Science Explorations 2019-2020, Volume 9

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SCIENCE EXPLORATIONS Saint Ann’s School VOLUME 9

2019 – 2020

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Table of Contents

Examining Gene Therapy Strategies Through the Lens of Sickle Cell Anemia Cuatro V. (Teresa Chiang)….……………………………………….…………………………………………..……3 Sleeping with The Fishes: Upside Down Jellies and Circadian Rhythm Lee G. (Jessica Zayas).……………………………………..…………………………………………………………11 Using Bacteriophages to Combat Antibiotic Resistance Emily D. (Leah Kaplan)………………………………………………….………………..………………………….17 Bomb Calorimetry 101 Eliza B. & Sam S.-M. (Jared Cross)……………………………….…………………….…………….…..…….30 Hydrophobic Coagulation in Pressed Tofu: An At-home Study Una R. & Ayla S. (Liz Velikonja)…………………………..………………………………………………………33 Simulating Ecosystems for Evolutionary Exploration Aaron F. (Mike Roam)………………….…………………..……………………..……………….………………..41 Melting Glaciers Viv W. (John Baierl)……………….……….……………………………………………………..…………….….…48 The Effects of Climate Change on Marine Life Noah R. & Ezra G. (Gretta Reed)…………………………………………………………………….….…......50 Maxwell’s Equations from the Principle of Least Action Luca S. (Daniel Yaverbaum)………………..………………………………………………………..……….……56 An Exploration of Spectroscopic Techniques and Their Use in Tandem William T. (Nicholas Harbison)………..….………………………………………………………………..…….68 “Let’s Pretend That…”: The Role of Dramatic Play in Language Development Lily S.-K. (Virtue Sankoh)…………………………..………………………………….….……………….........83

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Examining Gene Therapy Strategies Through the Lens of Sickle Cell Anemia Cuatro V. Mentor: Teresa Chiang

Abstract Since the discovery of the human genome, it has been a goal of the scientific community to modify specific points in this genetic code. Gene therapy is the treatment that allows such modification; it is a way to correct mutated genes by transplanting genetically normal genes into the affected cells. In the experimental portion of this project, by conducting bacterial transformations, the insertion of DNA into bacteria parallels the transfer of DNA into a different living organism — a fundamental process in gene therapy. In recent years, curing genetic diseases has become a reality with sickle cell anemia being cured through several methods of genetic therapy. Sickle cell disease is caused by a single point mutation in the β-globin subunit of hemoglobin — the body’s oxygen transporter. Whether it be through inserting a healthy version of β-globin into patients’ blood stem cells or reverting adult hemoglobin to fetal hemoglobin, in numerous patients, sickle cell anemia has been cured. In this paper, research regarding these gene therapy strategies combating sickle cell disease are compiled. Examining these methods will elucidate the path forward in curing other genetic diseases such as cystic fibrosis, Huntington's disease, muscular dystrophy, spinal muscular atrophy, and many more.

Introduction Every human genome is composed of approximately three billion DNA base pairs, yet even if one of these pairs exhibits a mutation, the effects can be physiologically astronomical. An apt example of such a phenomenon is sickle cell disease. The defining mutation of this monogenic disorder is a point mutation in the β-globin gene, encoding a single protein chain of 147 amino acids. The mutation, in the sixth amino acid of βglobin, is a base pair substitution from adenine to thymine, causing the corresponding amino acid to be valine as opposed to what is typically glutamic acid. This substitution of amino acids permits inoperative hemoglobin tetramers to form. The defective tetramers polymerize when deoxygenated and cause red blood cells (RBCs) to sickle — hence the name sickle cell anemia. These deformed RBCs break down prematurely, damage endothelial cells, and create blockages in the bloodstream causing extreme inflammation and waves of hemolysis (Figure 1).

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Figure 1: The sequence of changes from the original DNA mutation to the RBC blockages.

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Adapted from Chacko, Ron. “Sickle Cell Anemia - New Research from Chicago Offers Hope.” Heartland Health Centers, 31 July 2019 & “A Case Study of the Effects of Mutation: Sickle Cell Anemia.” A Case Study of the Effects of Mutation: Sickle Cell Anemia

On a symptomatic level, patients typically experience cut-off oxygen to the limbs, hypertension, organ injury, and episodes of extreme pain. With approximately 300,000 babies being born annually with sickle cell anemia world-wide, the disease is the most common inherited blood disorder. While treatments include certain medications and blood transfusions, the only current cure available to the public is a bone-marrow transplant. Hematopoietic stem cells (HSCs) — the blood cell factories — are removed from a healthy matched donor’s bone marrow and infused into the patient. While a sixyear survival period has been reported in over 90% of cases with matched sibling donors, fewer than 14% of patients have such donors. When the transplant is successful, the donor's stem cells will create normal RBCs in the patient’s body and the disease is cured; however, the sickle cell disease community remains hesitant to embrace the HSC transplant. In cases with matched, yet unrelated donors, graft-versus-host disease, graft rejection, and other immunological barriers often arise. These side effects are among many that contribute to the bone-marrow transplant’s high short-term morbidity and mortality rates. For male patients the median lifespan is 38 and for females it is 42.

Considering the inefficacy of the current sickle cell disease cure, scientists and doctors are developing novel genetic therapies that may lead to a significant advance.

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It was amid the 1960’s and early 70’s when the concept of gene therapy arose. During this time, cell transformation techniques were in development due to infections caused by the simian vacuolating virus 40 and papovaviruses. Recombinant DNA techniques increased cloned genes’ availability and clarified that genetic disease phenotypes could be corrected in vitro with foreign genes. In 1990, after several decades of research, scientific advancement, and ethical debate, the first gene therapy trial commenced.

Ashianthi DeSilva, a four-year-old patient with severe combined immunodeficiency due to a missing enzyme called adenosine deaminase (ADA), underwent a twelve-day treatment. A functioning copy of the gene ADA was introduced into DeSilva’s immune cells using a benign viral vector, and successfully cured her. Indeed, DeSilva’s story was one of success and a milestone for the gene therapy movement, yet this wave of triumph would be short-lived.

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In 1999, Jesse Gelsinger, an 18-year-old boy, and his father went to the University of Pennsylvania for a clinical trial in gene therapy. Jesse had ornithine transcarbamylase: a disease caused by a mutated ornithine carbamoyltransferase (OTC) gene that compromises the liver’s urea cycle. In the trial, the intent was to introduce a healthy OTC gene to Jesse’s body through another virus vector; however, four days later, he died due to an immune reaction to the injection. The laboratory’s gene therapy program was suspended, and the FDA launched 69 investigations on U.S. gene therapy trials.

After Jesse's death, the world of gene therapy was brought to a halt.

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Throughout the world gene therapy was at a roadblock both due to the public safety concerns and the extreme cost in gene therapy technology. It is only in recent years, with the development of gene editing technology, that gene therapy has begun, once again, to gain momentum. Today, there are approximately 2,600 gene therapy trials worldwide. After numerous biotechnological and genetic advances, sickle cell disease is one of the first diseases to be cured using gene therapy. With many clinical trials underway, different forms of gene therapy are developing. We are on the brink of a novel era of genomic medicine.

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Methods In the experimental portion of this project, conducting bacterial transformations, the insertion of DNA into bacterial cells, parallels the fundamental process in gene therapy of transferring DNA into living human cells. In the transformation, Vibrio fischeri — a luminescent bacteria found in the light organ of the pinecone fish, Monocentris japonicus — was used. Action from the enzyme luciferase on a specific aldehyde facilitates V. fischeri’ s light production. This process is not only highly regulated as it requires at least 10% of the cell’s energy, but also requires the involvement of numerous genes. The luciferase enzyme, required in this light production, is encoded by lux genes. These genes from V. fischeri are placed in a plasmid named pVIB; this plasmid also contains ampicillin resistant genes. If the transformation is successful, then the bacteria should be able to make this luminescent protein and will be resistant to ampicillin.

In two sterilized 15mL tubes, the first marked “+plasmid” and the second one “plasmid,” 250 µL of iced calcium chloride was added. After placing both tubes on crushed ice, an isolated E. coli colony (approximately 2-5 mm in diameter) was transferred from an agar starter plate to the +plasmid tube using a sterile plastic inoculating loop. To ensure all cell mass entered the tube, the loop was spun rapidly and the tube was held up to light to see if any remains lodged on the plastic. The cells were suspended until there were no cell clumps by pipetting gently, as to not create bubbles.

Once the suspension was white, with an appearance like milk, the +plasmid tube was returned to crushed ice. The same E. coli cell transfer and suspension method was

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repeated to the -plasmid tube. Using a sterilized plastic inoculating tube, plasmid DNA was transferred to the +plasmid tube’s cell suspension and mixed with the bacterial cells. Afterwards, both tubes were returned to the crushed ice and left for 15 minutes.

Four separate luria broth (LB) agar plates were labeled. The experimental plate with LB and ampicillin was labeled “LB +Amp +plasmid.” A negative control plate, also with LB and ampicillin, was labeled “LB +Amp -plasmid.” The final two plates, while containing LB, do not have ampicillin and are labeled “LB +plasmid” and “LB -plasmid.”

After a 15-minute cooling period, both the +plasmid and -plasmid tubes were “heat shocked” by submerging them in a 42°C water bath for 90 seconds while gently stirring them. After returning the tubes to ice for 60 seconds, 250 µL of room-temperature LB was gently pipetted and incorporated to each tube’s cell suspension. The new mixtures were left to recover at room-temperature for 10 minutes. After recovery, 100 µL from the +plasmid or -plasmid tube was pipetted to the appropriate agar plates and spread using a glass cell spreader. The end of the cell spreader was sterilized by dipping into a beaker with 70% ethanol, and once removed from the ethanol, lit with a flame. The spreader was first set on a portion of the agar that does not already have cells to cool the instrument, then the bacterial mixture was immediately spread. The plates were incubated for approximately 30 hours at exactly 30°C.

Results As expected, nothing grew on the Negative Control plates, with no bacteria and no DNA. In Control groups A and B, because no ampicillin was present, a lawn of bacteria grew.

Even though Control A includes bacteria with added DNA, there is no way to tell whether the bacteria have picked up any ampicillin resistance. On the experimental plate, distinct bacterial colonies formed, because the cells contained ampicillin resistance; furthermore, these bacteria display luminescence (Figure 3). By examining each of these factors it is evident that the DNA successfully transformed the bacteria: the presence of the bacterial colonies underscores the ampicillin resistance gene’s functioning, and the glowing indicates that the bacteria can make the luminescent proteins.

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Figure 2 (left): Image of plates under white light. Figure 3 (right): Image of plates in the dark to observe luminescence.

Discussion While the experimental portion of this project only changes bacterial cells’ luminescence and resistance to ampicillin, it demonstrates the undeniable value of gene therapy. If we manipulate DNA and inject it into a living organism, we can change the protein that an organism produces. This basic process underlies the power of gene therapy.

Using gene therapy to combat sickle cell anemia not only presents a cure, but does so in a way that largely eliminates risks of morbidity and mortality associated with a bone marrow transplant — by using a patient’s stem cells to cure their own disease, there is no conflict between the patient and the host's cells. The basic process starts with the removal of a patient’s stem cells. These cells are then corrected to contain a healthy version of the mutated gene through some form of gene editing (such as CRISPR), employing a viral vector, using a gene therapy drug, or a combination of these processes. In this paper, three forms of sickle cell disease gene therapy are analyzed.

The first method, currently conducted in a clinical trial at Bluebird Bio, uses LentiGlobin BB305, a viral vector gene therapy drug, to correct the mutated β-globin gene through insertion of the healthy version. Stem cells are first harvested from patients. While these cells are then transported to a facility to undergo insertion of the healthy gene using LentiGlobin BB305, patients receive three to four blood transfusions over the course of a month and a four-day round of intensive chemotherapy to remove as many sickle cells

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as possible. Once the stem cells are ready for reinsertion into the patient, they are frozen, shipped from the facility, and infused into the patient. It takes approximately a day for patient’s immune system to recover and an additional three months for complete recovery, but patients are potentially cured for life, producing normal RBCs.

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In a clinical trial at Boston Children’s Hospital, there is a different gene therapy strategy.

Humans have two different types of hemoglobin, one fetal and the other adult, encoded by different genes. Fetal hemoglobin expression is typically turned off shortly after birth, and adult hemoglobin takes over. Rather than changing the specific point mutation that causes sickle cell in the sixth amino acid of β-globin (in adult hemoglobin), scientists silence the BCL11A gene, which codes for a protein that turns off fetal hemoglobin production. When BCL11A is silenced, fetal hemoglobin may restart production and the adult hemoglobin will phase out. Seeing as sickle cell anemia only affects adult hemoglobin, once the BCL11A gene is silenced in stem cells, which are reintroduced to a patients’ bodies, they will begin to produce fetal hemoglobin and normal RBCs, and be cured.

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While results are preliminary, a third strategy uses CRISPR as the gene editing tool, as opposed to viral vectors. At the Sarah Cannon Research Institute in Nashville, Tennessee, a patient named Victoria Gray is one of the first patients to be helped using CRISPR gene therapy. This approach also targets the switch from adult to fetal hemoglobin, yet does so by directly disrupting the BCL11A gene in Gray’s stem cells using the CRISPR-Cas9 system. Four months after Gray was reinjected with her stem cells, 94.7% of her RBCs contained fetal hemoglobin. While Gray hasn’t been completely cured, her condition is improving dramatically — her case is a milestone for CRISPR-mediated gene therapy.

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All three of the gene therapy strategies analyzed in this paper have changed the lives of sickle cell patients. Both advanced viral vector drugs and CRISPR gene therapy methods show immense promise. Questions can now be asked as to how to apply gene therapy to other genetic diseases. Looking at sickle cell anemia’s genetic qualities, development, and cultural history, may clarify what makes a disease a viable candidate for gene therapy. Table 1 depicts numerous diseases that, like sickle cell disease, are monogenic and may, therefore, be easier to target with gene therapy. The fact that these diseases are all caused by mutations in a single gene is one of many genetic qualities that may be examined when deliberating the next diseases to undergo gene therapy clinical trials.

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Table 1: Examples of monogenic diseases and respective defining mutations.

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Genetic Disease:

Gene Mutation:

Cystic fibrosis

Cystic fibrosis conductance transmembrane regulator (CFTR)

Huntington's disease

Huntingtin (HTT)

Duchenne muscular dystrophy

Dystrophin (DMD)

Sickle-cell anemia

Beta hemoglobin (HBB)

Spinal muscular atrophy

Survival motor neuron (SMN1)

Source: Adapted from Chial, Heidi. “Rare Genetic Disorders: Learning About Genetic Disease Through Gene Mapping, SNPs, and Microarray Data.” Nature News, Nature Publishing Group, 2008.

Historically, because sickle cell mainly affects people in lower income communities mainly of African, Indian, and Saudi Arabian descent, it hasn’t received as much attention until recent years. While there is surely a medically revolutionizing future in gene therapy, currently there are several barriers hindering the path forward. Firstly, gene therapy is an immensely costly endeavor. Completing one gene therapy trial for sickle cell anemia can cost upward of $700,000 per patient. Moreover, all gene therapy approaches are currently in clinical trial phases. To be accessible to the public, the technology will have to undergo a major transition to lower costs for the millions of individuals suffering from potentially curable genetic diseases. While optimism is warranted for the future of gene therapy, it is essential to remain cognizant of the major changes that must be involved to make this science accessible.

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Bibliography 1 - Clancy, Suzanne. “A Single Base Change Can Create a Devastating Genetic Disorder or a Beneficial Adaptation, or It Might Have No Effect. How Do Mutations Happen, and How Do They Influence the Future of a Species?” Nature News, Nature Publishing Group, 2008, www.nature.com/scitable/topicpage/genetic-mutation-441/.

2 - Chacko, Ron. “Sickle Cell Anemia - New Research from Chicago Offers Hope.” Heartland Health Centers, 31 July 2019, www.heartlandhealthcenters.org/sickle-cell-anemia-new-research-from-chicagooffers-hope/.

3 - “A Case Study of the Effects of Mutation: Sickle Cell Anemia.” A Case Study of the Effects of Mutation: Sickle Cell Anemia, evolution.berkeley.edu/evolibrary/article/0_0_0/mutations_06.

4 - Kolata, Gina. “These Patients Had Sickle-Cell Disease. Experimental Therapies Might Have Cured Them.” The New York Times, The New York Times, 27 Jan. 2019, www.nytimes.com/2019/01/27/health/sickle-cell-gene-therapy.html.

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5 - “Sickle Cell Anemia.” Mayo Clinic, Mayo Foundation for Medical Education and Research, 30 Jan. 2020, www.mayoclinic.org/diseases-conditions/sickle-cell-anemia/diagnosis-treatment/drc-20355882.

6 - Hoban, Megan D, et al. “Genetic Treatment of a Molecular Disorder: Gene Therapy Approaches to Sickle Cell Disease.” Blood, American Society of Hematology, 18 Feb. 2016, www.ncbi.nlm.nih.gov/pmc/articles/PMC4760089/.

7 - Lanzkron, Sophie, et al. “Mortality Rates and Age at Death from Sickle Cell Disease: U.S., 1979-2005.”

Public Health Reports (Washington, D.C. : 1974), Association of Schools of Public Health, 2013, www.ncbi.nlm.nih.gov/pmc/articles/PMC3560868/.

8 Friedmann, T. “A Brief History of Gene Therapy.” Nature Genetics, U.S. National Library of Medicine, 1992, pubmed.ncbi.nlm.nih.gov/1303270/.

9 - “OTC Gene - Genetics Home Reference - NIH.” U.S. National Library of Medicine, National Institutes of Health, 12 May 2020, ghr.nlm.nih.gov/gene/OTC. 10 - Mitha, Farhan. “The Return of Gene Therapy.” Labiotech.eu, 15 May 2020, www.labiotech.eu/indepth/gene-therapy-history/.

11 - Ginn SL;Amaya AK;Alexander IE;Edelstein M;Abedi MR; “Gene Therapy Clinical Trials Worldwide to 2017: An Update.” The Journal of Gene Medicine, U.S. National Library of Medicine, 19 Apr. 2018, pubmed.ncbi.nlm.nih.gov/29575374/.

12 - Nowogrodzki, Anna. “Medicine Is in the Blood.” Media.Nature.com, Nature, 13 Dec. 2018, media.nature.com/original/magazine-assets/d41586-018-07646-w/d41586-018-07646-w.pdf.

13 - Fliesler, Nancy. “Sickle Cell Gene Therapy Boosting Fetal Hemoglobin Shows Promise.” Boston Children's Discoveries, Boston Children's Hospital, 31 Jan. 2020, discoveries.childrenshospital.org/sicklecell-gene-therapy/.

14 - Kolata, Gina. “At 16, She's a Pioneer in the Fight to Cure Sickle Cell Disease.” The New York Times, The New York Times, 11 Jan. 2020, www.nytimes.com/2020/01/11/health/sickle-cell-disease-cure.html.

15 - Haematology, The Lancet. “CRISPR-Cas9 Gene Editing for Patients with Haemoglobinopathies.” The Lancet Haematology, vol. 6, no. 9, 2019, doi:10.1016/s2352-3026(19)30169-3.

16 - Stein, Rob. “Gene-Edited 'Supercells' Make Progress In Fight Against Sickle Cell Disease.” NPR, NPR, 19 Nov. 2019, www.npr.org/sections/health-shots/2019/11/19/780510277/gene-edited-supercells-makeprogress-in-fight-against-sickle-cell-disease.

17 - Chial, Heidi. “Rare Genetic Disorders: Learning About Genetic Disease Through Gene Mapping, SNPs, and Microarray Data.” Nature News, Nature Publishing Group, 2008, www.nature.com/scitable/topicpage/rare-genetic-disorders-learning-about-genetic-disease-979/.

18 - “History of Sickle Cell.” Sickle Cell Association Of New Jersey, www.sicklecellnewjersey.org/aboutscanj/history-of-sickle-cell/.

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Sleeping with The Fishes: Upside Down Jellies and Circadian Rhythm Lee G. Mentor: Jessica Zayas

Abstract How do we define sleep? It’s a complicated question, usually answered by a vague phrase about decreased brain activity. But what about creatures without brains? From that definition, they can by definition not sleep; does that mean that they truly cannot, or that the human definition of sleep is too narrow? I propose the latter. Upside-down jellyfish, also known as cassiopeia, are the only creatures without brains ever observed going into a sleep-like state; a 2017 study from CalTech postulated that this state should, in fact, be defined as sleep and may provide insight on the origins of this still mysterious biological phenomenon. This project attempts to expand upon this research by providing answers on the nature of the cassiopeia circadian rhythm---whether it exists in the first place, and its parameters if it does. Finding answers to questions of the jellyfishes’ circadian rhythm could provide strong evidence about whether these creatures can, in fact, sleep.

