were performed on the TS optimized structure. If only one imaginary (negative) frequency was found in the vibrational frequency calculation, then an intrinsic reaction coordinate (IRC) calculation was performed on the TS structure. In the 2014 Schmidt et al. paper from which this paper’s chemical models were derived, B3LYP/6-31G(d) model chemistry was used in all of their calculations. This model chemistry was probably chosen because it is a good midpoint between the accuracy of ab initio methods and the CPU conservation ofsemi-empirical ones, which makes it extremely popular among computational chemists. Their geometries for the two model systems were compared to those determined using the methodologies in this paper via percent error calculations. Using the data obtained from the IRC calculations, the Gibbs free energy profiles of the two methylation reactions were constructed using Mathematica 11.0.
over the reaction path can be seen in figure 6. The relative inaccuracy of the measurement for α1 (angle between S, C, and H in the methyl donor molecule) in the N-7 reaction makes sense because the optimized angles between the methyl donor and its methyl group components change a lot over the course of the reaction, and therefore would be more likely to have calculation inaccuracies. The relative inaccuracy of the reactants’ geometries in the N-7 reaction likewise makes sense due to the large amount of potential energy in this stage of the reaction and corollary potential for interaction between the molecules.
Figure 4. Lists and compares the PM3 determined geometry values for differing stages in the N-7 methylation reaction. Distances (d#) are in angstroms and angles (α#) are in degrees.
3. Results and Discussion
Figure 5. Lists and compares the PM3 determined geometry values for differing stages in the 2’-O methylation reaction. Distances (d#) are in angstroms and angles (α#) are in degrees.
The computational chemistry server located at NCSSM was used to determine the important distances and bond angles in both reactions for each of the reaction stages (reactants, transition state, products), as well as the reaction dynamics of the two methyltransferase reactions in DENV, N-7 and 2’-O. Figures 4 and 5 depict the geometries determined using MOPAC PM3 andcompare them to the DFT geometry values determined in the 2014 Schmidt et al. paper using percent error calculations. The most accurate geometries calculated were for the transition state of the N-7 reaction (Fig. 4). The most accurate measurement overall was the distance between the acceptor and the donor atom (d2). The measurement that was least accurate overall was the bond angle between the donor, carbon atom, and hydrogen atom (∞1). The reactant stage had the largest percent errors of any stage in the reaction. Percent errors for the differing measurements
The relative accuracy of d2 (distance between acceptor and donor atom) in the N-7 reaction makes sense, as the distance between the donor and acceptor atoms should not change that much over the course of the reaction. The donation of the methyl group to the acceptor atom (at least schematically, Fig. 3) does not involve much movement on the part of the donor/acceptor atoms. The total percent errors for each of the N-7 reaction stages were all around 105%, but the stage with the least overall percent error was the transition state. This is probably because before running each geometry calculation, each molecular system was “pre-optimized” with a comprehensive mechanics calculation, the goal of which was to make the energy of the system as low as possible prior to the actual geometry optimization. The cleanup likely arranged the reactants and products (separately) in conformations unlike how they arrange in vivo, which is why they were less accurate than the measurements of transition state of
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the reaction. Before running the transition state optimization calculation, distances and angles between atoms had to be edited, so there was no cleanup prior to the running the calculation. Lack thereof may have conferred some degree of accuracy to that stage of the reaction. The most accurate geometries calculated were for the products stage of the 2’-O reaction (Fig. 5). The most accurate measurements were the distances between the acceptor and the donor atom (d2), the acceptor atoms and the transferring methyl group (d3), and the bond angle between the proton donor, proton, and proton acceptor (α2). The least accurate measurement by far was the distance between the proton donor and the transferred proton (d4); the transition state had an outstanding percent error value of 366.731%. Overall, the stage of the reaction with the least accurate measurements was the transition state. The percent errors for the differing measurements over the reaction path can be seen in Figure 7.
is bonded to the nitrogen atom). The measurement for d2 (distance between the acceptor and donor atom) was likely accurate for the same reason that d2 was accurate in the N-7 reaction: the 2’-O reaction does not involve much movement of the acceptor and donor atoms. The measurement for d3 (distance between the acceptor atom and transferring methyl group), though it involves the transferring methyl group, is relatively accurate because it also involves another atom that stays fairly static throughout the reaction, the acceptor atom. The most accurate geometries were determined for the products stage of the 2’-O reaction. This makes sense, as the products stage of the reaction should have the lowest potential energy of anywhere on the reaction path and thus have a low energy and potential to interact with the other molecules around it. This leaves little ambiguity in determining the geometry of this stage, ergo the low overall percent error. The structures of the relative reaction stages (reactants, transition state, products) can be seen in figures 8 and 9 (located in the “Figures and Tables” section). The transition state should appear as an intermediate between the reactants and products. The following had to occur in each reaction’s transition state in order for the appropriate products to form.
Figure 6. Percent errors of the relative measurements for each stage of the N-7 reaction pathway (reactants, transition state, products). The inaccuracy of d4 in the 2’-O reaction was likely due to the arrangement of molecules in the system upon TS optimization. This involved arranging the three molecules in the system into a conformation capable of forming the appropriate products and was likely different than that of the Schmidt et al. paper. The problem with determining transition state geometries is that they are relatively subjective in their setup, with each computational chemist likely to choose slightly different distances/angles for the transition state of their molecules. The large degree of inaccuracy (overallpercent error of 672.765%) for the transition state geometry of the 2’-O reaction probably occurred for the same reason that the measurement of d4 was highly inaccurate — human error. Because the α2 angle involves three atoms and a bond alternation of one of those atoms to the other atom, the reaction had to involve a relatively static angle between the hydroxy group and the nitrogen atom in the lysine moiety (the hydroxy group loses its hydrogen group, which then CHEMISTRY RESEARCH
Figure 7. Percent errors of the relative measurements for each stage of the 2’-O reaction pathway (reactants, transition state, products). The reactants for the N-7 reaction were a SAM-mimicking methyl donor and a guanosine-mimicking methyl acceptor, an N-methylimidazole. In order for the products to be formed — the methyl donor with two remaining methyl groups and an 1,3-dimethylimidazole molecule — the geometries changed in the following ways. The distance between the nitrogen atom accepting the methyl group on the Nmethylimidazole molecule decreased, and the distance between the reactive sulfur atom of the methyl acceptor and its transferred methyl group increased. The reactants for the 2’-O reaction were a SAM-mimBroad Street Scientific | 2016-2017 | 13
icking methyl donor, the methyl acceptor ribose moiety, and part of the side chain of lysine, which acts as a proton acceptor. In order for the products to form — the methyl acceptor with an accepted methyl group, the methyl donor with two remaining methyl groups, and the imitation SAM methyl donor with an additional hydrogen atom — the geometries changed in the following ways: the bond length increased between the hydrogen atom and the oxygen atom in the methyl receptor, and the bond length between the reactive sulfur atom of the methyl acceptor and its transferred methyl group likewise increased. The Gibbs free energy difference between product and reactant was -25.78771 kcal/mol for the N-7 reaction and -55.37757 kcal/mol for the 2’-O reaction (See Figs. 10 and 11, located in the Figures and Tables section). The percent errors of these values, when compared to the DFT-calculated values, are 9.7% and 227.7%, respectively. 4. Conclusions In general, determining the geometries of the molecules in the different stages of these two reactions and comparing them to set, more “accurate” measurements (defined as those determined using DFT methods in Gaussian in the Schmidt et al. paper) allows the identification of potential “weak spots,” or areas in the molecular systems that are more volatile or reactive than the rest of the system. In summary, the “variable” and “static”distances/angles in the N-7 and 2’-O reactions were identified as: “Variable” distances and angles: • N-7 Reaction: α1 (angle between donor, C, and H) • 2’-O Reaction: d4 (distance between proton donor and transferred proton) “Static” distances and angles: • N7 Reaction: d2 (distance between acceptor and donor atom) • 2’-O Reaction: • d2 (distance between acceptor and donor atom) • d3 (distance between acceptor atom and transferring methyl group) • α2 (angle between proton donor, proton, and proton acceptor) Because the “variable” distances and angles determined here are more apt to change or react with surrounding molecules, they are a possible target for antiviral therapies for DENV MTase. Chemicals that could inhibit the catalytic areas on DENV MTase that interact with the donors (methyl donor for the N-7 reaction or proton donor for the 2’-O reaction) are of special interest, as these molecular donors are what help drive the two methylation reactions and also house the “weak points” of the reaction. The Gibbs free energy profiles of the two reactions showed that the activation energy of the two reactions was similar, but that the heat released from the reaction (25.78771 kcal/mol vs. 55.37757 kcal/mol) differed significantly, indicating that the 2’-O model system stored more potential energy than the N-7 system. However, the large 14 | 2016-2017 | Broad Street Scientific
discrepancy between the Gibbs free energy difference of the reactants and products for the 2’-O reaction (close to 230% error) indicates that the PM3 calculation for the 2’-O reactionmay not have been very accurate. A computational analysis studying the nature of the methyltransferase reactions in DENV, such as that conducted in this paper, is very helpful in gaining insight into possible mechanisms by which an antiviral therapy could be created. As it is difficult to ascertain the geometries of reactant/transition state structures through experimentation, a computational approach or mathematical approach can provide valuable information which could otherwise not be ascertained. Analyzing the geometries of the constituent molecules in each reaction and comparing them to other, more comprehensive studies’ results is especially helpful, as it pinpoints possible “weak points” in each molecular system that are highly reactive or variable. Points such as these could therefore interact with other introduced chemicals, halting the normal course of the reaction, the formation of the RNA cap, and ultimately replication of DENV. This paper presents a method by which possible targets within the DENV methyltransferase reactions, N-7 and 2’-O, could be determined for use in developing antiviral therapies for DENV. Though this study chose a relatively simplistic computational method (MOPAC PM3) to determine the geometries of its modelsystems, it was through this simple calculation choice that highly reactive or variable points in the molecular systems could be identified. Hopefully future studies will be able to investigate the computationally determined results here through handson experimentation, as well as launch their own investigations into developing antiviral therapies based on some of the basic reaction geometry information presented here and in other studies. 5. Acknowledgements The author thanks Mr. Robert Gotwals for assistance with this work, as well as the North Carolina School of Science and Mathematics online program for offering a course in Computational Chemistry. Appreciation is also extended to the Burroughs Welcome Fund and the North Carolina Science, Mathematics, and Technology Center for their funding support for the North Carolina High School Computational Chemistry Server. 6. References Dong, H., Chang, D. C., Xie, X., Toh, Y. X., Chung, K. Y., Zou, G., et al. (2010). Biochemical and genetic characterization of dengue virus methyltransferase. Virology, 405(2), 568-578. Potisopon, S., Priet, S., Collet, A., Decroly, E., Canard, B., & Selisko, B. (2014). The methyltransferase domain of dengue virus protein NS5 ensures efficient RNA synthesis initiation and elongation by the polymerase domain. NuCHEMISTRY RESEARCH
cleic Acids Research, 42(18), 11642-11656.
7. Figures and Tables
Zhou, Y., Ray, D., Zhao, Y., Dong, H., Ren, S., Li, Z., et al. (2007). Structure and Function of Flavivirus NS5 Methyltransferase. Journal of Virology, 81(8), 3891-3903.
Schmidt, T., Schwede, T., & Meuwly, M. (2014). Computational Analysis of Methyl Transfer Reactions in Dengue Virus Methyltransferase. The Journal of Physical Chemistry B, 118(22), 5882-5890. The North Carolina High School Computational Chemistry Server, http://chemistry.ncssm.edu. (Accessed January 2017). Schmidt, J.R.; Polik, W.F. WebMO Enterprise, version 17.0.008e; WebMO LLC: Holland, MI, USA, 2017; http:// www.webmo.net (Accessed January, 2017).
Universal Protein Resource [Database]. (n.d.). Retrieved January 10, 2017, from http://www.uniprot.org/uniprot/ O43148. UniProtKB entry for mRNA cap guanineN7 methyltransferase. MOPAC Version 7.00, J. J. P. Stewart, Fujitsu Limited, Tokyo, Japan. Wolfram Research, Inc., Mathematica, Version 11.0, Champaign, IL (2016) Products
Figure 8. Optimized structures of reactants, transition state, and products for the N-7 reaction.
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Figure 10. Gibbs free energy profile for the N-7 reaction. The first point indicates the energy of the reactants stage, the local maximum indicates the energy of the transition state, and the final point on the graph indicates the energy of the products stage. Because ΔG is negative, this reaction is exothermic.
Figure 11. Gibbs free energy profile for the 2’-O reaction. The first point indicates the energy of the reactants stage, the local maximum indicates the energy of the transition state, and the final point on the graph indicates the energy of the products stage. Because ΔG is negative, this reaction is exothermic.
Figure 9. Optimized structures of reactants, transition state, and products for the 2’-O reaction.
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ANALYSIS OF ELECTROCYCLIC REACTIONS USING WOODWARD-HOFFMANN RULES AND FRONTIER MOLECULAR ORBITAL THEORY Katherine Mueller & Neil Palkar Abstract In this investigation, the conrotatory or disrotatory behavior of several different electrocyclic reactions was analyzed using Woodward-Hoffmann rules and frontier molecular orbital theory. To use Woodward-Hoffmann rules, the number of pi bonds involved in each reaction and the source of energy for each reaction were found to determine whether the behavior was conrotatory or disrotatory. To use frontier molecular orbital theory, the p orbitals of the highest occupied molecular orbital were analyzed for each reactant molecule. Finally, MOPAC PM3 was used to run molecular orbital calculations on all molecules involved in each reaction to visualize the highest occupied molecular orbitals. It was found that the thermal electrocyclic ring closure of 1,3,5-hexatriene was disrotatory, the thermal electrocyclic ring opening of cyclobutene was conrotatory, and the thermal and photechemical ring opening electrocyclic reactions of (2E,4Z,6E)2,4,6-octatriene were disrotatory and conrotatory, respectively. It was also found that vitamin D3 is produced from a photochemical, conrotatory elecrocyclic ring closure of 7-dehydrocholesteral and a sigmatropic reaction of provitamin 3D, yielding vitamin 3D. These results are important because the conrotatory or disrotatory behavior of a molecule determines the steriosomer produced and because the studied electrocylic reactions are common unimolecular reactions with various aplications. 1. Introduction Computational chemistry encompasses a wide range of methods to analyze molecular transformations. Through such practices, we are able to learn more about pericyclic reactions, that is, reactions which involve cyclic transition states. Two types of pericyclic reactions are electrocyclic and sigmatropic reactions. Pericyclic reactions are considered to be rearrangement reactions because they reorganize bonds to produce a more stable structure. Electrocyclic reactions are results of carbon ring closures from conrotatory and disrotatory reactions, while sigmatropic reactions are shifts in the arrangement of bonds through the transition of one sigma bond to another sigma bond (Pericyclic Reactions, n.d.). Both of these pericyclic reactions will be analyzed through common reaction examples by examining molecular orbitals. The potential to use molecular orbitals to analyze pericyclic reactions comes from the frontier molecular orbital (FMO) theory. This theory describes that the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) can be used to analyze the reactivity of pericyclic reactions. In electrocyclic and sigmatropic reactions, specifically, the LUMO will not be analyzed. Due to their unimolecular nature, these reactions simply use the the p orbitals at the termini of the HOMO of the reactant. This means that the p orbitals at each end of each HOMO of the open ring structure will interact with each other (Pericyclic Reaction Chemistry, n.d.). They do so by orientating their orbitals based on parameters that will be covered later on in this passage. FMO theory will be implemented in the observation of specific electrocyclic reactions. CHEMISTRY RESEARCH
As stated earlier, electrocyclic reactions are one of the three classes of pericyclic reactions. They are characterized by the breaking or the formation of one sigma bond in a carbon ring structure. This idea is shown in Figure 1 through the example of a generic six-carbon ring.
Figure 1. Electrocyclic reactions (Pericyclic Reactions, n.d.). In the left example of Figure 1, the carbon structure is removing a sigma bond to form an open structure, while the right example of Figure 1 is showing the creation of a single sigma bond that closes the ring. The change can be noted by looking at the number of double bonds held in this molecule at a given time. These electrocyclic reactions can occur in either of two fashions: conrotatory or disrotatory reactions (Pericyclic Reaction Chemistry, n.d.). While both of these methods result in correct orbital overlap for sigma bonds, they have different ways of doing so. Keeping this idea in mind, there are two ways for the two p orbitals at the termini of the HOMO to rotate and form a sigma bond. This formation of a sigma bond through the reorientation of p orbitals can occur in two ways. The first way is conrotation, and it is defined by the same rotational movement of both orbitals to form a sigma bond between the two atoms on the opposite ends of the ring. The second way is known as disrotation, and it involves the orbitals rotating in opposite directions in Broad Street Scientific | 2016-2017 | 17
order to form a sigma bond between the two atoms on the opposite ends of the ring. In other words, conrotation describes both orbitals moving clockwise, and disrotation shows one orbital moving counterclockwise, while the other moves clockwise, as can be seen in Figure 2 (Pericyclic Reactions Electrocyclizations, n.d.).
Figure 2. Conrotation of a four carbon compound and disrotation of a six carbon compound (Pericyclic Reaction Chemistry, n.d.). When discussing the conrotatory and disrotatory behavior that takes place in unimolecular systems, stereospecificity must be discussed. Electrocyclic reactions can be characterized as completely stereospecific. This indicates that the ring closure of a specific reactant under specific conditions can only yield one product. Conditions involving the energy source of a reaction control which products are formed from the electrocyclic reaction. For example, cyclization of 2,4-hexadiene as a result of heat can form trans groups only, whereas cyclization of the same compound with light can form cis groups only (Pericyclic Reactions, n.d.). This is due to the difference between the energy sources of the reaction. In electrocyclic reactions involving heat, the two atoms at each end of the ring use the highest occupied molecular orbital. On the other hand, photochemical electrocyclic reaction utilize the excited state HOMO, meaning that one electron is excited by the light source, causing it to move up one molecular orbital energy level. For an example of the difference in steriosomers as a result of different energy sources, refer to Figure 3.
Figure 3. 2,4,6-octatriene: photochemical conrotation and thermal disrotation (Pericyclic Reaction Electrocyclizations, n.d.). In Figure 3, the rightmost reaction shows a thermal electrocyclic reaction. When this reaction is altered by using a light energy source, the orbitals of the reactant are changed to display methyl groups on opposite sides of the molecular plane (Pericyclic Reactions, n.d.). This causes the reaction on the left to proceed with conrotation in 18 | 2016-2017 | Broad Street Scientific
order to form the sigma bond, while the reaction on the right proceeds with disrotation. The rules that delineate these parameters were forged by extremely influential scientists. American chemists Robert Burns Woodward and Roald Hoffmann attempted to explain certain aspects of electrocyclic reactions. They used molecular orbitals to better understand the stereospecificity of such reactions. The product of their research was a set of rules known today as the Woodward-Hoffmann rules, which describe in which situations an electrocyclic reaction will occur through conrotatory or disrotatory means. Woodward and Hoffman used the symmetry of the orbitals to help determine this behavior. They found that certain isomers of the molecules would not form because they were not “symmetry allowed.” Rather, they were “symmetry forbidden.” This means that the p orbitals involved in a conrotatory reaction must be symmetric with respect to a C2 axis of symmetry whereas the p orbitals involved in a disrotatory reaction must be symmetric with respect to a mirror plane of symmetry (Electrocyclic and Cycloaddition Reactions, n.d.). Thus, the symmetry of the p orbitals involved in the electrocyclic reaction determine whether the reaction is conrotatory or disrotatory, which in turn determines whether the cis or trans isomer is the product of the electrocyclic reaction, thus explaining the stereospecificity of such reactions. This research conducted by Woodward and Hoffman allowed for electrocyclic reactions to be better understood. It also led to the creation of the Woodward-Hoffman rule, which are summarized in Table 1. Number of π bonds Even Odd
Thermal reaction Conrotatory Disrotatory
Photochemical reaction Disrotatory Conrotatory
Table 1. Woodward-Hoffmann rules (Pericyclic Reactions, n.d.). While the explanation that Woodward and Hoffmann developed to explain stereospecificity in electrocyclic reactions was correct, it required analysis of all of the molecular orbitals of both the reactants and products of electrocyclic reactions. To simplify this, Kenichi Fukui used his frontier molecular orbital theory to help explain the conrotatory and disrotatory pathways of electrocyclic reactions. FMO theory uses the frontier orbitals of molecules in pericyclic reactions to describe their reactivity. Fukui found the pi bonding in the HOMO of a molecule undergoing an electrocyclic reaction could predict whether the reaction would be conrotatory or disrotatory. In molecules where the two p orbitals of the HOMO involved in the reaction were in phase, the reaction would be disrotatory. In molecules where the two p orbitals of the HOMO involved in the reaction were out of phase, the CHEMISTRY RESEARCH
action would be disrotatory. These rules, however, only applied to thermal reactions. In photochemical reactions, one of the electrons moves to an excited state, causing the HOMO to change to what used to be the LUMO. The p orbitals of this excited state HOMO, therefore, are used to determine the conrotatory or disrotatory behavior of photochemical electrocyclic reactions (Pericyclic Reaction Electrocyclizations, n.d.). An example of this can be seen for the thermal and photochemical electrocyclic ring closures of 1,3-butadiene in Figure 4.
can be seen in Figure 5.
