2014 rosandic and paar codon sextets with leading role of serine create ideal symmetry by Eppur si muove

Gene 543 (2014) 45–52

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Codon sextets with leading role of serine create “ideal” symmetry classiﬁcation scheme of the genetic code Marija Rosandić a, Vladimir Paar a,b,⁎ a b

Croatian Academy of Sciences and Arts, Zrinski trg 11, 10000 Zagreb, Croatia Faculty of Science, University of Zagreb, Bijenička 32, 10000 Zagreb, Croatia

a r t i c l e

i n f o

Article history: Received 6 March 2014 Accepted 3 April 2014 Available online 5 April 2014 Keywords: Genetic code Amino acids Codon symmetries Codon sextets Evolution

a b s t r a c t The standard classification scheme of the genetic code is organized for alphabetic ordering of nucleotides. Here we introduce the new, “ideal” classification scheme in compact form, for the first time generated by codon sextets encoding Ser, Arg and Leu amino acids. The new scheme creates the known purine/pyrimidine, codon–anticodon, and amino/keto type symmetries and a novel A + U rich/C + G rich symmetry. This scheme is built from “leading” and “nonleading” groups of 32 codons each. In the ensuing 4 × 16 scheme, based on trinucleotide quadruplets, Ser has a central role as initial generator. Six codons encoding Ser and six encoding Arg extend continuously along a linear array in the “leading” group, and together with four of six Leu codons uniquely define construction of the “leading” group. The remaining two Leu codons enable construction of the “nonleading” group. The “ideal” genetic code suggests the evolution of genetic code with serine as an initiator. © 2014 Elsevier B.V. All rights reserved.

1. Introduction In 1943, Schrödinger proposed in his lectures at the Trinity College in Dublin that the hereditary material must take the form of an “aperiodic crystal” (Schrödinger, 1944). In a metaphoric sense this could imply the presence of symmetries in the structure of DNA. This was a guiding idea in several studies of genetic code. Here we consider amino acids encoded by six codons as generators of symmetries underlying the pattern of classification scheme of the genetic code. The nucleic acid code for protein synthesis is composed of four different nucleotides, U, C, A, and G, assembled in linear arrays that are read as 64 three-nucleotide codons. The 61 codons code for 20 amino acids and the remaining three (UAG, UGA, and UAA) code for stop signals, and the codon AUG for Met also codes for the start codon and most of the amino acids are specified by multiple codons (Craig et al., 2010). Five amino acids are encoded by four codons to fill out the same four-codon box, where the first two nucleotides in codons are sufficient for their specification. Three amino acids, Ser, Arg and Leu, are specified by six codons, and each includes combination of codons from two different boxes, four codons from one and two from another box. The empirically determined codon–amino acid catalogue usually is displayed as a scheme of alphabetically organized table, referred to as the standard genetic code (Nirenberg et al., 1965, Nirenberg, 2004; Woese, 1965). In this scheme the U, C, A, G nucleotides are used to Abbreviations: D, direct; RC, reverse complement; C, complement; R, reverse. ⁎ Corresponding author at: Faculty of Science, University of Zagreb, Bijenička 32, 10000 Zagreb, Croatia. E-mail address: paar@hazu.hr (V. Paar).

label consecutively the first, second and third positions in codons. Codons are grouped into boxes or families of four codons that mutually differ only in nucleotide at the third position within each codon. In general, a box is not split if the nucleotides at the first two positions in codons are of the type NC or SK (N = any nucleotide, S = strong bases (C,G), and K = keto bases (G,U)) (Lagerkvist, 1978; Nikolajewa et al., 2005); otherwise, a box is split. In some boxes there is a “binary splitting”, that is a quartet of codons within a box loses codons in pairs. Similarly, some pairs of codons split into singlets. In light of this, the amino acids of multiplicities different from 4 can be considered as arising from combinations 4 = 2 + 2, 2 = 1 + 1, 6 = 4 + 2, and 3 = 2 + 1 (Bashford et al., 1998). Thus, an outstanding feature of the genetic code is degeneracy (more than one codon associated with the same amino acid). The appearance of degeneracy in science generally is a consequence of some kind of symmetry that acts as an organizing principle. In analogy, possible symmetries have been considered for genetic code (Antonelli and Forger, 2011; Bashford et al., 1998; Findley et al., 1982; Forger and Sachse, 2000; Forger et al., 1997; Hornos and Hornos, 1993; Kozirev and Khrennikov, 2010; Michel and Pirillo, 2013; Ramos et al., 2010). In some studies, classification scheme of the genetic code was reorganized using alternative nucleotide orders or purine–pyrimidine contents (Fimmel et al., 2013; Jimenez-Montano, 2009; Nikolajewa et al., 2005; Wilhelm and Nikolajewa, 2004; Zhang and Yu, 2011) or permutation of nucleotides at some positions within codons (Itzkovitz and Alon, 2007). A classification scheme introduced by Wilhelm and Nikolajewa (Nikolajewa et al., 2005; Wilhelm and Nikolajewa, 2004), was based on purine–pyrimidine binary encoding of nucleotides (Yagil, 2004), with eight binary triplets. This allows the genetic code to be represented using an 8 × 4 matrix; each element corresponds to two codons where