Introduction

Jellyfish, a class of invertebrate of the subphylum Medusozoa, are aquatic creatures characterized by their distinctive physiology. Their composition is 98-99% water, with bodies made of two layers: the outer ectoderm and the inner endoderm, with a thick gelatinous muscle cell layer called the mesoglea between them. They have neither hearts nor lungs, and do not have a central nervous system of any kind. Instead, they have a diffuse nerve net, a system of neurons spread throughout their bodies. These neurons are not homogeneously spread; instead they form clusters with designated functions within the larger nervous system. Exact structures and location of neuron clusters vary between the orders, demonstrating many different evolutionary strategies

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for neuronal integration. One of these orders is Scyphozoa, or “true jellyfish.” Jellies in this order have the most organized nervous systems in the jellyfish world, divided into three broad sections.

A diagram of upside-down jellyfish anatomy. (Santhanakrishnan, A., Dollinger, M., Hamlet, C. L., Colin, S. P., & Miller, L. A. (2012). Flow structure and transport characteristics of feeding and exchange currents generated by upside-down Cassiopea jellyfish. Journal of Experimental Biology, 215(14), 2369–2381. https://doi.org/10.1242/jeb.053744)

The first major section of the Scyphozoan nervous system are the rhopalia. There are eight or more per jelly and they are found in the bell, especially around its circumference. These nerve clusters contain ocelli, which are structures that sense light, and statocysts, which sense gravity. It also contains neurons that set the jellyfish’s swim rhythm. Though individual rhopalia exist distinctly from each other, they are connected and bilaterally symmetrical to each other. The second major section is the motor nerve net, which directly activates muscle contraction in response to the aforementioned swim rhythm neurons, called pacemakers. The neurons of this system are randomly oriented and widely spread throughout the entire under surface of the jelly, forming bidirectional chemical synapses where they overlap. Due to these synapses, signals can travel in any direction through the system all at once, allowing for synchronized muscle contraction. The third and final major section is the general diffuse nerve net. These neurons perform several roles such as indirectly relaying sensory information to the pacemaker neurons, regulating the motor nerve net, and even controlling immunoreactivity to antibodies that would harm the jelly. With such a relatively simple nervous system, it would seem as if Scyphozoan jellyfish are incapable of complex neurological function, and yet a certain species of them are the first creatures without brains ever observed sleeping.

Rhizostomeae--- a subcategory of Scyphozoans defined by their frilled arms and spongy, mouthless undersides---contains a genus of jellyfish known as Cassiopeia, commonly called the mangrove or upside-down jelly. Found in the swamps and mudflats of Florida, the Caribbean, and Micronesia, these small, unassuming filter feeders lazily float on the silt of shallow tropical waters, using their symbiotic algae to photosynthesize while they

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eat passing zooplankton and small invertebrates. They rely on the sun during the day, but at night they enter a low-activity state similar to what we humans define as sleep.

But what even is sleep?

Sleep is defined by the Oxford English Dictionary as “a condition of body and mind which typically recurs for several hours every night, in which the nervous system is inactive, the eyes closed, the postural muscles relaxed, and consciousness practically suspended.” This definition works fine for humans, but what about creatures without eyes, in whom we can only theorize the nature of consciousness? Some scientists think that only creatures to whom this description fits truly sleep, while others believe this definition is too narrow in the first place. Three CalTech students decided to push the boundaries of the generally accepted definition of sleep. In their experiments with Cassiopeia, whose behavior they described as “behavioral quiescence,” they proved that these jellies not only become less active during periods of the night, they also show reduced responsiveness to stimuli during their quiescent state and molecular conservation of sleep regulation. They also observed that their behavioral quiescence seemed to be regulated by homeostatic systems and found some proof that they may be regulated by a circadian system as well.

A circadian rhythm is a natural, internal biological rhythm that determines when an organism is asleep vs. awake. To be called circadian, a process must 1. be endogenous (originating from within the organism) and endogenously follow a ~24 hour pattern, 2. be reset by exposure to external stimuli (light, temperature, weather, etc), and 3. retain periodicity in a wide range of physiological temperatures, also known as temperature compensation. Circadian rhythms have been observed in animals, plants, fungi, and even some bacteria---every human on Earth has one. A circadian rhythm is necessary for many creatures because it regulates sleep, which organisms need for proper function. It also keeps nocturnal and diurnal creatures on their respective schedules, and allows creatures to respond to external stimuli, especially periodic stimuli, without their bodies going radically out of balance. In creatures with brains, circadian rhythm is timed by melatonin production from the pineal gland and core body temperature minimum. In creatures without brains, things become more complicated. Generally, it can be measured by using the aforementioned criteria to examine biological patterns.

Cassiopeia jellyfish sleep, but do they have a circadian rhythm?

Materials and Methods I hypothesized that these jellies would, in fact, show evidence of a circadian rhythm. My plan was to take some upside-down jellies, one of which would be the control, and see how light impacted their biological rhythms. The experiment was planned to involve using a number of jellyfish, some of which are the controls. First, I would have to build a saltwater tank.

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The location of the tank is vital; it must be away from windows, heaters, ACs, and outside doors that could change its temperature. First, I would rinse out the tank to remove any dust, debris, and other foreign contaminants. Then, I would use a carpenter’s level and make sure the tank is set up flat. Next would be to add water of desired volume, temperature, and pH, which for mangrove jellies are 72-78° F, dKH 812, pH 8.1-8.4, sg 1.023-1.025, and a low-medium flow. After filling the tank ⅓ full and checking for leaks and cracks, I would fill the tank fully and run a nitrogen cycle to convert any ammonia into friendly bacteria. I would then make sure the filtration, temperature, pH, etc are all working well. all of these qualities should be stable for 48 hours before adding anything to the tank. Finally, before adding the jellies, I would add any additions--in this case, just sand--and check to see if they have changed the water chemistry at all. If this is not the case, then it would be time to add the jellyfish; first, leaving them in their original water bag to acclimate to their new environment and prevent shock, then allowing them to swim freely. Then it would be time to keep an eye on them for a couple minutes to make sure they’re doing ok. For every gallon it holds, the tank would weigh ~8 lbs, so it would also be extremely heavy, meaning the jellies would have to stay in one location and could not be easily moved.

After the tank is set up, and jellies had at least 48 hours to adjust to their surroundings, the experiment would begin. First, for ten days, there would be a 12-12 hour light cycle on all the jellies; 12 hours light, 12 hours no light. 10 times a day for one minute, 10 minutes a day for 10 days--or 100 minutes total--I would count the number of jellyfish pulses to measure their activity. The CalTech students used a similar method, though they had access to an imaging system that I do not have access to due to price, so I would just be using my eyes. I would also be feeding them at the same time every day during this process.

Next, for ten days, the controls would continue to have a 12-12 hour light cycle while the others would have constant lighting. I would be measuring the pulses the same way and feeding them at the same time. Finally, I would do the opposite: the controls still on a 12-12 hour light cycle, but the others in constant darkness, once again measuring pulses and feeding them at the same time. Then, I would put all the data together and analyze any changes. The total experiment time, not including data analysis, would be about 6 weeks, though this could easily be shortened or lengthened.

Results While I was not able to perform the experiment due to the onset of the coronavirus pandemic, I plan on performing the aforementioned experiment in the future as soon as possible. Much of my project, however, was based on the experiments of the aforementioned CalTech study, which can be found here and whose results I found extremely compelling. Once completing my original experiment, possible continuations

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could involve altering feeding times to observe their impact on the circadian rhythm of the jellyfish, as well as finding ways to see if jellyfish take sleeping cues from each other or if their systems are not socially oriented.

Discussion Jellyfish are vastly underestimated, endlessly fascinating creatures, and though they look nothing like us, they may have much more in common with us and other vertebrae than we initially thought. I hope to continue my experiments in the future and hopefully solve this mystery as to whether jellyfish can, in fact, sleep. The evidence I have collected so far, as well as the evidence produced by the CalTech study, points towards the conclusion that they do, in fact, sleep, but I will want to produce experimental evidence before I solidify that result. If they do, not only would it open a new realm of jellyfish neuroscience for study, it would give insight into humankind’s questions about the origins of sleep and what exactly happens in us while we’re sleeping.

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Peroxiredoxins are conserved markers of circadian rhythms. Nature, 485(7399), 459–464. https://doi.org/10.1038/nature11088 Katsuki, T., & Greenspan, R. J. (2014). Jellyfish Nervous Systems. Current Biology, 23(14), 592–594.

Retrieved from https://www.cell.com/current-biology/pdf/S0960-98221300359-X.pdf Marshall, N. B., & Marshall, O. (1971). Ocean Life. New York, NY: Blandford Press Ltd. Meinkoth, N.A. (1981). National Audubon Society: Field Guide to Seashore Creatures(pp. 363-364). New York, NY: Alfred A. Knopf, Inc. Moore, P. D., & Turner, B. D. (1991). Saline Wetlands. In P. Moore (Eds.), Encyclopedia of Animal Ecology (pp. 88-89). Hong Kong: The Promotional Reprint Company Limited Nath, R. D., Bedbrook, C. N., Abrams, M. J., Basinger, T., Bois, J. S., Prober, D. A., … Goentoro, L. (2017).

The Jellyfish Cassiopea Exhibits a Sleep-like State. Current Biology, 27(19), 2984-2990.e3. https://doi.org/10.1016/j.cub.2017.08.014 National Institute of General Medical Sciences. (2019, March 4). Circadian Rhythms. Retrieved from https://www.nigms.nih.gov/education/fact-sheets/Pages/circadian-rhythms.aspx Pappas, S. (2017, September 21). Jellyfish Don’t Have Brains, But They Do Sleep. Retrieved from https://www.livescience.com/60476-jellyfish-sleep.html

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Reitzel, A. M., Tarrant, A. M., & Levy, O. (2013). Circadian Clocks in the Cnidaria: Environmental Entrainment, Molecular Regulation, and Organismal Outputs. Integrative and Comparative Biology, 53(1), 118–130. https://doi.org/10.1093/icb/ict024 Santhanakrishnan, A., Dollinger, M., Hamlet, C. L., Colin, S. P., & Miller, L. A. (2012). Flow structure and transport characteristics of feeding and exchange currents generated by upside-down Cassiopea jellyfish.

Journal of Experimental Biology, 215(14), 2369–2381. https://doi.org/10.1242/jeb.053744 The Editors of Encyclopaedia Britannica. (2010, April 13). Cassiopea | jellyfish genus. Retrieved from https://www.britannica.com/animal/Cassiopea The Editors of Encyclopaedia Britannica. (2020, March 18). jellyfish | Characteristics, Habitat, Diet, Anatomy, & Facts. Retrieved from https://www.britannica.com/animal/jellyfish Yong, E. (2017, September 21). Even Jellyfish Sleep. Retrieved from https://www.theatlantic.com/science/archive/2017/09/even-jellyfish-sleep/540432/

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Using Bacteriophages to Combat Antibiotic Resistance Emily D. Mentor: Leah Kaplan

Abstract The use of bacteriophages--viruses that target and kill specific strains of bacteria--to treat bacterial infections has faded out of western medicine, but due to the increase in antibiotic resistance, it may be making a comeback. With experimentation and literary research, I looked into using a combination therapy of bacteriophages and antibiotics to combat antibiotic resistant bacteria. Phage-antibiotic synergy (PAS) is a theory that sublethal concentrations of antibiotics can promote phage productivity, thus increasing bacterial decline. I focused on PAS in my research, looking at its mechanisms and potential implications for clinical use. Using coliphage T4r and E. coli strain B which we made resistant to the antibiotic ampicillin, we set up a plaque assay to assess whether phage and antibiotics used together would have a higher bacterial suppression than antibiotics or phage alone. We repeated the plaque assay twice, as we had difficulties pouring the molten agar in the first round, and added different titers of phage in the second round. The results from round one supported the hypothesis that phages and antibiotics may be synergistic, however the results from round two were inconclusive, possibly owing to contaminants in the bacteria which we later discovered. We made plans for additional trials with new resistant bacteria and a more reliable method to quantify bacterial suppression using liquid cultures to hopefully see any phage-antibiotic synergy more clearly. While we were unable to continue our experimentation due to school closures, the research done supports the idea that using phages and antibiotics synergistically is a viable treatment option for resistant infections as we move into the post-antibiotic era.

Introduction After Alexander Fleming received the Nobel Prize for his discovery of penicillin in 1945, he issued caution against the emergence of penicillin resistance: “The thoughtless person playing with penicillin is morally responsible for the death of the man who finally succumbs to infection with the penicillin-resistant organism�(16). His words of caution were not heeded. Between just 1940 and 1962, pharmaceutical companies introduced more than twenty new classes of antibiotics to the drug market(16). Pharmaceutical companies ignored the signs of resistance, reasoning they could stay a step ahead by continuously developing new drugs. Figure 1 illustrates the emergence of clinical resistance to many different antibiotics.

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Figure 1: “The Diminishing Effectiveness of Antibiotics�(18)

Scientists have estimated that, at the rate bacterial resistance is emerging, they would need to develop thirty-five new classes of antibiotics every century. However, no new class of antibiotics has entered the market since 1980 (16).

The continuous presence of antibiotics creates selective pressure on bacteria to develop resistance. Thus, their widespread use has resulted in the rise of resistant bacteria throughout the world. As the pharmaceutical companies have been occupied with developing antibiotics, bacteria have continued to evolve rapidly. According to the Centers for Disease Control, in hospitals in the United States, over 30% of antibiotics have been inappropriately and unnecessarily prescribed(12). In most of the developing world, antibiotics are sold over the counter. Additionally, 80% of the antibiotics sold in the US goes to animals, which inevitably leads back to us through water, air, dust and the meat they become(12). Antibiotic resistance is now one of the World Health Organization’s most pressing public health concerns; they estimate that by 2050, over 10 million people will have died from a resistant bacterial infection(1). In the United States alone, currently 2.8 million people acquire antibiotic resistant infections each year, and approximately 40,000 people die from them(1). As of now, there are no approved therapies to combat these deadly bacteria. The use of bacteriophages is emerging as a promising method, however.

There are more bacteriophages on the earth than every living organism combined(14).

These abundant entities exist in the form of DNA or RNA held in a protein capsid.

Attached to the capsid are tail fibers, which are used to bind to receptors on the surface of specific bacteria that they infect. Phages reproduce through two possible life cycles: lysogenic or lytic. Lytic phages bind to the outside of bacteria, then inject their genetic material. It is transcribed and translated, producing proteins and viral DNA to build new

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viruses. Phage production stops when the bacterium is filled up; at this point endolysin, an enzyme that punctures a hole in the cell wall, is produced and the phages escape, effectively killing the host cell and creating more phages(14). Lysogenic phages are not used therapeutically, because instead of killing the host cell they remain dormant, using the host cell as a refuge to reproduce.

Bacteriophages offer many advantages over antibiotics as antibacterial agents.

Compared to most broad-spectrum antibiotics, their specificity causes less disruption to the host’s bacterial flora--many of which are vital to the organism’s ecological balance.

Few side effects, such as allergic reactions that can result from antibiotics, have been observed with phage therapy(13). When using phages to combat localized infections, phages have the special advantage that they can continue to multiply and penetrate deeper for as long as the infecting bacteria are present, rather than having concentration-dependent killing like antibiotics(13). Another advantage to phage therapy is that unlike antibiotics, phages can evolve, so any resistance mechanism the bacteria evolve, phages may change to counter it. Finally, large amounts of phages can be prepared relatively easily and cost efficiently. The process of isolating and selecting new phages is less expensive, in terms of both time and money, than the development of new antibiotics--it can take numerous years and millions of dollars to develop a new antibiotic drug(17). The growing library of phages at institutions in the United States and throughout the world(13) will continue to make available phages that can target more and more bacterial infections.

Phage therapy was actually used to treat bacterial infections before the appearance of antibiotics. In 1919, Félix d’Herelle discovered bacteriophages in association with diarrheal illnesses(17). He introduced the idea of laboratory-produced phages as both prophylactic and therapeutic agents against bacterial infections. In 1934, d'Herelle established an institute to study phages in the Soviet Republic of Georgia. Phage therapy was developed and widely used in the Soviet Union. It was even administered to the German army during World War II, as the first antibiotics were only available to the Allies(17). Upon the advent of antibiotics, the use of phage therapy diminished in the western world. Combined with the fact that at the time, antibiotics were cheaper and more efficient than phages(17), after World War II all things “communist” weren't to be trusted in the West, including scientific knowledge. Therefore, because phage therapy was popular in the Soviet Union, it got caught up in international politics and eventually faded out of western medicine.

Phage therapy is now making a comeback, however. Fifteen-year-old cystic fibrosis patient Isabelle Carnell had a resistant Mycobacterium abscessus infection, against which all treatments failed. After just six weeks of phage therapy, her infection was completely under control. She was also the first person to be treated with genetically engineered phages--two of the three phages in her cocktail were lysogenic phages and thus had to be converted to lytic phages so they killed their bacterial hosts (4). A 41year-old male developed an infection after a knee surgery, including multi-drug resistant

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Klebsiella pneumoniae and Acinetobacter baumannii. He commenced phage therapy which eradicated the infection in under two weeks. This man’s wound healed completely, so he was able to avoid above knee amputation(4).

Thomas Patterson is another example of a successful case, and his treatment depended on bacteriophages in combination with antibiotics. He developed a resistant Acinetobacter baumannii infection while vacationing in Egypt. A Perfect Predator, a memoir co-written by him and his wife Steffanie Strathdee, chronicles his battle with this infection and how he eventually survives through the use of bacteriophages. It was while reading this book that I came across the idea of Phage-Antibiotic Synergy (PAS), which is when antibiotics and phages are coadministered and a stronger bacterial suppression is observed. In Patterson’s case, his phages were synergistic with the antibiotic minocycline. The antibiotics alone had little to no antibacterial effect, but when combined with phages, the bacteria became more susceptible to minocycline and Patterson fully recovered(16).

While the exact mechanism of PAS is not yet completely understood, Comeau, et al. suggest that the success of PAS may be related to the activation of bacterial filamentation and/or the SOS response in E. coli(3). The presence of antibiotics and phage drastically increase cellular stress responses in bacteria. When E. coli grows in the presence of sub-lethal concentrations of antibiotics, there is an effect on cell morphology--they divide poorly and form long, multinucleated filaments, which phages can take advantage of(3). The SOS response is one mechanism that has been linked to the process of filamentation. The SOS response is controlled by the LexA and RecA proteins, which are activated in the presence of DNA lesions(11). Upon activation, SOS genes are derepressed, among which is the sulA gene, which stops cell division and activates filamentation. Beta-lactam antibiotics, which inhibit cell wall synthesis, can induce the SOS response in E. coli through a two-component signal transduction system(11). However, in a study done by Ryan et al., filamentation was observed owing to an unknown mechanism independent of the SOS pathway--PAS was apparent in mutant E. coli with a RecA deletion(11). They did indeed find that the PAS effect was almost always accompanied by filamentation or swelling of the cell.

Another possible mechanism behind PAS is that antibiotics may delay lysis of the host cell, allowing for more phage replication(9). Generally, phage holins, small proteins that control the degradation of the cell wall, accumulate in the bacterial membrane until a signal triggers the transport of endolysins. More phage holins than usual will continue to accumulate in the presence of antibiotics, because due to filamentation, the surface area of the membrane is increased(11). Consequently, the cycle is prolonged, and lysis is delayed, leading to a lengthened assembly of phage precursors. This means that upon lysis, there exists a greater concentration of phages. It is also suggested that the filamentous state induces perturbations in the peptidoglycan layer, leading to an increased sensitivity to these phage lysis genes(3).

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Another aspect to PAS is the eradication of biofilms. Biofilms are densely packed communities of microbial cells that adhere to living or non-living surfaces. The cells within biofilms are encased in a protective matrix. Medically, biofilms are extremely important as they have been involved in many deadly antibiotic resistant infections, such as the Pseudomonas aeruginosa biofilms, which cause chronic lung infections in cystic fibrosis patients. Biofilms have been identified as a leading cause of antibiotic resistance. Phage alone are not effective against the matrix, either. Extracellular polysaccharides prevent the virus from penetrating the biofilm by shielding the phage receptors on the cell(6). In a study done by Ryan et al., however, it was shown that the use of phage and antibiotics in synergy significantly enhanced biofilm eradication, although little further research has been done on its mechanism(6).

One obvious limitation to phage therapy is the probability that bacteria would readily develop resistance to phages. One possible phage resistance mechanism is the alteration of the expression of phage receptors on the bacteria, allowing them to escape phage infection. However, these phage resistance mechanisms often come with a cost to the bacteria. Using phage and antibiotics together could be a way to exploit the genetic trade-off phenomenon--in which an organism evolves one trait that improves fitness while compromising performance in another trait(2). For instance, phages have been shown to interfere with bacterial conjugation, thus preventing the spread of plasmid-mediated antibiotic resistance(2). Basically, phage therapy exerts a selective pressure on bacteria that compromises their antibiotic resistance. This, along with biofilm eradication, has exciting clinical implications--through PAS we can essentially “re-discover�(2) new classes of antibiotics that have already been clinically approved, but are out of use due to resistance.