Figure 4. Shows how molecular orbital diagrams can be used to determine conrotatory or disrotatory behavior (Electrocyclic and Cycloaddition Reactions, n.d.). In this work, the electrocyclic reactions of four different molecules will be analyzed. The first reaction involves the thermal electrocyclic ring closure of 1,3,5-hexatriene, resulting in 1,3-cyclohexadiene. The second reaction involves the thermal electrocyclic ring opening of cyclobutene, resulting in 1,3-butadiene. The third reactant molecule being analyzed is (2E,4Z,6E)-2,4,6-octatriene. An electrocyclic ring closure can occur with this starting molecule in either thermal or photochemical conditions. This will result in two different stereoisomers of the product, 5-6-dimethyl- 1,3-cyclohexadiene. This can be attributed to the excited state of one of the electrons involved in the photochemical reaction. This causes whether the reaction is conrotatory or disrotatory to change from the thermal reaction based on which orbital is the HOMO in each reaction, thus resulting in two different stereoisomeric forms (Pericyclic Reactions, n.d.).) The fourth molecule being analyzed was 7-dehydrocholesterol. When a photochemical electrocyclic ring opening reaction occurs, it produces a molecule known as provitamin D3. When a sigmatropic reaction occurs with provitamin D3 as the starting molecule, vitamin D3 is produced and can be used in this form in the liver. Not all vitamin D3 synthesis can be explained by an electrocyclic reaction mechanism, however. The second step in the two-part shift from 7-dehydrocholesterol to vitamin D3 is the sigmatropic reaction that converts provitamin D3 to vitamin D3. This also results in a change in the pi bond arrangement of the molecule. In the case of provitamin D3, one of the hydrogen atoms changes the atom to which it bonds (Pericyclic Reaction Chemistry, n.d.). The process of 7-dehydrocholesterol being converted to vitamin D3 CHEMISTRY RESEARCH
Figure 5. Vitamin D3 synthesis using electrocyclic and sigmatropic reactions (Electrocyclic and Cycloaddition Reactions, n.d.). In conclusion, electrocyclic reactions are unimolecular reactions that occur due to a change from pi to sigma bonding (in the case of a ring closure) or from sigma to pi bonding (in the case of a ring opening). They can occur through the addition of either heat or light to the starting molecule. However, the use of light will result in a different isomer than an electrocyclic reaction which uses heat. This is due to the conrotatory or disrotatory movement of the p orbitals involved in the changing bond. Whether an electrocyclic reaction is conrotatory or disrotatory can be determined by the number of pi bonds involved in the reaction and the type of reaction (thermal or photochemical). These reactions are important in the synthesis of many different molecules, such as vitamin D3, which aids in calcium absorption in the human body. The purpose of this investigation is to analyze the molecular orbitals of various molecules involved in electrocyclic reactions in order to understand how WoodwardHoffmann rules and pi bonding in the HOMO can be used to predict whether each reaction was conrotatory or disrotatory. Broad Street Scientific | 2016-2017 | 19
2. Computational Approach In this study, the electrocyclic reactions that occur with four different reactant molecules were analyzed. The conrotatory or disrotatory behavior of each reaction was predicted using both the Woodward-Hoffmann rules and analysis of pi bonding in the HOMO of each open ring molecule. Then, the pi and sigma bonds in the HOMO for the reactant of each reaction and the product of each reaction were viewed using molecular orbitals calculations. These bonds were then analyzed to show how an electrocyclic ring closure converts a pi bond to a sigma bond and how a ring opening converts a sigma bond to a pi bond. The four reactant molecules analyzed were 1,3,5-hexatriene, cyclobutene, (2E,4Z,6E)-2,4,6octatriene, and 7-dehydrocholesterol. For the thermal electrocyclic ring opening reaction involving 1,3,5-hexatriene, the number of pi bonds in the molecule involved in the reaction was determined in order for the Woodward-Hoffmann rules to be applied. Once this number of pi bonds was found, whether the reaction was conrotatory or disrotatory was determined by whether the number of pi bonds was even or odd. Next, analysis of pi bonding in the HOMO of the molecule was performed to again predict whether the reaction was conrotatory or disrotatory. This was done by drawing the potential configurations of the p orbitals involved in the reaction, sorted by energy level, and then determining and analyzing the HOMO configuration. Whether the p orbitals on the atoms involved in forming the sigma bond were in phase or out of phase was used to determine whether the reaction was conrotatory or disrotatory. Finally, a molecule of 1,3,5-hexatriene and a molecule 1,3-cyclohexadiene (the product of the reaction) were built and molecular orbitals calculations were performed on each using MOPAC PM3. PM3 was the chosen method because it does not require a large amount of computing time and a high level of accuracy was not necessary for this study. The orbitals of the HOMO were then viewed and the change in the pi bond to a sigma bond was analyzed by comparing the HOMO of 1,3,5-hexatriene to that of 1,3-cyclohexadiene. A geometry optimization was only performed on the closed ring structure (1,3-cyclohexadiene) because a geometry optimization altered the proper structure of the opened ring structure (1,3,5-hexatriene). It was found that a comprehensive cleanup was sufficient to provide a proper structure for a molecular orbitals calculation to be performed on the opened ring structure. Next, the thermal electrocyclic ring opening reaction converting cyclobutene to 1,3-butadiene was analyzed using the same procedure as above. However, instead of analyzing and performing a molecular orbitals calculation on 1,3,5-hexatriene as the reactant and a geometry optimization and molecular orbitals calculation on 1,3-cyclohexadiene as the product, cyclobutene was analyzed and had a geometry optimization and molecular 20 | 2016-2017 | Broad Street Scientific
orbitals calculation performed on it as the reactant, and 1,3-butadiene had the molecular orbitals calculation performed on it as the product. The only other alteration made to this procedure for the cyclobutene reaction was that rather than viewing the change in the pi bond to a sigma bond using the molecular orbitals viewer, the change in the sigma bond to a pi bond was viewed due to the fact that this electrocyclic reaction is ring opening rather than ring closing. For the ring closing electrocyclic reaction involving 2,4,6-octatriene as the reactant, both the thermal and photochemical reactions were analyzed. For both reactions, Woodward-Hoffmann rules were used to predict whether each reaction was conrotatory or disrotatory. Then, the pi bonding in the HOMO of the (2E,4Z,6E)- 2,4,6-octatriene was analyzed to predict the conrotatory or disrotatory behavior of the thermal reaction, and the pi bonding in the excited state HOMO of the (2E,4Z,6E)-2,4,6-octatriene was analyzed to predict the conrotatory or disrotatory behavior of the photochemical reaction. Finally, a molecular orbitals calculation was performed on (2E,4Z,6E)-2,4,6-octatriene using MOPAC PM3, followed by a geometry optimization and molecular orbitals calculation on the product of the thermal reaction (cis-5,6-dimethyl- 1,3-cyclohexadiene) and the product of the photochemical reaction (trans-5,6-dimethyl1,3-cyclohexadiene). The orbitals in the HOMO of each molecule were then viewed to analyze the pi bond to sigma bond shift due to the electrocyclic reaction. For the photochemical ring opening electrocyclic reaction of 7-dehydrocholesterol, WoodwardHoffmann rules and pi bonding in the HOMO of 7-dehydrocholesterol were once again used to predict the conrotatory or disrotatory behavior of the reaction converting 7-dehydrocholesterol to provitamin D3. Next, molecular orbitals calculations were performed on 7-dehydrocholesterol, provitamin D3, and vitamin D3 in addition to an initial geometry optimization performed on 7-dehydrocholesterol. The HOMO of each molecule was viewed. The HOMO of 7-dehydrocholesterol was compared with that of provitamin D3 in order to analyze the conversion from a sigma bond to a pi bond due to the electrocyclic ring opening. Next, the HOMO of provitamin D3 was compared with that of vitamin D3 in order to analyze the movement of a sigma bond and rearrangement of the pi bonding due to the sigmatropic reaction.
3. Results and Discussion Reactant
1, 3, 5-hexatriene cyclobutene (2E, 4Z, 6E)-2, 4, 6-octatrine (2E, 4Z, 6E)-2, 4, 6-octatrine provitamin D3
Number of Thermal Pi Bonds or Photochemical 3 thermal
Conrotatory or Disrotatory disrotatory
Table 2. Predictions using Woodward-Hoffman rules. Table 2 shows the predictions made as to which reactions were conrotatory and which were disrotatory using Woodward-Hoffmann rules. The number of pi bonds involved in the electrocyclic reaction was determined by looking at the molecular model of the open ring molecule in each reaction. The number of double bonds in the open ring was determined to figure out the number of pi bonds. Then, the number of bonds (even or odd) and whether the reaction was thermal or photochemical were plugged into Table 1 to determine whether the reaction was conrotatory or disrotatory.
Figure 7. 1,3,5-hexatriene electrocyclic reactant and product (The NC HS Server, n.d.). Figure 7 demonstrates the ring closure of the molecule 1,3,5- hexatriene. This is a thermal reaction because it occurred between the end atoms of the highest occupied molecular orbital of the leftmost image. Since it was thermally electrocyclic and there were three pi double bonds, the disrotatory reaction that was predicted with Woodward-Hoffmann rules was verified in this circumstance. The formation of sigma bonds can be observed in the rightmost image of Figure 7 through the blue orbitals that extend towards each other in the direction of the bond responsible for closing the ring.
Figure 8. Cyclobutene molecular orbitals.
Figure 6. 1,3,5-hexatriene molecular orbitals. Figure 6 shows the pi orbitals for 1,3,5-hexatriene. It was determined that the third level was the HOMO because it would consist of three pi bonds, as does 1,3,5-hexatrieneâ€™s HOMO. Looking at the two end orbitals on the HOMO, it can be seen that they are in phase. Therefore, disrotatory behavior would be required to convert one of the pi bonds into a sigma bond.
Figure 9. Cyclobutene electrocyclic reactant and product (The NC HS Server, n.d.). The example in Figure 9 presents a simple reaction based on the opening of a ring structure. This is another representation of a thermal electrocyclic process and shows the properties of cyclobutene through a reaction Broad Street Scientific | 2016-2017 | 21
where the sigma bond was lost and a pi bond was formed on an open ring structure. The reactant had sigma bonds and a pi double bond, while the product gained a pi double bond after the reaction took place. Refer to Figure 8 to see the out of phase orientation of the two p orbitals on the HOMOâ€™s ends.
Refer to Figure 10 to see the in phase orientation of the p orbitals at the end of the HOMO. The rightmost figure shows the result of a photochemical reaction with electrocyclization. However, since the highest occupied molecular orbital became the excited state HOMO, the odd number of pi double bonds led to conrotation. Conrotatory reactions with 2,4,6-octatriene led to a specific stereochemistry as well. This product is known as trans-5,6-dimethyl- 1,3-cyclohexadiene because the methyl groups are on opposite sides of the molecular plane. Refer to Figure 10 to see the out of phase orientation of the two p orbitals at the end of the excited state HOMO. From this information, it can be concluded that in a thermal electrocyclic process with (2E,4Z,6E)-2,4,6octatriene, the stereospecific nature of the reaction will only yield cis products, and in a photochemical electrocyclic process, (2E,4Z,6E)-2,4,6-octatriene will only yield trans products.
Figure 10. (2E,4Z,6E)-2,4,6-octatriene molecular orbitals.
Figure 11. (2E,4Z,6E)-2,4,6-octatriene reactant and products (The NC HS Server, n.d.). The three molecules shown in Figure 11 are those involved in the thermal and photochemical electrocyclic reactions using 2,4,6-octatriene as the reactant. The leftmost molecule is the reactant of the electrocyclic reaction. It is important to observe this molecule because it shows the two pi orbitals that are on the verge of forming a sigma bond. The sigma bond completion is shown in two separate reactions, the products of which are shown as the middle and rightmost molecules of Figure 11. In the middle diagram, the molecule was formed from a reaction that underwent a thermal electrocyclic process. Due to the odd number of pi double bonds in the reactant, the reaction must proceed using disrotation. As disrotatory changes occur, a sigma bond forms in the opening and is shown in the middle molecule by the two red orbitals that extend across the bond. To further characterize this product, it can be named a cis product because its methyl groups are on the same side of the molecular plane. This product is known as cis-5,6-dimethyl- 1,3-cyclohexadiene. 22 | 2016-2017 | Broad Street Scientific
Figure 12. Provitamin D3 molecular orbitals. Figure 12 shows the pi orbitals for provitamin D3. Because this reaction is a photochemical reaction, the light that interacts with the molecule causes one of the electrons from the HOMO to move to its excited state, causing what would have been the LUMO to be an excited state HOMO. This became the orbital analyzed to determine the behavior of the reaction. Because the two orbitals at the ends of the excited state HOMO are out of phase, it was determined that conrotatory behavior was required to complete the electrocyclic reaction converting 7-dehydrocholesterol to provitamin D3.
Figure 13. 7-dehydrocholesterol, provitamin D3, and vitamin D3 HOMO orbitals from left to right, respectively (The NC HS Server, n.d.). Figure 13 shows from left to right 7-dehydrocholesterol, provitamin D3, and vitamin D3, respectively. As can be seen, during the photochemical electrocyclic ring closure that converts 7-dehydrocholesterol to provitamin D3, the conversion from 7-dehydrocholesterol to provitamin D3 involves a ring closure and the formation of a pi bond. This shows that a sigma bond was converted to a pi bond once the ring was opened. The sigmatropic reaction that converted provitamin D3 into vitamin D3 can also be seen because of the rearrangement of the pi bonds. 3. Conclusions The reaction involving 1,3,5-hexatriene is a thermal electrocyclic process; therefore, it was discovered that the orbitals located on the end of the molecule in the highest occupied molecular orbital were in phase. We can conclude that the reaction will take place through disrotatory changes in order to form a sigma bond between atoms that were previously held together with a pi bond. Cyclobutene was a unique aspect of this experiment because it showed the reverse reaction of a ring closure with the opening of a 4 carbon ring. This reaction is also a thermal electrocyclic reaction and contains an even number of pi bonds in the open structure; therefore, the out of phase p orbitals that were formed at the ends of the ring lost a sigma bond through conrotation to form two pi bonds. For analysis of (2E,4Z,6E)-2,4,6-octatriene, both thermal and photochemical reactions were demonstrated. As predicted through the Woodward-Hoffmann rules as well as the FMO theory, the molecule completed the electrocyclic ring closure in two distinct fashions. In the thermal reaction, the orbitals were in phase and participated in disrotation in order to form a sigma bond. In the photochemical reaction the orbitals were out of phase and participated in conrotation in order form the sigma bond. It was found from both the Woodward-Hoffmann rules and analysis of the HOMO of 7-dehydrocholesterol, provitamin D3, and vitamin D3 that the electrocylic reaction that converts 7-dehydrocholesterol to provitamin D3 is conrotatory. It was also seen that the reaction that converts provitamin D3 into vitamin D3 is a sigmatropic reaction based on the shift in pi orbital arrangement that can be seen from the HOMO illustration created using the CHEMISTRY RESEARCH
North Carolina High School Computational Chemistry Server. Electrocyclic reactions play an important role in chemistry. The change from pi to sigma bonding during a ring opening or closing reaction due to electrocyclic behavior governs many unimolecular reactions that play important roles. For example, the electrocyclic ring opening reaction that converts 7-dehydrocholesterol to provitamin D3 allows for the eventual production of vitamin 3D, which is vital to calcium absorption in humans. In addition, analysis of the conrotatory and disrotatory behavior is important because it allows for the stereoisomer being produced in the reaction to be predicted. 4. Acknowledgements The authors thank Mr. Robert Gotwals for assistance with this work. Appreciation is also extended to the Burroughs Welcome Fund and the North Carolina Science, Mathematics and Technology Center for their funding support for the North Carolina High School Computational Chemistry Server. 5. References Electrocyclic and Cycloaddition Reactions H. (n.d.). Retrieved January 14, 2017, from http://higheredbcs. wiley.com/legacy/college/solomons/0470401419/spetops/ special topic h.pdf Electrocyclic and Cycloaddition Reactions H. (n.d.). Retrieved January 14, 2017, from http://higheredbcs. wiley.com/legacy/college/solomons/0470401419/spetops/ special topic h.pdf Pericyclic Reactions. (n.d.). Retrieved January 14, 2017, from https://www.asu.edu/courses/chm332/ PericyclicReactions.pdf Pericyclic Reaction Chemistry. (n.d.). Retrieved January 14, 2017, from http://www.meta-synthesis.com/ webbook/49 pericyclic/pericyclic.html Pericyclic Reactions Electrocyclizations, Cycloadditions and Sigmatropic Rearrangements. (n.d.). Retrieved January 14, 2017, from http://pms.iitk.ernet.in/wiki/index. php/Pericyclic Reactions Cycloadditions nd Sigmatropic Rearrangements Schmidt, J.R.; Polik, W.F. WebMO Pro, version 7.0; WebMO LLC: Holland, MI, USA, 2007; available from http://www.webmo.net (accessed January 2017). The North Carolina High School Computational Chemistry Server, http://chemistry.ncssm.edu (accessed January 2017). Broad Street Scientific | 2016-2017 | 23
FASCIN EXPRESSION AND PURIFICATION AND FORMATION OF FASCIN-ACTIN PARACRYSTAL AS A SCAFFOLD FOR FUTURE PLASMONIC NANOFIBERS Tejas Pruthi Abstract Actin is a structural protein that is found in the body. This protein is bound together with fascin: a protein that is able to adhere bundles of actin to produce paracrystalline structures. Gold nanorods are nanoparticles that have plasmonic properties which allow them to transduct optical and electrical signals. In the experiment, cells were transformed with the fascin plasmid so that they would produce fascin. After the fascin was extracted from the cell, it was combined with actin to produce the paracrystals. Next, these paracrystals were then decorated with gold nanorods and tested for surface plasmon resonance. The samples showed a shift in longitudinal surface plasmon resonance, which could suggest horizontal coupling of the gold nanorods; this provides us with a scaffold for work on future plasmonic nanofibers. Key words: Gold nanorods, surface plasmon resonance, Actin, Fascin, plasmonic, cell transformation 1. Introduction Actin is a structural protein found in most eukaryotic cells; actin is used in cell processes like cell division, and muscle contraction. The protein comes in two forms, Globular actin and Filamentous actin. Globular actin, or G-actin, is the monomer form of actin. Filamentous Actin, or F-actin, is the polymer form that is produced in linear strands. Adenosine Tri-phosphate (ATP) is needed by the actin to maintain its structure over time, however the chemical phalloidin can be added to the actin to “freeze it” (Doherty & Mcmahon, 2008). The phalloidin prevents the depolymerization of the actin filaments by locking the individ ual monomers to each other, which occurs because the phalloidin will stick to the monomers more than the monomers do each other. Since the phalloidin makes the actin stay in tighter bonds, the structure does not suffer destabilization (Gunning, Ghoshdastider, Whitaker, Popp, & Robinson, 2015). This process is important to preserving the structural integrity of the actin bundles without the need of a constant supply of ATP (Cooper, 1987). Fascin is an actin-binding protein found in humans and other vertebrates, this protein is a fundamental part of the production of filopodia. Fascin binds F-actin bundles to each other, the protein is spaced out around in 11 nanometer(nm) intervals on the F-actin strands. Fascin has four main Beta-Trefoil domains, the first and third domains serve as binding sites for the actin filaments. The binding sites on the fascin will line up two parallel F-actin strands and bind them (Jansen et al., 2011; Bryan & Kane, 1978). Gold Nanorods are metal nanoparticles that are about 10 nanometers(nm) in diameter and 1-100 nm in length. These particles exhibit surface plasmon resonance; when light is introduced to the gold nanorods, the free electrons 24 | 2016-2017 | Broad Street Scientific
in the nanorods start to oscillate, creating an electromagnetic field. Coupled gold nanorods exhibit the same electromagnetic field, furthermore, this system of coupled nanorods has the ability to transduct an optical or electrical signal (Perezjuste, Pastorizasanto, Lizmarzan, & Mulvaney, 2005). Due to the nanoparticles rod-like shape, it has two “directions” of absorption, the transversal and the longitudinal. The transversal band refers to the shorter axis of the nanoparticle, while the longitudinal refers to the longer axis. This property of gold nanorods can give us an idea about which direction they have coupled (Stone, Jackson, & Wright, 2010; Liao et al., 2013). A wavelength vs. absorption graph can show transversal and longitudinal surface plasmon resonance. Gold nanorods have absorption in the wavelength spectrum of 300-900 nanometers, which includes the visible light spectrum (400-700 nm). For the gold nanorods, the absorption has peaks at two points: 515 nm and 900 nm. These peak at 515 nm correlates to the transversal axis and the 900nm peak correlates to the longitudinal axis. A wave shift in either of the peaks can mean a change in the coupling of the samples. A wave shift is when the absorption of a certain wavelength shifts over to another (Link, Mohamed, El-Sayed, 1999). For example, a .7 absorption ratio for 750 nm could shift to a 850 nm wavelength after a chemical reaction (Mcmillan et al., 2005). Gold nanorods, modified with polyethylenimine (PEI) polymer, bind to proteins. The polymer works by attracting the negatively charged outer surfaces of cells (Vancha et al., 2004). With the information provided, we conducted an experiment where we sought to create a scaffold for a plasmonic nanofiber using fascin, actin, and gold nanorods.
2. Materials and Methods Fascin and actin were gathered for the experiment. Actin was available at the facility, however fascin needed to be expressed and purified. Gold nanorods were bought from Nanopartz. The nanorods were coated with PEI polymer, they measured 10 nanometers in diameter and 45 nanometers in length. 2.1 – Fascin Preparation Competent Escherichia Coli (E.coli) were grown in LB media overnight, then placed in SOB++ media until the OD600 was between 0.4 and 0.6. Cells were placed on ice for 15 minutes and then centrifuged(4 Celcius(C), 8000 rpm) for 10 minutes. The supernatant was poured out and 5 milliliters of TB buffer (5mL buffer for the initial 25mL of cells) was mixed with the cells. Cells were placed on ice for 15 minutes and then centrifuged(4 C, 8000 rpm) for 10 minutes once more. The supernatant was poured out, and 2 ml TB buffer with 7 percent Dimethyl Sulfoxide (DMSO) was added to the cells (2ml for 25 ml initial cell culture). Tubes of cells were prepared, 200 microliters of cells per tube. The solution was frozen with liquid nitrogen and placed in -80 C storage. A tube of BL21(DE3) was thawed on ice for 10 minutes. Two 14-mL BD Falcon tubes polypropylene round-bottom tubes were chilled. 100 mL of cells were aliquoted into each of the Falcon tubes. 1.7 microliters of 1.5M 2Mercaptoethanol was added to each tube. Solution was incubated on ice for 10 minutes. 4 microliters of fascin plasmid was added to one Falcon tube. Tubes were incubated for 30 minutes. The SOC medium was heated to 42 C in a water bath. The Falcon tubes were put in a 42 C water bath for 45 seconds, and put in ice immediately afterwards. 880 microliters of SOC media and 20 microliters of Magnesium sulfate was added to each tube. Four ampicillin-coated agar plates were gathered. 100 microliters of solution from each tube were spread onto plates. Then, 900 microliters of solution from each tube was spread onto the remaining plates. These plates were incubated for 16 hours at 37 C. Individual colonies were taken from plates and grown in growth media. The transformed cells were collected and washed with the MES buffer. The cells were suspended in Buffer A and sonicated. The sonicated cells were spun down. The chitin resin was prepared and washed with milliQ water and Buffer A two times. The supernatant with cells was mixed with the resin and loaded into the column. Column was washed with Buffer B, then flushed with Buffer C. The column was left overnight and then the resin was eluted with Buffer A. 2.2 – Actin-Fascin Bundling G-actin was spun down and polymerized into F-actin by centrifuging it in F-buffer. Half of the sample was CHEMISTRY RESEARCH
mixed with phalloidin, while the other half was mixed with fascin. The fluorescence marker, Alexa-555, was added to both of the solutions. A confocal microscope was used to view the bundles. 2.3 – Paracrystal Decoration with Gold Nanorods Four samples were created with the protein samples. The first sample was G-actin and gold nanorods. 11 microliters of G-actin, 39 microliters of G-Buffer, and 50 microliters of Gold nanorods were put together to create a solution. 15.8 microliters F-actin, 34.2 microliters F-buffer, and 50 microliters of gold nanorods were mixed to create the Factin/Gold nanorods solution. 5 microliters of F-actin+phalloidin, 45 microliters of F-buffer, and 50 microliters of gold nanorods to create the F-actin+Phalloidin/gold nanorod solution. 50 microliters of F-actin+fascin, and 50 microliters of gold nanorods were mixed to create the F-actin+fascin/ gold nanorod solution. These solution were left overnight at room temperature. 3. Results 3.1 – Protein Preparation The cells from the bacterial transformation grew following a logistic curve. The rate of growth increased until about time 60 minutes where the rate growth started to slow (Figure 1). The original cells were not resistant to the ampicillin on the agar plates. The fascin plasmid included a gene for antibiotic resistance, this shows that the cells growing on the ampicillin agar plates contain the gene for antibiotic resistance and fascin production (Figure 2). The grown cells likely contain the fascin. The cells were put through a fascin purification process to get rid of excess cell parts and cellular proteins. After the process, fascin was found on the gel at 54 kD (Figure 3).
Figure 1. Cell Growth of E.coli with Fascin Plasmid. The optical density of the solution with the cells was measured at 600nm. The cell growth followed a logistic curve as shown by the red line. The cells were taken out of incubation at time 120 minutes. Broad Street Scientific | 2016-2017 | 25
Figure 2. Growth of cells implies successful transformation. The agar plates were coated with antibiotic. The left plate contains 900 microliters of cells with the fascin plasmid. The right plate contains 100 microliters of cells with the fascin plasmid. Figure 4. F-actin yields miniscule bundles. This solution contains F-actin and phalloidin. The image was taken with a confocal microscope at 40x magnification. The actin is labeled with a fluorescent marker.
Figure 3. Fascin was produced by the transformed cells. SDS PAGE gel was run. Throughout the Fascin purification process, samples were taken for the gel. The first sample was the supernatant after the sonicated cells were spun down, sample 2 came from pellet of the centrifuged solution. Sample 3 was from the supernatant and resin solution. Sample 4 and 5 were Buffer B and C, respectively. Sample 6 was fascin after the column, and sample 7 was the resin after the column. 3.2 â€“ Actin-Fascin Bundling The labeled actin appears white on the images; the brighter the white, the more actin there is concentrated in one area. The F-actin was mixed with phalloidin to stabilize the F-actin bundles. The bundles made by the F-actin and phalloidin were small and scarce, the bundles were about 10 nanometers in diameter (Figure 4). The fascin and F-actin solution produced much denser and abundant bundles than Fascin and phalloidin (Figure 5).
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Figure 5. F-actin and Fascin create bigger bundles. This solution has F-actin and Fascin. The image was taken with a confocal microscope at 40x magnification. The actin is labeled with a fluorescence marker. 3.3 â€“ Paracrystal Decoration with Gold Nanorods Transversal surface plasmon resonance is the vertical movements of electrons in the gold nanorod, while the longitudinal surface plasmon resonance shows the horizontal movement of electrons. The shift in peaks in the 870-900 range shows the electrons seem to not be moving on the same wavelength (Figure 6).