For experimentation, I decided to see if the infection rate of a standard bacteriophage could be affected by the simultaneous presence of an antibiotic. We first needed to generate bacteria that were known to be susceptible to a bacteriophage but were also resistant to an antibiotic. In order to assess bacteriophage infection rates, we did a plaque assay, using ampicillin-resistant and non-resistant E. coli. A viral plaque is formed when a virus infects a cell which lyses and spreads the infection to adjacent cells. There, the cycle is repeated. The infected cell area will create a plaque (an area of infection surrounded by uninfected cells) which can be seen visually, thus can be counted manually on each plate. The more plaques on a plate, the more effective the phage is in eradicating the bacteria. Varying the phage titer in plaque assays can show whether there is a different effect based on the amount of viral particles present. We tested four different combinations of antibiotics and bacteria with the phage: resistant E. coli with ampicillin in the soft agar and base layer agar, resistant E. coli without ampicillin, and ampicillin sensitive E. coli. We also tested resistant E. coli with ampicillin on just the base layer mistakenly, but it was inhibited the same as with the ampicillin in the soft agar as well. With these combinations, we could test for PAS between ampicillin and T4 phage, and also whether phages infect resistant and sensitive bacteria equally. We hypothesized that using a combination of phages and antibiotics against resistant

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bacteria would be more successful in clearing the bacterial lawn than phage or antibiotics alone. While results were not truly conclusive due to inconsistencies in sample growth and contaminants in our ampicillin resistant samples, key methods were developed for future research.

Materials and Methods 1. Generation of ampicillin resistant E. coli: We began experimentation with the development of ampicillin resistant bacteria using a disc diffusion method. We ordered E. coli strain B from Carolina Biological, and made our own tryptone slant agar plates, both with and without ampicillin (50μg/mL), following a recipe also from Carolina(19).

Figure 2 First, we spread 100μL of resuspended strain B cells onto a tryptone plate, then placed discs containing 10 μg of ampicillin on top, letting them grow in an incubator overnight.

We selected colonies nearest to the zone of inhibition (ZOI)--figuring they were partially resistant--to grow overnight and re-plate using the same methods. We wanted a singular colony because it means they should all come from one cell, and thus all be genetically identical.

After 4 trials, the bacteria appeared to have become resistant, because they were able to grow in the ZOI. We took several samples and grew them in a broth containing 50 μg/ml ampicillin, then spread them on plates containing ampicillin to verify resistance.

2. Growth rate comparison: To determine the growth rate of our newly created amp resistant strain and verify that it could be compared to strain B for the growth-based plaque assay procedure, we measured the growth rates of liquid cultures of ampicillin resistant strain B (“E2C”) and strain B using a spectrophotometer at 600nm. Overnight cultures were normalized to a

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starting OD600 of 0.1, and we took readings every 45 minutes for 3 hours. We had four different samples of bacteria. Three of these were from different colonies or areas of the ampicillin resistant plates and grown in broth containing ampicillin, and one sample was sensitive strain B, grown in nutrient broth without any ampicillin.

3. Plaque assay: Different dilutions of phage suspension were mixed with host bacteria in a soft agar solution and then distributed to solidify on a standard agar plate (or “base layer�). We ordered coliphage T4r from Carolina and followed Carolina’s plaque assay protocol (B).

The T4r culture had a titer of 1.5x1010 virions per milliliter, and 10-2 through 10-9 serial dilutions were set up in nutrient broth. This demonstrates what we added to the soft agar and base layer agar for each combination of phage/antibiotics/bacteria:

E2C with antibiotics

Base layer agar

Soft agar

ampicillin

Ampicillin, phage and E2C

E2C E2C with base-layer antibiotics Sensitive strain B

Phage and E2C ampicillin

Phage and E2C Phage and sensitive strain B

We heated up two 1 mL tubes of soft agar in a water bath set at 48 degrees Celsius until molten. Then, 0.1 mL of the 0.1 OD600 normalized bacteria was mixed into each tube, along with 1 mL of the phage solution. The molten agar was quickly poured onto the base layer and was left at room temperature for two or three hours to solidify. After solidifying, they were transferred to an incubator where they grew overnight. For our second round of experimentation, we repeated the procedure, but also plated phage titers of 10-4, 10-6 and 10-10.

4. Testing for contaminants: After round two, we tested our E2C resistant bacteria plate to see if it was contaminated. Taking a sterilized toothpick, we streaked one colony from the plate we used for the plaque assay onto a trp amp plate in an attempt to get a singular colony that we could look at under the microscope. To visualize the cells we added crystal violet, which stains the cell wall.

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Results In the end, we successfully induced antibiotic resistance, and ended up with several different samples to use for the phage experimentation. In Figure 3, colonies are observed growing in the ZOI. In Figure 4, resistant bacteria are able to grow on an amp plate after being streaked with a toothpick the day before.

Figure 3

Figure 4

For the growth curve, we compared the growth of several samples of resistant bacteria (grown in amp broth) and sensitive bacteria. Similar growth rates were seen between the amp-resistant strains and the amp-sensitive strain B (figure 5).

Figure 5 Growth rate as measured by spectrophotometry (B denotes sensitive strain B, the rest are from different resistant samples)

We had several different samples of resistant bacteria, so we had to choose one to use for the plaque assays. Our choice was somewhat arbitrarily based on the fact that we thought we could select just one colony from the plate E2. This is advantageous because singular bacterial colonies should have homogenous genetic information. However, the

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complications that later arose due to contamination may have been because the E2C plate had heterogenous growth to begin with--it had a lawn of bacteria with colonies growing on top.

Phage assay: No phage

10-4 virions/mL

10-7 virions/mL

10-8 virions/mL

Row 1: Strain B + T4 phage

Row 2: E2C + T4 phage:

Row 3: Ampicillin + E2C + T4 phage:

Inconclusive

Figure 6: Plaque assays

Row 1 of Figure 6 shows that the T4 bacteriophages were infecting the bacteria properly, and that with decreasing concentrations of phage, the amount of phage infection (or presence of plaques) decreases as well. The bacteria grew well, as shown by lawn on the plate with no phage, but at 10-4 virions/mL the phage suppressed all bacterial growth. At 10-7 and 10-8 countable plaques appeared, with fewer on the 10-8 plates due to a lower concentration of phage.

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Row 2 shows that T4 phage will infect amp-resistant E2C as well. The only striking difference between row 1 and row 2 is that at the 10-4 concentration, there were opaque dots and a cloudy film over the soft agar indicating more growth of E2C than strain B even in the presence of high concentration of T4. Additionally, while the amount of plaques was roughly the same in the 10-8 concentrations, at 10-7 the E2C resistant bacteria had fewer plaques.

Row 3 shows T4 infection of resistant E2C in the presence of ampicillin. The amount of plaques followed the same trends as other combinations, but each plate seemed to have a consistently higher amount of bacterial suppression. At 10-4 there was no growth on the plate, as expected at such a high concentration of phage. The 10-7 and 10-8 plates seemed to have less growth than the other combinations, (more individual colonies of bacteria were visible). However, the plates that didn’t contain phage were inconclusive due to problems with pouring the molten top agar. This means that we were unable to verify that this sample was growing at a similar rate to the other samples.

Plaque assays round 2: The second round of plaque assays did not yield conclusive results. There were issues with pouring the molten agar, so that on many plates there was lumpy top agar that made it hard to quantify any plaques. In addition, the resistant strain E2C with amp and without amp seemed to have very different growth rates, which also may have been the case with round 1. This big difference made us wonder about the heterogeneity of our sample, and whether there was a contaminant in the bacterial culture we were using. To investigate this, we streaked samples from the plate of resistant bacteria and looked at a colony under a microscope. We found that there was contamination on our plates, as evidenced by the different organisms we observed. This prompted us to look at the sensitive strain B, which was also contaminated. We were unsure at what point in the experimentation the E2C and strain B cultures had become contaminated, meaning that it also could have affected the results of round 1.

So, we ordered more strain B and repeated the ampicillin resistance-induction procedure to generate new resistant samples (see figure 7). We looked at these resistant samples along with the newly purchased strain B under a microscope and were able to determine they were homogenous.

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Figure 7

Discussion The similar patterns and amount of plaques seen in E2C and strain B demonstrate that the ampicillin resistance mechanism of E2C does not significantly affect how T4 infects resistant bacteria. E2C actually was able to be infected by T4, regardless of the presence of the ampicillin antibiotic. This is desirable because it implies that the resistance mechanisms of E2C may not prevent virus entry/replication. We had hypothesized that through the phage-antibiotic synergy phenomenon, the antibiotic ampicillin would increase the effect of T4 infection, resulting in more plaques. In round 1 the plates with E2C and antibiotics had a bit less growth than E2C and phage alone. The small effect was perhaps not surprising because in other studies done (2) (3), phages were most productive at lower concentrations of antibiotics. In our experimentation, we didn’t vary the antibiotic concentrations for the plaque assays, so there conceivably could have been a higher combinatorial effect at lower concentrations of ampicillin.

On the other hand, the results of the two rounds also raised questions about the relative growth rates of E2C with and without ampicillin, regardless of the presence of T4. Since our cultures of E2C and strain B had become contaminated over the ten weeks we had been using them, our next step was to test the growth rates of the new resistant strain B with and without ampicillin and compare them to strain B as well. Additionally, we also learned of a different method for testing phage/PAS productivity through the use of liquid cultures, by loosely following a procedure developed by Chan et. al (2).

Along with heightened sterile procedures, we planned on using the same three combinations of phage, bacteria and antibiotics in the form of liquid cultures. We would use a spectrophotometer to measure the amount of bacterial suppression (“clearance” of the cultures) of each combination. This seems a preferable method because it is much easier to quantify any growth and would mean that we wouldn’t have to use the soft agar, which we consistently had difficulty pouring to the point where it inhibited plaque quantification. However, since school closed, we were unable to test this new method. Instead, we can turn to all of the promising research that is gaining traction and the new phage institutes that are beginning to open across the United States, such as

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Adaptive Phage Therapeutics. Once more research and clinical trials on phage therapy have been completed, antibiotic resistant infections may just become less of a global threat.

References 1 "Antibiotic Resistance." World Health Organization, 5 Feb. 2018, www.who.int/news-room/factsheets/detail/antibiotic-resistance. Accessed 23 Mar. 2020.

2 Chan, B., Sistrom, M., Wertz, J. et al. Phage selection restores antibiotic sensitivity in MDR Pseudomonas aeruginosa. Sci Rep 6, 26717 (2016). https://doi.org/10.1038/srep26717 3 Comeau, André M et al. "Phage-Antibiotic Synergy (PAS): beta-lactam and quinolone antibiotics stimulate virulent phage growth." PloS one vol. 2,8 e799. 29 Aug. 2007, doi:10.1371/journal.pone.0000799 4 “Compassionate Use Case Studies” Adaptive Phage Therapeutics, http://www.aphage.com 5 Dever LA, Dermody TS. Mechanisms of Bacterial Resistance to Antibiotics. Arch Intern Med. 1991;151(5):886–895. doi:10.1001/archinte.1991.00400050040010 6 Elizabeth M. Ryan, Mahmoud Y. Al Kawareek, Ryan F. Donnelly, Brendan F. Gilmore, Synergistic phageantibiotic combinations for the control of Escherichia coli biofilms in vitro, FEMS Immunology & Medical Microbiology, Volume 65, Issue 2, July 2012, Pages 395–398, https://doi.org/10.1111/j.1574-695X.2012.00977.x 7 Haq, I.U., Chaudhry, W.N., Akhtar, M.N. et al. Bacteriophages and their implications on future biotechnology: a review. Virol J 9, 9 (2012). https://doi.org/10.1186/1743-422X-9-9 8 Jansen, M., Wahida, A., Latz, S. et al. Enhanced antibacterial effect of the novel T4-like bacteriophage KARL-1 in combination with antibiotics against multi-drug resistant Acinetobacter baumannii. Sci Rep 8, 14140 (2018). https://doi.org/10.1038/s41598-018-32344-y 9 Kim, Minjin, et al. "Phage-Antibiotic Synergy via Delayed Lysis." Applied and Environmental Microbiology, 22nd ser., vol. 84, nos. 02085-18, 30 Oct. 2018. American Society for Microbiology, doi:10.1128/AEM.02085-18. Accessed 11 Apr. 2020.

10 Krut, Oleg, and Isabelle Bekeredijian-Ding. "Contribution of the Immune Response to Phage Therapy."

The American Association of Immunologists, 9th ser., vol. 200, nos. 3037-3044, 23 Apr. 2018. The Journal of Immunology, doi:https://doi.org/10.4049/jimmunol.1701745. Accessed 11 Apr. 2020.

11 Maiques, Elisa, et al. "β-Lactam Antibiotics Induce the SOS Response and Horizontal Transfer of Virulence Factors in Staphylococcus Aureus." Journal of Bacteriology, Mar. 2006, doi:10.1128/JB.188.7.2726-2729.2006. Accessed 14 Apr. 2020.

12 McKenna, Maryn. Superbug: The Fatal Menace of MRSA. New York, Free Press, 2011.

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13 "Phage therapy." World of Microbiology and Immunology, edited by Brenda Wilmoth Lerner and K. Lee Lerner, Gale, 2007. Gale In Context: Science, https://link.gale.com/apps/doc/CV2644650333/SCIC?u=broo17331&sid=SCIC&xid=0abc1649.

Accessed 12 Apr. 2020.

14 Schmidt, Charles. "Phage Therapy Could Beat Drug-Resistant Illnesses." Scientific American Archive Online, Springer Nature America, Nov. 2019, www.scientificamerican.com/article/phage-therapycould-beat-drug-resistant-illnesses/. Accessed 7 Apr. 2020.

15 Spratt, B G. "Distinct Penicillin Binding Proteins Involved in the Division, Elongation, and Shape of Escherichia coli K12." Proceedings of the National Academy of Sciences of the United States of America, vol. 72, no. 8, Aug. 1975, doi:10.1073/pnas.72.8.2999. Accessed 15 Apr. 2020.

16 Strathdee, Steffanie A., et al. The Perfect Predator: A Scientist's Race to save Her Husband from a Deadly Superbug. New York, Hachette Books, 2019.

17 Summers, William C. "The strange history of phage therapy." Bacteriophage vol. 2,2 (2012): 130-133. doi:10.4161/bact.20757 18 “The Diminishing Effectiveness of Antibiotics” Adaptive Phage Therapeutics, http://www.aphage.com 19 “Techniques for Studying Bacteriophages of Escherichia Coli” Carolina Natural Resources, https://www.carolina.com/teacher-resources/Document/techniques-for-bacteriophagecultures/tr30206.tr

30 Bomb Calorimetry 101 đ&#x;’Ľ Eliza B. & Sam S.-M. Mentor: Jared Cross

Abstract We started the year with the intention of constructing a bomb calorimeter, a type of calorimeter which uses water and a constant-volume chamber to measure the heat of combustion of reactions. We decided to first try to repurpose a can and a bike pump, but experimentation quickly proved that due to the can’s limited ability to contain any pressure from the inside, it would not be particularly suitable for our purposes. After several aborted trials, we settled on purchasing a keg to hold our bomb calorimeter, hoping it would be better able to handle the pressure, and were making headway on our planned experiments when, unfortunately, everything ground to a halt due to coronavirus. Since all of our materials are currently imprisoned at school, we began focusing on research instead. In the weeks following our move to online school, we have begun watching a series of lectures on thermodynamics from a professor at MIT and will probably continue to do so until the end of the year.

Introduction

fig. 1

A calorimeter is an instrument used to measure the heat produced by chemical reactions or physical changes and to measure heat capacity. In order to calculate the enthalpy change of a particular reaction performed in an ideal calorimeter, we can use the following equation, where Cv is the heat capacity of the calorimeter: q = Cv (Tf – Ti)

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Of course, no calorimeter is truly ideal, but some approach adiabaticity. A bomb calorimeter is a constant-volume calorimeter used to measure the heat of combustion of a reaction with as little heat exchange with its surroundings as possible. The sample is placed in the chamber (fig. 1) and is combusted via the ignition unit. The temperature change of the reaction is measured by the heat increase of the water around it, and the dewar is double walled in order to prevent heat loss so that the result is as accurate as possible. Since the reaction will generate gas, the chamber must be built to withstand large pressures. The heat capacity of the instrument is found using the following equation, where substance A is of a known heat of combustion (Hc): Cv = ΔHc (substance A) × ma + ΔHc (fuse wire) × mfuse wire This allows us to use equation 1 to calculate the enthalpy change of a reaction.

Procedures and Results We began by buying a regular calorimeter from Amazon. Unfortunately, it didn’t last long: the first reaction we tried with the calorimeter involved hydrochloric acid, at which point we discovered that the vessel was made of aluminum.

Our next idea was to test whether a normal can could hold enough pressure to serve as the chamber for our bomb calorimeter. It could not. We attempted to give our can as strong of a seal as possible with wax and hot glue and then pumped air into it with a bike pump to see the maximum pressure it could contain before the seal (or the can) broke, but it couldn’t hold much more than 1 atm.

We needed a container able to withstand pressure from the inside -- thus, the keg. For our first experiment we performed a simple exothermic, non-gas-producing reaction: CaCl2 (s) + H2O(l) → Ca2+(aq) + Cl-(aq) + H2O(l) Since a large amount of water would be needed to immerse the keg, the heat of any reaction the keg would be able to contain would only increase the water temperature imperceptibly and thus we decided that instead of measuring water temp we would measure the increase in temperature on the outside wall of the keg. Although a noticeable heat increase was measured on the inside of the keg -- and even on the interior wall of the keg itself -- we were unable to detect an increase in temperature on the exterior. We concluded that the keg walls were far thicker than the Amazon product description stated, so we would need to try something else to measure the heat change.

One of the ideas we had was to try to increase the conductivity of the actual reaction vessel. Instead of glass beakers, we opted for copper shot glasses given copper’s high

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conductivity in comparison to glass. Ideally, this would have allowed a more even heat distribution inside of the keg, resulting in a noticeable outer wall temperature increase.

Unfortunately, we had no such luck. Although the copper reaction vessel increased in temperature significantly, the walls of the keg were still too thick for any noticeable temperature change on the exterior.

Given the infeasibility of creating a reaction that would generate enough heat to transfer to the outer wall of the keg, we had to switch to measuring the temperature increase of the air on the inside of the keg instead. That meant that we now had to find a way to get a thermometer inside of the keg without compromising its seal. The best option would have been to use a Bluetooth thermometer, since it would not need a physical connection to the outside of the keg, but due to restraints of budget and time we decided to use a school thermometer instead. We modified it, removing much of the plastic casing so that it would fit comfortably inside of the keg without touching the bottom, and threaded it through one of the keg’s pre-existing valves. However, just as we were ready to test our new calorimeter, Saint Ann’s made the move to online school.

Discussion Before the end of the year, we had planned to continue testing our keg calorimeter, and eventually move on to constructing our own bomb calorimeter from scratch (using a youtube video of a similar independent science project as our guide). Since our project was entirely experimental in nature it was impossible to continue in an online setting, so we decided to move towards studying the theory behind our project instead. We began to work our way through MIT OpenCourseware’s Thermodynamics & Kinetics, meeting in our usual period to discuss the problems.

If you enjoyed this lab report, please like, comment, and subscribe! See you next time, science fans.

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Hydrophobic Coagulation in Pressed Tofu: An At-home Study Una R. & Ayla S. Mentor: Liz Velikonja

Abstract

Tofu has been a staple of many Asian countries' cuisines for centuries. Its existence was first recorded 2000 years ago in China, and it is still eaten all over the world today. The soybean curd is most often bought in pre-packaged blocks because of the inconvenience of isolating the necessary soy proteins. Commercial tofu is made with a mixture of coagulants including glucono-delta-lactone (GDL) and various salts. We set out to make tofu in a home kitchen, focusing on the various coagulants used in the process. We used nigari (MgCl2) as our control, and also tested epsom salt (MgSO4), gypsum (CaSO4), CaCl2, and KCl. We mixed some of the salts together in different proportions and found that it was possible to get a block of well-coagulated tofu using nigari and calcium chloride in a 5:1 ratio. Other areas of exploration were making silken tofu using GDL, and attempting to coagulate soy milk using citric acid as suggested in several online recipes. While there were subtle variations between the textures and densities, there was not a significant difference in the taste of tofu made from most of the coagulants we tested. Gypsum and citric acid were the only ones that coagulated notably differently. Potassium chloride did not work, which led us to believe that to coagulate the milk the metal in the salt has to be an alkali earth metal. Overall, making tofu by hand is labor intensive but a fun and rewarding chemistry project to undertake at home.