Figure 6. Gold Nanorods exhibit surface plasmon resonance. This solution has F-actin and Fascin. The peaks at 515 nm represents the transversal surface plasmon resonance of the gold nanorods. The peak at 900 nm represents the longitudinal surface plasmon resonance of the gold nanorods. 4. Discussion In the first experiment, we were able to create fascin using bacterial transformation, and fascin purification. We knew that our cells were capable of producing the Fascin because we gave them the Fascin plasmid. We grew the cell on antibiotic coated agar plates, however, the original cells were not resistant to the antibiotic. The fascin plasmid contained a gene for antibiotic resistance, since cells grew on our agar plates we were able to conclude that our cells had successfully obtained the fascin plasmid. In the fascin purification process, we aimed to extract the fascin from the cells. After putting the cells through various chemicals we were able to find pure fascin. We were able to reach this conclusion because we tested our fascin with an SDS PAGE gel. The results of the gel showed the fascin sample weighed 54 kilodalton. In the next experiment we showed that fascin is able to bind to actin to create ordered, paracrystalline structure. F-actin by itself produces a small strands of actin while F-actin and fascin produce large bundles that are ordered in nature. In the final experiment, we were able to show that the gold nanorods exhibited coupling and surface plasmon resonance. The frameshift in the wavelengths of the Gold nanorods only to the Factin+fascin/gold nanorod soltuions shows that the gold nanorods may be horizontally coupled. This could suggest the possibility of producing a plasmonic nanofiber that is able to transduct an optical or electric signal. 5. Conclusion One of the fastest forms of communication we have today is fiber optic communication. This type of commuCHEMISTRY RESEARCH
nication relies on the use of light to transfer information from point A to point B. Many communication companies have taken advantage of this technology to deliver faster and more reliable connections for consumers, for example tech giants like Google and AT&T have set up their fiber services in neighborhoods all across America . These programs work by setting up large fiber cables underground that connect to a big hub in a nearby area. This allows for faster internet speeds as well as other benefits. However, fiber optics is usually associated with a larger scale. The work that we have done is aimed at finding new solution for a smaller scale, especially in fields like nanocomputing. Computers have come a long way from their original form. They used to be big bulky machines that took up rooms, and they could only do 1 operation at a time. However, every new generation of computer has become smaller and faster. The processors in the computer have gotten smaller and smaller, to the point where the size of the nodes are reaching levels where quantum tunneling is occurring within them. With the size of computer constantly decreasing, the need of small scale communication devices is increasing. Nanocomputing may be the next big thing in the hardware side of computers. Having computers-with their fundamental parts-that are smaller than a few nanometers could open opportunities to make incredibly fast computers (Waldner, 2008). However, one downside to going to this scale is the communication between the computers and their individual parts. Unfortunately, fiber optics have a physical limitation. The radius of a fiber that a light is travelling through has to be at least four times the wavelength of the light. In other terms, the fiber has to have a diameter of at least half the wavelength (Genet & Ebbesen, 2007). For example, a 500 nanometer light can go through a 250 nm diameter fiber, and nothing smaller without any major attenuation. This presents a problem because most fiber technology works with light between the 800-1550 nm wavelengths. This is where gold nanorods and other nanoparticles can come into play. The wavelength of light is not a barrier for the gold nanorods because they just translate light into electron oscillations. The nanorods have electromagnetic properties that allow for nearby nanorods to copy the same electron oscillation, which can be used to carry a signal (Perezjuste et al., 2005). The goal of this project was to try to test if building some type of nanofiber was possible. The fascin-actin bundles functioned as a support for the nanorods, this relationship is similar to how a computer case is there to hold the parts of the computer together. The bundles keep the gold nanorods attached to one central line so that they can be close enough to carry on a signal. The gold nanorods are where the actual action happens. In the future, we would like to test the viability of this structure as a data transmission medium. Another test would be to find any attenuation that occurs in the gold nanorods. This project is really Broad Street Scientific | 2016-2017 | 27
taking the idea of high speed fiber optic technology and making it suitable for a smaller scale: a place where fiber optic technology may not be able to work as efficiently. 6. Acknowledgements I would like to thank UNC Charlotte for allowing me to come and use their resources. I would like to thank Dr. Shagufta Raja and the Center for STEM Education for giving me the opportunity to participate in a research program. I would like to thank Dr. Yuri Nesmelov with the Department of Physics and Optical Science for allowing me to work in his lab, as well as mentoring me throughout this project. I would lastly like to thank Joel Solomon, Jinghua Ge, and Kylen Blanchetta for helping me out in the lab. 7. References Doherty, G. J., Mcmahon, H. T. (2008). Mediation, Modulation, and Consequences of Membrane-Cytoskeleton Interactions. Annual Review of Biophysics, 37(1), 65-95. Gunning, P. W., Ghoshdastider, U., Whitaker, S., Popp, D., Robinson, R. C. (2015). The evolution of compositionally and functionally distinct actin filaments. Journal of Cell Science,128(11), 2009-2019.
tion of the Optical Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the Effect of the Medium Dielectric Constant. The Journal of Physical Chemistry B,103(16), 3073-3077. Mcmillan, B. G., Berlouis, L. E., Cruickshank, F. R., Pugh, D., Brevet, P. (2005). Transverse and longitudinal surface plasmon resonances of a hexagonal array of gold nanorods embedded in an alumina matrix. Applied Physics Letters,86(21), 211912. Vancha A. R. et al. . Use of polyethyleneimine polymer in cell culture as attachment factor and lipofection enhancer. BMC Biotechnology. 4, 23â€“34 (2004). Google Fiber. (2017). Fiber.google.com. Retrieved 10 January 2017, from https://fiber.google.com/about/ ATT Fiber Make High Speed Internet Even Faster. (2017). Att.com. Retrieved 10 January 2017, from https://www. att.com/internet/gigapower.html Waldner, J. (2008). Nanocomputers and swarm intelligence. London: ISTE. Genet, C., Ebbesen, T. W. (2007). Light in tiny holes. Nature, 445(7123), 39-46.
Cooper, J. A. (1987). Effects of cytochalasin and phalloidin on actin. The Journal of Cell Biology,105(4), 1473-1478. Jansen, S., Collins, A., Yang, C., Rebowski, G., Svitkina, T., Dominguez, R. (2011). Mechanism of Actin Filament Bundling by Fascin. Journal of Biological Chemistry,286(34), 30087-30096. Bryan, J., Kane, R. E. (1978). Separation and interaction of the major components of sea urchin actin gel. Journal of Molecular Biology,125(2), 207-224. Perezjuste, J., Pastorizasantos, I., Lizmarzan, L., Mulvaney, P. (2005). Gold nanorods: Synthesis, characterization and applications. Coordination Chemistry Reviews,249(17-18), 1870-1901. Stone, J., Jackson, S., Wright, D. (2010). Biological applications of gold nanorods. Wiley Interdisciplinary Reviews: Nanomedicine and Nanobiotechnology,3(1), 100-109. Liao, Y., Shiang, Y., Chen, L., Hsu, C., Huang, C., Chang, H. (2013). Detection of adenosine triphosphate through polymerization-induced aggregation of actin-conjugated gold/silver nanorods. Nanotechnology,24(44), 444003. Link, S., Mohamed, M. B., El-Sayed, M. A. (1999). Simula28 | 2016-2017 | Broad Street Scientific
TARGETING CANCER THROUGH ALTERING HYALURONAN SYNTHESIS AND DEGRADATION Emma Garval Abstract Hyaluronan (HA), a polymer that is a component of the extracellular matrix, is present in all vertebrate cells. In healthy cells the rates of synthesis and degradation of HA are equal, but when the rate of degradation becomes greater than the rate of synthesis, fragments of HA can accumulate. HA fragments increase cell proliferation and can lead to malignancy. However, other research has shown that excessive HA synthesis also leads to cancer. In this experiment HA synthesis and degradation were altered in mouse breast cancer cells, in order to determine whether inhibiting HA fragmentation or HA synthesis would be a better cancer treatment. The cells were treated with different combinations of HA promoters and inhibitors in order to determine the optimal combination that leads to the least cancer cell density and most cancer cell mortality. L-ascorbic 6-hexadecanote (L-Hex) and Tiopronin inhibited HA degradation, while 4-methylubelliferone (4MU) inhibited HA synthesis and 12-O-tetradecanoyl-phorbol-13- acetate (TPA) promoted HA synthesis. The inhibition of HA synthesis with 4-MU caused a significant decrease in cancer cell density and increase in cancer cell mortality. In addition, the combination of TPA and L-Hex prevented HA fragmentation through promoting HA synthesis and inhibiting HA degradation, and showed a trend in decreasing cell proliferation and increasing cell mortality. Through altering HA synthesis and degradation in cancer cells, this experiment indicates that inhibiting HA synthesis with 4-MU is a more effective cancer treatment than inhibiting HA fragmentation with TPA, L-Hex, or Tiopronin. 1. Introduction Hyaluronan (HA), along with the enzymes that produce and degrade it, can inhibit or facilitate cancer depending on its molecular weight and type. Hyaluronan is a component of the extracellular matrix of vertebrate cells that is a form of a glycosaminoglycan (Sironen et al., 2011). It is a polymer composed of alternating units of N-acetyl glucosamine (GlcNAc) and glucuronic acid (GlcA) (Girish and Kemparaju, 2007). HA is present in the tissues of all vertebrates, with an elevated concentration in the connective, nervous, and epithelial tissues (Girish and Kemparaju, 2007). Furthermore, HA is distinguished by its high native molecular weight ranging between 2×10⁵ and 10×10⁷ Da, which gives it many of its unique properties such as the ability to bind to large amounts of water and to form viscous gels (Sironen et al., 2011). HA serves an important function in joint mobility as a component of cartilage and synovial fluid, and facilitates skin hydration (Liang et al., 2015). In recent years, HA has also gained attention due to its role in the many stages of cancer in humans. The results of several experiments point toward the degradation of HA into low molecular weight hyaluronan (LMW-HA) as being a significant cause of malignancy and a predictor of negative cancer outcomes (Cowman et al., 2015). Normally HA has a high rate of turnover, with new HA constantly being produced as old HA is degraded, but fragmentation is caused when the rate of HA degradation is greater than the rate of HA synthesis (Cowman et al., 2015). Fragmentation causes HA’s normal high molecular weight to be broken down into smaller fragments that are less than 10⁵ BIOLOGY RESEARCH
DA (Alaniz, 2008). Hyaluronan is synthesized by the enzyme hyaluronan synthase (HAS), and is degraded by both the enzyme hyaluronidase (HYAL) and oxidative degradation (Liang et al., 2015) (Fig. 1). In its native form, HA has a high molecular mass, so when it is fragmented by HYALs in tumors, the fragmentation encourages inflammation, making the tumor cells more likely to survive (Schwertfeger et al., 2015). In a clinical study (Wu et al., 2014), serum collected from breast cancer patients was used for a cell culture. The most highly invasive breast cancer cells had increased levels of LMW-HA (molecular weight of 10⁵ DA) and increased HYAL activity (Wu et al., 2014).
Figure 1. Pathway of HA synthesis to degradation. The enzyme HAS synthesizes HA, which is degraded into HA fragments by the enzyme HYAL and by oxidative degradation. While HA fragmentation has been shown to lead to cancer, conflicting research has indicated that excessive HA synthesis facilitates cancer growth. When HA synthesis in prostate cancer cells was inhibited by the drug Broad Street Scientific | 2016-2017 | 29
4-methylumbeliferone (4-MU), migration was decreased (Cheng et al., 2015). Similarly, 4-MU had antitumor effects in canine mammary cells through decreasing cell proliferation and inducing apoptosis (Saito et al., 2013). The drug 4-MU acts as a competitive inhibitor of HA synthesis by becoming the acceptor of the substrate of UDP-GlcUA, which lowers the amount of UDP-GlcUA that can bind to HA (Morohashi et al., 2006) (Table 1, Fig. 2). In contrast, 12-O-tetradecanoyl-phorbol-13-acetate (TPA) was used in pancreatic cancer cells to promote HA synthesis through the activation of the protein kinase C. The TPA caused the cancer cells to increase migration (McAttee et al., 2014). However, lower concentrations of TPA have been used to inhibit cancer growth (Table 1, Fig. 2). In one experiment, a low dose TPA was combined with the anti-cancer drug Taxol, and effectively inhibited the growth of human prostate cancer cells (Zheng et al., 2006). Several inhibitors specifically target HYAL1, which degrades a variety of weights of HA. The highest level of inhibition was achieved by L-ascorbic 6-hexadecanote (L-Hex) (McAtee et al., 2014) (Table 1, Fig. 2). L-Hex was tested in streptococcal and bovine testicular hyaluronidase, and inhibited HYAL1 by having the L-ascorbic acid part binding to the catalytic site of HYAL1 (Botzki, 2004). Drug
Effect on HA Synthesis/Degradation Inhibits HA synthesis
Promotes HA synthesis
for HA degradation, HA can also be degraded by reactive oxygen/nitrogen species (ROS/RNS). This degradation is caused by the production of free radicals like OH and mediated by metals like copper ions (Valachova et al., 2015). The drug Tiopronin contains an SH- group which donates H+ and can counteract oxidative degradation (Table 1, Fig. 2). This structure enabled Tiopronin effectively stop the oxidative degradation of HA in joints (Valachova et al., 2015). While Tiopronin was tested against HA degradation associated with acute joint inflammation, it could also be effective in retarding the oxidative stress associated with HA fragmentation in cancer cells.
Effect on Cancer
Decreases cancer cell proliferation and cell migration (Saito et al., 2013). High concentrations increase cancer cell migration (McAttee et al., 2014); low concentrations inhibit cancer cell growth (Zheng et al., 2006). Has not been tested on cancer cells
Inhibits synthesis through inhibiting HYAL Inhibits synHas not been tested on thesis through cancer cells inhibiting oxidative degradation
Table 1. The effect of drugs that alter HA synthesis (4MU, TPA) and degradation (L-Hex, Tiopronin) on HA synthesis/degradation and cancer. While a lot of research points towards increased HYAL activity or decreased HAS activity as being a mechanism 30 | 2016-2017 | Broad Street Scientific
Figure 2. The effect of the drugs TPA, 4-MU, L-Hex, and Tiopronin on the degradation pathway of HA. TPA promotes HA synthesis, 4-MU inhibits HA synthesis, L-Hex inhibits HYAL degradation of HA, and Tiopronin inhibits oxidative degradation of HA. HA is an integral component of cancer progression, impacting cell proliferation, migration, metastasis, and angiogenesis. The results of some experiments point toward hyaluronan fragmentation as being a cause for malignancy, while other experiments point toward excess HA synthesis leading to cancer. Several inhibitors and promoters of HYAL and HAS have been shown to be effective in either increasing or decreasing the activity of these enzymes. HA degradation has also been targeted through drugs that donate electrons and prevent oxidative degradation. While these drugs have been tested on their ability to alter HA synthesis or degradation, their effect on cell proliferation and mortality has often not been tested. Testing cancer cell proliferation and mortality under different HA synthesis and degradation altering treatments could provide new insights into how the balance of HA synthesis and degradation can promote or inhibit cancer. In addition, the effect of combining different inhibitors and promoters of BIOLOGY RESEARCH
hyaluronan synthesis and degradation has not previously been tested, but would enable further control over the rate of synthesis and degradation of HA. The drug 4-MU could be used to inhibit HA synthesis, the drug TPA could be used to promote HA synthesis, the drug L-Hex could be used to prevent the HA degradation through inhibiting HYAL, and Tiopronin could be used to prevent the oxidative degradation of HA. This method of controlling the rate of synthesis and degradation of HA could be a novel cancer treatment that could be catered to different types and stages of cancer. 2. Materials and Methods 2.1 – Experimental Design for Experiments Combining Hyaluronan Synthesis Altering Drugs (4-Mu, TPA) and Hyaluronan Degradation Altering Drugs (L-Hex, Tiopronin) The drugs that inhibit HA Degradation (L-Hex and Tiopronin) were combined with drugs that alter HA synthesis (TPA and 4-MU). The combination of different drug treatments and the control treatment created 9 treatment groups: TPA, 4-MU, L-Hex, TPA+L-Hex, 4-MU+L-Hex, 4-MU+Tiopronin, TPA+ Tiopronin, and 4-MU+Tiopronin. Cell density and percent cell mortality was measured as the response variable. 3 trials with a sample size of n=3 were conducted, to give a total sample size of n=9 (Fig. 3).
Synthesis Altering No Synthesis Inhibitor/ Promoter No Degradation Inhibitor
HYAL Inhibition (L-Hex) Oxidative Degradation In hibition (Tiopronin)
Figure 3. Experimental design; cell density and percent mortality were measured as the response variable. 2.2 – Cancer Cell Culture CRL-2116, mouse epithelial, mammary, adenocarcinoma cells were obtained from ATCC. This cell line was established in 1983 from a mammary adenocarcinoma tumor along the midline of a female BALB/c mouse (ATCC). The cells were grown in RPMI media (Sigma) that contained 10% fetal bovine serum (Sigma) and 1% Penn Strep (Sigma), and were incubated at 37° C and 5% CO2. The cells were split every 2-3 days at a 1:5 ratio when they reached BIOLOGY RESEARCH
70-80% confluence. 2.3 – Reagents 4-MU, Tiopronin, L-Hex, and TPA were obtained from Sigma Aldrich. Each of these drugs were dissolved in 1 mL of DMSO, and vortexed to ensure that they dissolved. 4 stock solutions were made: 1 M 4-MU, 0.1 M Tiopronin, 0.1 M L-Hex, and 1 ng/mL TPA. These drugs were stored at in 100 µL aliquots at -20 °C and defrosted an hour before use. 2.4 – Preliminary Dosage Experiments Each drug was tested at 3 different concentrations to determine the optimal dosage for lowering the cell density of the CRL-2116 cells. Dosage ranges for each drug were obtained from the literature, and based on those values, a wide range of dosages were chosen for the preliminary experiment. First, a 10 mL solution of RPMI media and drugs was made. Different amounts of each drug were added to the media, but the amount of DMSO in each solution was adjusted to ensure that the different treatments contained the same amount of DMSO. A control media solution was also made that contained the same amount of DMSO as the different drug treatments. The amount of DMSO was also adjusted so that each plate would have less that 0.2% DMSO. Next, a 100 mm diameter, 15 mL plate of CRL-2116 cells was trypsinized and split into two 6-well plates. Each well in the 6 well plates was plated with 133 µL of cells to maintain a 1:5 ratio of cells to media. Then, 1867 µL of the media mixtures containing the different concentrations of the drugs was added to each of the wells, so that each well contained a total of 2 mL. Each concentration of drug had 3 replicates, giving each dosage experiment a total sample size of N=12. 2.5 – Experiments With Combinations of Drugs Based on the results of the preliminary experiments, 0.5 mM 4-MU, 10 µM Tiopronin, 5 µM L-Hex, and 10 ng/mL TPA were used for the experiments that combined drugs. First, 9 different 7 mL mixtures of media and drugs were prepared for the 9 treatment groups. The concentration of DMSO in each solution was adjusted so that each solution would have 15 µL of DMSO, making the final concentration of DMSO in the cell culture less than 0.25%. The control media mixture also had 15 µL of DMSO added to it. Then, the same procedure from the preliminary dosage experiments was followed to split a 15 mL plates of cells into 6-well plates, and to add the drugged media mixtures to these plates. After the plates were seeded with the CRL2116 cells and the drug media mixtures were added to the plates, the plates were incubated at 37 °C and 5% CO2. After 3 days, the cell density of the plates were scored using a hemocytometer that was stained with Trypan blue (Sigma), and viewed through an inverted scope (Bark, 2005). Broad Street Scientific | 2016-2017 | 31
The experiment was repeated 3 times, with each of the 9 treatment groups having 3 replicates. From these 3 trials, each treatment group had 9 replicates, and the entire experiment had a total sample size of N=81. 2.6 – Protocol Change In Trial 1 of Main Experiment In the first trial of the experiment, the 35 µM of L-Hex and 1 mM of 4-MU were used instead of 5 µM L-Hex and 0.5 mM 4-MU used in trial 2 and 3. However, these higher concentrations of L-Hex and 4-MU precipitated when added to the RPMI media. Since this occurred when the rest of the experiment was already set-up, the trial was continued with these drugs that precipitated. However, to avoid precipitation in the second trial, the concentration of 4-MU was reduced to 0.5 mM and the concentration of L-Hex was reduced to 5 µM. Besides these changes in concentration of 4-MU and L-Hex, this trial followed the same procedure as trial 2 and trial 3. 2.7 – Cell Density Assay After the cells had grown in the 6-well plates for 3 days, the cell density of each plate was recorded using a hemocytometer. The cells were stained by mixing 50 µL of cells with 50 µl of Trypan blue in a micro centrifuge tube. 20 µL of the cell-Trypan blue mixture was pipetted into the hemocytometer. The hemocytometer was then viewed under an inverted scope, and the number of alive and dead cells in 3 different locations were counted. The number of alive cells for the 3 locations were averaged, and this number was multiplied by 2x104 to find the cell density per mL. 2.8 – Statistical Analysis JMP statistical analysis software was use to perform Student’s T-Tests, analysis of variance tests, ANOVA, and Tukeys HSD tests. Excel was use to graph the data. 3. Results 3.1 – Preliminary Dosage Experiments The results of the preliminary dosage experiments were measured and analyzed with a Student’s T-Test (JMP) to determine significance. Based on the results, in the subsequent experiments, 0.5 mM 4-MU, 10 ng/mL TPA, and 10 μM Tiopronin were used, as they gave statistically lower cell densities than the controls (Fig. 4). Though 500 μM L-Hex led to the lowest cell density, both 500 μM and 50 μM concentrations precipitated in the media, so 5 μM L-Hex was used in the subsequent experiment.
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Figure 4. A. Cell density after 3 days for cells treated with 0.1 mM, 0.5 mM, and 1 mM 4-MU. The concentration 1 mM had significantly lower cell density than the control. B. Cell density after 3 days for cells treated with 1 ng/mL, 10 ng/mL, 100 ng/mL TPA. The 10 ng/mL dosage had a significantly lower cell density than the control. C. Cell density after 3 days for cells treated with 5 µM, 50 µM, 500 µM L-Hex. The 500 µM had no cell growth, so it was statistically lower than the control. D. Cell density after 3 days for cells treatment with 10 µM, 55 µM, 100 µM of Tiopronin. No concentrations of Tiopronin had a significantly lower cell density than control. 3.2 – Percent Mortality Compared Across Synthesis Altering Drugs, Degradation Altering Drugs, and Combinations of Synthesis and Degradation Altering Drugs An analysis of variance test (JMP) determined that the variation in percent cell mortality between all of the drug treatments did not occur by chance and was statistically significant with p=0.0001. An ANOVA (JMP) determined that there was a significant effect of the synthesis altering drugs (4-MU and TPA) on percent mortality of the CRL-2116 cells on day 3, with p = 0.0195 (Table 2). A Tukey’s HSD test (JMP) showed that specifically drug treatments with 4-MU (4-MU, 4-MU+L-Hex, 4-MU+Tiopronin) caused a significantly higher percent mortality than the treatments with no synthesis altering drugs (control, L-Hex, Tiopronin) (Fig. 5). A Tukey’s HSD test also showed that treatments with TPA (TPA, TPA+L-Hex, TPA+Tiopronin) fell in between 4-MU and the control in terms of percent mortality, but was not statistically different from either treatments with 4-MU or treatments with no synthesis altering drugs (Fig. 5). There was also a significant effect of the degradation altering drugs (L-Hex and Tiopronin) on percent mortality of the CRL-2116 cells at day 3, with p=0.0379 (Table 2). A Tukey’s HSD Test BIOLOGY RESEARCH
showed specifically that cells treated with L-Hex (L-Hex, 4-MU+L-Hex, TPA+L-Hex) had significantly more cell mortality than the cells treated with Tiopronin (Tiopronin, 4-MU+Tiopronin, TPA+Tiopronin) (Fig. 6). The cells treated with no degradation altering drugs (Control, 4-MU, TPA) fell in between the L-Hex and Tiopronin in their percent mortality, causing there not to be a detectable difference between L-Hex percent mortality and the control or Tiopronin percent mortality and the control (Fig. 6). The ANOVA also revealed that there was not significant effect of the combination of synthesis and degradation drugs on percent mortality, with p=0.7468 (Table 2). Source Synthesis Altering Degradation Altering Synthesis Altering*Degradation Altering Trial
F Ratio 4.1687
Prob > F 0.0195*
Table 2. ANOVA test from JMP. Shows that the synthesis altering drugs (4-MU and TPA), degradation altering drugs (L-Hex and Tiopronin), and the 3 trials have statistically significant differences in their percent mortality, with p<0.05.
Figure 5. Mean percent mortality after 3 days for treatments with L-Hex (L-Hex, 4-MU+L-Hex, TPA+LHex), treatments with no degradation altering drugs (control, 4-MU, TPA), and treatments with Tiopronin (Tiopronin, 4-MU+Tiopronin, TPA+Tiopronin). Different letters signify statistically different percent mortalities, with L-Hex having a significantly higher percent morality than Tiopronin. Error bars are plus 1 standard error of the mean.
Figure 6. Mean percent morality after 3 days for treatments with 4-MU (4-MU, 4-MU+L-Hex, 4-MU+Tiopronin), treatments with TPA (TPA, TPA+L-Hex, TPA+Tiopronin), and treatments with no synthesis altering drugs (control, L-Hex, Tiopronin). Different letters signify statistically different percent mortalities, with 4-MU having a statistically higher percent mortality than treatments with no synthesis altering drugs. Error bars are plus 1 standard error of the mean. 3.3 – Cell Density Compared Across Synthesis Altering Drugs, Degradation Altering Drugs, and Combination of Synthesis and Degradation Altering Drugs An analysis of variance test (JMP) determined that the variation in cell density between all of the drug treatments did not occur by chance and was statistically significant with p<0.0001. An ANOVA (JMP) determined that there was a significant effect of the synthesis altering drugs (4MU and TPA) on the cell density of the CRL-2116 cells at day 3, with p<0.0001 (Table 3). A Tukey’s HSD (JMP) test determined that 4-MU treated cells had a statistically significantly lower cell density than the control. The test also revealed that the TPA treated cells had a lower cell density than the control cells and a higher cell density than the 4-MU treated cells. However, the test did not detect a significant difference in cell density between TPA treated cells and control cells, or TPA treated cells and 4-MU treated cells. The ANOVA also that determined there was a significant effect of the synthesis altering drugs (L-Hex and Tiopronin) on the live cell density of the CRL-2116 cells at day 3, with p=0.0216 (Table 3). A Tukey’s HSD test determined that the Tiopronin treated cells had a statistically higher cell density than the L-Hex treated cells. The test also showed that the control cells had a lower cell density than the Tiopronin treated cells and a higher cell density than the L-Hex treated cells, but were not significantly different from either Tiopronin or L-Hex. The ANOVA also determined that there was a significant effect of the combinations of synthesis and degradation altering drugs, with p=0.0314 (Table 3). A Tukey’s HSD test determined that the cell density of the Tiopronin treated cells was significantly different from cell treated Broad Street Scientific | 2016-2017 | 33
with L-Hex, TPA+Tiopronin, TPA, 4-MU, 4-MU+L-Hex, and 4-MU+Tiopronin (Fig. 7). The test also determined that the control cells were significantly different from the cells treated with 4-MU, 4-MU+L-Hex, and 4-MU+Tiopronin (Fig. 7). The drug treatments could be ordered from lowest to highest cell density: 4-MU+Tiopronin, 4-MU+L-Hex, 4-MU, TPA+L-Hex, TPA, TPA+Tiopronin, L-Hex, Control, and Tiopronin (Fig. 7). Additionally, the areas of significance and overlap between all the different treatment groups were analyzed (Fig. 7). Source Synthesis Altering Degradation Altering Synthesis Altering*Degradation Altering Trial
F Ratio 26.0814
Prob > F < .0001*
Table 3. ANOVA test for percent mortality from JMP. Shows that synthesis altering drugs (4-MU and TPA), degradation altering drugs (L-Hex and Tiopronin), the combination of synthesis altering and degradation altering drugs, and the trials have statistically significant differences in their percent mortality, with p<0.05.
Figure 7. The mean cell density after 3 days of growth for the drug treatments: control, TPA, 4-MU, L-Hex, Tiopronin, TPA+L-Hex, 4-MU+L-Hex, TPA+Tiopronin, and 4-MU+Tiopronin. Errors bars are plus 1 standard error of the mean. Letters signify statistical differences between treatments, with non-overlapping letters indicating significantly different treatments.
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4. Discussion 4.1 â€“ Effect of Synthesis Altering Drugs, Degradation Altering Drugs, and Combination of Synthesis and Degradation Altering Drugs on Cell Percent Mortality The combination of 4-MU and L-Hex had the highest percent mortality, significantly higher than that of the Tiopronin treated cells or the control cells. However, there was a lot of overlap in percent mortality between the drug treatments, and not a significant difference between the 4-MU+L-Hex treatment, and the 4-MU, TPA, TPA+LHex, L-Hex, 4-MU+ Tiopronin, or TPA+Tiopronin treatments. These treatments were also not significantly different from the control. Additionally, while not significant, the data showed a trend of increasing cancer cell mortality across all of the other drug treatments except Tiopronin. These results showed that the combination of inhibiting HA synthesis with 4-MU and inhibiting HA degradation with L-Hex caused significantly higher percent mortality than the control. While altering HA synthesis and degradation had a definite effect on cancer cell mortality, further research will need to be done to understand the nature of this effect. 4.2 â€“ Effect of Synthesis Altering Drugs, Degradation Altering Drugs, and Combination of Synthesis and Degradation Altering Drugs on Cell Density Overall, cells treated with 4-MU had the lowest cell density at day 3. The combinations of 4-MU+Tiopronin and 4-MU+L-Hex had a slightly lower cell density than just 4-MU alone, but since L-Hex and Tiopronin treated cells were not statistically different from the control, it is likely that the 4-MU alone was responsible for the decrease in cell density in these drug combinations. These results demonstrate that through inhibiting the synthesis of HA in cancer cells, 4-MU decreased the cancer cells ability to proliferate. This data aligns with previous experiments, which showed that 4-MU decreased cancer cell density (Saito et al., 2013). While the cell density of L-Hex treated cells were not statistically significantly lower than control cells (p > 0.05), there was a definite trend towards decreasing cell density with L-Hex. The L-Hex had slightly over 33% of the mean cell density of the control, and with a larger sample size to account for the large variation in the data, this effect might be significant. These results suggest that preventing the degradation of HA through inhibiting HYAL (the enzyme that degrades HA) had some effect on cell proliferation, but was not significant. In addition, L-Hex had not been tested in cell culture prior to this experiment, and consequently there were unanticipated difficulties with solubility and precipitation of L-Hex. The higher concentrations of L-Hex where the drugs would precipitate killed almost all of the cells, but this was likely due to the large chunks of precipitate floating in the cell media. Due to this precipitaBIOLOGY RESEARCH
tion, only low concentration of L-Hex could be used in the experiment. Finding a way to prevent the L-Hex from precipitating at higher concentrations would be key for further research involving L-Hex and cell culture. In addition, other drugs that inhibit HYAL might be more compatible with cell culture than L-Hex. While the cell density of TPA treated cells was not significantly different than the cell density of control, there was a definite trend towards decreased cell density in the TPA treated cells, with these cells having less than 33% the mean cell density of the control cells. This suggests that promoting HA synthesis with TPA decreased cell density in cancer cells, but that this decrease was not significant at this sample size. Similarly, the difference between the TPA treated cells and the TPA+L-Hex treated cells was not significant, but there was a slight trend in the data. The combination of TPA and L-Hex caused cells to have only about 75% of the cell density of the cells treated with either TPA or L-Hex alone. This shows that the combination of inhibiting HA degradation (L-Hex) and promoting HA synthesis (TPA) to reduce HA fragmentation could be more effective for treating cancer than just inhibiting degradation or promoting synthesis alone. The Tiopronin treated cells did not have a statistically different cell density than the control cells, and actually had the highest mean cell density across the nine different drug treatments. This suggests that inhibiting the oxidative degradation of HA with Tiopronin was not an effective cancer treatment, and trends in the data suggest that Tiopronin even promoted cancer cell growth. In the preliminary dosage experiment, there had been a decrease in cell density with a 10 ÂľM dose of Tiopronin, but since the preliminary sample size was small, this dosage response was likely an artifact of the experiment. Prior to this experiment Tiopronin had not been tested on cells, so it is likely that the Tiopronin did not significantly impact the hyaluronan content in the cells, and therefore did not impact their cancer growth. It is also likely that the dosage of Tiopronin was too low to have an effect, and that a higher dosage could decrease cancer cell growth.
(TPA). Inhibiting the oxidative degradation of HA with Tiopronin had no effect on cancer cell density or percent mortality. Like previous research involving the effect of HA synthesis and degradation (Schwertfeger et al., 2015), this experiment showed that the effects of altering HA synthesis and degradation are complex. While inhibiting HA synthesis led to significantly less cell proliferation and more cell mortality, preventing HA fragmentation through HYAL inhibition and HAS promotion also showed a trend in decreasing cell density and increasing mortality. To fully understand the role of HA in cancer progression, further research would need to be done, testing more combinations of drugs that alter HA synthesis and degradation. In the future, this project could be expanded upon by measuring the hyaluronan content in the cancer cells under each drug treatment. The Hyaluronan Quatikine Elisa Kit measures HA concentrations greater than 35 kDA in cell culture supernatants, allowing the concentration of HA in cells to be measured, and the amount of HA fragmentation to be quantified (Yuan et al., 2013). Through quantifying the HA content under the different drug treatments, the effect of the HA synthesis and degradation altering drugs on HA content could be determined. In addition, the HA content could be compared to the cell density in each drug treatment, to determine if there is a correlation between the content of HA in cancer cells and the ability of these cells to proliferate. The drugs 4-MU, TPA, L-Hex could also be tested on a similar type of non-cancerous cells, to determine how manipulating HA content effects normal cell growth. This would also determine if the drugs 4-MU, TPA, and L-Hex are toxic to non-cancerous cells. Since Tiopronin showed a trend in increasing cancer cell density and decreasing cell mortality, it would not make sense to use Tiopronin in future trials. Lastly, the effect of additional drugs that alter HA synthesis and degradation could be tested to determine if other drugs, such as the HYAL inhibitor Dextran Sulfate (Wu et al., 2014), are more effective in decreasing cancer cell density and mortality.
5. Conclusion and Future Work
I would like to acknowledge Dr. Amy Sheck for advising and supporting me though all steps of the research process, Dr. Michael Bruno for advising me on how to dissolve drugs, Dr. Kim Monahan for advising me on cell culture, Dr. Zermeena Marshal for showing me cell culture techniques, Ms. Julie Graves for advising me on statistical analysis, The Research in Biology Class of 2016 for mentoring me and teaching me research skills, The Research in Biology Class of 2017 for providing moral support and camaraderie, the Glaxo Smith Kline Endowment for providing funding, and The North Carolina School of Science and Mathematics for providing funding and facilitating this research opportunity.
This project demonstrated that altering HA synthesis and degradation has a significant effect on cancer cell density and mortality, but that the interactions between altering synthesis and degradation are multifaceted. The data showed that inhibiting HA synthesis with 4-MU significantly decreased cell proliferation and cell mortality and could therefore be an effective cancer treatment. This effect of 4-MU on cancer cells is consistent with previous research (Saito et al., 2013). While not significant, the paper showed a trend of decreasing cell density and cell mortality when HA fragmentation was prevented through inhibiting HYAL degradation (L-Hex) and promoting synthesis BIOLOGY RESEARCH
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7. References Alaniz, L., Rizzo, M., Malvicini, M., Jaunarena, J., Avella, D., Atorrasagasti, C., Aquino, J., Garcia, M., Matar, P., Silva, M., & Mazzolini, S. (2009). Low molecular weight hyaluronan inhibits colorectal carcinoma growth by decreasing tumor cell proliferation. Cancer Letters, 278, 9-16. Bark, K. At the Bench: A Laboratory Navigator. Cold Spring Harbor, NY: Cold Spring Harbor Laboratory, 2005. Botzi, A., Braun, D., Nukui, S., Salmen, M., Dove, J., Jedrzejas, S., & Buschauer, A. (2004). L–ascorbic acid 6-hexadecanoate , a potent hyaluronidase inhibitor. The Journal of Biological Chemistry, 279, 90-91. Cheng, X., Kohi, S., Koga, A., Hirata, K., & Sato, N. (2015.) Hyaluronan stimulates pancreatic cancer cell motility. Oncotarget, 11, 1-11. Cowman, M., Hong-Gee, L., Schwertfeger, K., McCarthy, J., & Turley, E. (2015). The content and size of hyaluronan in biological fluids and tissues. Frontiers in Immunology, 6, 261-269. Fuchs, K., Hippe, A., Schmaus, A., Sleeman, J. S., & Orian Rousseau, V. (2013). Opposing effects of high- and low-molecular weight hyaluronan on CXCL12-induced CXCR4 signaling depend on CD44. Cell Death and Disease, 4, 1-11. Girish, K., Kemparaju, K., Nagaraju, S., & Vishwanath, B. (2009). Hyaluronidase inhibitors: a biological and therapeutic perspective. 2009. Current Medicinal Chemistry, 16, 61-88. Kuppusamy, H., Ogmundsdottir, H., Baigorri, E., Warkentin, A., Steingrimsdottir, H., Haraldsdottir, V., Mant, M., Mackey, J., Johnston, J., Adamia, S., Belch, A., & Pilarski, L. (2014). Inherited polymorphisms in hyaluronan synthase 1 predict risk of systemic B cell malignancies but not of breast cancer. PLOS One, 9, 91-101.
Saito, T., Dai, T., and Asano, R. (2013). The hyaluronan synthesis inhibitor 4-methylumbelliferone exhibits antitumor effects against mesenchymal like canine mammary tumor cells. Oncology Letters, 5, 1068-1074. Schwertfeger, M., Cowman, P., Talmer, E., Turley, A., & McCarthy, J. (2015). Hyaluronan, inflammation, and breast cancer progression. Frontiers in Immunology, 6, 236-248. Sironen, R., Tammi, M., Tammi, R., Auvinen, P., Anttila, M., & Kosma, V. (2011). Hyaluronan in human malignancies. Experimental Cell Research, 317, 383-391. Valachová, K., Ba, M., Topol, D., Sasinková, V., Juránek, I., Collins, M., & Soltés, L. (2015). Influence of tiopronin, captopril and levamisole therapeutics on the oxidative degradation of hyaluronan. Carbohydrate Polymers, 134, 516-523. Weigel, P., & Deangelis, P. (2007). Hyaluronan synthases: A decade-plus of novel glycosyltransferases. Journal of Biological Chemistry, 282, 77-81. Wu, M., Cao, M.,He, Y., Liu, Y., Yang, C., Du, Y., Wang, W., & Gao, F. (2014). A novel role of low molecular weight hyaluronan in breast cancer metastasis. The FASEB Journal, 1, 1-9 . Yuan, H., Tank, M., Alsofyani, A., Shah, N., Talati, N., LoBello, R., & Cowman, M. K. (2013). Molecular mass dependence of hyaluronan detection by sandwich ELISA-like assay and membrane blotting using biotinylated hyaluronan binding protein. Glycobiology, 23(11), 1270–1280. Zheng, X., Chang, R., Cui, X., Avila, G., Garzotto, V., Shih, W., Lin, Y., Lu, S., Rabson, A., Kong, A., & Conney, A. (2006). Effects of 12-O-tetradecanoylphorbol-13-acetate (TPA) in combination with paclitaxel (Taxol) on prostate Cancer LNCaP cells cultured in vitro or grown as xenograft tumors in immunodeficient mice. Clinical Cancer Research, 12, 3444-51.
Liang, J., Jiang, D., & Noble, P. (2015). Hyaluronan as a therapeutic target in human diseases. Advanced Drug Delivery Reviews, 14, 1-18. Morohashi H., Atsushi, K., Nakaia, M, Yamaguchi, M., Kakizaki, I., Yoshihara, S., Sasaki, M., & Takagaki, K. (2006). Study of hyaluronan synthase inhibitor, 4-methylumbelliferone derivatives on human pancreatic cancer cell. Biochemical and Biophysical Research Communications, 345, 1454-1459. 36 | 2016-2017 | Broad Street Scientific
DRASTIC CONDITIONS CALL FOR DRASTIC MEASURES: THE VIABILITY OF TERRESTRIAL EXTREMOPHILES IN SIMULATED MARTIAN UV RADIATION Ana Sofia Uzsoy Abstract The harsh ultraviolet (UV) radiation at the Martian surface prevents viability of life as we know it by causing potentially lethal single and double-stranded DNA breaks. However, there are a few organisms on Earth that could survive in the low wavelength and high intensity radiation of Mars. This experiment tested the radioresistant properties of Halobacterium salinarum, a halophile, and Deinococcus radiodurans, a radioresistant extremophile. The organisms were exposed to simulated Martian UV radiation under 3 different conditions: unshielded, shielded with a physical shield consisting of powdered meteorite and simulated Martian soil (artificial meteorite), or shielded with NaBr in growth media (salt shield). The unshielded radiation resistance of D. radiodurans was much higher than that of H. salinarum; however, with the artificial meteorite shield, the survival ratios of the two species were not significantly different. The salt shield showed a positive trend in survival ratio for H. salinarum, but a negative trend for that of D. radiodurans, most likely caused by inhibited growth. There was a significant difference among shields (p = 0.0007), with results indicating that the artificial meteorite shield ameliorated the effects of the UV radiation in both species, leading to survival rates indistinguishable from those of the no-radiation control. This suggests that the soil on Mars could potentially shield terrestrial organisms from the UV radiation. Overall, the results of this experiment can be used to further develop radiation shielding techniques in the pursuit of one day allowing terrestrial life to survive on Mars. 1. Introduction Many have often wondered if terrestrial life could possibly survive on Mars, but only recently has the prospect of survival for terrestrial organisms on a Martian planet been seen as a realistic research subject (Haynes and McKay, 1992 and Horneck, 2008). As technology continues to advance, it seems increasingly plausible that humans will be traveling to, and possibly even colonizing, the red planet sometime in the future. Knowledge of which terrestrial microorganisms would be viable in Martian conditions would contribute to knowledge of the origins of life and climate change, as well as increasing potential for the discovery of extraterrestrial life and interplanetary exploration. Condition Temperature Pressure Liquid Water Atmospheric Composition Radiation Intensity UV Wavelength
Earth 16°C 100,000 Pa Abundant Mostly Nitrogen/ Oxygen Relatively Low
Mars -60 ±100°C 560 Pa Not present Mostly Carbon Dioxide Very High
Table 1. Comparison of average environmental conditions on Earth and Mars. Any of the extreme surface conditions (Table 1) would BIOLOGY RESEARCH
make Mars a wholly unsuitable place for most terrestrial organisms. When tested, organisms such as the fungus Wangiella dermatitidis, the worm Caenorhabditis elegans, the haloarchaeon Natronorubum, and seven different strains of Bacillus spores could not survive in a simulated Martian environment, mostly due to extreme desiccation (Johnson et al., 2011; Peeters et al., 2010; Schuerger and Nicholson, 2006). The most deadly feature of the Martian environment is the ultraviolet (UV) radiation. Mars receives up to one thousand times more UV radiation than Earth because its atmosphere lacks ozone (Schuerger et al., 2006). On Mars, UV wavelengths can be as low as 190 nm while on Earth they range from 290-300 nm (Haynes and McKay, 1992 and Schuerger et al., 2006). UV radiation of this wavelength is lethal because the absorbed energy alters DNA bases, causing single and double stranded breaks that eventually impede life-sustaining processes, such as DNA replication, cell division, and protein production (Battista, 2016). However, some organisms have the potential to survive in the harsh Martian radiation. Halorubrum chaoviator, a halophilic extremophile archaea found in a saltern (a pool of evaporating seawater) in Mexico, had a 100% survival rate in the simulated Martian environment, showing that it could withstand damage from the UV radiation on Mars (Johnson et al., 2011). Given its survival rate, testing more halophiles and other extremophiles could be a promising route to finding life forms that could survive the Mars environment. A number of traits that aid organisms in tolerating the rough climate have been identified. A “salt shield” has been Broad Street Scientific | 2016-2017 | 37
tested against ionizing radiation, which also causes DNA breaks by producing a hydroxyl (OH-) radical (Kish et al., 2009). Halobacterium salinarum grown in media with high KCl or KBr concentrations showed up to 2.6 times fewer double-stranded DNA breaks than in regular buffer solutions (Kish et al., 2009). This is because the Cl- and Brions, which are less reactive with DNA bases, replaced the hydroxyl radicals, thus causing less DNA damage (Kish et al., 2009). High concentrations of Cl and Br ions have been found on Mars by rovers, which could make this shield plausible for use on Mars (Kish et al., 2009). Other organisms have DNA repair proteins that are able to repair the lesions as they occur, allowing them to withstand large radiation doses (Battista, 2016). Such may be the case with D. radiodurans (Battista, 2016). A physical covering of some kind could also help protect organisms from the harmful Martian UV rays (Battista, 2016). Martian soil, whose composition is shown in Table 2, could potentially provide some shielding from the UV rays. Interestingly, an “artificial meteorite” layer composed of a mixture of simulated Martian soil, terrestrial clay, terrestrial sandstone, and powdered meteorite helped Bacillus spores survive the simulated Martian environment just as well as those that were not exposed to the UV rays (Rettberg et al., 2004). In the quest to colonize Mars, these findings will help us modify the organisms’ environment with protective technologies to improve survival rates by reducing or potentially eliminating the effects of UV radiation. Compound SiO2 FeO CaO MgO Al2O S H2O
cus radiodurans to simulated Martian UV radiation. 2. Methods This experiment, whose design is summarized in Figure 1, involves two extremophile microorganisms. Halobacterium salinarum is a halophilic archaeon that thrives in extreme salt concentrations. It maintains an osmotic balance by taking in ions to create an intracellular salt concentration that is equal to that of its environment. This high salt concentration creates an environment of extreme desiccation, causing DNA breaks similar to those caused by radiation, thus allowing halophiles to survive in high radiation doses (Kish et al., 2009). Other halophiles have previously been found to have high percent survival rates in simulated Martian UV radiation, most notably Halobrium chaoviator with a 100% survival rate after 40 days of exposure (Johnson et al., 2011). In this experiment, H. salinarum was grown on 4.28 M NaCl Halobacterium agar plates. Deinococcus radiodurans is a bacterium known for being able to survive large radiation doses due to its high concentration of manganese (II) ions and high Mn/Fe ratio (Battista, 2016). It can quickly and efficiently repair radiation-induced DNA lesions and is thus able to continue replicating in the face of high radiation doses (Battista, 2016). It is found all over the world, most notably in Antarctica, whose climate conditions resemble those of Mars more than anywhere else on Earth. D. radiodurans was grown on TGY (tryptone, glucose, yeast) agar plates.
% Composition 43.0 16.2 5.8 6.0 7.2 3.5 <1
Table 2. Percent Composition of major components of Martian soil. The Mars One program plans to send humans to Mars by 2027, having them live in inflatable structures equipped with life support units and extract water from the tiny amount that exists in the Martian regolith (Do et al., 2016). The characteristics of organisms that can withstand the conditions of Mars help us develop technology and materials to protect less hardy organisms. In order for survival on Mars to become a possibility for Earth-born species, more organisms must be tested for their ability to survive the harsh, but possibly tolerable, Martian conditions. This experiment investigated the effects of a NaBr “salt shield” and an “artificial meteorite” shield on the resistance of the extremophiles Halobacterium salinarum and Deinococ38 | 2016-2017 | Broad Street Scientific
Figure 1. Experimental Design. n = 5 replicates per experimental condition. The wavelength of the UV radiation of Mars, which varies from 200-300 nm was simulated using a UVP Mineralight Lamp Model UVGL-55 that emits UV radiation with a wavelength of 254 nm (Haynes and McKay, 1992). This short-wavelength subset of UV radiation is referred BIOLOGY RESEARCH
to as UV-C. The advantage of using this source to simulate Martian radiation is that its distance from the organism, which impacts the intensity of the received radiation, can be controlled. The radiation dose used in this experiment was 500 J/m2. A short-wave UV meter (UVP) was used to measure the flux from the lamp and determine the time needed to get the correct dose. The UV lamp was given 30 seconds for the reading on the meter to stabilize, after which the reading was recorded and the necessary time of exposure calculated. The “salt shield” consists of increased NaBr concentration in the growth media of the organisms. Preliminary experiments were conducted with both model organisms to ensure that the NaBr concentrations would not unduly inhibit bacterial growth. For H. salinarum, the concentration used was 2.6 M, as in the work of Kish et al. (2006). The NaBr replaced NaCl in the media, so there was only 1.7 M NaCl in the “salt shield” media, yielding a total salt concentration of 4.3 M. For D. radiodurans, which is much more sensitive to salts, the concentration of NaBr used was 0.1 M, which did not inhibit growth. The regular TGY Media used for D. radiodurans in other trials did not have any salt in it. The “artificial meteorite” shield consisted of equal parts of powdered meteorite and simulated Martian soil. The composition of this shield is meant to mirror that of the Martian surface. This experimental condition was motivated by the work of Rettberg et al. (2004), who showed that the presence of a similar substance completely eliminated UV sensitivity in Bacillus spores, causing survival rates to be the same with and without the simulated Martian radiation. To create this shield, a Muong Nong Tektite, obtained from meteorites-for-sale.com, was crushed into powder with a rock hammer, and then sieved to obtain a consistent particle size. Three grams of this powder was mixed with three grams of JSC-1A Martian Simulant soil, acquired from Orbitec. A uniform layer of powder approximately 1 mm in thickness was applied over a quartz plate that was then placed on top of the petri dish containing the cultured organism. UV radiation can pass through quartz, so this plate did not provide any additional shielding. The purpose of the quartz plate is to allow the physical shield to be applied over the organisms during irradiation while still allowing bacterial/archaea colonies to be counted in the dish afterwards, when collecting data. Overnight cultures of H. salinarum and D. radiodurans were placed in 42°C and 30°C water baths, respectively, and left to grow for at least five hours. For the “salt shield”, the media used in the overnight cultures was 2.6 M NaBr + 1.7 M NaCl Halobacterium media (for H. salinarum) and 0.1 M NaBr TGY media (for D. radiodurans). All other conditions used 4.28 M NaCl Halobacterium media and TGY media. The cultures were then diluted to an optical density of 0.006 ± 0.001 using a spectrophotometer from Amersham Biosciences, and spread evenly on petri dishes using the “lawn” bacterial spreading technique. Five petri dishes BIOLOGY RESEARCH
were made for each shield condition and for each organism, making 30 petri dishes in total (Figure 1). The plates were then immediately irradiated. A glass shield was placed over half of the dish (as shown in Figure 2), to create a “No UV” control condition. UV radiation cannot pass through glass, so its presence over half of the petri dish did not allow any radiation to reach the organisms under it. The other half was completely exposed to the radiation. The glass shield was placed directly on top of the petri dish for the no shield and salt shield conditions, and was placed over the powder on the quartz place in the artificial meteorite shield condition. After irradiation, the plates were immediately transferred to incubators of temperature 42°C and 30°C for H. salinarum and D. radiodurans, respectively.