Introduction Tofu originated around 2000 years ago in China. Legend has it that it was discovered when a Chinese cook accidently put seaweed in a pot of hot soy milk and it subsequently curdled. It was first mentioned in writing in a Chinese document, the Qing Yilu, in 965 CE. It was introduced into Japan around the eight century A.D. by the name “okabe,” and was first mentioned in Japanese writings in 1183. In 1457, the word tofu as it is in modern Japanese was first written. In 1665 tofu and its cooking process was mentioned by Domingo Fernández de Navarrete in his book recounting his travels—the first time tofu was mentioned specifically by a Westerner. It is marked in his book as an exclusively Chinese food, and he says it is “one of the most remarkable things in China.”

Benjamin Franklin made reference to tofu in a letter written to John Bartram on January 11th, 1770. He was the first American to mention tofu, and also made note of “runnings of salt” that is used to coagulate the milk. Tofu was first made on a commercial scale by Wo Sing ＆ Co., a San Francisco based business, in 1879. In 1911 Ota Tofu shop, America's oldest tofu shop, was founded—it is still open today in Portland, Oregon.

Throughout the early to mid 1900’s, many more tofu shops and manufacturers began to

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open around the world. In 1958, the world's first packaged tofu was sold in Los Angeles

by Matsuda Hinode Tofu Co. The blocks of tofu were placed in plastic bags filled with water, heat sealed, and placed in cartons with wire handles — previously, all tofu was sold in vats of water, and not individually packaged. In 1965, the name of “tofu” was officially established by the Library of Congress for the pressed soybean curd. Tofu continued to gain popularity as the vegetarian movement grew throughout the 70’s. By April of 1982, there were 173 tofu manufacturers in the United States. In October of 1999, the U.S. FDA officially recommended that soy protein as a substitute for meat can help reduce the risk of heart disease. This generated a surge in public interest in tofu products. As of 2017, annual U.S. tofu sales reached $91 million, and are expected to reach $24 billion worldwide by 2022. Tofu continues to be a popular vegetarian, cost effective source of protein worldwide.

What comes to mind when one thinks of tofu is most likely tofu of the firm type, sold in a rigid plastic container in the supermarket. Such tofu is marketed as “soft,” “medium firm,” “ extra firm,” and everything between. However, the processes behind these seemingly varied products are essentially the exact same. Once coagulant is added to fresh soy milk, the product is poured into a mold and pressed. The only variation is the pressure of the weight and the time spent pressing. The only tofu that truly differs is “silken” tofu, which is not pressed at all. Instead, coagulant is added to soy milk in the same container that will be used for eating.

Coagulants vary by region: in Japan, the most widely used one is nigari, or magnesium chloride, an extract from brine or seaweed. In China, the most common coagulants are gypsum and calcium sulfate, the latter of which is used in Korean tofu as well. We also experimented with calcium chloride, another coagulant sometimes used in China, and epsom salts. Tofu is eaten in many other countries in Asia, with the above coagulants being the most common ones used.

Materials and Methods Coagulants Nigari (MgCl2) - SoyaJoy® Epsom Salt (MgSO4), unscented - Rite Aid Gypsum (CaSO₄·2H₂O) - LD Carson Potassium chloride (KCl) - Micro ingredients Citric acid (C₆H₈O₇) - Milliard™ Glucono delta-lactone - Modernist Pantry Soy milk Soy milk was made based on Andrea Nguyen’s recipe from Chefsteps. Each batch called for the submerging of 170g dry soybeans (using either Laura’s Soybeans or Soymerica Non-GMO soybeans) in water and soaking until the beans expanded and were able to

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split easily, approximately overnight. The beans were strained and ground with 2 cups (473mL) of the reserved soaking water in a blender until reaching a “milkshake” consistency. The blended mixture was added to 5 cups (1.18L) of reserved soaking water, with an additional ½ cup (118mL) of water to help rinse the blender, and heated for up to 10 minutes, until it frothed. The hot mixture was poured into a nut milk bag and the soy milk was strained out by squeezing the cloth, with an additional ½ cup of water to rinse the solids. The leftover solids were baked into banana bread and fed to chickens.

Pressed tofu 8 cups (1.89L or ½ gallon) of soy milk was heated to a gentle simmer and cooled for about 3 minutes. 1.5 teaspoons (7.39mL) of coagulant was dissolved in ½ cup of water and added, ⅓ at a time, to the hot soy milk. The curds were transferred to a mold lined with a fine-weave cloth and weighted with 867.4g for fifteen minutes, and then removed from the cloth and fully cooled in ice water.

Silken tofu Silken tofu was made according to MyKitchen101en. 1.5L of soy milk made using the above directions was heated until steaming, then divided into 5 containers, each already containing .5g GDL dissolved in 5g tap water. Soy milk was mixed well and left to coagulate untouched, for 10-40 minutes.

Results Salts We tried five salts in total, starting with Nigari (MgCl2 ). It is the traditional coagulant used in Japan, and is extracted from seawater or seaweed after the table salt has been dried out. It is sold in both salt and liquid form, though the liquid is a less powerful coagulant than the salt. It is a highly soluble salt that coagulates very quickly. It produces a slightly sweet, not very beany, tofu that has a tight, small, curd structure.

Epsom salt (MgSO4), a commonly used household product and marketed as a muscle soother in the US, was the next coagulant we tested. It coagulated quickly, although the base recipe we used instructed us to let the coagulated soy milk stand for three minutes longer then the nigari before pressing. It produces a small curd structure and a relatively beany tofu.

Gypsum (CaSO4), or drywall, was the most unique coagulant we tested. It produced a cloud-like large curd and the heaviest block of tofu out of the four. It coagulated rapidly, although the gypsum itself did not dissolve as readily in water. The tofu tasted very similar to the epsom salt block, it had the same beany flavor.

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Calcium chloride (CaCl2) was the last coagulant we tried. It is sold in little pellets that dissolve quickly in water, and produces very similar results to nigari. The curd size is slightly bigger than nigari’s and the tofu itself tasted a tiny bit beanier, but other than that the outcome was the same as nigari.

Potassium chloride was completely unsuccessful. After following normal procedure and even after allowing extra time for the milk to show curds, there was no significant solidification in the soy milk.

We also tried mixing some of the salts together. We attempted to coagulate tofu with equal portions of the gypsum, epsom, and nigari to meet the 1 ½ tsp. our recipe called for. The soy milk barely coagulated which may be due to the salts contracting each other in some way, although we are not really sure.

We next mixed 1tsp. of nigari and ½ tsp. of calcium chloride, which did coagulate the milk although the block itself did not hold together when turned out of the cloth. When adjusted to the concentrations of 1 ¼ tsp. nigari to ¼ tsp. calcium chloride the block did hold together and was able to cook up like a regular block of tofu would. We concluded that the perfect concentration for nigari-calcium chloride tofu would be somewhere between the two that we tried.

Acids Many recipes suggest using either citric acid or lemon juice as a coagulant. We attempted this, using the same 1 ½ tsp. coagulant to 8 cups water ratio. The tofu did coagulate, but with an extremely unpleasant sour taste and a crumbly texture.

Silken Tofu GDL, which on addition to water converts into gluconic acid, performed extremely well as a coagulant. It was notable that after heating the full 1.5 L of soy milk at the same time and stirring the 5 portions for approximately 30 seconds each after adding the milk to the coagulant, the cooling that took place over that time caused the last portion to take several hours to coagulate, where the portion made with the hottest soy milk coagulated much faster, in around ten minutes.

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Ionic coagulants are summarized in the table below: Coagulant

Cation

Anion

Effect

Nigari

Mg2+

Cl-

control

Epsom salt

Mg2+

SO42-

smoother texture, beanier taste

Gypsum

Ca2+

SO42-

tighter curd

Calcium chloride

Ca2+

Cl-

looser curd

Potassium chloride

K+

Cl-

no coagulation

Discussion Based on the failure of KCl and success of all other ionic coagulants, it seems that the cation must be an alkali earth metal to coagulate tofu, while a different anion charge works either way. The difference between Mg2+ and Ca2+ was difficult to distinguish, but the tofu made from a coagulant with SO42- was softer, with a smaller curd structure overall.

As for the failure of citric acid and the success of GDL, it may be attributed in part to the difference in acidity of the compounds. Perhaps due to the acidity of citric acid (pKa1 = 3.13 pKa2 = 4.76 pKa3 = 6.39, 6.40), it released “too many protons” and would have worked better at a lower concentration or temperature. GDL, in contrast, has a singular pKa of 3.7. (pKa is a measure of the extent to which an acid ionizes/releases protons, with stronger acids having smaller pKas).

Further directions for these experiments include adding oils as well as coagulants and observing the change in texture, coagulating tofu with enzymes such as papain or bromelain, mixing acids with salts, and experimenting with nontraditional salts such as aluminum chloride (although not eating it!).

Figures: (A) Nigari block soaking in water after being unmolded; (B) epsom salt block; (C) calcium chloride curds before pressing; (D) gypsum block soaking in water after being unmolded; (E) citric acid “tofu” unable to form a block; (F) GDL silken tofu with part removed to demonstrate texture.

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A.

B.

C.

D.

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E.

F.

References Kang, Chang Soo, Guan Ho Byun, and Ik Hyun Yeo. Tofu Manufacturing Process. US Patent US20140302199A1, filed Apr. 7, 2014, and issued Oct. 9, 2014.

Kohyama, Kaoru & Sano, Yoh & Doi, Etsushiro. (1995). Rheological Characteristics and Gelation Mechanism of Tofu (Soybean Curd). Journal of Agricultural and Food Chemistry - J AGR FOOD CHEM. 43.

10.1021/jf00055a011.

Lewin, Jo. "The Health Benefits of Tofu." BBC Goodfood. Accessed May 20, 2020. https://www.bbcgoodfood.com/howto/guide/ingredient-focus-tofu.

Liu, Keshun. "Food Use of Whole Soybeans." In Soybeans: Chemistry, Production, Processing, and Utilization, by Richard Galloway, Lawrence Alan Johnson, and Pamela J. White. 2nd ed. Urbana, Ill.: AOCS Press, 2010. https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/glucono-deltalactone.

McHugh, Tara. "How Tofu Is Processed." Institute of Food Technologists. Last modified February 1, 2016.

Accessed May 20, 2020. https://www.ift.org/news-and-publications/food-technologymagazine/issues/2016/february/columns/processing-how-tofu-is-processed?page=viewall.

Mujoo, Rajani, Dianne T. Trinh, and Perry K.W. Ng. "Characterization of Storage Proteins in Different Soybean Varieties and Their Relationship to Tofu Yield and Texture." Food Chemistry 82, no. 2 (August 2003): 265-73. https://www.sciencedirect.com/science/article/abs/pii/S0308814602005472.

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Nguyen, Andrea. "How to Make Homemade Tofu." The Splendid Table. Accessed May 20, 2020. https://www.splendidtable.org/story/how-make-homemade-tofu.

Ono, T. "Soy (Soya) Cheeses." In Encyclopedia of Food Sciences and Nutrition, by Benjamin Caballero, Luiz C. Trugo, and Paul M. Finglas, 5398-402. 2nd ed. Amsterdam: Elsevier, 2003. https://www.sciencedirect.com/science/article/pii/B012227055X011135.

Pevreall, Katie. "Annual US Tofu Sales Reach a Staggering $91 Million." Live Kindly. Last modified September 27, 2017. Accessed May 20, 2020. https://www.livekindly.co/annual-us-tofu-sales-reach-astaggering-91-million/.

Saio, Kyoko. "Tofu - Relationships between Texture and Fine Structure." Food and Agriculture Organizations of the United Nations. Last modified 1970. Accessed May 20, 2020. https://agris.fao.org/agris-search/search.do?recordID=US8017009.

Shurtleff, William, and Akiko Aoyagi. History of Tofu and Tofu Products (965 CE to 2013): Extensively Annotated Bibliography and Sourcebook. Lafayette, CA: Soyinfo Center, 2013. Accessed May 20, 2020. https://books.google.com/books?id=gGrUNvZt0_YC&printsec=frontcover&dq=tofu+history&hl=en&sa=X &ved=2ahUKEwjhltioteTkAhXnRd8KHSd6DhoQ6AEwAXoECAAQAg#v=onepage&q=isbn&f=false.

"Smooth Hot Tau Fu Fa (With GDL, No Gypsum Powder)." MyKitchen101en. Last modified May 2, 2018.

Accessed May 22, 2020. https://mykitchen101en.com/smooth-hot-tau-fu-fa-with-gdl-no-gypsumpowder/.

"Soymerica Non-GMO Soybeans - 7 Lbs (Newest Crop). Identity Preserved (IP). Great for Soy Milk and Tofu. 100% Product of USA." Amazon. Accessed May 20, 2020. https://www.amazon.com/SoymericaNon-GMO-Soybeans-Identity-Preserved/dp/B0763GC8SB. Starostinetskaya, Anna. "Global Tofu Industry to Reach $24 Billion by 2022." VegNews. Last modified May 2018. Accessed May 20, 2020. https://vegnews.com/2018/5/global-tofu-industry-to-reach-24-billion-by2022.

Sukiyaki (Homemade Tofu). Directed by Jun Yoshizuki. 2018.

"Tofu." McGill University. Last modified 2007. Accessed May 20, 2020. https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/t/Tofu.htm.

Wu, A. H., P. L. Horn-Ross, and A. M. Nomura. "Tofu and Risk of Breast Cancer in Asian-Americans."

American Association for Cancer Research. Accessed May 20, 2020. https://cebp.aacrjournals.org/content/5/11/901.short.

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Simulating Ecosystems for Evolutionary Exploration Aaron F. Mentor: Mike Roam

Abstract Evolution usually takes place on a timescale too large to be directly observed, but with computer simulation, we can break through this barrier. We spent the year designing a simple digital ecosystem, complete with reproduction and selection pressure, to watch evolution play out at high speed. After watching the simplest of creatures evolve to gather food more efficiently, we moved on to the creation of simple brains to see if our creatures could truly “learn” through evolution. While obstacles in execution prevented our simulation from running for particularly long times, we were able to observe the partial development of simple common sense.

Materials and Methods For natural selection to occur, three things are necessary: the existence of creatures with variable traits, the ability of creatures to reproduce with mutation, and some form of selective pressure. The selective pressure we chose was starvation.

Because the longer a creature does not starve, the more opportunities naturally arise for it to reproduce, creatures with advantageous traits will contribute more to future generations. Thus, these advantageous traits will be passed down, mutating to even better serve our creatures, and hopefully eventually creating an optimal (or at least highly successful) set of creatures. This is the basic principle of natural selection, and we hoped our three rules would be enough to spur it into action.

For the first real version of our simulation, we created a simple world containing patches of food and creatures (figure 1.1, below). The creatures move around the environment as determined by a set of traits to be discussed below (figure 1.2, below).

As they move, they use up energy, eventually dying of starvation. In particular, their energy consumption is proportional to their size and movement speed, which introduces a possible tradeoff. (With a larger body, they are more likely to collide with a piece of food, but also have more bulk to lug around, for example). But if they happen upon a food patch as they wander, they consume it, regaining energy, and staving off starvation for some period of time.

Size and movement patterns are controlled by these traits. The first trait is radius, as each of our creature’s is represented by a simple circle. The second and third traits are forward movement speed, and rotation speed: how fast, on average, they move in the direction they’re facing, and how quickly that direction changes over time. But to stop

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them from making perfect circles, we had to introduce a fourth and fifth trait, those being ranges for random deviation in their forward movement and rotation, respectively. With large enough random deviations, their movement becomes properly unpredictable while still being quite dependent on these four numbers together. As a final note on these traits, it is quite important to realize that these creatures have no sense whatsoever of their surroundings. They move around the environment dependent on these numbers, never seeking out food intentionally or trying to find mates, because they have no concept of the world.

Figure 1.1: Creatures are shown in red and food in green.

Figure 1.2: A creature’s five traits are displayed visually.

Now we arrive at the second major ability that creatures possess: reproduction. When two creatures collide, there is a chance that they will have a child, and that child will inherit their traits. Specifically, since each trait is a decimal number, a child receives a simple arithmetic mean of its parent’s values. And while not strictly necessary, we decided to add a slight mutation of up to five percent in each trait to keep evolution possible once the population’s traits have generally converged.

So now, to run the simulation and see what happens. If we graph the average values within the population of each of these five traits over time, we end up with something as shown in the following graph:

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The first thing we can see in this graph is that the creatures’ radii changed dramatically over the generations, and in one consistent direction. The question then is whether this change was the result of active natural selection, or if the value of this trait was unimportant to a creature’s reproductive success and thus varied semi-randomly.

Perhaps lugging a body of radius 15 (which we started the creatures at as a blind guess) was simply not worth the extra area food could be eaten from, and so large creatures died and over time they shrunk, or perhaps we’re essentially looking at a radius random walk.

Another trait which varied fairly dramatically was the level of random deviation in rotation speed. This one though changed in two directions over the course of the simulation. Perhaps that means this trait’s movement truly was due to chance and not to a selective force. While we could presumably utilize some nuanced statistical technique (such as p-values or the like) to determine which changes are random and which are evolution, it seems far easier to simply run the simulation a whole bunch more times and see where the results are similar.

In particular, the radius often converges to a number around 3 (as in this graph), and at least always trends steeply in the downward direction, which seems quite good evidence that evolution is at work here. The random deviation in rotation speed did entirely different things in each run, suggesting the value of this trait is simply not important in determining evolutionary success.

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While this is not directly related to evolution, we then took a moment to graph the number of creatures and number of food patches over time. In a representative run of the simulation, we ended up with this graph:

By looking at these (degree-ten) polynomial trendlines, we can see very clearly that both populations oscillate over time, and that they do so in alternation. This has a very straightforward explanation: When there are many creatures, they eat much of the food but then they cannot be sustained, and some creatures die off, allowing the food to replenish itself. This cycle will theoretically continue indefinitely. While this is interesting in itself, it has been observed in real-life ecosystems, which provides a welcome sign that our incredibly simple simulation might be doing something correctly.

For the second version of our simulation, we decided to grant our creatures some level of awareness of their surroundings, and along with that awareness, a decision-making process. To provide this awareness, we added a singular eye to the front of each creature, an eye capable of seeing a single object directly in front of itself (figure 2.1, below). Essentially the creature could tell if what was closest in front of it was a piece of food, another creature, or the boundary of the simulated environment, as well as the distance to this object. (We achieved this quite simply by tracing a ray forward from the creature’s eye until collision, though this did add somewhat to the running time of the simulation).

Now that we had established the specifics of its information on the environment, we had to decide on a processing scheme. While we considered designing a more explicit decision-making capability, such as some sort of decision tree, we settled on using a

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very simple artificial neural network to most simply provide our creatures with a large array of possible strategies for interpreting the results of their sight. And we decided as well that this neural network would have two outputs, one to determine the speed with which the creature would move forward on a given frame, and one to determine the speed with which it would rotate (figure 2.2, below).

We experimented with a number of different network architectures, but found that, for the most part, a single hidden layer of three neurons gave the creatures as much freedom as they would be able to use. (It wasn’t particularly important to the simulation’s outcome, but we settled on a hyperbolic tangent activation function as well.)

And the final decision to make concerned the processes of evolution, specifically how the passing down of traits from parent to child would be simulated, and how mutations would occur. To keep things simple, we made the decision to simply pairwise average the corresponding weights and biases in each parent’s brain, and add a mutation of up to five percent, before bestowing this value upon the child. In total the fifteen weights (3 x 3 + 3 x 2) and five biases (3 + 2) give our creatures a total of twenty traits.

Figure 2.1: Creatures shown in blue, with red lines illustrating their lines neural of sight.

Figure 2.2: The structure of a creature’s network brain.

Now to run this second simulation. The first thing to notice is that while in version one, all creatures started out moving around the environment in relatively coherent ways (even if that meant running circles around the simulation’s edges, or some such suboptimal behavior), the neural network approach taken in this second version allows for much more nonsensical movement patterns. Many creatures barely moved at all.

Some jittered rapidly without making any meaningful motion in any direction, rotating clockwise and counter clockwise in succession as the object in their vision changed.

Some entirely ignored what they were seeing and moved in circles like the creatures from version one.

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We hoped that the creatures exhibiting the most anti-advantages of these behaviors will die off quickly, and evolution will be able to proceed. In running this simulation, we were successful in seeing a general coherence of strategy develop, meaning that creatures would continuously move and in a reasonably smooth pattern as to cover decent distance. This already is a sign that natural selection is having some effect.

Additionally, while we never got to a point of creatures truly seeking out food, we did start to see them accelerate forward in a burst of energy when food passes through their line of sight. This is progress in the direction of tracking down visible food, although we never fully got there. Unfortunately, since the weights and biases of creatures’ neural network brains are on their own essentially meaningless, we were unable to come up with a useful way to quantify or graph results. This is a thought project for the future.

Discussion Before concluding, it’s worth discussing impediments we faced and some of the changes we would like to explore in the future. On the first point, even in simulation, evolutionary progress takes time, but keeping the environment functioning smoothly for long stretches proved difficult. Often, all but one of the creatures present would die, halting evolution in its tracks. Other times, our creatures multiplied out of control (which occurred especially when their movement was slow) and lagged out the simulation too much for it to continue progressing. And a third problem was caused by random crashes that we were never able to fully eliminate. Because of these simulationstopping problems, we were never able to reliably run the simulation for more than a few tens of generations, which stopped us from attaining the evolutionary complexity we were hoping to achieve.

If we continue this project into the future, there are many possibilities we never took the time to explore. One such area is more nuanced methods of reproduction. While in our simulation two parents simply average each of their numerical traits, adding in some random mutation, real-world creatures pass on their traits through mix-and-matched genes. Designing some type of simplified DNA-like method of encoding traits would be quite an interesting area of exploration.

Another idea would be to simply complify the environment, and the abilities of the creatures. Adding predators to the simulation would be quite interesting, though after attempting it very briefly we discovered that balancing an ecosystem so neither creatures goes extinct is exceptionally difficult. Giving our creatures more nuanced perception of their environment (as opposed to a single eye) and increasing the complexity of their brains is another avenue to be explored. Also allowing the structures of their neural-network brains to evolve along with their specific weights and biases could lead to the development of more efficient (and thus more interesting) brain

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structures. Furthermore, we are committed to writing more code tests, rooting out runtime bugs, and finding a solution for our program’s often-short lifespan.

The full code can be found on GitHub: https://github.com/aaronfink01/creatureEvolution References Designing Neural Networks through Neuroevolution A review article in Nature by Kenneth O. Stanley, Jeff Clune, Joel Lehman, and Risto Miikkulainen https://www.nature.com/articles/s42256-018-0006-z Polyworld: Using Evolution to Design Artificial Intelligence A Google Tech Talk by Larry Yaeger https://www.youtube.com/watch?v=_m97_kL4ox0 Simulating Evolution: How Close do Computer Models Come to Reality An article in The Conversation by Christoph Adami https://theconversation.com/simulating-evolution-how-close-do-computer-models-come-to-reality57538 Coding Adventure: Simulating an Ecosystem A project by Sebastian Lague https://www.youtube.com/watch?v=r_It_X7v-1E

48 Melting Glaciers Viv W. Mentor: John Baierl

Abstract Given the role of melting glaciers in climate change, researching ways to slow their melting will invariably play a role in combating climate change. I have used a very smallscale model of glaciers to model different methods of slowing melting. I modeled two of the major proposals: building sea walls to insulate glaciers, and seeding the air with sulfide to block the sun and mimic an o-zone layer. All of the ice was shaped into a 350ml container. The sea walls are used for underwater glaciers. At the bottom of the glacier, the density is .92g/ml. I used a block of ice submerged in 67 degree water and found the melt rate to be 1.9ml/ minute. When coated in silicone, the melt rate lowered to 1.5ml/ minute. To model how the tops of glaciers are affected by an artificial ozone, I first modeled a control at the density of .32g/ml by shaving ice and slightly compressing it. When this ice was exposed to a sun lamp it melted at the rate of 2.26 ml/minute.

When the light was removed, it melted at the rate of 1.85ml/minute. Although each of these proposals significantly lowered the melt rate, that does not necessarily mean they are viable options for glaciers. The first concern would be the expense of having robots build walls underwater and having planes circle the arctic and seed sulfide. The second concern would be the ecological effect. The underwater walls could interfere with the sea life, and the sulfide has yet to be tested in the environment and may affect surrounding wildlife. The last concern with these proposals would be the long-term effects on the thinking surrounding climate change. Such methods could create the illusion that they are long term fixes for climate change and slow the systemic changes that need to happen.

Introduction The motivation for my project came from the urgent need to protect our glaciers. First and foremost, the only way to stop glaciers from melting and restore them is to stop emitting carbon dioxide, and capture the excessive carbon dioxide in the air. Because of this urgency, there are many proposed plans to slow glaciers from melting until we have a more permanent solution. I decided to test the efficacy of these plans with small scale models, and research their ecological impacts.

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Materials and Methods In order to keep my results as consistent as possible, I used the same volume for all of my glacier models: 350ml. I measured their melting in ml/minute my dividing the 350ml volume with the number of minutes it took for the ice to fully melt under different conditions. All of these tests were conducted in a 68 degree Fahrenheit environment.

Results Through my models I found both models to be effective—insulation and ‘sulfate seeding.’ However, I cannot compare the two results as they were designed to protect two different types of glaciers, and there is no way to calibrate the effects of my manipulation with the effects it would have on a glacier. The sea glacier was preserved with underwater walls, which I modeled by insulating the solid ice (at a density of .92) with silicon and submerging it in water. When coated in silicon, the melt rate went from 1.9ml/minute to 1.5ml/minute. The tops of glaciers were modeled with compressed shaved ice which were a density of .32. To model the sulfate seeding which would act as an artificial o-zone, I used sun lamps as my variable. When these ‘glaciers’ were exposed to the sun lamp, they melted at a rate of 2.26 ml/minute. When the lamps were removed, the average melt rate lowered to 1.85ml/minute. Both methods showed a significant decrease in melt rate, showing that these methods could potentially be successful in lowering the melting rate of glaciers.

Discussion Although both of these methods show promise, there are still many concerns that are keeping them from being practiced. The primary concern is cost. Both of these proposals would be extremely costly, and many argued that this money would be better spent on carbon capture technology, or renewable energy research. The second concern is the environmental impact. This applies mostly to the sulfate proposal. This method has been researched in a very limited manner, and there is limited information as to how strong the impact of the sulfate would be, and how frequently it would need to be re-seeded into the atmosphere. The third concern would be the ecological impacts of these technologies. With the proposal to build underwater insulating walls there are many areas of concern. The actual construction of walls may interfere with the surrounding habitats. In addition, once the walls are built, the luminescence may be different than that of ice, potentially confusing animals. As for the sulfate proposal, the long-term ecological impact is largely unknown, which must be tested before proceeding with the plan.

50 The Effects of Climate Change on Marine Life Noah R. & Ezra G. Mentor: Gretta Reed

Abstract We worked throughout the beginning of the year to look at the impacts of climate change on sea-faring organisms. Specifically, we wanted to explore different environmental variables such as, salinity, pH, eutrophication, and acidity on marine life to see how our test subjects would react. We started our planned series of experiments using planaria, and their regenerative abilities to test the effects of these conditions on the freshwater organism. Our results were relatively surprising. At the conclusion of the 10-day experiment, the most successful planarians (disregarding control) were those immersed in salt water (keep in mind these were freshwater organisms). The salt water had originally appeared to kill the planarian, however, they came back stronger than ever. We feel this was due to a combination of factors including natural selection by change in habitat, and the planarian regenerative process. The eutrophication planaria were the least successful, as all of them died within two days after the start of the experiment. We had originally planned to replicate our experiment with a series of other marine organisms such as, slugs, snails, and crabs. However, due to COVID-19 we were unable to complete our research. We have read a series of articles that attempted to monitor the effects of salinity changes in pH, eutrophication, and acidity on other marine organisms, and we have discovered that our results with the planarian fit within the general scientific consensus.

Introduction The goal of our project was to test the effects of climate change on different sea-faring organisms and then determine if those changes could affect any other species in its ecosystem. For example, Algae which are photosynthetic eukaryotes are being hit hard by the increase in fresh water storms, and increases in temperature, which is placing their survival in jeopardy. However, their survival is critical not just for the preservation of their species, but also for many others that depend on them. One example of this is with the anemone, which has a symbiotic relationship with algae. The algal cells soak in energy from the sun, providing the host anemone with nutrition in return for safekeeping. When the temperatures reach a certain limit, which they are on pace to reach, the algae will be forced to leave their host and most likely die. The anemones, who can tolerate temperatures a bit better, now cannot sustain themselves putting their survival at risk. But the chain reaction doesn’t end there. Another symbiotic partner of the anemone is the clownfish. The anemone, who is not at risk, protects the clownfish by concealing it within its poisonous arms (which the clownfish is immune to) and leaving scraps of its meals for the clownfish to consume. In return, the clownfish

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rids the anemone of parasites and wards away predators. With the inevitable loss of the anemone the clownfish will need to seek out a new form of protection, which is not guaranteed. This is just one example of how climate change can affect a whole sector of the ecosystem by rooting on one piece. Everything in the ocean relies on other organisms for its survival. And removing one piece can jeopardize the survival of many more. What motivated us was that the mainstream story has been focused on the threats to individual species and not making the connection the inevitable chain reaction throughout the ecosystem. We wanted to address the severity of the problem by presenting all the challenges we will face in the future. For our experiment we first chose to use planaria (Platyhelminthes) and we tested them under 4 different conditions: A control (room temperature pond water, CO2, salinity, and eutrophication).

Eutrophication, which is an excessive amount of nutrients in a lake or other body of water, is a consequence of using excess fertilizer in agriculture and having too many flat concrete surfaces near lakes, rivers, and oceans, because the water, along with the excess nutrients and pollutants, then has nowhere to be absorbed. Salinity was our next variable because, with the increase in temperature and hurricanes, more freshwater waterways will be filled with excess salt. Finally, we tested CO2 because it is being absorbed by water all across the globe because of increases in fossil fuels in our atmosphere. Similar experiments have been conducted in the past, however we had different results and a different end goal. By testing the planria’s reproduction rate, survival, and regeneration time, we could figure out how they would be affected, but also how much their symbiotic partners would be affected. We had a hypothesis for how the planira would fare. We believed that overall, Salinity would be the worst for the planaria, and, besides the control, the tests subjects in the CO2 would do the best.

Materials and Methods

For each experiment we conducted (eutrophication, acidity, etc.) We maintained three subgroups that were set up exactly like each other in order to make sure our results replicated themselves and were not due to lab error. Within each subgroup we placed one planaria that we did not cut or expect to regenerate, and one planaria that we had cut in half. Therefore, in a scenario with 0% mortality and 100% regeneration by the end of experimentation we would have had three fully formed planarians in each petri dish.

Habitats (75ML per container) Control Group: Pre-purchased freshwater. (Salinity .08 PPT) Eutrophication: Resembled control. An additional 2ML of plant food was added.

Acidity: Resembled control. An additional 2ML of carbonic acid was added every 7 days.

Salinity: Resembled control. (Salinity 1.64PPT)

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Results

The mortality rate for control was relatively even and minor throughout the experiment.

The mortality rate for salinity spiked in the early days of the experiment and then was relatively even and minor throughout the remainder of the experiment.

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The mortality rate for eutrophication was 100%. All planarians died within four days of the experiment.

The mortality rate for CO2 / Acidity spiked in the early days of the experiment and then was relatively even and minor throughout the remainder of the experiment.

Regeneration: All groups that survived the experiment exhibited some form of regeneration (we took note of the days when planarians were fully regenerated).

Control: Regenerated fully after roughly 12 days and reached a size of .9cm

Salinity: Regenerated fully after roughly 13 days and reached a size of .6cm

CO2 / Acidity: Regenerated fully after roughly 14 days and reached a size of .8cm

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Discussion By examining planarian regeneration in a multitude of environmental settings we are able to deduce the effects of salinity, CO2, and eutrophication have on planaria. Our results were unexpected. We hypothesized that planaria would not be able to survive, much less regenerate, in an environment that was dramatically different from their natural habitat. Although our results did not match our initial perceptions, we gathered insight into the adaptation abilities of planarians. Because we only had time to test their regeneration and survival abilities, we couldn’t determine precisely how else they were affected by the climate change variables. Also because of time constraints we could only test one organism, which seems to be tolerant of many of the variables. Planaria in waters with increasing eutrophication, seem to be the only ones in immediate danger.

The rest were able to adapt to their new circumstances. In this situation, there isn’t a chain of detrimental effects of the planaria’s ecosystem. However, if we had the time to test other organisms, such as slugs, crabs, fish, and snails, we are sure we could have found an example similar to the algae, anemone, and clownfish case. If we had more time, we would have tested more species, with more variations in our variables (25% salinity, 50% salinity, etc.), and we would have looked for more effects on the organism instead of just studying their survival and reproduction rate. Overall, we did not answer the questions we had in September; however, we did create a sound experiment with a lot of potential that someone else can hopefully expand on.

References

Auerbach, Christensen, Bamber, Brownell, Calabrese, Davis, . . . Havas. (1982, January 01). Impacts of ocean co 2 disposal on Marine life: I. a Toxicological assessment INTEGRATING CONSTANTCONCENTRATION LABORATORY ASSAY data WITH VARIABLE-CONCENTRATION field exposure. Retrieved May 25, 2020, from https://link.springer.com/article/10.1023/A:1019029931755

Bunse, C., Lundin, D., Karlsson, C., Akram, N., Vila-Costa, M., Palovaara, J., . . . Pinhassi, J. (2016, January 11). Response of MARINE bacterioplankton ph Homeostasis gene expression to elevated co 2. Retrieved May 25, 2020, from https://www.nature.com/articles/nclimate2914

Contributor. (2019, September 15). How sea anemones feel the pinch of climate change. Retrieved May 25, 2020, from https://www.sfexaminer.com/news-columnists/how-sea-anemones-feel-the-pinch-ofclimate-change/

Gall, S., & Thompson, R. (2015, February 10). The impact of debris on marine life. Retrieved May 25, 2020, from https://www.sciencedirect.com/science/article/abs/pii/S0025326X14008571

Morgan, T. H. (1898). Experimental studies of the regeneration Of Planaria Maculata. Leipzig: W. Engelmann.

Reddien, P., Bermange, A., Murfitt, K., Jennings, J., & Alvarado, A. (2005, May 02). Identification of GENES needed for Regeneration, stem cell function, and TISSUE homeostasis by SYSTEMATIC Gene perturbation In planaria. Retrieved May 25, 2020, from https://www.sciencedirect.com/science/article/pii/S1534580705000924

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Rising CO2 levels threaten global marine life. (n.d.). Retrieved May 25, 2020, from https://www.pri.org/stories/2017-11-05/study-rising-co2-levels-threaten-global-marine-life

Riutort, M. (2013, December 11). Dugesia sicula (Platyhelminthes, Tricladida): The colonizing success of an asexual Planarian. Retrieved 2013, from https://link.springer.com/article/10.1186/1471-2148-13-268

Simon, M. (n.d.). How is the coronavirus pandemic affecting climate change? Retrieved May 25, 2020, from https://www.wired.com/story/coronavirus-pandemic-climate-change/

Spary, S. (2020, April 17). Space images of Venice show how Coronavirus has changed the City's iconic canals. Retrieved May 25, 2020, from https://www.cnn.com/2020/04/16/europe/venice-space-satelliteimages-canals-scli-intl-scn/index.html

US Department of Commerce, & National Oceanic and Atmospheric Administration. (2017, October 05).

What is eutrophication? Retrieved May 25, 2020, from https://oceanservice.noaa.gov/facts/eutrophication.html

Wang, M., & Shi, W. (2011, June 03). Satellite-Observed algae blooms in China's Lake taihu. Retrieved May 25, 2020, from https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2008EO220001

56 Maxwell’s Equations from the Principle of Least Action Luca S. Mentor: Daniel Yaverbaum

Abstract This project endeavored to determine whether Maxwell’s Equations can be derived from the principle of least action. Maxwell’s Equations here refer to the four laws governing electricity and magnetism, and the principle of least action is a fundamental theorem that determines the equations of motions of objects. Indeed, we found that it is possible, and this paper outlines one of the known derivations. The motivation for this project is to show just how wide-ranging and fundamental the principle of least action is. Maxwell’s Equations, unlike say, Newton’s Laws, describe fields rather than discrete objects. In order to be able to produce Maxwell’s Equations, the principle of least action has to be formulated in terms of fields and their interactions with objects, instead of just interaction between physical objects. We used this field version of the principle of least action for a specific case, the laws of electricity and magnetism, but by formulating the principle of least action to include fields, we are left with the basis for a broader classical field theory.

1 Introduction The question of whether or not it was possible to get to Maxwell’s Equations from the Principle of Least Action was an open one. The Principle of Least Action is formulated in terms of particles, discrete objects with masses. Maxwell’s Equations, on the other hand, are formulated in terms of fields. Our project was a search for a reformulation of the Principle of Least Action in terms of fields, and this paper provides a condensed and explained version of one such formulation. In order to derive Maxwell’s Equations, we need to formulate the principle of least action in terms of fields instead of particles. To do this, we will rely on several principles, ones that also are the foundations of many other theories: Least Action, Locality, Lorentz Invariance, and Gauge Invariance.

1.1 Principle of Least Action The principle of least action states that the action (the abstract quantity outlined below) is always minimized (more rigorously, extremized) along any physical path. The action đ?‘†, ! is âˆŤ! ! â„’ đ?‘‘đ?‘Ą, where classically, â„’ = đ?‘‡ − đ?‘‰, the kinetic energy minus the potential energy. "

The Lagrangian in other cases can be something more complicated and can be represented as any function of generalized coordinate đ?‘ž and its velocity đ?‘žĚ‡. In classical mechanics, the principle of least action reproduces all of our familiar equations, đ??š"#! = đ?‘šđ?‘Ž and such.

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!!

�� = � 1 ℒ (�, �̇) �� = 0 !"

When one goes about the process of minimizing the action, one gets general equations of motion, called the Euler-Lagrange Equations: đ?œ• đ?œ•â„’ đ?œ•â„’ = đ?œ•đ?‘Ą đ?œ• đ?‘žĚ‡ đ?œ•đ?‘ž 1.2 Locality The principle of locality states that things can only affect neighboring things. Whatever happens at one position and time can only be related to things at neighboring positions and times. It’s a fundamental principle of classical mechanics, and it prevents action at a distance. The way this is mathematically represented is that a Lagrangian will only depend on the coordinates and their first derivatives. Having just first-order derivatives or lower makes sure that the equations of motion produced are differential equations that relate locally. If there were higher order derivatives in the Lagrangian, derivatives with order 2 or above would appear in the equations of motion, which is not physical.

1.3 Lorentz Invariance Lorentz invariance makes sure that the theory fits with special relativity. The field theory necessary to derive Maxwell’s equations will be a relativistic theory (this makes it the most complete theory possible, and we know from experiment that the laws of electrodynamics are relativistic). A Lorentz invariant quantity is a quantity that doesn’t change under Lorentz transformations (coordinate transformations in a relativistic coordinate system). Scalars are Lorentz invariant, whereas vectors are not.

When we are dealing reference frames moving relative to one another, the geometry of the coordinate system (where time is one axis and space the other) is warped (see diagram below). Because of this, the quantities that are invariant in regular Euclidean space, like the distance from the origin, đ?‘Ľ $ + đ?‘Ś $ , are no longer invariant. One quantity that is invariant is something called proper time, đ?œ?. đ?œ? $ = đ?‘Ą $ − đ?‘Ľ $ . Proper time measures the number of ticks of a clock along one path in the coordinate system, through spacetime. This quantity is invariant for all observers.

One note on notation: throughout this paper, we will use units so that the speed of light, đ?‘? = 1.

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2. Methods Our new action integral for fields must include a term for the field and a term for the interaction with a particle. Let’s first begin with the particle term.

2.1 Action Integral 2.1.1 Interaction Term Our action needs to be Lorentz invariant and obey Locality. So, we cannot have a higher order derivative than a first derivative and it must be constructed from invariant quantities. Our new action will also have two terms: one that describes the particle, essentially the "interaction" with the field, and one that describes the field itself. Here we begin with the interaction or particle term.

Instead of constructing the integral using time, we will use proper time. So, the action will look like: %

đ?‘† = đ?‘’1 đ?‘‘đ?œ? &

We have a constant in front of it for consistency. Let’s make this constant − đ?‘š, and using using đ?‘‘đ?œ? = √1 − đ?‘Ł $ đ?‘‘đ?‘Ą, we can write our action integral as: %

đ?‘† = −đ?‘š âˆŤ& √1 − đ?‘Ł $ đ?‘‘đ?‘Ą, with the Lagrangian being â„’ = −đ?‘šâˆš1 − đ?‘Ł $ '

If one were to expand this Lagrangian out, the first order term would be $ đ?‘šđ?‘Ł $ , our good old kinetic energy. The constant, −đ?‘š, in front makes it so that we reproduce our old known kinetic energy.