Figure 2. Irradiation Procedure.
Figure 3. Example irradiated D. radiodurans plate. The survival ratio is 0.332. Data were collected after the H. salinarum plates had grown for seven days and the D. radiodurans plates had grown for three days. Each plate, as shown in Figure 3, was placed over a grid with 24 complete 1 cm2 squares for sub-sampling. Partial squares on the perimeter of the dish were not counted, due to the fact that colonies near the edges of the dish could have received additional shielding from the sides of the dish (the “edge effect”). Each square was assigned a number, and five squares from each side were randomly chosen, giving a total of 10 cm2 sampled from each plate, 5 cm2 from each side. The number of colonies in each square were counted and recorded. Colonies that were partially in the square were counted as in, due to the low probability that adjacent squares would be selected. This random sampling should give an accurate measure of how many colonies were on each side of the plate. Broad Street Scientific | 2016-2017 | 39
3. Results The survival ratio for each plate was determined by dividing the sum of the number of colonies in five squares of the irradiated side by the sum of colonies in five squares on the control side for each plate. This provides a ratio of the number surviving the UV condition to the number surviving the “No UV” condition, capturing the effects of the radiation on the organisms. A smaller ratio indicates that the radiation had a strong effect on the organism because the side exposed to UV had a much lower survival than that not exposed to UV. A higher ratio indicates that both sides had similar survival, suggesting that the radiation did not have as harmful an effect on the organisms. An increase in the survival ratio’s value indicates an increase in radiation resistance. Tukey’s mean separation test was conducted using JMP, a statistical analysis software, to determine the statistical significance among the different species-shield conditions. As seen in Figure 4, under the no shield condition, D. radiudurans had relatively higher radiation resistance than H. salinarum, with H. salinarum showing almost no survival in the radiation without a shield. The survival ratios of both species with the artificial meteorite shield reach and even surpass a value of 1, indicating very strong radiation resistance. An Analysis of Variance (ANOVA) test conducted using JMP found no significant different between the responses of the different species (p = 0.0864) across all three shield conditions, and that there was no significant difference among the different species-shield combinations (p = 0.4980).
Figure 5 shows the difference in survival ratio between the shielded conditions and the no shield condition. This may be interpreted as the amount of increase in survival ratio caused by the shield, which could be due to protection by the shields. As seen in Figure 5, the salt shield raised the radiation resistance of H. salinarum compared to the no shield condition, but actually lowered that of D. radiodurans compared to the no shield condition. The artificial meteorite shield raised the radiation resistance of both organisms relative to the no shield condition.
Figure 5. Effect of shields on survival rates. Error bars within one standard error. Y axis is the difference between the survival ratios with respective shields and the no shield condition. Figure 6 shows the overall effectiveness of the shields. Using the results of the Tukey’s analysis, it was determined that the survival ratios with the artificial meteorite shield were statistically significantly different from those of the salt shield and no shield conditions. An ANOVA test conducted using JMP indicated that there was a very significant difference among the survival ratios with the different shield conditions (p = 0.0007*). The artificial meteorite shield far outperformed the other two shield conditions, having a much higher survival ratio across both species.
Figure 4. Survival ratios of species-shield combinations. Error bars within one standard error. Letters indicate significance groups from the Tukey’s analysis. Levels not connected by the same letter are significantly different. Dotted lines represent no shield condition survival ratio for comparison.
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Figure 6. Overall effectiveness of shields across both species. Error bars within one standard error. Letters indicate significance groups from the Tukey’s analysis. Levels not connected by the same letter are significantly different. p = 0.0007*. Due to the paired nature of the experiment (the experimental and control conditions were on both sides of the same petri dish), an additional “Matched Pairs” statistical analysis was conducted using JMP. The paired quantities were the number of colonies on the control side and the number of colonies on the irradiated side, and the analysis conducted an ANOVA on the differences between them. Figures 7a and 7b show the results of this analysis, which found no statistically significant difference between species (p = 0.0661), but identified a significant difference among shields (p = 0.0116*). These results are in agreement with the ANOVA test conducted on the survival ratios using JMP.
Figures 7 a,b. Results of Matched Pairs analysis. Figure 7a shows analysis between species (p = 0.0661). Figure 7b shows analysis among shields (p = 0.0116*). Y axis shows difference between number of colonies on the control and irradiated sides. 4. Discussion The two organisms featured in this experiment are quite different. H. salinarum’s radioresistance is a result of its halophilic tendencies, which arise from its maintenance of a high salt concentration inside of its cells that is equal to that of its environment, striking an osmotic balance (Kish et al., 2009). D. radiodurans is one of the most radioresistant organisms on Earth, and its radioresistance comes from its ability to repair DNA breaks as soon as they occur and its high Mn/Fe ratio (Battista, 2016). It is thus expected that the radiation resistance of D. radiodurans is much higher than that of H. salinarum, proven in the no shield category of this experiment. All statistical analyses conducted (ANOVA, Tukey’s, and Matched Pairs) reported the radiation resistance as not differing significantly between species across all shield conditions. This is presumably because, as shown in Figure 4, the survival ratios of both organisms were relatively close under the artificial meteorite shield condition, and very close under the salt shield condition. These similarities likely offset the disparity between the survival ratios of both species under the no shield condition and led to the overall lack of statistical difference in radioresistance between species across all shield conditions. The mixed effects of the salt shield (shown in Figure 5) can be attributed to the different structures and functions of the two species. Since the radioresistance of H. Broad Street Scientific | 2016-2017 | 41
salinarum is a byproduct of its halophilic tendencies, the presence of NaBr would have a larger effect on it. A potential reason why the salt shield would increase the radioresistance of H. salinarum would be the increase in molecular weight of bromine when compared with chlorine. The cell would have to take in the same amount of Br to equalize charge and salt concentration, but would be absorbing a larger atom, which could cause it to be stronger and therefore more resistant to radiation damage. In contrast, the salt shield actually affected D. radiodurans negatively, causing it to have a lower survival ratio than when it was not shielded at all. This could be caused by the fact that the presence of NaBr in the TGY media inhibited the growth and resistance of D. radiodurans. It was not grown in its optimal growth media, and therefore was weaker and exhibited less radioresistance than usual. Even though the H. salinarum + salt shield and the D. radiodurans + salt shield were not significantly different, its negative effects that it had on the D. radiodurans makes the salt shield a less than ideal shielding technique for all species; however, its positive effects on H. salinarum indicate that it may serve as an effective radiation shield for halophiles and similar organisms. The H. salinarum + artificial meteorite shield and the D. radiodurans + artificial meteorite shield did not have a statistically significant difference, and were the two species + shield combinations with the highest survival ratios. The survival ratios of both species with the artificial meteorite shield were much higher and much closer to each other than their survival ratios under the no shield condition. So, although H. salinarum had relatively poor unshielded radioresistance compared to that of D. radiodurans, the artificial meteorite shield gives it a nearly equal chance of survival in simulated Martian UV radiation. This shows that the artificial meteorite shield increased radioresistance of both organisms considerably, regardless of their differences in structure and function. This statement is supported by the results of the ANOVA and Matched Pairs statistical analyses, which reported the shields to be significantly different with a p = 0.0007 and p = 0.0116, respectively. The Tukey’s analysis (Figure 6) also reported the survival ratios with the artificial meteorite shield to be statistically different from those under the other shield conditions. The work of Rettberg et al. (2006) showed that a homologous shield demonstrated a similar increase in the radioresistant properties of Bacillus spores. This, combined with the results of this experiment, strongly suggests that the artificial meteorite can be considered an effective radiation shield for diverse kinds of organisms, and its effectiveness is not limited by the different infrastructures of the species themselves. As previously mentioned, the artificial meteorite shield consists of an approximately 1mm layer of a powder made of equal parts powdered meteorite and simulated Martian soil spread on a quartz plate that is placed over the petri dish. The composition of the shield is meant to mimic extraterrestrial surfaces like that of Mars. It prevents the 42 | 2016-2017 | Broad Street Scientific
radiation from damaging the DNA by blocking it before it reaches the organisms. The meteorite used was a tektite (which contains glass), which reflects the radiation in the opposite direction. Some of the soil particles would also absorb the radiation, preventing it from passing down to the organism. This nature of the artificial meteorite shield allows it to work for many different kinds of organisms. The soil on the Martian surface could act as this type of shield, and organisms could survive underground, protected from the radiation. 5. Conclusions and Future Work This experiment investigated the effects of an NaBr “salt shield” and an “Artificial Meteorite” shield on the resistance of the extremophiles Halobacterium salinarum and Deinococcus radiodurans to simulated Martian UV radiation. The unshielded radioresistance of H. salinarum was much lower than that of D. radiodurans. The salt shield increased the survival ratio of H. salinarum but was actually detrimental to the resistance of D. radiodurans. This can be attributed to the differences in the structure of the species and the mechanisms of each organism’s radioresistance or the osmotic tolerance of each species. Notably, there was no significant difference between the survival ratios of the two species when the artificial meteorite shield was applied. The results of the artificial meteorite shield condition when compared to the no-radiation control suggest that a physical shield like that used in this experiment would be an effective way to protect organisms from radiation. It is important to note that the artificial meteorite shield would allow all kinds of organisms to be very radioresistant, regardless of their structure and function. The Martian soil could provide this kind of shield, allowing organisms to live underground on Mars with the soil protecting them from the radiation. Further research should definitely be conducted to investigate other ways that organisms resist radiation. The genetic basis of radiation resistance in organisms such as D. radiodurans is still not completely understood. A better understanding of these aspects might allow genetic engineering to give other species the same advantage and increase their unshielded radioresistance. Evidence has also been found that the presence of pigments such as bacterioruberin and scytonemin contributes to radiation resistance (Battista, 2016). The carotenoid pigments that make D. radiodurans red are a factor in its radioresistance (Pogoda de la Vega et al., 2007). It would be meaningful to investigate if increasing pigments in species increases their radioresistance. The Earth is not faced with such harmful, short-wavelength radiation because of the presence of the ozone layer, but as climate change continues and more of the ozone layer is depleted, shielding from UV-C radiation might become necessary. In this case, more research may need to be conducted on the effects of UV-C radiation on more BIOLOGY RESEARCH
complex organisms. This experiment used only UV radiation to simulate the radiation on Mars. Ionizing radiation is also prevalent on Mars and on other astronomical bodies. Ionizing radiation causes DNA breaks by bouncing electrons off the DNA, causing breaks and producing the unstable hydroxyl radical from water (Kish et al., 2009). Organisms with high UV resistance also usually have high resistance to ionizing radiation, but it has been shown that the mechanisms can be independent of each other (Battista, 2016). Ionizing radiation is also prevalent on other planets and throughout the universe, and it could be worthwhile to study whether UV shields prevent damage from it, too. Of course, the radiation is only one aspect of the harsh Martian climate. Other factors, such as temperature, lack of water and atmospheric composition could also affect the type of organism that could survive on Mars. Extremophiles that thrive in extremely cold environments or desert-like conditions could also be good candidates for survival on Mars. The viability of extremophiles in simulated Martian UV radiation is only the beginning. We must continue to investigate how to increase radioresistance in order to protect microorganisms from the harmful radiation. Subsequently, more complex organisms can be tested and the shieldsâ€™ effectiveness re-evaluated for them. It is only after there is a substantial amount of knowledge on radiation shielding and other ways of allowing different kinds of species to survive in extreme environments that there could be a possibility of human colonization of Mars. 6. Acknowledgments I would like to thank Dr. Amy Sheck for her continued guidance and support over the course of my RBio experience, Dr. Dan Teague for his help with data analysis, Dr. Jonathan Bennett for his help with radiation calculations and smashing meteorites, Dr. Michael Bruno for his help acquiring media ingredients, Dr. Amy Schmid for her advice and providing H. salinarum, Dr. John Battista for his advice, information, and providing D. radiodurans, Mr. Charlie Payne for his help finding a reliable source of meteorites and simulated Maritan soil, Dr. Julian Parris for his help with JMP software, the NCSSM Research in Biology Classes of 2016/2017 for providing a sense of community, moral support, and fun times, the Glaxo Endowment to NCSSM for providing funds and lab space, and the NCSSM Foundation for enabling students like me to pursue our passions. 7. References Battista, J.R. 2016. Radiation Tolerance. In: eLS. John Wiley & Sons, Ltd: Chichester. De Vera, J. 2012. Lichens as survivors in space and on Mars. Fungal Ecology 5:472-479. BIOLOGY RESEARCH
Do, S., A. Owens, K. Ho, S. Schreiner, and O. de Weck. 2016. An independent assessment of the technical feasibility of the Mars One mission plan â€“ Updated analysis. Acta Astronautica 120: 192-228. Haynes, R. and C. McKay. 1992. The implantation of life on Mars: feasibility and motivation. Advances in Space Research 12: 133-140. Horneck, G. 2008. The microbial case for Mars and its implication for human expeditions to Mars. Acta Astronautica 63: 1015-1024. Johnson, A., L. Pratt, T. Vishnivetskaya, S. Pfiffner, R. Bryan, E. Dadachova, L. Whyte, K. Radtke, E. Chan, S. Tronick, G. Borgonie, E. Mancinelli, L. Rothschild, D. Rogoff, D. Horikawa, and T. Onstott. 2011. Extended survival of several organisms and amino acids under simulated martian surface conditions. Icarus 211: 1162-1178. Kish, A., G. Kirkali, C. Robinson, R. Rosenblatt, P. Jaruga, M. Dizdaroglu, and J. DiRuggiero. 2009. Salt shield: intracellular salts provide cellular protection against ionizing radiation in the halophilic archaon, Halobacterium salinarum NRC-1. Environmental Microbiology 11: 1066-1078. Peeters, Z., D. Vos, I. ten Kate, F. Selch, C. van Sluis, D. Sorokin, G. Muijzer, H. Stan-Lotter, M. van Loosdrecht, and P. Ehrenfreund. 2010. Survival and death of the haloarchaeon Natronorubum strain HG-1 in a simulated Martian environment. Advances in Space Research 46: 1149-1155 Pogoda de la Vega, U., P. Rettberg, and G. Reitz. 2007. Simulation of the environmental climate conditions of martian surface and its effect on Deinococcus radiodurans. Advances in Space Research 40: 1672-1677. Rettberg, P., E. Rabbow, C. Panitz, and G. Horneck. 2004. Biological space experiments for the simulation of Martian conditions: UV radiation and Martian soil analogues. Advances in Space Research 33: 1294-1301. Schuerger, A. and W. Nicholson. 2006. Interactive effects of hypobaria, low temperature, and CO2 atmospheres inhibit the growth of mesophilic Bacillus spp. under simulated martian conditions. Icarus 185: 143-152. Schuerger, A., J. Richards, A. Newcombe, and K. Venkateswaran. 2006. Rapid inactivation of seven Bacillus spp. under simulated Mars UV irradiation. Icarus 181: 52-62.
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VARIATION OF MAXIMUM LEVITATION DISTANCE IN TYPE-II SUPERCONDUCTORS DUE TO CHANGING MAGNETIC DIPOLE MOMENTS Omkar Apte Abstract Superconductors are special materials that conduct electricity with zero resistance when they are below a certain temperature. This property leads to the material having unique electrical and magnetic properties, most notably the Meissner effect, which is the focus of this study. We hypothesized that there is linear relationship between the strength of a magnet and the height at which it levitates. In order to test this, YBCO and BSCCO ceramic superconductors (these are type-II) were placed on an upside down Styrofoam cup. A camera was set up to image the N52 neodymium magnet when placed on the superconductor when cooled using liquid nitrogen. The distance was measured using the image analysis tool in LoggerPro. The data suggest that the levitation heights are continuous range that was expected. However, there appeared to be an odd pattern in the data, and we determined that it warranted further investigation. The results of this experiment could provide more information on the microscopic theory of type-II superconductors because the BCS Theory fails to explain key aspects of high temperature superconductivity. 1. Introduction The aim of this project is to identify a relationship between the magnetic dipole moment of an externally applied magnetic field and the levitation distance of the magnet above Yttrium-Barium-Copper Oxide (YBCO) and Bismuth-Strontium-Calcium-Copper Oxide (BSCCO) polycrystalline superconductors. High temperature superconducting cuprates have a unique perovskite crystal structure that lets them be superconductive at much higher critical temperatures. The unique nature of superconducting cuprates has puzzled physicists since their discovery because the presence of vortex states and their high critical temperatures don’t fit within the proposed BCS model (Serway et al., 2005). Superconductivity was discovered in 1911 by Kamerlingh Onnes, who was studying the properties of metals at liquid helium temperatures. In 1933, Walther Meissner discovered the exclusion of magnetic flux from the bulk of the superconductor, and led to the London brothers’ phenomenological theory of superconductivity (Serway et al., 2005). This exclusion of magnetic flux, named the Meissner effect, is the focus of this study. The London theory was important in that it established a key difference between perfect conductors and superconductors. 1.1 – Defining the Difference between Perfect Conductors and Superconductor As demonstrated in the Meissner effect, all magnetic flux is expelled from the superconductor. Thus, B=0 everywhere inside the bulk of the superconductor. This is not the case in perfect conductors. This can be shown using Newton’s Second Law in a perfect conductor. B is constant in time for perfect conductors, but not necessarily zero. However, the Meissner effect clearly shows that the magnetic flux within the bulk of a superconductor is zero. 44 | 2016-2017 | Broad Street Scientific
By defining ns as the superconducting electron density, and Js as the superconducting current density, a charge carrier with charge e and mass m, will experience an electric field E. (1) London’s phenomenological theory imposes the condition that: (2) Defining the London Penetration depth constant as, (3) The solution to (2) is then: (4) Equation 4 shows that the magnetic field in a superconductor exponentially decays to zero from the surface to the London penetration depth, and is zero within the bulk of the superconductor (Howe, 2014). This explains the mechanism behind the Meissner effect. 1.2 – Bardeen-Cooper-Schrieffer (BCS) Theory In the BCS theory, pairs of electrons (called Cooper Pairs) can interact through distortions in lattice ions (this interaction is mediated by phonons). The Cooper Pair behaves like a boson, even though it is composed of electrons, which are fermions. The fact that the pair of electrons can act like a boson, which has an integer multiple of spin, means that they do not obey the Pauli Exclusion Principle. PHYSICS AND ENGINEERING RESEARCH
The theory states that as a consequence of this, particles can exist in a lower energy state at low temperatures, and that all of the Cooper Pairs in the metal can be described by a single wave function (Serway et al., 2005). This creates an energy gap, so when an electric field is applied that makes the pairs move, they do not collide with any of the lattice ions because they are in their lowest energy state and cannot give energy to the lattice ions, thus there is no resistance. The energy gap varies between materials and can be modeled according to the following equation: (5) where t is defined as T/TC, and δ represents the energy gap (Sheahen, 1994). This relationship shows that the energy gap decreases as T approaches TC, and becomes zero at TC, thus breaking superconductivity. The BCS model is invalid for temperatures greater than 50K because the thermal energy of the lattice ions at temperatures higher than 50K are greater than the binding energies of Cooper Pairs, thus making phonon-mediated superconductivity impossible. There are many theories behind high temperature superconductivity because the BCS model breaks down for high temperature superconducting cuprates (Mourachkine, 2002). There were over 100 theories posed from 1987 to 2002. There is no currently accepted theory that can explain high temperature superconductivity, but a combination of the bisoliton model and spin-fluctuation can explain it most reasonably. 1.3 – Type-II Superconductors Type-II superconductors experience a different kind of Meissner effect, known as the mixed-state Meissner effect, in which single quanta of flux will penetrate through the superconductor. Type-II superconductors have two critical magnetic fields, one upper and one lower. When the external magnetic field Ba is greater than the lower critical field Bc1, flux begins to penetrate the superconductor. These quantized vortices of penetration are arranged in a triangular lattice andas B increases, the spacing decreases At the upper critical field Bc2, the spacing becomes zero, allowing all of the flux to penetrate the superconductor, thus removing it of its superconductive properties. Cuprate superconductors exhibit an average Bc1 of 1 cT, and an average Bc2 of 100 T or more (Badía-Majós, 1990). This indicates that cuprate superconductors have enormous levitation potential because they can withstand objects that can be magnetized with large magnetic fields. The vortex state observed in high temperature superconductors contains many interesting properties including flux pinning and second magnetization peak (also known as fishtail). different vortex dynamical mechanisms have been observed in cuprate superconductors, such as elastic to plastic (E-P) vortex creep, vortex order-disorder phase transition, vortex lattice structural phase transition, and surface barriers, which were all a result of the second magnetization peak that occurs within the vortex PHYSICS AND ENGINEERING RESEARCH
state temperature range (Van der Laan et al., 2001). All of these phenomena affect the distance and strength of flux pinning, but under closer analysis, all of these effects can be expressed as a combination of the temperature and the magnetic dipole moment of the magnetized object. The goal of this study was to examine the relationship between the magnetic dipole moment of a magnet and the levitation height above the superconductor. We hypothesized that as the magnetic dipole moment increases the levitation height should proportionally increase because the Meissner effect causes the induced field in the superconductor to be exactly equal and opposite to the magnet, so if the induced field is larger, then the levitation height should also be larger. 2. Methods In order to maximize the levitation height, we selected magnets that were very strong relative to their weight, so that the largest levitation distance could be observed. We bought 30 Grade N52 Neodymium-Iron-Boron permanent magnets that were 1/8” in diameter and 1/16” inch thick from K&J Magnetics. The maximum operating temperature for these magnets is 80° C, and the Curie temperature is about 300° C. In order to change the magnetic dipole moment, without changing any other properties of the magnets, 15 magnets were baked at various temperatures between 120° C and 225° C, thus decreasing the magnetic dipole moment. The sixteenth magnet in the study was an unbaked magnet. This experiment was conducted with two different superconductors, Yttrium-Barium-Copper Oxide (YBCO), and Bismuth-Strontium-Calcium-Copper Oxide (BSCCO). These were selected because they were readily available and relatively inexpensive to acquire. For both trials, the superconducting disc was placed in a Styrofoam cup, cooled using liquid nitrogen, and the magnet was placed on top. A camera was set up parallel to the setup such that it could take a close up picture with minimal light distortion. Figure 1 (shown below) details the basic setup of the experiment.
(2b) (3) Figures 1, 2a, 2b, 3. Setup of experiment including levitation of Superconductors Broad Street Scientific | 2016-2017 | 45
For the first trial, each magnet was imaged with each pole facing the camera. First, a photo was taken of the North pole facing the camera, pictured in red (see Figure 2a). Then a second photo was taken of the South Pole facing the camera (see Figure 2b). Each image was analyzed in LoggerPro. The scale was set (shown by the green line in Figure 3) using the diameter of the superconductor because the diameter >> levitation distance. Then the measure tool was used to calculate the distance from the center of the magnet to the surface of the superconductor (shown by the black line in Figure 3). The center of the magnet was chosen as the starting point of the measurement because it was the only consistent point of reference across all of the magnets. This was repeated for all 16 magnets on both superconductors. This was to ensure that there was no difference between the sides of the magnet. The measured height for both sides was averaged and plotted with the magnetic dipole moment. For the second trial, the magnet was placed as in Figure 1, displaced from equilibrium, allowed to settle back to equilibrium, and then imaged. This process was repeated 3 times for each magnet and both superconductors. The heights were averaged and plotted with the magnetic dipole moment. Because these averages were calculated using 3 data points each, we could calculate error in the height using the average deviation. 3. Results and Data Analysis We measured the levitation height of the BSCCO typeII superconductor against the magnetic dipole moment. Figure 4 is the plot of the levitation height vs magnetic dipole moment for the first trial.
Figure 5. Second trial for the experiment As before, the y-axis shows the levitation heights, and the x-axis shows the magnetic dipole moment (µ). The YBCO data are shown as blue circles, and the BSCCO data are shown as red squares. 4. Discussion Based on these graphs, we can see that there is evidence for the directly proportional relationship that was hypothesized. The correlation of the linear fit for both sets of data is approximately .95, which is a very strong correlation. However, it is important to note that towards the larger µ, there appears to be a relatively stable levitation height, and a discontinuous jump at about µ = .015 Am2. This was very strange, seeing as the linear fit showed a very strong correlation that supported the hypothesis. This was the reason for the second trial, in which we calculated the error in our measurements in order to confirm whether this odd pattern merited further investigation. Once again the linear fits have a very strong correlation that supports the hypothesis that there is a directly proportional relationship between the levitation height and magnetic dipole moment. The error bars shown in this data set indicate that there is some merit to investigating the odd discontinuity, which occurs in this data set again at about µ = .015 Am2. Currently, the hypothesis is very well supported by the data that was collected in this experiment. 5. Conclusion
Figure 4. Levitation vs magnetic dipole moment for the YBCO and BSCCO superconductor The y-axis shows the levitation heights, and the x-axis shows the magnetic dipole moment (µ). The YBCO data are shown as blue circles, and the BSCCO data are shown as red squares. As shown in trial 1, there is a major discontinuity at 0.015 Am2. We performed a second trial in order to verify this phenomenon. Figure 5 shows the results of the second trial. 46 | 2016-2017 | Broad Street Scientific
We propose that the discontinuity could be investigated using a similar setup with an electromagnet, but in reverse. The electromagnet will be on the bottom, and the superconductor will be suspended above it. This way, the pull force of the two end wires of the electromagnet do not need to be taken into account. One advantage of an electromagnet is that it will allow for a much wider range of magnetic dipole moments to be tested, which will show if these discontinuities appear at other magnetic dipole moments. The other advantage is that the current can be very accurately controlled, so that the location of the discontinuities can be determined more accurately. We suspect PHYSICS AND ENGINEERING RESEARCH
that there may be topological effects that are also playing a role in this phenomenon, arising from way that that supercurrents form in the copper oxide layers of the superconductors used in this experiment. Investigating this phenomenon will be the goal of future studies. Until then, we conclude that the proposed model is well supported by the data collected in this study. 6. Acknowledgements I would like to acknowledge Dr. Bennett, NCSSM Physics department; Dr. Shoemaker, Research/Mentorship Coordinator; and Dr. Roberts, Chancellor of NCSSM. 7. References Serway, R. A., Moses, C. J., & Moyer, C. A. (2005). Modern Physics (3rd ed.). Thompson Learning. Howe, B. A. (2014). Crystal Structure and Superconductivity of YBa2Cu3O7−x (Unpublished master’s thesis). Minnesota State University Mankato. Retrieved July 29, 2016 Mourachkine, A. (2002). High-temperature superconductivity in cuprates: The nonlinear mechanism and tunneling measurements. Dordrecht: Kluwer Academic. Badía-Majós, A. (2006). Understanding stable levitation of superconductors from intermediate electromagnetics. American Journal of Physics, 74(12), 1136-1142. Van der Laan, D. C., Van Eck, H. N., Ten Haken, B., Schwartz, J., & Ten Kate, H. J. (2001). Temperature and magnetic field dependence of the critical current of Bi2Sr2Ca2Cu3Ox tape conductors. APPLIED SUPERCONDUCTIVITY, 11(1). Retrieved May 20, 2016. Sheahen, T. P. (1994). Introduction to high-temperature superconductivity. New York: Plenum Press.
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THE EFFECTS OF SHAPE AND MASS OF A PARTICLE ON ITS STABILITY IN A STANDING WAVE ACOUSTIC LEVITATION SYSTEM Renzo Benavides & Brendan Kane Abstract This work examined the stability of object shapes and object sizes suspended in a Standing Wave Acoustic Levitation (SWAL) system. In the experiments, objects with varying shapes of different sizes were suspended in a SWAL system and their movements were recorded during a period of approximately 90 seconds. The average displacement for each shape and size was determined and their stabilities were compared. In this study, it was found that an object with a flat plane shape is the most stable in a SWAL system. In addition, objects with particle sizes of 5mm or 6mm and with the density of Styrofoam were found to be highly effective at levitation. The implications of the results suggest that shape, size and density should be carefully considered when designing objects for levitation in a SWAL system. 1. Introduction Advancements in technology, while bringing about many benefits, have also brought about complications inherit with the technology. Needs have arisen to transport hazardous materials without human contact to eliminate the dangers of handling toxic compounds and the cleaning and construction of high precision instruments and materials. A relatively new method to achieve these needs is acoustic levitation. Acoustic levitation is a process in which objects are levitated against the force of gravity by sound waves. The two main type of acoustic levitation are SWAL (Standing Wave Acoustic Levitation) and NFAL (Near Field Acoustic Levitation). The implications of acoustic levitation could be useful in the medical and biomedical fields, the construction or cleaning of high precision instruments or the handling of hazardous materials. This paper aims to study the effects of SWAL on a variety of shapes and sizes. Research that has been done in this field in the past includes new ways to levitate objects by using a single side of transducers and a concave reflector, eliminating the need for a static reflector and allowing the reflector to be at any distance from the transducer (Andrade, Perez, Adamowski, 2015). This allows an easier setup of the SWAL system. Zhang, et al directed sound waves and created self-bending wave packets. This completely eliminates the need of a reflector and allows more control of the particles, although it presents a more complex system. The particles can translate on a preset path or rotate around an axis (Zhang, et al., 2014). New ways to achieve the precise standards in which acoustic levitation can occur were also researched (Andrade, Perez, Adamowski, 2015). Liu, Hu and Zhao studied the dependence of acoustic trapping capabilities on the orientation and shape of particles between two metal strips in ultrasonic vibration. (Liu, Hu, Zhao, Dependence of Acoutic Trapping Capability on the Orientation and Shape of Particles, 2010). The method of NFAL was first recorded in 1975 by 48 | 2016-2017 | Broad Street Scientific
Whymark. (Whymark, 1975). Most research in acoustic levitation has been conducted in refining these processes or examining the mathematical and physical attributes of the entire system. In the past decade, the field has slowly advanced. Park investigated adjusting the angle of the transducers to transport a particle along a path. (Park, 2014). Andrade, Perez, and Adamowski have made it easier to achieve levitation by presenting a new configuration in non-resonant acoustic levitation in which the distance between the reflector and transducer can continuously change (Andrade, Perez, Adamowski, 2015). Marzo, et al introduced a new method of Standing Wave Acoustic Levitation, in which only a single side of transducers were used, without opposing reflectors or transducers, and were able to spin and translate the particle in a preset trajectory (Marzo, et al., 2015). Ochiai, Hoshi, and Rekimoto introduced a novel entertainment system in which small objects are trapped in the acoustic beams of standing waves. By adjusting the distribution of the acoustic-potential field, graphics can be generated from the levitated objects. (Ochiai, Hoshi, Rekimoto). In the field of acoustic levitation, there have been few studies conducted to determine if the role of a particleâ€™s mass and shape affects the stability of a set frequency. Yanyan, Hu and Zhao studied the effectiveness of acoustic trapping capability on the orientation and shape of particles while being levitated in different mediums. (Liu, Hu, Zhao, 2010). Liu, Hu and Zhao studied the dependence of acoustic trapping capabilities on the orientation and shape of particles between two metal strips in ultrasonic vibration. (Liu, Hu, Zhao, Dependence of Acoutic Trapping Capability on the Orinetation and Shape of Particles, 2010). This paper adds to these works by testing different shapes with varying measurements. The methods that are used in this paper have been proven multiple times. The setup in which SWAL can be achieved hardly vary between experiments. In this paper, a single 25 kHz transducer will be used to induce SWAL, a proven method. The work researched in this paper aims PHYSICS AND ENGINEERING RESEARCH
to improve current methods. If the outcome of this experiment suggests that certain shapes and sizes are found to be more stable, researchers can use this information to conduct more effective experiments. This approach will be validated by using SWAL in this work. SWAL was chosen as the method of levitation due to its ability to hold an object in the node of a standing wave, giving the researchers the ability to more accurately measure the particle and its stability. We expect that this research will be beneficial into looking at the feasibility of building small, fragile components, cleaning precise instruments, handling hazardous materials safely, and as Ochiai, Hoshi and Rekimoto show, new forms of entertainment such as creating graphics from levitated particles (Ochiai, Hoshi, Rekimoto). We believe that the more spherical an object is, the more stable the particle will be. Most research is conducted using spheres, so this research will also determine if spheres are inherently better or if other shapes can be proven to be superior in a SWAL system. 2. Experimental Methods There are 3 phases for conducting this project. Phase 1 will consist of conducting trial runs to find the optimal running frequency of the transducer and the optimal height between the transducer and reflector. Phase 2 will consist of testing each shape with different sizes and collecting the data. Phase 3 will consist of analyzing the data. 2.1 – Test Apparatus The Bolt Clamped Langevin Transducer 25 KHz by Steiner Martins, INC. (Part Number: SMBLTD63F25H2) will be used to conduct the research. It will operate at a frequency of 25.428 KHz. The transducer will be set up similarly to Figures 1 and 1.1. Figure 1.1 (Park, 2014) presents the forces and pressures acting on a particle in a SWAL system. Figure 1.1 also presents a typical SWAL setup and its geometric parameters. SC refers to the sphere center, PN refers to the pressure node and F refers to the axial levitation force along the central axis (Foresti, Nabavi, Poulikakos, 2012). Figure 2 is a diagram of the setup that will be used in this paper. A Rigol DG1022 function/Arbitrary Waveform Generator will be used to create a sine wave signal at 25.428 KHz. The signal will be fed into a PYLE PCA3 Stereo Power Amplifier, which will then fed into the transducer, creating a standing wave. The levitated objects will be cut out of Styrofoam. A Canon EOS Rebel T5 will be used to record the levitating objects. It will be placed directly in front of the levitating object at an 180° angle to the stand. A white backdrop will be used to contrast the Styrofoam for the camera to get better footage. This setup is pictured in Figure 2. The distance from the tranducer to the reflector can also be calculated. This distance can be calculated with the equation in Figure 3 in which K is a constant. PHYSICS AND ENGINEERING RESEARCH
Figures 1, 1.1, 2, 3. (Park, 2014), (Foresti, Nabavi, Poulikakos, 2012). Pictures from: (Bizrate, 2016) and (Rigol, 2016). 2.2 – Phase 1 A trial run will be conducted to determine the optimal frequency and the optimal distance between the reflector and the transducer. This will be determined by first putting a small object of Styrofoam on the top plate of the transducer. The transducer will be run starting at 25 KHz, and the frequency will be increased by 0.1 KHz. When the Styrofoam object begins to vibrate around the plate, the value that is in the 0.1 place will be kept and the frequency will then be again increased by 0.001. The value that results in the most excitement from the particle will be used as the operating frequency. Using the newly determined frequency, the plate will be placed above the transducer at an arbitrary height and slowly moved up or down until the small Styrofoam object begins to levitate. The distance between the transducer and the reflector can also be calculated using the formula in Figure 3. 2.3 – Phase 2 Phase 2 will begin with testing different shape with varying sizes. The chart in table 1 shows the different shapes with their varying sizes.
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Triangles Base (mm)
Diameter (mm) 4.5 Flat Plane Length (mm)
2 3 8.4 8
5 6 7 5
7 8 9 10 6 7 8 4
Width (mm) Height (mm)
5.8 8 1 1
7 5 1 2
6 7 8 4 2 2 2 2
Table 1. While the tranducer runs, each shape will be placed into the area above the transducer. The sample will be placed using a folded piece of small tubular plastic. The object will begin to levitate and the plastic will be removed to leave the object levitating in the SWAL system. The camera will record approximately 1:30 minutes of footage. 2.4 – Phase 3 Phase 3 will consist of analyzing the data. The stability of the levitated object will be defined as the average displacement the object undergoes over time. The footage will be placed into the video analysis program Tracker (Douglas). Tracker will track the object and plot the x and y coordinates over time. The coordinates will then be placed into Excel and the difference between successive x coordinates and successive y coordinates will be found. The average between the positive differences, which is the positive slope of graphed displacement, and the average between the negative differences, which is the negative slope of displacement, will be found. The average of the negative differences will be subtracted from the average positive differences to find the overall average displacement. These average displacements will then be compared and analyzed. The humidity level in the air will be kept constant by performing the tests inside. This is to ensure that the amount of water vapor in the medium, the atmosphere, stays constant and will not affect the results. The tests will also be performed in a partially empty room with minimal sounds to ensure that the sound waves from other objects, such as people, loud voices or breezes, will not cause a deviation in the results.
frequency and optimal distance between the transducer and reflector. 3. The Camera will be set up at an 180o angle in front of the transducer. 3.2 – Phase 1 1. The transducer will begin running at 25KHz 2. A small piece of Styrofoam will be placed on the top of the transducer. 3. The frequency will be changed by a factor of 0.1. 4. When the Styrofoam has the maximum excitement, the frequency at which this occurs will be recorded. 5. The frequency will then again be increased by a factor of 0.01. 6. When the Styrofoam has maximum excitement, the frequency will be recorded. 7. Repeat steps 3 through 4 increasing at a rate of 0.001. 3.3 – Phase 2 1. Each object will be placed into the area between the transducer and reflector with a small piece of plastic string. 2. When the object is levitating, the plastic will be removed from the system, leaving the object to levitate on its own. 3. The camera will record approximately 1:30 of footage. 4. Steps 1 through 3 will be repeated with each object. 3.4 – Phase 3 1. Each video will be placed into Tracker. The program will track the data and plot its coordinates over time. The coordinates will be recorded and the difference between each successive x value and each successive y value will be found. The average between the negative x differences will be subtracted from the average between the positive x values, giving the average displacement of x values. The same method will be used with the y coordinates.
3. Experimental Procedure 3.1 – Preparation 1. The SWAL System will be set up. 2. Preliminary tests will be conducted to find optimal 50 | 2016-2017 | Broad Street Scientific
Figure 4. An object suspended in the SWAL system.
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Triangles Triangle 1 Triangle 2 Triangle 3 Triangle 4 Cube Cube 1 Cube 2 Sphere
X displacement (mm) 1.95E-02 2.19E-02 1.01E+01 5.48E-02
Y displacement (mm) 1.94E-02 5.98E-03 1.04E+00 7.78E-03
Base (mm) 3 4
Height (mm) 3 4
X displacement (mm) 1.95E-01 9.98E-02
Y displacement (mm) 6.76E-02 1.27E-02
Y displacement (mm) 0.00488
Len. Wid. Ht. X dis(mm) (mm) (mm) placement (mm) 5 5 1 0.0323
Y displacement (mm) 0.00374
X-Displacement (mm) Average Displacement Excluding Triangle 3
6 7 8 4
6 7 8 4
2 2 2 2
0.0107 0.00807 0.156 0.0167
0.00406 0.00556 0.0396 0.00851
Flat Plane 1 Flat Plane 2 Flat Plane 3 Flat Plane 4 Flat Plane 5 Flat Plane 6 Flat Plane 7 Flat Plane 8 Flat Plane 9 Flat Plane 10
Height (mm) 5 6 2 2
Diameter X displace(mm) ment (mm) 4.5 0.0691
Sphere 1 Flat Plane
Base (mm) 5 6 5 4
The shapes with their respective x and y coordinate displacements are listed above in Table 2. Figure 5 is the graph of all of the x and y displacement coordinates. From visual observation of the graph it can be seen that there exists a large outlier, making it harder to observe the other data points. Figure 6 is the x and y displacement coordinates excluding the outlier, Triangle 3. A grouping of approximately eight points lie in the lower left plane of the graph. These points have the lowest average displacement out of all of the data. These points are recorded in Table 3 and are plotted in Figure 7. Y-Displacement (mm)
X-Displacement (mm) Flat Plane 8
Flat Plane 7
Flat Plane 5
Flat Plane 6
Flat Plane 10
Flat Plane 3
Figures 5, 6. Table 3.
Table 2. PHYSICS AND ENGINEERING RESEARCH
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From these eight points, six are shaped in a flat plane. These flat planed shapes are also grouped closer to the origin of the graph, revealing that they have the least average displacement out of the objects in Table 3. However, this could be due to the fact that a large amount of data was recorded for the flat plane shape, giving it more probability to have a lower average displacement. Our hypothesis suggested that a sphere would be the most stable. The sphere was not in the lower area of the graph that correlated with a lower average displacement. The radius of the sphere that was used, 4.5 mm, was close to the length and width of Flat Plane 10 (4mm x 4mm x 2mm) and yet Flat Plane 10 was much closer to the origin than Sphere 1. However, this does not necessarily mean that a flat plane is more stable than a sphere. Due to the lack of sample sizes, this report suggests that a larger sample size with more correlating dimensions be used. Y-Displacement (mm)
Eight Lowest Average Displacements
X-Displacement (mm) Figure 7. From the flat plane dimensions that were grouped in the 8 shapes with the lowest average displacement, 2 of these has correlating dimensions with other shapes in that group. Flat Planes 6 and 7 had a length and width of 5mm and 6mm respectively. Triangle 1 and 2 also had a base and height of 5mm and 6mm respectively as well. This points to the conclusion that a levitating shape of either 5mm or 6mm would have the most stability. There are a few reasons as to why the flat plane shape had the most success at having the lowest average displacement. One reason is due to its large surface area versus the small amount of mass above it. The larger base allows for more sound wave pressure to suspend it in mid-air. The low mass above this base, as opposed to a larger shape with more mass above its bases, allows for less stress to be put on the sound wave, thus leading to a more effective levitation. Overall, the data suggests that the flat plane shape is the most stable in a SWAL system. The data also suggests that a shape of 5mm or 6mm with the density close to Styrofoam would be very effective at levitation as well. These results, however, need more conclusive data to reach a solid result. A larger sample size of all of the shapes would be recommended. A more controlled environment and a more advanced video analysis software would be beneficial as well. A few errors might have plagued the results, such as 52 | 2016-2017 | Broad Street Scientific
unknown sound waves, different temperatures, humidity levels and atmospheric pressures and unknown air currents circulating throughout the room. 6. Conclusion This work aimed to study the effects of shapes and sizes of objects suspended in a Standing Wave Acoustic Levitation system. The experiments sought to determine if certain shape and size were found to be more stable while suspended in a SWAL system consisting of a Bolt Clamped Langevin Transducer operating at a frequency of 25.428 KHz. A pilot test first identified the optimal running frequency of the transducer and the optimal height between the transducer and reflector. Levitation experiments then tested objects with various shapes and sizes. The results identified the Flat Plane shape as the most effective at levitation. Furthermore, a shape with a similar density to Styrofoam with the dimensions of 5mm or 6mm would be highly effective for levitation as well. The data and analysis did not support the earlier conclusion that proposed that the sphere was the most effective at levitation. A limitation of this work includes a low sample size as well as a handful of unknown errors that may have affected the data. A larger sample size of all of the shapes is recommended along with a better controlled environment. Furthermore, a more advanced video analysis software would be beneficial to future work. This work is poised to contribute to the field of acoustic levitation. For example, with the holographic display system introduced by Ochiai, Hoshi, and Rekimoto, the results of this study would be beneficial in creating a more advanced and concrete entertainment system by allowing researchers to know the most stable particle shape and size. In the field of handling hazardous material with a SWAL system, the knowledge shed by this study of the shape of the material container or the shape of the hazardous material itself would be very beneficial and could lead to increasing the safety of this application, ultimately resulting in less accidents. Lastly, having the knowledge of the most stable particle shape and size would be beneficial in assembling instruments through levitation. This knowledge would help to determine if certain components could be precisely fitted together, of if constructing them in a SWAL system would be too unstable. In conclusion, the work researched in this paper is poised to improve current SWAL methods. If a certain shape and size is found to be more stable than others, researchers will be able to use this information to conduct more stable experiments. Further research should be conducted on this topic to expand on the current knowledge. Future work should include a larger sample size, a more controlled environment to limit interacting and external influences during suspension, and advanced video analysis software.
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7. References Andrade, M., Perez, N., & Adamowski, J. C. (2015). Analysis of a Non-resonant Ultrasonic Levitation Device. Physics Procedia, 68-71.
Xie, W. J., & Wei, B. (2001). Parametric study of single-axis acoustic levitation. Applied Physics Letters. Zhang, P., Li, T., Zhu, J., Zhu, X., Yang, S., Wang, Y. et al. (2014). Generation of acoustic self-bending and bottle beams by phase engineering. Nature communications.
Bizrate,. (2016). Pyle PCA3 Mini Stereo Power Amplifier. Retrieved from http://www.bizrate.com/receivers/1230879949.html.
Zhao , S., & Wallaschek, J. (n.d.). A standing wave acoustic levitation system for large planar objects. Archive of Applied Mechanics.
Brown, Douglas. Tracker. Computer software. Tracker Video Analysis and Modeling Tool. Vers. 4.92. N.p., n.d. Web. 12 Feb. 2016. (http://physlets.org/tracker/). Cheol-Ho Kim, & Jeong-Guon Ih. (2007). On the horizontal wobbling of an object levitated by near field acoustic levitation. Ultrasonics, 331-335. Foresti, D., Nabavi, M., & Poulikakos, D. (2012). On the acoustic levitation stability behaviour of spherical and ellipsoidal particles. Journal of Fluid Mechanics, 581-592. Hashimoto, Y., Koike, Y., & Ueha, S. (1996). Near-field acoustic levitation of planar specimens using flexural vibration. The Journal of the Acoustical Society of America. Liu, Y., Hu, J., & Zhao, C. (2010). Dependence of Acoustic Trapping Capability on the Orientation and Shape of Particles. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 1443-1450. Marzo, A., Drinkwater, B. W., Seah, S., Sahoo, D. R., Long, B., & Subramanian, S. (2015). Holographic acoustic elements for manipulation of levitated objects. Nature communications. Matsuo, E., Koike, Y., Nakamura, K., Ueha, S., & Hashimoto, Y. (2000). Holding charactteristics of planar objjects suspended by near-field acoustic levitation. Ultrasonics , 60-63. Ochiai, Y., Hoshi, T., & Rekimoto, J. (n.d.). Pixie Dust: Graphics Generated by Levitated and Animated Objects in Computational Acoustic-Potential Field. Park, J.-K. (2014). Feasibility of Non-contact Manipulation of a Small Object using Standing Wave Acoustic Levitation. Rigol,. (2016). Retrieved from https://www.rigolna.com/ products/waveform-generators/dg1000/dg1022/ Thomas, G., Andrade, M., Adamowski, J. C., Silva, E. (2015). Acoustic Levitation Transportation of Small Objects Using a Ring-type Vibrator. Physics Procedia, 59-62. Whymark, R. R. (1975). Acoustic field positioning for containerless processing . Ultrasonics. PHYSICS AND ENGINEERING RESEARCH
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USING DIFFERENTIAL EQUATIONS TO DETERMINE THE EFFECTS OF BT CORN ON MONARCH BUTTERFLY (DANAUS PLEXIPPUS) POPULATIONS Amber Detwiler Abstract Monarch populations have been declining rapidly over the past decade, largely in part to herbicide and pesticide use. In this study, pesticide in the form of Bt corn is examined. Vensim (Vensim, 2010) simulation software was used to create a model of monarch population over the course of five generations, based on differential equations from Messan et al. 2011. The model was then altered to include data of Bt corn pollen exposure and its effects on death rate and growth rate. Bt corn pollen, when consumed by as little as 1.6 percent of the monarch population, was found to have a substantial effect. Decreased growth rate caused by Bt corn pollen lowered the population even further, proving the need to limit the quantity of Bt corn grown in the US. Future studies should adapt the model to show monarch populations year after year and determine the long-term consequences of Bt corn pollen on monarchs. 1. Introduction D. plexippus and other Lepidoptera â€”the order of insects accounting for moths and butterfliesâ€”are valued internationally for their beauty and importance to the health of an ecosystem as pollinators (Butterfly Conservation, n.d.). Monarchs are famous for their distinct orange and black coloring and their annual 2000 mile trip from Mexico to Canada, in which researchers and scientists track their flight and breeding patterns (The Monarch Butterfly in North America, n.d.). During the the course of their long journey, monarchs are important pollinators, spreading pollen further distances than more localized pollinators (Silovsky et al., 2016). In 2010, $10 billion worth of US crops were pollinated by insects other than honey bees (Silovsky et al., 2016).