2.1.2 Fields We need to establish what we mean when we talk about fields. A field is an abstract thing that permeates space and affects a particle. At each point in space, the field has a value. There are two types of fields: scalar fields and vector fields. An example of a

59

scalar field would be something like temperature: at every point in space and time, there is a value for the temperature measured at that point. An example of a vector field would be something like wind or gravity: at every point in space and time there is a vector determining how it would affect a particle if placed at that point. We will be dealing mainly with vector fields in this paper: electric and magnetic fields. The way we represent fields is by having a function of space and time that describes the value of the field at every point, đ?›ˇ(đ?‘Ą, đ?‘‹ ( ). In our Euler-Lagrange equations, this function đ?›ˇ would take the place of our generalized coordinate đ?‘ž, and we would have four Euler-Lagrange equations, one for time and three for space. Just as đ?‘ž(đ?‘Ą) describes the trajectory of a particle, đ?›ˇ(đ?‘Ą, đ?‘‹ ( ) describes the "trajectory" of a field. đ?œ• đ?œ•â„’ đ?œ•â„’ = ) *+ đ?œ•đ?‘‹ đ?œ•đ?›ˇ *, #

2.1.3 Field Term We must add a term to the action that describes the field. This term must be Lorentz invariant and must be local. One way to make it Lorentz invariant is to make it a scalar.

This new term must also be an integral over space and time, as our field is a function over space and time and not only time.

In order to accomplish this, let’s create an abstract quantity đ??´) . This is called the vector potential. It is related to the electric and magnetic fields, and we will see how soon. It is a more basic (and harder to grasp) quantity and makes it so we can include the electric and magnetic fields in the action integral.

Just as we did with the particle action term, let’s construct the simplest case we can.

The simplest option is to not include any derivatives of đ??´) , just đ??´) itself. The simplest way to make it a scalar is to multiply and sum it over the coordinates, đ?‘‹) . Our integral will be: %

đ?‘ž 1 đ?‘‘ đ?‘‹) đ??´) (đ?‘Ą, đ?‘Ľ) &

We included a constant in front, just as we did with the particle term.

The constant this time is charge, and we will see how it appears below.

So our new relativistic particle and field action will be: %

%

đ?‘† = 1 − đ?‘šE1 − đ?‘ĽĚ‡ $ đ?‘‘đ?‘Ą + đ?‘ž 1 đ?‘‘ đ?‘‹) đ??´) (đ?‘Ą, đ?‘Ľ) &

&

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2.2 Gauge Invariance Here we will talk briefly about the concept of gauge invariance. Let’s take a look at our action integral. We see that we can add a derivative of any scalar to the vector potential without changing the equations of motion. "

! "đ??´! (đ?‘Ą, đ?‘Ľ) + #

" " " đ?œ•đ?‘† đ?œ•đ?‘† ! ! ! đ?‘‘đ?‘‹ = ! đ??´ (đ?‘Ą, đ?‘Ľ)đ?‘‘đ?‘‹ + ! đ?‘‘đ?‘‹ = ! đ??´! (đ?‘Ą, đ?‘Ľ)đ?‘‘đ?‘‹! + đ?‘†(đ?‘?) − đ?‘†(đ?‘Ž) ! ! đ?œ•đ?‘‹! đ?œ•đ?‘‹ # # #

The quantity đ?‘†(đ?‘?) − đ?‘†(đ?‘Ž) does not change the action. When we go about the minimization process of the action, we wiggle the action along the path, but we fix the end points. The variation of the end points is necessarily zero because the end points are fixed and do not vary. Therefore, adding a derivative of any scalar to the vector potential does not affect the resulting equations of motion. Adding this derivative of a scalar is called fixing a gauge. This is much like fixing a zero point or ground for a regular potential.

This is a fundamental principle of many theories. It allows us to look at different parts of a system without affecting the resulting equations of motion. We will see this principle used below when we deal with charges and currents in Maxwell’s equations.

2.3 Lorentz Force Law We have an expression for the force on a particle with charge đ?‘ž moving at a velocity đ?‘Ł due to an electric field đ??¸ and a magnetic field đ??ľ: đ??š = đ?‘ž(đ??¸ + đ?‘Ł Ă— đ??ľ).

This is a previously known result, and our new action should reproduce the expression.

We have our new action: %

%

đ?‘† = 1 − đ?‘šE1 − đ?‘ĽĚ‡ $ đ?‘‘đ?‘Ą + đ?‘ž 1 đ?‘‘ đ?‘‹) đ??´) (đ?‘Ą, đ?‘Ľ) &

&

We must now plug the Lagrangian from the new action integral into the Euler − Lagrange equation. However, the second term in the new action expression is an integral over đ?‘‹) the space and time coordinates, and is not expressed in terms of a Lagrangian, though we can manipulate it do be expressed in terms of one. %

1 đ?‘‘ đ?‘‹) đ??´) = 1 &

%

&

đ?‘‘đ?‘‹) đ??´ đ?‘‘đ?‘Ą đ?‘‘đ?‘Ą )

Now we see that Lagrangian of our new action expression is:

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đ?‘‘đ?‘‹) đ??´) đ?‘‘đ?‘Ą -, # The quantity -! can be expressed as two different terms, a zeroth (time) term and a â„’ = −đ?‘šE1 − đ?‘ĽĚ‡ $ + đ?‘ž

spatial term. When split up, the Lagrangian becomes −đ?‘šE1 − đ?‘ĽĚ‡ $ + đ?‘ž đ?‘ž đ?‘ž

-, % -!

-, % -!

đ??´( . The time term

-, $ -!

-, $

-! $

đ??´. +

= 1, so the Lagrangian becomes −đ?‘šE1 − đ?‘ĽĚ‡ + đ?‘žđ??´. +

đ??´( . Now we can plug this into our Euler-Lagrange equations:

đ?‘‘ đ?œ•â„’ đ?œ•â„’ ( = đ?‘‘đ?‘Ą đ?œ• đ?‘‹Ě‡ đ?œ•đ?‘‹ ( Let’s start with the left side: ( đ?œ•â„’ đ?‘š đ?‘‹Ě‡ + đ?‘žđ??´( (đ?‘Ą, đ?‘Ľ) ( = đ?œ• đ?‘‹Ě‡ E1 − đ?‘ĽĚ‡ $ ( đ?‘‘ đ?œ•â„’ đ?‘‘ đ?‘š đ?‘‹Ě‡ = R + đ?‘žđ??´( (đ?‘Ą, đ?‘Ľ)S đ?‘‘đ?‘Ą đ?œ• đ?‘‹Ě‡( đ?‘‘đ?‘Ą E1 − đ?‘ĽĚ‡ $

Then for the right side: đ?œ•â„’ đ?œ•đ??´. " đ?œ•đ??´" = đ?‘ž ( + đ?‘ž đ?‘‹Ě‡ ( đ?œ•đ?‘‹ đ?œ•đ?‘‹ đ?œ•đ?‘‹ ( Now we have both sides of our Euler Lagrange Equation: đ?‘‘ đ?‘š đ?‘‹Ě‡( đ?œ•đ??´. " đ?œ•đ??´" R + đ?‘žđ??´( (đ?‘Ą, đ?‘Ľ)S = đ?‘ž ( + đ?‘ž đ?‘‹Ě‡ đ?‘‘đ?‘Ą E1 − đ?‘ĽĚ‡ $ đ?œ•đ?‘‹ đ?œ•đ?‘‹ ( This is starting to look a little more like the force law.

We can see that the first term on the right is a time derivative of the momentum (relativistic momentum), which is force. For low velocities, that term becomes mass times acceleration.

Notice we lowered the index in the first term in order to make the indices on both sides agree.

We can do that because it represents only the space components. đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ ) đ?‘‘ đ?‘š đ?‘‹Ě‡( đ?œ•đ??´. " đ?œ•đ??´" +đ?‘ž = đ?‘ž ( + đ?‘ž đ?‘‹Ě‡ đ?‘‘đ?‘Ą E1 − đ?‘ĽĚ‡ $ đ?œ•đ?‘Ą đ?œ•đ?‘‹ đ?œ•đ?‘‹ ( đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ) đ?‘‘ đ?‘š đ?‘‹Ě‡( đ?œ•đ??´. " đ?œ•đ??´" = đ?‘ž ( + đ?‘ž đ?‘‹Ě‡ −đ?‘ž ( đ?‘‘đ?‘Ą E1 − đ?‘ĽĚ‡ $ đ?œ•đ?‘‹ đ?œ•đ?‘‹ đ?œ•đ?‘Ą

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Let’s deal with that last term, �

*/% (!,2) *!

.

đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ ) đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ ) đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ) " = + đ?‘‹Ě‡ đ?œ•đ?‘Ą đ?œ•đ?‘Ą đ?œ•đ?‘‹ " So, collecting the terms, we have: đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ) đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ) " đ?‘‘ đ?‘š đ?‘‹Ě‡( đ?œ•đ??´. " đ?œ•đ??´" = đ?‘ž ( + đ?‘ž đ?‘‹Ě‡ −đ?‘ž −đ?‘ž đ?‘‹Ě‡ ( đ?‘‘đ?‘Ą E1 − đ?‘ĽĚ‡ $ đ?œ•đ?‘‹ đ?œ•đ?‘‹ đ?œ•đ?‘Ą đ?œ•đ?‘‹ " đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ) đ?œ•đ??´( (đ?‘Ą, đ?‘Ľ) " đ?‘‘ đ?‘š đ?‘‹Ě‡( đ?œ•đ??´. " đ?œ•đ??´" =đ?‘ž (−đ?‘ž + đ?‘ž đ?‘‹Ě‡ −đ?‘ž đ?‘‹Ě‡ ( đ?‘‘đ?‘Ą E1 − đ?‘ĽĚ‡ $ đ?œ•đ?‘‹ đ?œ•đ?‘Ą đ?œ•đ?‘‹ đ?œ•đ?‘‹ " Or: đ?œ•đ??´( đ?‘‘ đ?‘š đ?‘‹Ě‡( đ?œ•đ??´. đ?œ•đ??´( " đ?œ•đ??´" = đ?‘žT ( − U + đ?‘ž đ?‘‹Ě‡ T ( − " U đ?‘‘đ?‘Ą E1 − đ?‘ĽĚ‡ $ đ?œ•đ?‘‹ đ?œ•đ?‘Ą đ?œ•đ?‘‹ đ?œ•đ?‘‹ Now this looks even more familiar. We have a force term on the left side of the equation, and we have two terms that include the vector potential on the right hand side, one of which also involves velocity.

This looks a lot like the Lorentz Force Law. We can state the following in order to get the first term of the Lorentz Force Law: đ??¸( =

đ?œ•đ??´. đ?œ•đ??´( − đ?œ•đ?‘‹ ( đ?œ•đ?‘Ą

Now let’s deal with the term involving velocity.

We can compare this term component by component with the components of (đ?‘Ł Ă— đ??ľ), and we can see that: đ??ľ2 =

đ?œ•đ??´5 đ?œ•đ??´2 đ?œ•đ??´4 đ?œ•đ??´5 đ?œ•đ??´2 đ?œ•đ??´4 − , đ??ľ5 = − , đ??ľ4 = − đ?œ•đ?‘Ś đ?œ•đ?‘§ đ?œ•đ?‘§ đ?œ•đ?‘Ľ đ?œ•đ?‘Ľ đ?œ•đ?‘Ś

We recognize that these are the components are the components of the curl of đ??´, so: XX⃗ = XX⃗ đ??ľ đ?›ť Ă— Xđ??´âƒ—

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So now we have reproduced the Lorentz Force Law by relating the electric and magnetic fields to the new, more abstract quantity that appears in our Lagrangian, the vector potential.

2.4 Field Tensor Right now, we have the electric and magnetic fields as two different quantities, relating to the vector potential in two ways. We would like to describe the two in a possibly more compact way. You notice that the components of đ??¸ and đ??ľ look quite similar, though one involves time and space components and the other only involves space components. In our relativistic view of things, however, we treat time and space as equal components of spacetime. Time is just another coordinate system axis. So, we */

*/

realize that we can write both đ??¸ and đ??ľâ€™s components in one matrix: *, #& − *,#& . We call this the Electromagnetic Field Tensor, đ??š)6 . Tensor is a scary word, and you can ignore it.

This is just a matrix that contains the components of đ??¸ and đ??ľ.

0 −đ??¸2 −đ??¸5 −đ??¸4 0 đ??ľ4 −đ??ľ5 ⎞ ⎛đ??¸2 đ??š)6 = đ?œ•) đ??´6 − đ?œ•6 đ??´) = ⎜ đ??¸5 −đ??ľ4 0 đ??ľ2 âŽ&#x; âŽ?

đ??¸4

đ??ľ5

−đ??ľ2

0

âŽ

This tensor describes the electric and magnetic fields as one quantity, and one relevant thing to figure out would be how the field tensor transforms.

We shall use the tensor version of the Lorentz transformation: 1 −đ?‘Ł 0 0 $ √1 − đ?‘Ł $ ⎛√1 − đ?‘Ł ⎞ −đ?‘Ł 1 ) đ??ż6 = ⎜ 0 0âŽ&#x; ⎜√1 − đ?‘Ł $ √1 − đ?‘Ł $ âŽ&#x; 0 0 1 0 âŽ? 0 0 0 1⎠The field tensor has two indices, so it will transform like this: ) đ??š 7)6 = đ??ż8 đ??ż69 đ??š)6 In matrix multiplication form: đ??ż đ??š đ??ż: Where đ?‘‡ is the transpose: it flips the rows and columns of a matrix.

Doing out the matrix multiplication, we get:

64 0

−đ??¸2

−đ??¸5 + đ?‘Łđ??ľ4

−đ??¸4 − đ?‘Łđ??ľ5

$

$

√1 − đ?‘Ł √1 − đ?‘Ł ⎞ ⎛ −đ?‘Łđ??¸ + đ??ľ −đ?‘Łđ??¸ 5 4 4 − đ??ľ5 âŽ&#x; ⎜ đ??¸ 0 2 ⎜ √1 − đ?‘Ł $ √1 − đ?‘Ł $ âŽ&#x; đ??š 7)6 = ⎜ âŽ&#x; đ??¸5 − đ?‘Łđ??ľ4 đ?‘Łđ??¸5 − đ??ľ4 0 đ??ľ ⎜ âŽ&#x; 2 $ √1 − đ?‘Ł $ ⎜ √1 − đ?‘Ł âŽ&#x; đ??¸4 + đ?‘Łđ??ľ5 đ?‘Łđ??¸4 − đ??ľ5 −đ??ľ2 0 âŽ? √1 − đ?‘Ł $ √1 − đ?‘Ł $ ⎠We see that the electric and magnetic fields become mixed up under a Lorentz transformation.

This means that one observer may measure just an electric field, but a second observer moving relative to the first will measure an electric and a magnetic field. The tensor description of the electric and magnetic fields is not only mathematically concise, it also contains in it the mixing of the electric and magnetic fields.

2.5 Maxwell’s Equations There are four Maxwell Equations, and getting the first two is pretty straightforward.

Just using the vector identities and definitions of đ??¸ and đ??ľ in terms of the vector potential, we can get the two Maxwell Equations that don’t depend on sources (the presence of charges or currents). Let’s see what happens when we take the divergence of đ??ľ Xđ?›ť X⃗ â‹… Xđ??ľ X⃗ = đ?›ť XX⃗ â‹… cđ?›ť X⃗ Ă— đ??´ X⃗d The divergence of the curl of any vector is always zero, so: XX⃗ â‹… Xđ??ľ X⃗ = 0 đ?›ť This is our first Maxwell Equation. Now to get the second equation that doesn’t depend on sources, let’s take the curl of the electric field.

XX⃗ X⃗ đ?œ•đ??´ đ?œ•đ??´ XX⃗ Ă— đ??¸ X⃗ = Xđ?›ťâƒ— Ă— Tđ?›ť X⃗ đ??´. − X⃗ Ă— đ?›ť X⃗ đ??´. − Xđ?›ťâƒ— Ă— đ?›ť U=đ?›ť đ?œ•đ?‘Ą đ?œ•đ?‘Ą The curl of a gradient of a scalar is always zero, and the curl of a time derivative is a time derivative of a curl, so we can rewrite this as: đ?œ• XX⃗ Ă— XX⃗ đ?›ť đ??¸ = − XX⃗ đ?›ť Ă— Xđ??´âƒ— đ?œ•đ?‘Ą The curl of the vector potential is the magnetic field, so now we have our second Maxwell equation: XX⃗ đ?œ•đ??ľ Xđ?›ť X⃗ Ă— Xđ??¸ X⃗ = − đ?œ•đ?‘Ą

65

Now the other two equations are a little harder to get. They involve charges and currents and require a little more doing. For this, we have to turn back to the Euler-Lagrange Equations and the field tensor.

Our Euler-Lagrange Equations in tensor notation, with a generalized coordinate đ?œ™, look like this: đ?œ•â„’ đ?œ•â„’ đ?œ•â„’ = 6 *; đ?œ•đ?‘‹ đ?œ•đ?œ™ *, &

Now we need to figure out what our Lagrangian will be in this case. Strictly, this is the Lagrangian density, as the action integral for fields is an integral over space and time.

We need our Lagrangian to obey locality and Lorentz invariance, and it must involve the field tensor somehow, as we need it to relate to the electric and magnetic fields.

For it to obey locality, it must only involve first derivatives. The field tensor is constructed from first derivatives of the vector potential, so using the field tensor in our Lagrangian will be legal.

The next requirement is that our Lagrangian be Lorentz invariant. That just means it has to be a scalar.

In our tensor notation, that means that the indices have to match up (wherever we have an upper index, we also need a lower index). We have two options here. Let’s try the first one, where we just match up the indices in the field tensor: ) đ??š) We quickly realize that this quantity is zero all the time. That represents only the diagonal components of the tensor, which are zero. So, matching up the indices on the tensor isn’t really meaningful, so we won’t include it in our Lagrangian.

The next simplest thing we can try is đ??š)6 đ??š)6 . This does work. We see that the indices match up, for one lower đ?œ‡ there is an upper đ?œ‡, likewise for đ?œˆ. Let’s use this as our Lagrangian. We will actually multiply this by −1/4 as a constant. This is a little bit of foresight, we will see that it cancels later. '

So we have our Lagrangian, â&#x2C6;&#x2019; < đ??š)6 đ??š)6 , and now we plug it into the Euler-Lagrange equations. We will use the vector potential, đ??´) , đ??´6 as our generalized coordinates. *â&#x201E;&#x2019;

*â&#x201E;&#x2019;

*, & '(# ')&

*â&#x201E;&#x2019;

= */

#

'

*/

*/

*/&

*/ #

#

&

â&#x201E;&#x2019; = â&#x2C6;&#x2019; < j*, #& â&#x2C6;&#x2019; *,#& k l*, â&#x2C6;&#x2019; *, m

Letâ&#x20AC;&#x2122;s now go through this case by case. Letâ&#x20AC;&#x2122;s try đ?&#x153;&#x2021; = đ?&#x2018;Ľ: *â&#x201E;&#x2019;

*â&#x201E;&#x2019;

*, & '(* ')&

*â&#x201E;&#x2019;

= */

*

' */

*/

*/&

*/*

â&#x201E;&#x2019; = â&#x2C6;&#x2019; < j *2& â&#x2C6;&#x2019; *,*& k j *2 â&#x2C6;&#x2019; *, k &

66

Now, for this one case of đ?&#x153;&#x2021; = đ?&#x2018;Ľ, letâ&#x20AC;&#x2122;s do đ?&#x153;&#x2C6; = đ?&#x2018;Ś: *â&#x201E;&#x2019; *â&#x201E;&#x2019; *5 '(* '+

*â&#x201E;&#x2019;

= */

*

' */

â&#x201E;&#x2019; = â&#x2C6;&#x2019; < j *2+ â&#x2C6;&#x2019;

*/ +

*/*

k j *2 â&#x2C6;&#x2019; *5

*/* *5

k

An upper space index is the same as a downstairs space index, so we can write our Lagrangian as: $ 1 đ?&#x153;&#x2022;đ??´5 đ?&#x153;&#x2022;đ??´2 â&#x201E;&#x2019;=â&#x2C6;&#x2019; T â&#x2C6;&#x2019; U 2 đ?&#x153;&#x2022;đ?&#x2018;Ľ đ?&#x153;&#x2022;đ?&#x2018;Ś ' ' We wrote â&#x2C6;&#x2019; $ instead of â&#x2C6;&#x2019; < because this term appears twice, when đ?&#x153;&#x2021; = đ?&#x2018;Ľ, đ?&#x153;&#x2C6; = đ?&#x2018;Ś and when đ?&#x153;&#x2021; = đ?&#x2018;Ś, đ?&#x153;&#x2C6; = đ?&#x2018;Ľ.