Figure 1. Annual cycle of the monarchs, separated into four generations (Lovett, n.d.) 54 | 2016-2017 | Broad Street Scientific
In addition, monarchs are one of the many insects that undergo complete metamorphosis. Their transition consists of four main phases: egg, larvae, pupa, and butterfly (The King of Butterflies, n.d.). The larval phase can be broken down further into stages called instars. Instars are the periods between molts when the caterpillar sheds its skin. This helps to separate the massive growth of the caterpillar from about 3 mm in length to 30 mm (Lovett, n.d.). Every year, monarchs make the over 2000 mile voyage from Mexico to Canada in a matter of months (Messan et al., 2011). Due to their short lifespan, the butterflies make their journey in multiple generations, the first being born in March-April and the last in late August (Monarch Butterfly, n.d.). Throughout their travels, the monarchs lay eggs on milkweed plants to continue the cycle after their generation dies. These eggs hatch and begin rapidly consuming milkweed. The last generation goes through the overwintering phase and flies the entire journey south, back to Mexico, in order to breed and begin the cycle again in the spring. Figure 1 provides a visualization of the journey divided into four generations of monarchs. However, please note that the computational model used in this research consists of five generations, although there can be anywhere from three to seven depending on the conditions (Messan et al., 2011). The species survival depends on two plants: milkweed and the Oyamel fir tree. Milkweed, the only food source for the larvae, is currently being destroyed by the herbicides used in many of their agricultural habitats (Messan et al., 2011). The Oyamel fir tree, which serves as shelter for the overwintering monarchs, is decreasing in population due to deforestation in Mexico. Because of their reliance on these two species, one of the main reasons for the decreasing population of monarchs is the use of herbicides and pesticides throughout the United States. Bacillus thuringiensis (Bt) bacterium has been used as pest control in crop production since 1928 (Niederhuber, 2015). The bacterium can be found naturally in many MATHEMATICS AND COMPUTER SCIENCE RESEARCH
environments, ranging from deserts to animal feces (Niederhuber, 2015). Bt is a USDA approved biopesticide and is even commonly used in organic farming (Niederhuber, 2015). It began to cause problems in 1995 when Bt genes were first added to corn (Niederhuber, 2015). Bt corn is genetically modified to kill European corn worms and other Lepidoptera that ingest the plant. Even though Bt corn was found to cause no harm to other insects, there is still evidence of toxin in its pollen (Oberhauser et al., 2001). This pollen, when spread onto nearby milkweed, can have harmful effects on monarch larvae like decreased growth rate, decreased weight, and eventually death (Hellmich et al., 2001). After consuming some of the Bt corn pollen, the toxin binds to receptors in the caterpillar’s gut, causing it to stop eating (University of California San Diego, n.d.). The toxins then build up and create holes in the cell wall, allowing Bt spores and natural gut-dwelling bacteria to access the rest of the larva’s body (Niederhuber, 2015). Eventually the larvae dies as the rest of its body is consumed by the spores and bacteria (University of California San Diego, n.d.). The effect of Bt pollen varies depending on the instar in which the larvae consumes it. When tested, second and third instar larvae were 12 and 23 times more tolerant, respectively, of the toxin than first instars (Hellmich et al., 2001). In this model, however, the death rate of monarchs who consume Bt corn pollen is not based on individual instars, but the larval phase as a whole. Because Bt corn only affects monarch larvae, this model only accounts for the portion of the cycle which contains butterflies in the larval phase —the spring/summer stage of the journey. This model tests the significance of Bt corn pollen on the whole monarch population. 2. Computational Approach Based on differential equations from Messan et al. 2011, this model was made with Vensim (Vensim, 2010) to study the effects of Bt corn pollen on monarch populations with the simple alteration of various variables. While up to a year could be spent finding similar results in a noncomputational manner, this simulation using Vensim (Vensim, 2010) takes a matter of seconds. The difficulty of measuring monarch populations in real life is immense. Additional problems would arise when trying to calculate the grains of Bt corn pollen consumed by each larvae as well. The computational method of modeling population allows for a quick and easy way to find the effects of certain variables. Still, error when using this computational model is inevitable. Most variables are just rough estimates of values, and some are not represented. Climate, for example, has an impact on monarch populations, but is too difficult to add to this computational model. However, this model can still be trusted to produce relatively accurate results when it comes to the effects of Bt corn on monarch populations. MATHEMATICS AND COMPUTER SCIENCE RESEARCH
The first model, shown in Figure 9 (located in the Figures and Tables section) involves population over the course of five generations, covering the spring/summer migration. Because the model only accounts for the spring/summer migration and not the fall migration and overwintering months, the model cannot cycle through to show population year after year. To begin with, Equations 1-7 (shown below) were used to model the change in generations up to i = 5. Larval deaths during each generation are represented by μ₁Li and butterfly deaths by μ₂Mi, i being the generation.
Equation 8 adds a predator-prey (monarch-milkweed) model and allows for experimentation with milkweed population. Figure 8 (located in the Figures and Tables section) provides a visual representation of the model. By changing variables like “Percent milkweed destroyed by herbicide”, the user can visualize how changing our agricultural habits can benefit monarchs.
The values for all variables are shown in Table 1 and stay the same unless otherwise noted. Most of the values in Table 1 are based on those given in Messan et al., 2011. The last four values are only Variable Biological Meaning γ Maturation rate of larvae μ₁ Death rate of larvae μ₂ Death rate of monarch buterfly α₁ Growth rate of larvae
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Variable Biological Meaning M₀ Population in central Mexico μ₀ Death rate of overwintering monarchs A Initial milkweed mass a Growth rate of milkweed K Carrying capacity of milkweed σ Percentage of milkweed destroyed by herbicide β Consumption of milkweed by larvae
0.008 - 0.09
η α₂ ρ
Percent population exposed to Bt corn pollen Death rate of larvae exposed to pollen Growth rate of Bt larvae Percent not exposed to Bt corn pollen
3. Results and Discussion The results below were all generated using an η value calculated with the equation η = ē0.³⁵⁸⁵³�/(x + ē0.³⁵⁸⁵³�), where E is the distance from the Bt corn in meters and x is the sensitivity to the pollen (Perry et al., 2011). In this case, “high” sensitivity was used when given the options of “extreme”, “very high”, “high”, “above average”, and “below average” (Perry et al., 2011). While the value for x was constant at 0.7190, the value of E alternated between 1 and 4 meters, to account for closeness to the Bt corn (Perry et al., 2011).
1/(larvae * day)
0.00 - 1.00
0.992 - 0.91
Figure 2. Monarch population in millions without Bt corn. All values used are equal to those given in Table 1.
Table 1: Initial values and constants for Equations 1-8 present in the second model (shown in Figure 10), as explained later, and are based on research gathered from Hellmich et al. 2001, Perry et al. 2011, and Zanger et al. 2001. Figure 10 (located in the Figures and Tables section) shows the original model with the added effects of Bt corn pollen. An extra death output was added to each generation of larvae and is represented mathematically in Equation 9. To find the effect of Bt corn pollen on monarch deaths, the user can experiment with the values of ω and η in Table 1. Because Bt corn pollen can also have an effect on growth rate, the variable α₂ was created based on data gathered from Zanger et al. 2001, which states that Bt corn pollen decreased caterpillar growth rate by a factor of three (Hellmich et al., 2001) (Zanger et al., 2001). The input of all larvae box variables was changed to include the decreased growth rate of larvae exposed to Bt corn pollen. This is also represented in Equation 9. The user can alter variables ω and ρ as long as ω + ρ = 1 remains true. The same output and input were added to each equation up to i = 5.
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Figure 3. ”Worst Case Scenario”. 9 percent exposure, E = 1 meter, decreased growth rate not included When only considering the deaths caused by Bt corn and not decreased growth rate, large changes in population were only noticed at 4 percent exposure. Four percent exposure is relatively accurate considering that 50 percent of the monarch population originates in the Corn Belt, which as of the year 2016 is made up of 79 percent Bt corn (Hellmich et al., 2001) (Wechsler, 2016). From 2000 to 2016, the percent of Bt corn grown in the US has more than quadrupled (Wechsler, 2016). In this research, the “worst case scenario” has been 9 percent exposure, and although 4 percent would be more reasonable at this point MATHEMATICS AND COMPUTER SCIENCE RESEARCH
in time, without the controlled production of Bt corn, it may become reality. The population difference between the monarch population without the lethal effects of Bt corn (Figure 2) can be compared to this “worst case scenario” in Figure 3.
Figure 6. Worst Case Scenario” with decreased growth rate. 9 percent exposure, E = 1 meter Figure 4. Exposure is 6 percent, E = 1 meter, decreased growth rate not included Another factor included in this model is distance from the Bt corn, E. Unfortunately, the model does not account for varying differences in locations of monarchs. When including distance from the corn, it acts as if the entire exposed monarch population is the same distance away from the Bt corn. When distances of one meter and four meters are used to find the death rate of the monarchs, significant differences in population begin to occur at 1.6 percent exposure. Differences in population based on E are shown in Figures 4 and 5. Bt corn was also found in various studies to have nonlethal —yet still detrimental— effects on monarchs, such as decreased growth rate (Hellmich et al., 2001). With the added effect of decreased growth rate, Bt corn appears to have an even larger impact on the monarch population. Figure 6 shows the “worst case scenario” as explained earlier with the added effects of decreased growth rate. This added aspect decreases the monarch population by almost 50 percent as compared to the model of the population without the effects of Bt corn pollen, proving the impact that this factor has on D. plexippus.
Figure 7 shows a more realistic graph of monarch population with both decreased growth rate and deaths caused by Bt corn. Even this graph, without other harderto-measure effects like milkweed consumption and weight, shows the impact of Bt corn. The results gathered from this research provide evidence of population decrease in the millions,
Figure 7. Exposure is 4 percent, E = 4 meters, includes decreased growth rate which will have a negative effect on the already declining species. If reliance on Bt corn continues to grow in the US, the monarch population will decline even more rapidly. 4. Conclusions
Figure 5. Exposure is 6 percent, E = 4 meters, decreased growth rate not included
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D. plexippus and other Lepidoptera are valued not only for their beauty, but for their role in a healthy ecosystem. The monarchs’ annual migration shows the phenomenon in which generation after generation follows in its ancestors’ steps to complete the journey north. Monarchs are important pollinators in the US as well, spreading pollen much further distances than other butterflies due to their 2000 mile migration (Silovsky et al., 2016). Unfortunately, their survival largely relies on milkweed, which is being diminished by herbicide. Of the milkweed that remains, some of it contains evidence of Bt corn Broad Street Scientific | 2016-2017 | 57
pollen. By altering variables like exposure to pollen, death rate, distance from the Bt corn, and decreased growth rate, estimates of monarch population were produced. The models created in this research help to prove the harmful effects on larvae that consume this pollen. As the percentage of Bt corn grown in the US increases, the monarch population is predicted to decrease. At just 4 percent exposure, the monarch population was found to decrease by about 5 million. At 9 percent exposure and with decreased growth rate included, the population decreased by almost 50 percent. Future adaptations of these models could determine the long term effects of Bt corn pollen on monarch populations. Altering the model could even determine the approximate year of monarch endangerment status if no changes are made to increase the population. Currently, D. plexippus is under review by the U.S. Fish and Wildlife Service to be listed as a threatened species (U.S. Fish and Wildlife Service, n.d.). Changes should also be made to account for the differing locations from Bt corn. The model shown in Figure 10 only allows for one E value (distance from Bt corn), meaning that all monarchs are the same distance away from Bt corn. In reality there are variations in distance, which results in differing quantities of pollen consumed by each larvae. Generally, the closer the monarch is to the Bt corn, the more pollen it will consume. There is no question that Bt corn has a negative effect on monarch populations. By limiting the amount of Bt corn produced in the US, we can try to lessen its impact on monarchs. For an already decreasing species that is critical to a balanced ecosystem, we need to use any means necessary to support their survival. 5. Acknowledgements The author thanks Mr. Robert Gotwals for his excellent teaching and advice. Without the information he provided over the past semester, this paper would not be possible. Appreciation is also extended to the North Carolina School of Science and Mathematics (NCSSM) for providing high school students with the opportunity to take a computational science course. The author finally thanks Ms. Kathleen Abraham and Ms. Rebecca Hanson for their help in editing this paper. 6. References Vensim, P. L. E. ”Ventana Systems, Inc.” Avaiable at: http://www. vensim. com (2010). Messan, K., Smith, K., Tsosie, S., Zhu, S., Suslov, S. (2011, December 20). Short and Long Range Population Dynamics of the Monarch Butterfly (Danaus plexippus). Retrieved from https://arxiv.org/pdf/1112.3991v1.pdf The King of Butterflies – The Monarch Butterfly. (n.d.). 58 | 2016-2017 | Broad Street Scientific
Retrieved from http://www.monarchbutterfly.com/ Lovett, J. (n.d.). Monarch Watch : Biology : Life Cycle. Retrieved from http://www.monarchwatch.org/biology Hellmich, R. L., Siegfried, B. D., Sears, M. K., Stanley-Horn, D. E., Daniels, M. J., Mattila, H. R., Lewis, L. C. (2001, August 17). Monarch larvae sensitivity to Bacillus thuringiensispurified proteins and pollen. In PNAS. Retrieved from http://www.pnas.org/content/98/21/11925.pdf Monarch Butterfly. (n.d.). Retrieved from http://www. nwf.org/wildlife/wildlifelibrary/ invertebrates/monarch-butterfly.aspx Oberhauser, K. S., Prysby, M. D., Mattila, H. R., StanleyHorn, D. E., Sears, M. K., Dively, G., et al. (2001, August 17). Temporal and spatial overlap between monarch larvae and corn pollen. In PNAS. Retrieved from http://www. pnas.org/content/98/21/11913.full Hellmich, R. L., Sears, M. K., Stanley-Horn, D. E., Oberhauser, K. S., Pleasants, J. M., Mattila, H. R., et al. (2001, August 17). Impact of Bt corn pollen on monarch butterfly populations: A risk assessment. In PNAS. Retrieved from http://www.pnas.org/content/98/21/11937.full. Perry, J. N., Devos, Y., Arapaia, S., Bartsch, D., Ehlert, C., Gathmann, A.,et al. (2011, November 11). Estimating the effects of Cry1F Bt-maize pollen on non-target Lepidoptera using a mathematical model of exposure. In Wiley Online Library. Retrieved from http://onlinelibrary.wiley.com/ Zanger, A. R., McKenna, D., Wraight, C. L., Carroll, M., Ficarello, P.,Warner, R., Berenbaum, M. R. (2001, June 21). Effects of exposure to event 176 Bacillus thuringiensis corn pollen on monarch and black swallowtail caterpillars under field conditions [Scholarly project]. In PNAS. Retrieved from http://www.pnas.org/content/98/21/11908.full Wechsler, S. J. (2016, November 3). Recent Trends in GE Adoption. Retrieved from https://www.ers.usda.gov/data-products/adoption-ofgenetically-engineered-crops-in-theus/recent-trends-inge-adoption.aspx Butterfly Conservation. (n.d.). Retrieved from http:// butterfly-conservation.org/45/why-butterfliesmatter.html The Monarch Butterfly in North America. (n.d.). Retrieved from https://www.fs.fed.us/wildflowers/pollinators/ MonarchButterfly/index.shtml Silovsky, P., Martin, P., Rader, J., Birrell, M., Shrack, C. (2016). Plight of the Pollinators (P.Silovsky, Ed.). On T.R.A.C.K.S., 24(1), 1-5.
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Niederhuber, M. (2015, August 10). Insecticidal Plants: The Tech and Safety of GM Bt Crops. Retrieved from http:// sitn.hms.harvard.edu/flash/2015/insecticidal-plants/
7. Figures and Tables
University of California San Diego. (n.d.). How does Bt work? Retrieved from http://www.bt.ucsd.edu/howbtwork.html U.S. Fish and Wildlife Service. (n.d.). Species Profile for monarch butterfly (Danaus plexippus plexippus). Retrieved from http://ecos.fws.gov/ecp0/profile/ speciesProfile?sId=9743 Figure 8. This is the predator-prey model which represents Equation 8.
Figure 9. This is the basic model without the effects of Bt corn. The line extending off of the screen-shot connects to Figure 8, the predator-prey model.
Figure 10. This model shows the effects of Bt corn with the addition of four new variables, which are changed accordingly to produce the results above. MATHEMATICS AND COMPUTER SCIENCE RESEARCH
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3-TONE K-COLORINGS OF GRAPHS Cary Shindell Abstract This project addresses a problem in graph theory called t-tone k-coloring. A t-tone coloring of a graph assigns t distinct colors to each vertex such that vertices e edges apart share less than e colors. The t-tone chromatic number of a graph is the lowest possible number of colors used in a t-tone coloring of the graph. The 2-tone chromatic numbers of many types of graphs have already been determined, but the methods used are quite different, partially due to the simpler nature of 2-tone coloring. Very little has been done so far with 3-tone colorings, which is why this work is new and opens many opportunities extensions and further work. Here we investigate and find values, formulas, or bounds for the 3-tone chromatic numbers of path, cycle, and tree graphs. These graphs and the methods used to find their 3-tone chromatic numbers yield interesting results that have multiple practical applications. The findings can potentially be extended to other types of graphs and even to solve or prove other mathematical problems. For instance, the concept of grouping colors together such that the colors themselves do not matter, only the groups do, which simplifies the problem and prompts various discoveries and formulas. The ”possibility tree” can also be applied to other problems to simplify and solve sequences with many possibilities, and make patterns more apparent. One possible area of application is genetics, such as long sequences of DNA. Overall, the results and novel methods of this investigation will lead to additional discoveries and solutions to similar problems in graph theory and other scientific fields. 1. Introduction Given a graph G, we create a t-tone coloring of each vertex (chosen from k colors) so that any two vertices a distance d apart share fewer than d common colors. The minimum integer, k, such that a graph has a t-tone k-coloring is known as the t-tone chromatic number. We will denote the t-tone chromatic number as Tt(G) = k. For example, a 2-tone 5-coloring of the path, P5, is shown below:
Figure 1. A 2-tone 5-coloring of the P5 graph. From the figure above, we can see that the 2-tone chromatic number T2(P5) = 5. The 2-tone chromatic number of certain graphs has already been explored fairly in-depth. We will explore the 3-tone chromatic number of the path graphs, cycle graphs, and tree graphs, which have yet to be thoroughly investigated by mathematicians. These graphs produce some very interesting results which can also be applied to other types of graphs, other t-tone values (for example, T4(X)), and even problems in graph theory and other mathematical fields. 2. 3-tone Chromatic Number 2.1 – Path Graphs Conjecture 1. For all path graphs with n ≥ 3 vertices, the 3-tone chromatic number is 8. Proof. Let there be 8 colors denoted by the letters abcdefgh. Group these colors into 3 groups: abc, def, and gh. Now use the notation xyz to dictate the coloring possibilities for a node, where x ≤ 3, y ≤ 3, and z ≤ 2, and 60 | 2016-2017 | Broad Street Scientific
x + y + z = 3. x indicates how many colors from the abc group the node has, y indicates how many from the def group, and z indicates how many from the gh group. We’ll call a notation possibility (i.e. eligible xyz combination) for a vertex a ”node”. So, without loss of generality, for any path let the first vertex have colors abc; its notation is 300, and that is the only node for the first vertex. Let the second vertex have colors def; its notation is 030. The third vertex has 3 different coloring possibilities, but its notation must be 102 because it has 1 color from the abc group and 2 from the gh group, so again there is only one node. The fourth vertex must have notation 210. From the 5th vertex onward, there are multiple nodes (notation possibilities), so we create a “possibility tree” to illustrate and investigate these. When traveling “down” the tree, we are going from one vertex to the next in the path. A given node will have one ”child” node for each possible notation for the next vertex in the path. For instance, the 4th vertex is 210, so the 5th vertex has 2 nodes (possibilities): 021 and 120. Then, if the fifth vertex is 021, the 6th vertex has 2 nodes: 201 and 111. This tree continues on indefinitely; however, there are only so many xyz possibilities; there will therefore eventually be repetitions, which we can use to simplify the tree. Now, note that the “children” of a given node or notation possibility are based on the node’s notation and the 2 preceding nodes’ notations. If we have a chain C of 3 nodes, the notation possibilities, or “child nodes”, that come after it are the same as those for any chain whose second and third nodes are identical in notation to those of chain C. This is true because the child nodes of Chain C are 3 lengths away from the first node of chain C so they cannot share 3 colors with the first node. Since we are using 8 colors, the first and second nodes of any length 3 chain must have different colors (6 total), so the first and third nodes must share 1 color. Since the child nodes MATHEMATICS AND COMPUTER SCIENCE RESEARCH
share no colors with the third node of the chains, there is necessarily 1 color that the first node does not share with the child nodes, regardless of the notation of the first node. Thus the first node of C does not affect the child nodes of C, which means any given chain of 2 nodes always has the same child nodes. So if a certain chain of 2 nodes appears multiple times in the possibility tree, we only need to investigate the child nodes of one instance, since the tree from that point onward will be the same for each instance. The first time a distinct chain of 2 appears in the tree, we will give the lowest vertex a label, starting with v1. So the first vertex, 300, would be v1, 030 would be v2, 102 would be v3, 210 would be v4, etc.. Note that all ”102” nodes are not necessarily v3; only those preceded by 030 are (a node is defined by its notation and its parent node’s notation). We label nodes in an order from top to bottom and left to right, like atomic number in the periodic table. If we find a node identical to one that has already been labelled, we give it the same label instead of drawing its child nodes. We can keep labelling nodes and cutting off the tree until the tree has been “completed”-all nodes are labelled, as shown in the diagram below.
Figure 2. Possibility Tree. Looking at the possibility tree, we see that v10 (012 preceded by 120) has 300 as a child node – thus it has v1 as its child node. This means we can repeat the sequence 300, 030, 102, 210, 120, 012 any number of times, so all paths of length 3 or longer must have a 3-tone chromatic number of 8. A path of length 2 has a 3-tone chromatic number of 6. The null graph has a 3-tone chromatic number of 3. Thus we know the 3-tone chromatic number for all path graphs. 2.2 – Cycle Graphs Conjecture 2. For all cycle graphs with n ≥ 8 vertices, the 3-tone chromatic number is 8 or 9. (We can find it for all cycles). Proof. A cycle graph on n vertices can be considered as a path on n vertices where the first and last vertex have been connected. Thus, for a cycles on n vertices, we can look at the possibility tree for paths and check if there is a chain of length n (starting with v1) that can be “wrapped”first and last vertices connected. For some values of n, there MATHEMATICS AND COMPUTER SCIENCE RESEARCH
will be no sequence, chain, or path that can be wrapped and still have a 3-tone 8 coloring. In fact, in the possibility tree, the only node that can be “wrapped” back to v1 is v10. So a cycle is only 3-tone 8 colorable if it has a corresponding path that ends in v10. Note that when traversing down the tree, whenever we encounter a “dead end”-i.e. a labelled node – we effectively go back up to the first occurrence of that node in the possibility tree. Thus there are many paths that end in v10. Some notable cycles that are 3-tone 8-colorable are those of length 6 + 3a, 8a, and 11a, where a is any positive whole number. We can determine if any given cycle is 8-colorable by checking if there is a path of the same length that ends in v10 - the possibility tree makes this fairly simple, and for larger n values one can extend the tree. Additionally, from the possibility tree we see that the shortest path that includes v25 and ends with v10 has length 14. When ”wrapped”, this path would be 3-tone 8-colorable. Since v25 can be followed by any number of additional v25’s, and this path has a v25, we can insert any number of v25’s next to the existing v25, which means we can obtain a path ending in v10 for any n ≥ 14. Thus all cycles of length 14 or more are 3-tone 8-colorable. Now consider cycles that aren’t 3-tone 8-colorable. • We see that if n = 7, when we “wrap” any of the possible nodes, we will have 2 or more contradictions – 2 colors minimum will need to be added, so the 3-tone chromatic number is 10 for n = 7. • If n = 8, we already know the 3-tone chromatic number is 8 (we can wrap the v10 that follows v11 to v1). • If n = 9, we can wrap v25 to v1, which creates only 1 contradiction; so one color must be added to eliminate it. Thus T3(C9) = 9 • If n = 10, we have v25 again, so T3(C10) = 9 We see from Figure 5. that v25 can be followed by any number of v25’s, any of which can be wrapped to v1 with only 1 contradiction. So for n ≥ 9, T3(Cn) ≤ 9. We already know T3(Cn) ≥ 8. Now we consider the cases where 3 ≤ n ≤ 5, as we know all other cases of n. • n = 3: Obviously we need 3 different colors for each vertex, so T3(C3) = 9 • n = 4: If we wrap v4 to v1, there are 2 contradictions so we must add 2 colors. Thus, T3(C4) = 10 • n = 5: If we wrap v5 to v1, we get 2 contradictions. Thus, T3(C5) = 10 Thus we can find the 3-tone chromatic number for any cycle. 2.3 – Trees Conjecture 3. The 3-tone chromatic number for a tree on v ≥ 3 vertices and a max degree of x is C= if C is even, or
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C= if C is odd. Proof. Let each letter in the alphabet represent a different color. Each tree has a ”main path”, which is the longest path in the tree, and this path has a 3-tone chromatic number of 8 (using colors abcdefgh) based on a previous conjecture. So, for a given tree G, let vk be a vertex on the main path of G, and vk−1 and vk+1 be the vertices preceding and following vk, respectively. Note that vk−1 and vk+1 can share exactly one color. Now allow vk to have any number of branches of length 1. We’ll use the notation vkx to represent the xth branch of vk. The first branch of vk, vk , can share one color 1 from vk−1, no colors from vk, and one color from vk+1. So we must introduce a 9th color, i, to the 3-tone coloring of the graph. Consider the maximum total number of times the color a can appear on vkx (the 1st vertex on each branch of vk. Each time a appears on a vkx with a set of 2 colors, each of those 2 colors can’t appear with each other or with a on any other vkx, because vkx’s can only share 1 color as they are a distance of 2 apart. So a can appear on a vkx for each distinct pair of non-adef colors. So with 8 colors, there are 8 − 4 = 4 colors (and 2 sets of 2) that aren’t adef, so a can appear on at most 2 vertices. Using 9 colors, there are still only 2 sets of 2 colors that aren’t adef, so a can still appear on 2 vertices at most. Using 10 colors, there are 10 − 4 = 6 colors that aren’t adef, so a can appear on at most 6/2 = 3 vertices (vkxs). We see that using C colors, a can appear on
we can expand and use the quadratic formula to express C in terms of α, split by even and odd C cases due to the % (mod) in the equation. • For even C:
For odd C:
However, this is not ideal because the cases are determined by the dependent variable, C. It is simpler to look at the highest α for each C value, then for a given α see what range or C value it corresponds to. Below is a table of those values: C 8 9 10 11 12 13 14 15 16 17
α 3.3 → 3 4 7 8 12 13.3 → 13 18.3 → 18 20 26 28
Table 1. C values and the Corresponding α. vkxs at most. The same thing applies for every other color not on vk(def). Since each vertex has 3 colors, the total number of vkxs (including vk−1 and vk+1) is the total number of times all non-def colors appear on vkxs divided by 3. There are C − 3 non-def colors, so with C colors we can properly color up to
We see right away that for some values of C, the graph cannot achieve its theoretical maximum α. For C = 8, we know that the actual α is 2, not 3. This is an exception caused by the restriction on the number of sets - only 2 ”sets” of 2 colors (bc and gh) are available, and both are taken by a. The values for C = 9 and C = 10 work, as shown below.
branches of vk. So with C = 9, vk can have up to 4 branches. Note that
is the maximum total number of times all non-def colors can appear in the branches (length 1) of vk. Since that value is not necessarily a multiple of 3, there may be 1 or 2 ”leftover colors”-that is, 1 or 2 colors may not be able to appear their maximum number of times. So when we divide said value by 3, we may not get an integer result for α (the maximum possible number of branches with C colors). We account for this by truncating or rounding down the result to the nearest integer. We want to know the 3-tone chromatic number given α branches for vk , so 62 | 2016-2017 | Broad Street Scientific
Figures 3, 4. C = 9. C = 10. However, the max α for C = 14 is actually 17, not 18 upon further investigation: The color a can appear 5 times. Assume WLOG that it appears as: abc, agh, aij, ahl, and amn. Now we establish a ”group” notation similar to that used in the ”possibility tree” for paths.
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Figure 5. Slot Notation. With this notation, we will not include the color whose sets we are listing (so for example, as 1st set is 200000) For any vertex or set except those with a, the notation cannot have a value greater than 1 in any slot, as that vertex would then share 2 colors with abc, agh, aij, akl, or amn. Also, a 1 in a given slot can appear up to 2 times in a given color set. Since there are only 4 slots available for a given color set, and no slot can appear more than twice, each available slot must appear exactly twice in a given color set (assuming each color appears 5 times total). as sets and the first set of each color are already locked in, so we’ll ignore those for now. Also, each set can only appear 4 times (not including sets with a). Assume set 000011 is in the ij group. We find that having set 000011 in the ij group means 101000 is also in the ij group, thus 001100 is in bc group, thus 000011 is in bc group, thus 000101 or 000110 is in bc group, both of which leads to contradictions. Thus 000011 cannot be in the ij group. Consider the sets of 2 that contain the last 3 groups only. There are 3 possibilities: 000011, 000101, and 000110. For the bc group , since the gh group must appear exactly twice, there are 2 sets per color (b, c) containing only colors from the last 3 groups. For the gh groups, bc appears twice, so there are 2 sets per color (g, h) containing only colors from the last 3 groups. For the ij groups, the only possible set containing only colors from the last 3 groups is 000011; however, we just showed that the ij group couldn’t have that set. We also know that if the bc group has 000011, it will have 001100. This means the ij group will have 000011, which is again a contradiction. Therefore the bc group can’t contain 000011. By similar reasoning, the gh group also cannot have 000011. Thus no group can have 000011. This means the 4 expected combination of 000011 cannot appear anywhere, so the last 4 colors can only appear 4 times, not 5. This explains why the formula for α and the value in the table, is 4/3 too high (18.3 instead of 17. See figure). It seems as though there could be a pattern for C ≥ 14. Perhaps the last 2 groups (the set 000...011) cannot appear together for certain C values, like C = 8 and C = 14, resulting in certain α values that are 4/3 too high. Further investigation would be needed to confirm this. So we know potential 3-tone chromatic numbers for trees with branches of length 1. Now we must consider branches of length 2 and greater; that is, the branches of vkxs branches. The situation (C and α values) for vk applies to any vertex with length 1 branches, so vkx (and its branches) will follow the same pattern as vk and its branches. The only difference between vkx and vk is that the first vertex of MATHEMATICS AND COMPUTER SCIENCE RESEARCH
any given branch of vkx (vkxy) cannot have the exact same colors as any vkx (each vkxy is 3 away from each vkx, except the vkx in question) so they can only share 2 colors). First we will show that a vkx has the same C and α values as a vk (for now, we will ignore the difference stated above).
a b c g h i j k
Vertex 1 200000 200000 200000 101000 101000 100100 100100 100010
Vertex 2 002000 001001 001001 100010 100010 100001 100001 100100
100100 100100 001100
100100 101000 001100
100100 101000 001100
Vertex 3 000200 001010 001010 100001 100001 100010 100010 100100
Vertex 4 000020 000101 000101 000101 000101 001001 001001 001100
Vertex 5 000002 000110 000110 000110 000110 001010 001010
Table 2. C = 14. For vk and its branches we assumed WLOG that a would appear on a vkx once with each set of 2 non-adef colors in order (bc, gh, ij, kl, mn, etc.). We’ll do the same for vkx and its branches- assume WLOG that d appears on a vkxy once with each pair of colors except for d and those on vkx in order (assume colors are paired in the order abcdefghij...). Now we can use similar notation as the group notation used for vk, but the groups are different. We want to keep the ”order” of groups the same, so group 1 for vkx is def (it was abc for vk), group 2 for vkx, whose colors cannot appear at all on any vkxy, is whatever colors are on vkx, since for vk group 2 was the colors on vk (def). For each subsequent group we take the list of available colors and order them abcdefghij... and remove d and whichever colors appear on vkx, then fill group 3 with the first 2 from the list, group 4 with the next 2, and so on until all groups have been filled. For example, if vkx was cjg and C = 10, group 1 would become def, group 2 would be cjg, group 3 would be abj, and group 4 would be hi. Now, since the groups correspond for each branch of vk there can be a corresponding branch on vkx with the same group notation (each using its respective groups). Ignoring the exception listed above, we know this is true because vkx is in the exact same situation that vk was in, and we already know the results of that situation in terms of branches and group notation. It turns out the exception does not actually change the situation. Recall that the difference was that vkxy could not share 3 colors with any vkx, as they are 3 lengths apart. We assumed that d will not share 3 colors with a vkx for any x. For vkxys without d, we’ll assign each color within a group for vkx to the corresponding color in the corresponding group for vk. For instance, if group 3 was gh for vk and ab Broad Street Scientific | 2016-2017 | 63
for vkx, g on a vkx would become a on a vkxy, and h on a vkx would become a b on a vkxy. Using this we can replicate and color each vkx into a vkxy (if bgi was a vkx, eah could be a vkxy if vkx was a cjg). Now, we find each vkxy that is identical in color scheme to a vkx. For each one, we choose one of its colors and swap each instance of that color on all vkxy with the other color from its group; we swap all instances of the other color on all vkxys with that color. So for example, if we chose i and i’s group was hi, we’d replace every instance of h on each vkxy with i, and every instance of i on each vkxy with h. We know that the resulting color combination for that vkxy will not share 3 colors with any vk because it x already shares 2 colors with a vkx, and no 2 vkxs can share 2 colors. So we repeat this until no vkxys share 3 colors with a vkx. Note that further investigation might be needed to confirm that there won’t be any chains formed from swapping that will lead to a contradiction (that is, at least one vkxy necessarily shares 3 colors with a vkx). We tested some cases - C ≤ 10 definitely does not give unexpected contradictions - and investigated some high C values and did not find any contradictions. Thus the aforementioned difference is inconsequential in terms of chromatic numbers. Therefore the situation (possible branches and their notations) for vkx is the same as that for vk. Now consider the branches of vkxys. Each vkxyz is at least 4 lengths away from all but one vkx (and its branches) and each vkxy, except for those on that vkxy. So those vertices don’t affect the situation. Each other vkxy, including vk, is 3 lengths away from each vkxy (of that vkxy), so those cannot share 3 colors; this is analogous to the difference in the vkx situation, which we showed was inconsequential. Each vkxyz is 2 lengths away from each other vkxyz (including vkx), which is the same condition as in the vk situation. Each vkxyz is 1 away from vkxy, which is the same condition as in the vk situation, where each vkx was 1 away from vk. We have accounted for all possible vertices on all possible branches of vkxy and found no differences from vkx’s situation; thus the situation for vkxy is the same as that of vkx, and by extension, the situations for all subsequent vertices on all subsequent branches of vkxy are the same as that for vkxy. This means that the situation for vk applies for any vertex in a tree. We know the resulting chromatic number given a vertex with α branches from the equation we derived previously:
if C is even. if C is odd.
Note that there are some exceptions to this as previously stated; further investigation would be necessary to account for these. We do know, however, that the values for C cannot be less than those listed in the table from the equations (Table 1). 3. Future Questions 1. Do chains form for C ≥ 11? in trees? 2. If we take the general case of t-tone colorings, how do graphs behave? 3. Why do exceptions occur for the formula for trees for certain C values? 4. How can we apply the concept of group notation to other problems, including practical applications? 4. Acknowledgements Thanks to Dr. Tamar Avineri for introducing me to the graph theory field, providing the inspiration for this project, and advising me and editing the paper. 5. References Bickle, A., & Phillips, B. (n.d.). T-Tone Colorings of Graphs. Retrieved from https://allanbickle.files. wordpress.com/2016/05/ttonepap
C= for even C and C= for odd C. Since C increases as α increases, the vertex in any tree with the highest degree among all vertices in the tree determines the 3-tone chromatic number for that tree. So for a tree with a max vertex degree x, the 3-tone chromatic number, C, of that tree is: 64 | 2016-2017 | Broad Street Scientific
MATHEMATICS AND COMPUTER SCIENCE RESEARCH
AN INTERVIEW WITH DR. RACHEL LEVY ‘85
From left, Sreeram Venkat, BSS Chief Editor; Dr. Jonathan Bennett, BSS Faculty Advisor; Dory Li, BSS Chief Editor; Dr. Rachel Levy ‘85, Professor of Mathematics at Harvey Mudd College; and Samuel Li, BSS Essay Contest Winner. What inspired you to pursue a career in math education? My brother Matt (NCSSM ’89) and I are both educators. Our parents are educators. When I was a little kid I played “school” for fun, and in some ways my job is like playing “school” for fun. It’s hard for me to remember a time that I didn’t think about education. While I was a student at NCSSM I tutored community college students. During college I taught math in the summer at the Duke TIP program. What do you think is the biggest misconception that people, especially students, have about math today? Actually, I don’t think the biggest problem is a misconception. From K-12 students experience mathematics in school, so they have a solid concept of what constitutes school mathematics. I think a big problem is the lack of connection between the mathematics people do in school and the mathematical thinking they can employ or enjoy in life. I want to help people make stronger connections between the power and beauty of the mathematics they experience in school and the power and beauty of mathematics they can experience in their lives and in their jobs. Some people love mathematics because it has inherent beauty and truth. Take 2+1=3. This equation has lovely and fundamental connections to our ideas about quantity FEATURE ARTICLE
and counting. Some school problems try to connect this idea to life by just adding units that refer to something concrete. For many people, just saying 2 apples + 1 apple = 3 apples doesn’t give the abstract idea more meaning or beauty. When “real life math” in school consists of contrived story problems, people generally don’t connect it with problems they see as important. If we want to create a more authentic real world math problem about apples that involves quantity, we can instead pose a question kindergarteners can discuss, such as “how many apples do we need for snack so that everyone gets enough?” This question still involves quantity, but also elicits beginning thoughts about division, fairness and apportionment. Kids can understand that it might be fair to give hungrier people more slices of apple. Here’s another example. Let’s say we have 3 kids at a party and we have a whole cake. The best way to divide the cake is probably not into thirds because the pieces would be too big. Maybe you’re twice as hungry as me or maybe someone is allergic to cake. Fair division doesn’t always mean taking whatever you have and dividing it by the number of people or things you need to divide it amongst. A problem relevant to my daily life is the need to pick a cell phone plan or buy an airplane ticket. The pricing can be intentionally confusing and complicated. Practicing some mathematics can help consumers get a handle on what’s Broad Street Scientific | 2016-2017 | 65
going on so that they can make good decisions. I enjoy helping people discover the relevance of mathematics in their life. When I travel and sit next to strangers, if they tell me what they do for their job, I often ask, “What’s a common problem in your job?” Then I listen to how they think about the problem. Sometimes I share a way a mathematician might approach the same problem. People are usually curious to see that there might be some insight gained. So, I have wonderful conversations with people who start out by saying that math has nothing to do with their life. By the end of the conversation they want to exchange cards and have further conversations about how mathematics might play a role in what they do. I wish more math lovers could engage with people by helping them see some math they find beautiful (which might be quite abstract), or by showing them certain ways of thinking that may impact their daily life and their biggest concerns! What do you think is the best way to improve math education at the K-12, undergraduate, and graduate levels? What I find very motivating for people in general is mathematical modeling, like the examples with the apples, the cake or cell phones. Through the IMMERSION program I work with elementary school teachers who help their students pose problems such as “how many words will I read this year?” Kids can start to think about what words count (Books? Comics? Texts? Signs?), and how to count (or estimate counts of) words. This naturally leads to rates such as words/page or books/week. It’s a sophisticated question, and kids really get it! Teachers notice that every kid has an entry point and personal connection to the problem. I’m trying to build the practice of mathematical modeling in schools all the way from kindergarten to high school and college. As their mathematical and analytical tools build, students can tackle more sophisticated problems. To give more students experiences using mathematical sciences in business, industry, and government, a group of us have started the BIG Math Network. The Network will help mathematical sciences students get internships and new job opportunities so that they understand what opportunities they have in the world. Many mathematics Ph.D.’s enter careers in business, industry, and government (BIG). How does your research in applied mathematics benefit from an interdisciplinary environment? If we’re not talking across disciplines, then we’re very likely to get something wrong and miss a perspective or insight. Often we’ll develop a model that isn’t flexible enough. In my work I’ve interacted with biologists, physicists, chemists, engineers, and artists to get different views on models describing fluid motion. All of those perspec66 | 2016-2017 | Broad Street Scientific
tives have made my research stronger. The times that we haven’t reached out soon enough are the times we’ve made incorrect assumptions. Conferences facilitate this reaching out. If I’m doing a problem related to biology, I’ll go to a biology conference so that I’m getting my work in front of the people who might be able to tell me, hey there’s something I’m missing. Or, they may get excited about it and extend the model some other way. Conferences organized by my professional society, the Society for Industrial and Applied Mathematics (SIAM), bring together people from a broad range of fields. Where do you see the future of mathematical modeling and applied mathematics? I hope that mathematics will help us make the world better. That means different things to different people. I hope that mathematics will be used to address issues of equity, fairness and health. Many very important questions are related to security, whether that means safety, cybersecurity or privacy. I think mathematics has the potential to change those spaces and is powerful enough to change them for the better or the worse. So my hope is that we not only create tools that can do good in the world, but that we choose to use them that way. What are you and the Society for Industrial and Applied Mathematics (SIAM) working to accomplish? SIAM aims to build cooperation between mathematics and the worlds of science and technology through our publications, research, and community. As Vice President of Education for SIAM, it’s very easy for me to promote those goals. One thing I get to do is to read comments from the students who don’t win the Moody’s Mega Math Challenge (a mathematical modeling competition for high school students). The competition asks them something like “What impact has this experience had on you?” Comments often say something like “I don’t care if I won or lost - I know what I want to do with my life now.” Or, “This is the most fun I’ve had all year in school!” There’s impact for you. Sometimes school mathematics can feel like a set of problems, often of the same type, with a pre-determined solution strategy, where you are at perpetual risk of getting red X’s and feeling stupid. So I don’t find it surprising when I say I am a mathematician and people immediately share a negative experience or feeling. I have seen how mathematical modeling can improve people’s dispositions towards mathematics. People who can talk with others about fun and creative experiences like the Moody’s Mega Math Challenge have the potential to build a citizenry with a more positive connection to mathematics.
School mathematics testing is also often a solitary activity. In the workplace I can’t think of a time I was not allowed to ask for advice or help from a colleague. I like to say mathematical modeling is a team sport. You bring everything you have to the table, then your group tries to develop a good enough answer to the problem. The problems are large, messy and complicated enough that you need all hands on deck.
However, the first grandmother who sent me her picture also included stories about how she knew the famous computer scientist Grace Hopper and how she’d been involved in the early days of computing. So instead of the fractal, I created a blog as a way to organize and share the stories while I was collecting the pictures. I still have yet to make the fractal!
In undergrad at Oberlin College, I studied math and English. I actually did my honors work in English and I got to do a practicum at NASA as my capstone in math, which were very formative experiences. At Harvey Mudd College, I actually teach writing as well as mathematics. I love to wear both hats. At Oberlin I also studied a lot of music.
As more people started sending me their stories, the blog was commented on by Cory Doctorow at boingboing.net. He posted something like, “I don’t know why geeks hate their grandmothers.” That just blew up in the comments and the Grandma Got STEM blog got tens of thousands of hits. I knew that I had reached my target audience when senior male physicists and computer scientists started contributing to the blog and promising to stop using those phrases. They were excited to share stories about women whose work they admired.
I’m really interested in languages. I see mathematics as a language, and art as a language, and programming as a language. I wish I had studied more languages. I love how they sound, and I like how they feel in your mouth. I like the culture that goes along with them. I would love to have the time and the brain capacity to pick up hundreds of languages. I’ve tasted a little bit of a lot of languages, but I can only have a philosophical conversation in English!
Around this time Grandma Got STEM was featured in Slate, on Australian radio, on NPR and in the Israeli and French press. It was a really exciting time! Now the site has a large body of posts that serve as a reference. When someone uses the Grandmother line in the press or in an advertisement, people point to my blog and say “hey, wait a minute, check out this blog and you’ll see that what you just said doesn’t make any sense.”
You have a blog called Grandma Got STEM. What was your inspiration for the blog, and how do you envision it changing the way that people perceive senior women in STEM?
What part of your NCSSM experience would you like to see changed or added?
Beyond mathematics, what are some of your other academic interests?
At talks and in classes, I often heard people say, “Explain it so that your grandmother could understand it.” Another phrase you might have heard is, “It’s so easy my grandmother could do it.” A few years ago I realized that I was likely to soon become a grandmother and realized that those phrases were problematic because they imply that maternity + gender + age = novice. People were not trying to be offensive, but they were not saying what they really meant. They meant to be saying, “Explain this so anyone can understand it.” I think they include the grandmother part, because the implicit expectation is that people have warm feelings toward their Grandmothers and would want them to understand their work. I have seen Einstein and Feynman both cited as originating this idea. I thought for a long time about how to change people’s perception about grandmothers and people’s inclination to use these phrases. I started by asking my students for pictures of their grandmothers who were in STEM fields. I planned to make a fractal-like art project so that if you zoomed in on the STEM grandmothers, you’d get more and more of them. I hoped this would give the perception that there are infinitely many grandmothers in STEM.
I never got to do an internship. I was in the 4th graduating class when NCSSM was just getting started. I had friends who did internships and it was very impactful for their careers. I wish I had experienced that opportunity. I also wish I had done more programming. I first learned in middle school on a 2K Pet computer (that’s only one page of text worth of memory to work with!). The funny thing was that my experience being exposed to computer programming at a young age was that computer programming was really easy. Math seemed more rich and complex and deep. I wanted to spend my time doing things that were hard, so I was more drawn to math than computing. It’s sort of funny to me looking back that in some ways, a lot of people were intimidated by computer science whereas I couldn’t see how I would use it. It wasn’t until a gazillion years later in grad school when I started getting back into programming. I really wish I had taken every opportunity to learn more computer science. I think it would have been fun, useful, interesting and challenging. Now I know a little bit of R, and a little bit of Python. I’ve used C++ and FORTRAN and software like Mathematica and MATLAB. I find it really exciting that programming languages are becoming accessible, and it is fun to see how the tools can facilitate Broad Street Scientific | 2016-2017 | 67
mathematical modeling. What was the most impactful part of your NCSSM experience? For me, something that was really impactful, something that I really carry with me, is that everyone works either on the grounds or in the cafeteria. I think that if this school ever loses that, it would be horrible. I have a strong appreciation for the people who do that kind of work at my own institution because I have a small bit of understanding about how hard their jobs are. So I would say that the most impactful experience was working in the dishroom
of the cafeteria. I can still smell the dish room if I think about it (not a lovely smell), but the camaraderie was super awesome. So I also learned the importance of camaraderie in a job, no matter what the job is. I love my job and I love the people I work with. The NCSSM alumni network continues to be tight. When students come to my college from Science and Math, it’s really exciting. It’s a connection to home, a connection to a place that I love. My husband Sam Kome and I are both class of ’85 so we have many longtime friendships in common.
FEATURED ELEMENTS (Opposite, from left)
The 2017 edition of Broad Street Scientific was redesigned in order to ensure that the journal retains a clean and modern look. The fonts featured in this edition are Old Standard TT and Crimson Text, both courtesy of Google Fonts.
Chemistry Section First identified in 1923, hafnium is a shiny, silver element commonly used in filaments and electrodes. Additionally, it is used in control rods in nuclear power plants due to its high neutron capture cross section.
Biology Section Iridium is one of the rarest elements in Earth’s crust, and only 3000kg of this metal are produced and consumed annually around the world. The salts it produces vary widely in color, leading to it being named after the Greek goddess of the rainbow, Iris.
Congratulations on your close reading of the 2017 edition of Broad Street Scientific. If you are able to find the three small unicorns hidden throughout the issue, e-mail Avra Janz at firstname.lastname@example.org with the numbers of the pages on which each of the unicorns are located. The first person to complete the challenge correctly will receive a small bag of candy.
Physics and Engineering Section With an entire age in human history named after it, copper has been perhaps one of the most instrumental elements in human advancement. Its alloy with tin to create bronze punctuated the beginning of the Bronze Age, and since, it has come to be used in plumbing, industrial machinery, and electrical wiring. Math and Computer Science Section At 22.59g/cm3, osmium is the densest metal on the periodic table. Though toxic alone, in alloys it provides extra durability with applications in electronics and other highwear materials. Back Cover While neon is the fifth most common element in the universe, it is actually quite rare on Earth. Discovered in 1898 along with other trace inert gases found in air, the bright red emission spectrum of neon has been used in advertisement signs, lasers, and high-voltage discharge tubes. ~ Karl Westendorff