Letâ&#x20AC;&#x2122;s plug this into our Euler-Lagrange Equation, starting with the left side: đ?&#x153;&#x2022;đ??´5 đ?&#x153;&#x2022;đ??´2 đ?&#x153;&#x2022;â&#x201E;&#x2019; =T â&#x2C6;&#x2019; U */* đ?&#x153;&#x2022;đ?&#x2018;Ľ đ?&#x153;&#x2022;đ?&#x2018;Ś *5

We notice that this is the the same as đ??š25 , which is also the same as đ??š 25 , because you can move space indices up and down. We can do this for other components of đ?&#x153;&#x2C6; and đ?&#x153;&#x2021;, and we get the general version: đ?&#x153;&#x2022;â&#x201E;&#x2019; = đ??š)6 */ #

*, &

So, the full left side of the Euler â&#x2C6;&#x2019; Lagrange equation will be: đ?&#x153;&#x2022; đ?&#x153;&#x2022;â&#x201E;&#x2019; = đ?&#x153;&#x2022;6 đ??š)6 đ?&#x153;&#x2022;đ?&#x2018;&#x2039; 6 */# *, &

*â&#x201E;&#x2019; */ #

Now letâ&#x20AC;&#x2122;s evaluate the right side of the Euler â&#x2C6;&#x2019; Lagrange equation: = 0, because our Lagrangian only has derivatives of đ??´, and no terms with just đ??´.

So we have our Euler-Lagrange equation: đ?&#x153;&#x2022;6 đ??š)6 = 0 Now this is the tensor form of our first two Maxwell Equations which donâ&#x20AC;&#x2122;t depend on sources.

Now letâ&#x20AC;&#x2122;s see what to do when we do have charges and curents.

We have to somehow add in đ??˝) , the four-current vector with đ?&#x153;&#x152;, the charge density as its 0th component, and đ??˝( , current density as the rest of its components. We must add this in in a gauge invariant way, that is, it cannot change the action. It turns out that adding the quantity đ??˝) đ??´) to the Lagrangian doesnâ&#x20AC;&#x2122;t change the action: it is gauge invariant. One could check this by plugging this modified Lagrangian into the action integral and using conservation of charge. So, what will our Euler-Lagrange equations look like with this added term?

67

1 â&#x201E;&#x2019; = â&#x2C6;&#x2019; đ??š)6 đ??š)6 + đ??˝) đ??´) 4

Because we didnâ&#x20AC;&#x2122;t add any more derivatives of đ??´) , the left side of the Euler-Lagrange equation will be the same: đ?&#x153;&#x2022;6 đ??š)6 . The right side this time will not be zero, because we have an đ??´) term in our Lagrangian now. đ?&#x153;&#x2022;â&#x201E;&#x2019; = đ??˝) đ?&#x153;&#x2022;đ??´) So we now have our Euler â&#x2C6;&#x2019; Lagrange equation that includes sources: đ?&#x153;&#x2022;6 đ??š)6 = đ??˝) These are the other two Maxwell equations that depend on sources. In a more familiar notation, they are: XXâ&#x192;&#x2014; đ?&#x203A;ť â&#x2039;&#x2026; XXâ&#x192;&#x2014; đ??¸=đ?&#x153;&#x152; Xâ&#x192;&#x2014; đ?&#x153;&#x2022;đ??¸ Xâ&#x192;&#x2014; = đ?&#x2018;&#x2014; + đ?&#x2018;? $ Xđ?&#x203A;ťâ&#x192;&#x2014; Ă&#x2014; Xđ??ľ đ?&#x153;&#x2022;đ?&#x2018;Ą 3 Conclusion We have outlined one of the known methods of reformulating the Principle of Least Action for fields and then deriving Maxwellâ&#x20AC;&#x2122;s Equations. We see how rich and complete the Principle of Least Action is. This search for a way to derive a specific set of equations brought us along a path of a much more fundamental reformulation of the Principle of Least Action. This process leaves us with the building blocks for other classical field theories, and opens up much more to explore.

4 Appendix: Notation There are two types of indices that appear in the paper. The indices đ?&#x2018;? and đ?&#x2018;&#x203A; runs from 1 â&#x2C6;&#x2019; 3, and represents just spatial coordinates. The indices đ?&#x153;&#x2021; and đ?&#x153;&#x2C6; run from 0 â&#x2C6;&#x2019; 3, and represent space and time coordinates.

This paper uses the Einstein Sum Convention, which is just a shorthand for writing out sums. Whenever an upper and a lower index (being the same index) appear next to each other, that means that the components are matched and summed, like a dot product: đ??´) đ??ľ) = đ??´. đ??ľ. + đ??´' đ??ľ' + đ??´$ đ??ľ$ + đ??´> đ??ľ>

When an upper and a lower index appear together and they are not the same index, they are not summed. The spatial components of an upper index are equal to those of a lower index, but an upper zeroth component is the negative of a lower zeroth component. đ??´( = đ??´( , đ??´. = â&#x2C6;&#x2019;đ??´.

More strictly, there is a difference in how they transform. đ??´7) =

*(, , )# *, &

đ??´6 ,

5 References

*, #

đ??´)7 = *(, , )& đ??´)

Susskind, Leonard. Special Relativity and Classic

68 An Exploration of Spectroscopic Techniques and Their Use in Tandem William T. Mentor: Nicholas Harbison

Abstract Spectroscopy, the study of interactions between matter and electromagnetic radiation, is essential to classification and understanding of molecular structures. However, all spectroscopic techniques have their limitations; we are motivated to investigate a method capable of overcoming some of these weaknesses. Building upon our initial understanding of quantum physics we researched the mechanics behind different spectroscopic techniques, specifically nuclear magnetic resonance (NMR), electron diffraction (ED), and X-ray diffraction crystallography (XRD), analyzing topics such as theoretical descriptions of NMR spectroscopy and basic diffraction theory. After gaining insights into the techniques we examined the practicality and recent applications of techniques combining NMR and ED, finding them capable of mitigating some of the constraints of each method. Of particular interest is the understanding of hydrogen bonding structures and determination of the structures of crystalline polymorphs with similar conformations. We present a summary of the two individual methods, along with a discussion of recent research into their combination. Future directions would include further investigating the mathematical theory behind NMR and ED, and exploring, more in depth, the mechanism and data interpretation methods behind their use together.

Introduction 1.1. Spectroscopy Originating from the study of light’s dispersion through prisms, spectroscopy has since grown into one of the most relevant and widely used fields of science. Since its inception, spectroscopy has been expanded to include any interaction with radiative energy. Although spectroscopy predominantly makes use of electromagnetic radiation, other types of waves such as matter, acoustic, and gravitational can be classified as radiative energy. Data is often represented as an emission spectrum in the frequency or wavelength domain. Spectroscopy’s variety of applications make it an essential tool in physics and chemistry, allowing the study of the composition as well as the physical and electronic structure of matter. There are also a wide variety of applications in the biomedical fields, such as tissue analysis and magnetic resonance imaging.

Two particularly interesting and widely used methods are nuclear magnetic resonance (NMR) and electron diffraction (ED). NMR consists of measuring the precession of a sample’s nuclear spin in a magnetic field, while electron diffraction measures patterns

69

created by electrons incident on the sample. However, all spectroscopic methods have limitations. Owing to the small size of hydrogen atoms, ED methods lead to ambiguity in determining their positions and can also fail to differentiate atoms with similar atomic numbers. With larger crystals NMR signals can become jumbled and difficult to interpret, and both NMR and ED can fail if molecular conformations are too similar.

Other techniques have similar problems â&#x20AC;&#x201D; powder X-ray diffraction (PXRD) requires a large amount of small highly isomorphic crystals with small lattices and X-ray diffraction (XRD) is seldom able to produce diffraction spots on small individual crystals even with high-intensity X-rays.

Given these challenges, there is motivation to develop techniques capable of overcoming these limitations. We investigated a recently developed technique called NMR Crystallography - a combination of NMR, ED, quantum computations, and analyzed some of the most recent applications.

Results 2.1 Diffraction Theory Electron diffraction uses the wave-particle nature of electrons by firing electrons at a crystal and observing the resultant interference patterns as the electrons diffract.

Instruments used, including transmission electron microscopes (TEM) and scanning electron microscopes (SEM), typically accelerate electrons to desired energies by way of electrostatic potentials, which are then diffracted off of a sample crystal.

This technique is very similar to X-ray diffraction and neutron diffraction apart from the type of radiation being used, and hence the three are united under diffraction theory. A basic overview of diffraction theory follows.

2.1.1 Braggâ&#x20AC;&#x2122;s Law

Figure 1 Diagram of diffraction by a crystal. Note that a. the angle between the incident radiation and the plane normal is equal to that between the normal and the diffracted radiation b. the angle between the diffracted and incident radiation is always 2đ?&#x153;&#x192;, called "the diffraction angle."

70

In many techniques involving diffraction by crystals it is important to know the particular condition in which the scattering from crystals and incident radiation is in phase with itself, producing detectable diffraction beams. Furthermore, if the incident radiation of wavelength đ?&#x153;&#x2020; strikes a crystal where all the atoms are placed in a regular periodic array with interplanar spacing đ?&#x2018;&#x2018;â&#x20AC;˛, sufficient intensity is only detected when such a condition is fulfilled. For this purpose, diffraction can be defined using Braggâ&#x20AC;&#x2122;s law: 2đ?&#x2018;&#x2018;â&#x20AC;˛sinđ?&#x153;&#x192; = đ?&#x2018;&#x203A;đ?&#x153;&#x2020;

where đ?&#x2018;&#x203A; is the order of reflection and đ?&#x153;&#x192; is the angle between the incident radiation and the plane normal. This is commonly rewritten as 2đ?&#x2018;&#x2018;sinđ?&#x153;&#x192; = đ?&#x153;&#x2020;

đ?&#x2018;&#x2018;â&#x20AC;˛ where đ?&#x2018;&#x2018; = đ?&#x2018;&#x203A; 2.1.2 Reciprocal Space While Braggâ&#x20AC;&#x2122;s law enables us to describe many diffraction phenomena exhibited by crystals, we still need a more general theory using the vector representation. To this end, we use a concept called the "reciprocal lattice," which is effective for handling all diffraction phenomena.

We first consider the crystal lattice with a unit cell defined by the vectors a1; a2, and a3.

We then obtain the corresponding reciprocal lattice, with unit cell defined by the vectors b1; b2, and b3, given by

Therefore every crystal has two lattices, the real-space lattice in the dimensions of ' đ?&#x2018;&#x2122;đ?&#x2018;&#x2019;đ?&#x2018;&#x203A;đ?&#x2018;&#x201D;đ?&#x2018;Ąâ&#x201E;&#x17D; and the reciprocal lattice in the dimensions of ?#"@!A. A diffraction pattern

produced by a crystal is then a map of the reciprocal lattice, which must then be Fourier transformed into real space. This is due to the fact that the reciprocal lattice represents a lattice in the Fourier space associated with each crystal.

71

2.1.3 Fourier Transforms In order to obtain the data required, often the electron density in real space, we utilize Fourier transforms:

where q represents a point in reciprocal space. This technique is, however, limited by what is called the phase problem. The phase problem is loss of information regarding the phase of the Fourier transform. Generally, the intensities of reflections observed give us the magnitudes, |F(q)|, of the transform but not the phase, with the full transform given by

In order to obtain phases, we collect full sets of reflections with specific alterations performed on the scattering, such as modulating the wavelength. The 2D images taken at different orientations, combined with atomic data allow us to construct our picture in reciprocal space. An ED pattern is displayed in (Fig. 2), along with two computer generated patterns.

2.2 Nuclear Magnetic Resonance Nuclear magnetic resonance, in contrast to diffraction methods, relies on a sampleâ&#x20AC;&#x2122;s nuclear spin and its interactions with magnetic fields. Hence, itâ&#x20AC;&#x2122;s worth noting that due to the fact that nuclei with an even mass number and an even atomic number exhibit no nuclear spin, these nuclei are not applicable to NMR spectroscopy. We will first treat

72

this method fairly classically and then apply a more accurate theory by way of quantum mechanics.

2.2.1 Nuclear Magnetism Nuclear magnetism and NMR spectroscopy are both results of a sampleâ&#x20AC;&#x2122;s intrinsically quantum mechanical nuclear spin angular momentum. Nuclear spin angular momentum is represented by the nuclear spin quantum number, đ??ź. The vector quantity corresponding to nuclear spin angular momentum, characterized by I has magnitude

Quantum mechanics tells us that only one of the three Cartesian components of I can be specified simultaneously with I2 and so by convention we specify the z-component with đ??ź4 = â&#x201E;?đ?&#x2018;&#x161;

with the magnetic quantum number, đ?&#x2018;&#x161;, ranging from đ?&#x2018;&#x161; = (â&#x2C6;&#x2019;đ??ź, â&#x2C6;&#x2019;đ??ź + 1, â&#x20AC;Ś , đ??ź â&#x2C6;&#x2019; 1, đ??ź), giving đ??ź4 2đ??ź + 1 possible values.

Nuclei with nonzero spin angular momentum also have corresponding nuclear magnetic moments. The nuclear magnetic moment is collinear with the vector representing the nuclear spin angular momentum and is given by đ?? = đ?&#x203A;žđ?&#x2018;°

đ?&#x153;&#x2021;4 = đ?&#x203A;žđ??ź4 = đ?&#x203A;žâ&#x201E;?đ?&#x2018;&#x161;

The gyromagnetic ratio, đ?&#x203A;ž, is a constant for a given nucleus. In the presence of an external magnetic field, nuclear spin states have energies given by

with B being the magnetic field vector. A spin then has minimum energy when the projection of đ?&#x153;&#x2021; onto B is maximized. The quantization of nuclear spin results in both the magnetic moment and magnetic energies being quantized, with these quantized energies proportional to the projection of đ?&#x203A;? along B. In the presence of a static magnetic field, the main action of the spin is to precess around the direction of the field, at its quantized energy. For a static field along the đ?&#x2018;§ axis, the convention in NMR, the energies become đ??¸B = â&#x2C6;&#x2019;đ?&#x203A;žđ??ź4 đ??ľ. = â&#x2C6;&#x2019;đ?&#x2018;&#x161;â&#x201E;?đ?&#x203A;žđ??ľ.

where đ??ľ. is the static magnetic field strength. We now define the bulk magnetic

73

moment, M, and the bulk angular momentum J. These are given by the vector sum of the corresponding quantities for each given nuclei. At thermal equilibrium, owing to Zeeman splitting and statistical mechanics, the transverse components of đ?&#x203A;? and I sum to zero. This along with small population differences between energies gives rise to a bulk magnetization parallel to the static magnetic field, which is central to NMR spectroscopy.

2.2.2 Bloch Formalism From a semiclassical standpoint the Bloch model is useful in describing a sample of noninteracting spin-1/-2 nuclei in a static field.

We first consider the torque on the bulk magnetic moment in the presence of a magnetic field, obtaining

We then transition to a frame of reference rotating with respect to our fixed laboratory axis, with the angular velocity of the rotating axis represented by the vector đ?&#x203A;&#x161;. The equations of motion in the laboratory and rotating frames are related by

Hence we see that the equations of motion are the same in both reference frames when the field B(t) is replaced by an effective field

When đ??&#x17D; = â&#x2C6;&#x2019;đ?&#x203A;žđ?? (đ?&#x2018;Ą), the effective field is zero and hence M(t) is time independent in the rotating frame. In the laboratory frame we see that M(t) precesses around B(t) with frequency given by đ?&#x153;&#x201D; = â&#x2C6;&#x2019;đ?&#x203A;žđ??ľ. For a static field, the precessional frequency, or Larmor frequency is đ?&#x153;&#x201D;. = â&#x2C6;&#x2019;đ?&#x203A;žđ??ľ.

We now see that in the absence of other fields, the bulk magnetization precesses at the Larmor frequency around the main static field. This represents a time varying magnetic field, which will produce a detectable electromotive force in a coil of appropriate geometry nearby. However, the collinearity of the bulk magnetization at thermal equilibrium results in no signal being produced. In order to produce a detectable signal, we make use of a short burst of radiofrequency (rf) electromagnetic radiation. These pulses displace the bulk magnetization vector from equilibrium, and when shut off the magnetization is generally no longer parallel to the static field. As a result, the bulk

74

magnetization precesses around the static field with its Larmor frequency at a detectable angle.

We write the magnetic component of an rf field linearly polarized along the x-axis as

Plugging this into our equation of motion, our solution is found by moving to a rotating frame which results in the perturbing field being time independent. The effective field in the rotating frame is given by

đ?&#x203A;Ľđ??ľ. is known as the reduced static field and đ?&#x203A;ş = đ?&#x153;&#x201D;. â&#x2C6;&#x2019; đ?&#x153;&#x201D;CD is the offset.

Figure 3 The orientations of B1, Br, and â&#x2C6;&#x2020;B0 in the rotating frame. Note: tanđ?&#x153;&#x192; =

-! .

.

Upon application of Brf, Mr(t) precesses around the effective field with an angular frequency đ?&#x153;&#x201D;C in the rotating frame, đ?&#x153;&#x201D;C = â&#x2C6;&#x2019;đ?&#x203A;žđ??ľC .

The effective rotation angle is then đ?&#x203A;ź = đ?&#x153;&#x201D; C đ?&#x153;?( =

E " 9% FGHI

.

If đ?&#x153;&#x201D;CD is equal to đ?&#x153;&#x201D;. then the radiation is on-resonance. When the radiation is onresonance, offset is zero, đ??ľC = đ??ľ' , and in the rotating frame the effective field is collinear with Brf (t). Hence the influence of the main static magnetic field has been removed, and bulk magnetization precesses around the axis defined by the Brf (t) field.

From here on out the rotating frame will be assumed unless otherwise specified

75

Figure 4 Precession of the magnetization around the effective field in the rotating reference frame. a The effect of an applied rf field with y-phase. b The effect of an on-resonance rf field, with Br along the y-axis and Mr rotating in the x-z plane orthogonal to Br. J

An ideal one-pulse experiment is one that achieves a $ rotation of M(t). While a discussion of this will be reserved for later, itâ&#x20AC;&#x2122;s worth noting that the maximum transverse magnetization is achieved by such a rotation, with the relevant pulse being a J pulse. After such a pulse, the magnetization will not continue to evolve in the $ transverse plane forever. In order to account for the signal decay, Bloch defined two processes. The first takes into account the state population movement back to thermal equilibrium and is called spin-lattice relaxation. Bloch assumed that this decay took the form

with đ?&#x2018;&#x2026;' being the spin-lattice relaxation rate constant. The second relaxation process is called spin-spin relaxation and takes into account decay of transverse magnetization in the x-y plane.

where đ?&#x2018;&#x2026;$ is known as the spin-spin relaxation rate constant.

76

By combining these two relaxation expressions with our original equation of motion for the magnetization we obtain the Bloch Equations, written here in matrix form

Brf (t) is commonly applied for a time đ?&#x153;?( << 1/đ?&#x2018;&#x2026;$ and 1/đ?&#x2018;&#x2026;' , simplifying the Bloch equations to

If both đ??ľ' and đ?&#x153;&#x2122; are not time dependent then the solution is represented by a series of rotations given by the rotation matrices, a discussion of which will be avoided here.

Now we return to the previously mentioned one pulse experiment. The maximum transverse magnetization, and hence maximum NMR signal, is detected when the bulk magnetization is perpendicular to the static field. An rf pulse of strength đ??ľ' , duration đ?&#x153;?( , and tilt angle đ?&#x153;&#x192; = đ?&#x153;&#x2039;/2 along the y-axis (đ?&#x153;&#x2122; = đ?&#x153;&#x2039;/2) results in the following magnetization after the pulse:

where đ?&#x203A;ź is the rotation angle and đ?&#x2018;&#x20AC;. is the equilibrium magnetization. Hence by adjusting the rotation angle, we can calculate where our magnetization will precess to.

J J For example, a $ pulse will rotate our magnetization $ degrees.

After the pulse is turned off the magnetization precesses around the static field during the acquisition period. This signal, called the free induction decay (FID), is composed of two components which are given by the Bloch equations in the rotating frame for the case of free precession (absence of an rf field).

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with the damping exponential factor resulting from the relaxation of the bulk magnetization.

Usually both parts of this complex signal are detected, taking the form of đ?&#x2018; K = đ?&#x153;&#x2020;đ?&#x2018;&#x20AC;K (đ?&#x2018;Ą), where đ?&#x153;&#x2020; is an experimentally determined constant. This is then Fourier transformed, L

đ?&#x2018;&#x2020;(đ?&#x153;&#x201D;) = 1 đ?&#x2018; K (đ?&#x2018;Ą)exp â&#x2C6;&#x2019; {đ?&#x2018;&#x2013;đ?&#x153;&#x201D;đ?&#x2018;Ą} đ?&#x2018;&#x2018;đ?&#x2018;Ą .

outputting

đ?&#x2018;Ł(đ?&#x153;&#x201D;) = đ?&#x153;&#x2020;đ?&#x2018;&#x20AC;.

đ?&#x2018;&#x2026;$$

đ?&#x2018;&#x2026;$

+ (đ?&#x203A;ş â&#x2C6;&#x2019; đ?&#x153;&#x201D;)$

along with a complex component. The function đ?&#x2018;Ł(đ?&#x153;&#x201D;) represents a absorptive Lorentzian lineshape, and is what is typically displayed as the NMR spectrum (Fig. 5).

Figure 5 The NMR spectrum of L-Histidine-B.

2.2.3 Quantum Mechanical NMR Spectroscopy Armed with this classical model, we now present a brief quantum mechanical description of the one pulse experiment. The initial state of our system is described via the equilibrium density operator. At thermodynamic equilibrium we assume that our nuclear spin states are at equilibrium with the lattice. By extension the values of the probability distribution, đ?&#x2019;Ť(đ?&#x153;&#x201C;) are constrained such that the populations of the stationary states take the form of a Boltzmann distribution. In addition, we require that the density matrix is diagonal at equilibrium due to the fact that the different subensembles are uncorrelated. These requirements lead us to

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which in the high temperature limit can be approximated to

đ?&#x2018; represents the dimensionality of the Hilbert space. For example, for đ?&#x2018;&#x20AC; spin -1/2 nuclei đ?&#x2018; = 2M . However, this term is a constant that doesnâ&#x20AC;&#x2122;t affect the NMR experiment and is usually not written. Removing this term and writing in the Zeeman Hamiltonian we obtain M

đ?&#x153;&#x17D;

#N

= â&#x2C6;&#x2019;ÂŞ OP'

â&#x201E;?đ?&#x153;&#x201D;. đ?&#x2018;&#x2DC; đ??ź đ?&#x2018; đ?&#x2018;&#x2DC;% đ?&#x2018;&#x2021; O4

The complex magnetization recorded during the acquisition period is given by

đ?&#x2019;Š is volume density of the number of spins, and F+ is

For a single spin, we have that đ?&#x153;&#x17D; #N â&#x2C6;? đ??ź4 and hence the effect of a pulse with x-phase and a rotation angle đ?&#x203A;ź applied to đ??ź4 is

J

when đ?&#x203A;ź = $ this becomes

This is identical to the result we expect via the Bloch model. We now consider the evolution of the â&#x2C6;&#x2019;đ??ź5 magnetization under the Zeeman Hamiltonian (in the rotating frame) â&#x201E;&#x2039;4 = đ?&#x203A;şđ??ź4

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Following this out, with the derivation omitted here, we obtain

đ?&#x153;&#x17D;(đ?&#x2018;Ą) = đ??ź2 sin đ?&#x203A;şđ?&#x2018;Ą â&#x2C6;&#x2019; đ??ź5 cos đ?&#x203A;şđ?&#x2018;Ą

Not only does this allow us to calculate the magnetization, it also implies that magnetization with a

positive resonance offset in the rotating frame precesses in the clockwise direction, looking along the â&#x2C6;&#x2019; đ?&#x2018;§ axis.

We can now calculate our detectable magnetization for a one-pulse sequence for a single isolated spin:

Hence our quantum mechanical formalism once again outputs the form expected using the Bloch model in the absence of relaxation.

3. NMR Crystallography Although both of these techniques are highly useful in their own right, individual spectroscopic methods can be insufficient to determine some structures. Having already discussed weaknesses of each technique, we turn our attention to the relative strengths. Unlike PXRD and XRD, the strong scattering power of electrons allows ED to observe diffraction patterns from micro to nanosized single crystals, even in mixtures of powders. In analyzing chemical shift values NMR can provide valuable information regarding hydrogen bonding and atom assignments. As hydrogen is one of the primary atoms we can magnetize, itâ&#x20AC;&#x2122;s natural that we can collect thorough data on it. For the same reasons, NMR also permits direct measurements of carbon, and nitrogen atoms, removing uncertainty in atomic assignments. Therefore, a combination of NMR and ED is a powerful approach for understanding crystal structures and hydrogen bonding networks, overcoming the limitations of each individual technique. ED is used to determine the nanocrystal structure, permitting the use of 3D reciprocal space using diffraction tomography and continuous rotation methods, while NMR is used for direct measurement of atoms via fast magic-angle sample spinning. Quantum computations are then used to link NMR chemical shifts to crystal structures.

One such use of this technique was applied by GuzmĂĄn-Alfonso et al. (2019) to determine the structure of and elucidate the hydrogen-bonding networks in L-Histidine as well as cimetidine form B, the structure of which was previously unknown. These studies further developed methods previously employed by Oikawa et al. (2017) and Martineau-Corcos et al. (2018).

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In the case of L-Histidine, the initial structure was solved from ED patterns (Fig. 6) collected while continuously rotating the sample around a single axis. To cover missing sections of data the patterns of five crystals were combined using computer software.

The obtained lattice parameters were đ?&#x2018;&#x17D; = 5.27(5), đ?&#x2018;? = 7.44(5), and đ?&#x2018;? = 18.99(8) all in angstroms. The space group was determined to be đ?&#x2018;&#x192;2'$"!" , and the crystal was found to exhibit orthorhombic symmetry. However, the solved molecule contained missassigned carbon, nitrogen, and oxygen atoms and many of the hydrogen atoms were missing. Even detected hydrogen atoms were shown to be inaccurate. Further refinement of the atom assignments with preexisting data, ambiguity in the structure remained. In accordance with the NMR crystallography approach, gauge included projected augmented wave calculations (GIPAW) were used. GIPAW calculations optimize a crystal structure by relaxing the atomic positions to local energy surface minima as well as providing isotropic chemical shifts and quadrupolar couplings.

Application of NMR methods to solve for the hydrogen positions, along with the use of GIPAW calculations revealed the most energetically favorable structure.

Figure 6 Select ED patterns of L-Histidine during continuous rotation. The number on each frame corresponds to the starting rotation angle of the pattern, with patterns obtained every 1.18â&#x2C6;&#x2DC; .

Similar strategies were used in the determination of cimetidine form B (CB). Cimetidine exhibits polymorphic behavior, with crystal forms B and C displaying very similar 13C chemical shifts (Fig. 7). Using the same method used for L-Histidine the initial crystal structure was solved using several sets of ED patterns. Three sets of data were merged to form the final structure. CB was shown to belong to the space group đ??ś2/đ?&#x2018;? and possessed monoclinic crystal symmetry with parameters đ?&#x2018;&#x17D; = 55.45(15), đ?&#x2018;? = 5.0, đ?&#x2018;? = 18.72(6), and đ?&#x203A;˝ = 100.4(5)â&#x2C6;&#x2DC; . However, there were still 2 conformations included in the crystal structure, and 4 candidate models were considered. The hydrogen positions and bond lengths were calculated and refined via NMR however, determination of the correct structure was still prevented. GIPAW calculations once again revealed the most energetically favorable structure, which was then validated by evaluating root-meansquare deviation values for chemical shifts.

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Figure 7 a 1D 13C NMR spectra of a mixture of cimetidine form B and C. b 2d 1H-13C spectra over the full spectral range. Regions of interest, as indicated by the blue and orange regions are expanded.

Discussion As a cutting-edge technique that is rapidly developing, much research is still being done to develop the field of NMR crystallography. As research by Oikawa et al. (2017), Guzmán-Afonso et al. (2019) and Martineau-Corcos et al. (2018). has shown, NMR crystallography is an extremely promising technique. The complimentary properties of ED and NMR permitting the differentiation of similar crystal conformations and elucidation of hydrogen-bonding networks have very powerful implications, paving the way for the determination of previously unknown structures and finding important applications in the field of spectroscopy.

References 1. Oikawa, T., Okumura, M., Kimura, T., & Nishiyama, Y. (2017). Solid-state NMR meets electron diffraction: determination of crystalline polymorphs of small organic microcrystalline samples. Acta Crystallographica Section C Structural Chemistry, 73(3), 219–228. https://doi.org/10.1107/s2053229617003084 2. Guzmán-Afonso, C., Hong, Y.-L., Colaux, H., Iijima, H., Saitow, A., Fukumura, T., … Nishiyama, Y. (2019).

Understanding hydrogen-bonding structures of molecular crystals via electron and NMR nanocrystallography. Nature Communications, 10(1). https://doi.org/10.1038/s41467-019-11469-2 3. Waseda, Y. (2014). X-ray diffraction crystallography. Springer.

4. Cavanagh, J. (2008). Protein NMR spectroscopy: principles and practice. Academic Press.

5. Comparison of Crystallography, NMR and EM. Creative Biostructure. https://www.creativebiostructure.com/comparison-of-crystallography-nmr-and-em_6.htm.

6. Martineau-Corcos, C. (2018). NMR Crystallography: A tool for the characterization of microporous hybrid solids. Current Opinion in Colloid & Interface Science, 33, 35â&#x20AC;&#x201C;43. https://doi.org/10.1016/j.cocis.2018.01.009

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“Let’s Pretend That…”: The Role of Dramatic Play in Language Development Lily S.-K. Mentor: Virtue Sankoh

Abstract The goal of this project was to explore how dramatic play aids language development among preschoolers. Dramatic play involves some form of representation of a scenario or “acting-as-if,” which involves the need to negotiate roles and coordinate actions, recruiting the use of a range of verbs as well as commentary and stage directions (e.g., I’m the baby; you be the mommy). Taking on and negotiating roles encourages children to practice more advanced linguistic forms. Developmentally, dramatic play is most prominent between the ages of three and five and entire preschool curricula are designed around it because of the evidence for its critical importance to children’s development. Observing at the Saint Ann's Preschool, as well as analyzing online videos of children at play, I gathered clips demonstrating interactions such as those which reproduced family scenarios ranging from cooking dinner to taking a trip to Japan. In conclusion, the role of dramatic play in language development is critical; it's a way for children to be contentedly engaged while learning novel vocabulary and practicing social interactions requiring the use of language.

Introduction I’m captivated by young children, specifically preschoolers around the ages of three to five, and how they create their unique imaginative play as well as how they develop cognitively. I wanted to tie these two interests together and what better way to do so than assessing how their play helps their cognitive development. I focused mainly on how dramatic play aids language development. Dramatic play implicates reenactment and pretending; it can be a reenactment of a situation that a child has seen, heard or read about, or derived from the child’s imagination, like an alternative reality that they project. There have been many prior explorations on the subject matter of how significant dramatic play is in children's development. Further, because of the evidence for its critical importance, entire preschool curricula are designed around pretend play. According to The National Association for the Education of Young Children: “Highlevel dramatic play produces documented cognitive, social, physical and emotional benefits.” The American Association of Pediatrics also says, “Play is essential to development...so important…that it has been recognized by the United Nations High Commission for Human Rights as a right of every child.” Thus, I decided to explore how much dramatic play does in fact help language development, an idea already theorized.

I started off by reading studies and experiments. As I was reading, I found that there was controversy on the topic of whether language helps kids play better, or whether play helps kids learn language better. This is a concept that is still being discussed today, as there is not definite proof on which helps which. However, I decided to take action myself by going to the Saint Ann’s preschool weekly, observing the kids play

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dramatically, and taking videos to analyze and transcribe later. Unfortunately, due to Coronavirus I was unable to do as much observing at the Saint Ann's Preschool as I would have liked to; however, I started examining online clips of children at play. Throughout all my research and observing it proved clear to me how critical the role of dramatic play is in language development. Even though there is still controversy on how helpful it really is and how much to incorporate it in preschools, there is no doubt that it is extremely captivating for children and a beneficial way for them to learn language and participate socially.

Background & Methods Developmentally, dramatic play is first seen around eighteen months in the form of object substitution, which is when one object is used as a stand-in for another. A classic example of this is a banana used for a telephone.

There are many other forms of dramatic play, most prominent between the ages of 3 and 5, the supposed “high season”; there is pretend with invisible objects, which is entirely in the child’s imagination, enactment play (e.g., dressing up as mommy and cooking with plastic food in a play kitchen), replica play: (e.g., using a doll in a doll house), and imaginary companions. However, enactment play is seen most.

Object substitutions in play are strongly linked to language learning and their absence can be a diagnostic marker of language delay. Props serve as symbols for real objects and this relationship between a prop and the object it represents, resembles the relationship of a word to its referent. Because both play and language share a representational character, play provides children with opportunities to practice forming symbolic relationships. Children also learn better using visual representations; by pretending a banana is a telephone, they are more likely to remember what a telephone is in the future. Frequency of symbolic play at thirteen months relates to the diversity of the child’s speech at twenty months.

Dramatic play also includes intense social encounters, and social interactions in play feed into language development. In sociodramatic play, children establish a play frame (e.g., going to the store) and collaborate to create it. Such frames often involve the need

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to negotiate roles and coordinate actions, which typically recruits the use of a range of verbs (e.g., want, explain). Further, children often switch back and forth between speaking within the play frame (Can you give me some milk?) and providing commentary or stage directions (I’m the baby; you be the mommy). These two activities, taking on roles and negotiating, encourage children to practice more advanced linguistic forms than they would use in other interactions.

Another factor that indicates why dramatic play helps language development is that the amount of language children hear and use strongly relates to their overall linguistic skills. Further, playing with others will bolster language development since it encourages greater language use. Increased time spent talking during play with peers in preschool, positively relates to the preschoolers’ vocabulary size in kindergarten, as well as to measures of early literacy and better comprehension.

Dramatic play is important for language development because when children are in control of an interaction they are engaged; they speak about and listen to what interests them. Similarly, a child is more likely to learn novel vocabulary items when an adult follows their interest as opposed to making the child follow the adult’s interest. When children learn solely by listening to a teacher or adult talk the information is not as likely to stay with them. However, when children take part in dramatic play, they tend to reenact things they have already seen or heard, so a strategy a lot of teachers use is to give children prior information and background knowledge about a certain subject that they can then base their pretend play off of. By doing this they will understand and remember the information better.

Observations & Results I captured enactment play and object substitution in full action through one of the videos I took at the Saint Ann’s Preschool. In the video, one of the preschoolers is pretending to be a mom and call the doctor about her sick baby, an example of enactment play, while her classmate is using a block as a “stinger” to play “bad guy,” an example of object substitution.

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The preschooler who is reenacting a scenario of a baby being sick, probably has observed something similar in her own life and is incorporating it into her play.

Moreover, she is experiencing what is around her and further learning it by using it.

Later in the same clip two preschoolers negotiate what they want to play. The first boy says to the other, “Do you want to play bad guy?” The second boy responds, “No, let’s play stinger!” The teacher then intervenes and gives them a different approach to their game by changing the wording but still having it be within the parameters. She says, “Why don't you play good guy?” However, they decide not to listen, and proceed to sting everyone in sight, although they did practice language and the skill of negotiating by deciding what they wanted to play.

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I investigated the strategy a lot of teachers had been using about giving children prior background knowledge about a certain subject that they can then use in their dramatic play to solidify the information. I watched an online video of a preschool that was based around dramatic play as a main way of teaching. In one of the classes, the teacher decided to explain baking, and did so through a dramatic game. Maureen Ostroff, the teacher said, “We read a nonfiction book about baking. When I asked them what they knew about baking, they kept on telling me, ‘You cook, you cook, you cook.’...Our dramatic play was a bakery this time. We tried it with just pictures on the wall to help them understand these concepts of cooking and working together and whose job is what.” She then goes on to show two kids arguing about who gets to put their cookies in the oven, and another teacher stepping in to resolve their conflict with the use of language: Teacher: “Alright Mia put those in the oven. And then she’s going to share with you.”

Child: “Tiffany go there.”

Teacher: “Well, say Tiffany excuse me please.”

Child: “Tiffany excuse me, please.”

Teacher: “I have to put my cookies in the oven.”

Child: “I have to put my cookies in the oven.”

Teacher: “See she moved for you, go ahead.”

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The little girl had to use language to get what she wanted in the dramatic play and she succeeded. This therefore reinforced the use of that particular language and next time she will most likely use it again since it worked. Sometimes it is important that teachers

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assist children when they’re interacting with one another, and help them have conversations, share ideas, and collaborate to create play themes. Later in the same clip of the bakery, object substitution is shown: Narrator: “They were using a lot of symbolic imaginary play; they were asking for money.”

Child: “I need three dollars. Three dollars. Thank you!”

Narrator: “They were pretending to go into their pocket and pull out the money... Even though everything else was very realistic, those were one of the parts that were very symbolic that they could use their imagination for...it is so important for them to use their brain and that higher-level thinking.”

The teaching of numbers is also shown using a kitchen timer: Teacher: “Alright I’m going to set the timer. It says how many minutes?”

Child: “Five.”

Teacher: “It says three.”

Child: “Three.”

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The sheer amount of language input in the bakery dramatic play helped the preschoolers learn immensely. They learned about different kitchen appliances, how to read a timer, ask for money for their cookies, as well as how to talk with their peers and negotiate different play scenarios. They were also learning about real life situations; most of them have probably seen someone in their family bake or cook before, and now they learned, through pretend play, how to do the same and will understand baking when they see it next.

Pretend play is also an extremely useful way to teach kids who have learning disabilities or autism since it’s engaging and they’re learning through enactment. One of the online videos I observed was of a teacher trying to teach language through dramatic play to a child with autism. They were set up with baby dolls, beds, plastic food, and a play bathtub. The strategy the teacher was using was to show an object and say what it was repeatedly until the child understood. She would also use actions to represent verbs.

For example, she would scrub the baby doll in the bathtub and say, “scrub, scrub, scrub,” or “wash, wash, wash.” The repetition, visual representations and constant engagement was extremely useful, for the little boy was indeed learning language.

When he would pick up plastic food, the teacher would say the name of it while he was looking at it. Throughout the video he was actively participating, following her words, and then repeating them himself.

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Discussion & Future Directions Due to Coronavirus, I did not get the chance to observe that much at the Saint Annâ&#x20AC;&#x2122;s Preschool. I plan to continue my research next year. Some of the questions I was hoping to further explore were: How do preschoolers express their emotions and what they are thinking through their play? How do children work through difficult things in their

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personal lives through their play? These two questions can be examined through the preschooler who called the doctor for her sick baby. Is she scared of getting sick, or has she been sick before and taken care of? Another question I was interested in was how does play influence and form friendships. This can be looked at through those two little boys who were negotiating what they wanted to play and that friendship forming from the decision to play â&#x20AC;&#x153;stinger.â&#x20AC;?

Language for young kids is mostly learned through hearing and observing and then reinforced by usage, which could be a dramatic scenario or game. The most important thing when kids are learning language is just for them to be actively using it, and so that is why dramatic play is seen so widely as one of the best ways. However, there are many other strategies for language development, and I hope to be able to research and compare them to dramatic play.

Iâ&#x20AC;&#x2122;m also interested in gender roles in dramatic play. Why do girls and boys have mostly different ways of expressing their dramatic play? I think what they are reading and watching around them, as well as the toys they are given at a young age, relate to how they play dramatically. Sadly, most girls are given dolls and things to dress up with, while boys are given toys and action figures that they can play "bad guy" with. The shows they watch and books they read usually have each gender defined into a very "stereotypical" role, for example Disney princess movies, and further what they are seeing they will use in their play. However, at the Saint Ann's preschool there is actually a merge between how boys and girls play dramatically; there are a few boys who love to play dress up and cook in the kitchen, as well as a few girls who love to play "stinger" or monster.

The final aspect that interested me was how preschools in lower-socioeconomic areas include dramatic play and how the preschoolers there play differently from the Saint Ann's preschoolers, as well as looking into the difference in their language development.

I assume if preschoolers do not partake in dramatic play, or play at all for that matter, that there will be some sort of delay for them, whether in language or just in the ability to interact with others. However, all kids have imaginations, and so even if their preschool does not focus on dramatic play, which many well-known preschools do not, they are probably still getting it in some sense, whether at home with siblings, or just by themselves using dolls or imaginary friends.

Conclusion What I would like to do next year is home in even more on the growth of language in dramatic play. I would do this by starting at the beginning of the year and focusing on two or three kids who I immediately noticed were playing dramatically. I would then track their language progression throughout the year and compare it to other kids who did not participate in as much, if any, dramatic play.

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Bibliography Lillard, A. S., Lerner, M. D., Hopkins, E. J., Dore, R. A., Smith, E. D., & Palmquist, C. M. (2013). The impact of pretend play on children's development: A review of the evidence. Psychological bulletin, 139(1), 1.

Ramani, G. B. (2012). Influence of a playful, child-directed context on preschool children's peer cooperation. Merrill-Palmer Quarterly (1982-), 159-190.

Smith, P. K. (2011). Observational methods in studying play. In The Oxford handbook of the development of play.

Weisberg, D. S. (2015). Pretend play. Wiley Interdisciplinary Reviews: Cognitive Science, 6(3), 249-261.

Twawick-Smith, Jeffery, narr (2015). The Bakery - Supporting Children to Succeed in the Dramatic Play Center. EarlyChildhoodVideos.

Responsive Interactions for Pretend Play, (2015). Vanderbilt EBIP.