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the third position is important only as purine or pyrimidine (in the binary manner). Thus the 32 binary codon space was used. In that representation several symmetries have been identified (Nikolajewa et al., 2005; Wilhelm and Nikolajewa, 2004). Zhang and Yu (2011) suggested that the six-fold degenerate codons and their amino acids could have important balancing roles for error minimization. A number of theories on the origin and evolution of the genetic code were proposed (Chechetkin and Lobzin, 2009; Di Giulio, 2005,2008; Freeland et al., 2003; Glazebrook and Wallace, 2012; Knight and Landweber, 2000; Knight et al., 2001; Koonin, 2010; Koonin and Novozhilov, 2009; Maizels and Weiner, 1987; Novozhilov et al., 2007; Rodin et al., 2011; Szathmary, 1999; Vetsigian et al., 2006; Woese, 1965; Wong, 1975,1976; Yang, 2005). It was pointed out that a real understanding of the code origin and evolution is likely to be attainable only in conjunction with a credible scenario for the evolution of the coding principle itself and the translation system (Koonin and Novozhilov, 2009). 2. Materials and methods A new classification scheme of the genetic code is constructed by combining three codon sextets encoding Ser, Arg, and Leu amino acids into a compact pattern with mutually connected sextets, serving as a core for the full 64-codon scheme. 3. Results 3.1. “Ideal” sextet's classification scheme of the genetic code Our guiding idea in creating the new classification scheme of the genetic code is the use of three codon sextets (Ser, Arg, Leu) as initial generators, Ser having the central role. This represents a novel mechanism

of creating the classification scheme. In this process we include pairing of A + T rich and C + G rich codons according to the trinucleotide classification in the framework of recent trinucleotide studies (Rosandić et al., 2011, 2013a, 2013b). The three sextets as initial building blocks for creation of the new scheme of the genetic code generate by themselves the patterns of A + U rich/C + G rich, purine–pyrimidine, weak–strong and amino–keto symmetries. In this approach, the symmetries are a consequence of sextet's dynamics. This approach also establishes a compact connected pattern of all three sextets that was not achieved previously. The new scheme (Table 1) is named the “ideal” sextet's classification scheme of the genetic code (in short, the “ideal” scheme). This scheme has the form of a 16 × 4 codon matrix that can be expressed in a block form as the 4 × 4 matrix of 4-codon boxes, forming the two 32-codon groups. They will be referred to as the “leading” and “nonleading” groups, respectively. Each group consists of A + U rich and C + G rich columns. An approach with “binary” A + U rich/C + G rich representation is in accordance with the general trinucleotide framework from Rosandić et al. (2013b). Each column is composed of four successive four-codon boxes. Each box is characterized by nucleotides at the first two positions in constituent codons, while the difference between codons is only at the third position. The pattern of box structure in “ideal” scheme differs from the standard classification scheme of the genetic code (Nirenberg et al., 1965, Nirenberg, 2004; Woese, 1965), and from the purine–pyrimidine classification scheme (Nikolajewa et al., 2005; Wilhelm and Nikolajewa, 2004). The differences of the “ideal” scheme with respect to the previous schemes are in combinations and ordering of boxes and in ordering of constituting codons within boxes. The “ideal” scheme is determined by biochemical properties of sextets, in contrast to the classification scheme of the standard genetic code where the alphabetic key was used for nucleotides within codons.

Table 1 “Ideal” classiﬁcation scheme of the genetic code created by sextets. “Leading” group Amino acid Box 1

“Nonleading” group I. AU rich

Start/Met AUG ————————————— AUA

II. CG rich

Amino acid

GCA GCG Ala

Ile

Box 2

Box 3

Box 4

AUC GCU AUU GCC ——————————————————————————————— — UAC CGU Tyr UAU CGC ————————————— Stop UAG CGA ————————————— Arg Stop UAA CGG ————————————— — GAG AGA Glu GAA AGG ——————————————————————————————— GAC AGU Asp GAU AGC ————————————— CUC UCU Ser CUU UCC Leu CUG UCA CUA

Amino acid

UCG

Val

III. AU rich

IV. CG rich

GUG

ACA

GUA

ACG

Amino acid

Purine- pirimidine representation code 101 101

Thr

GUC ACU GUU ACC ————————————————————————————————— CAC UGU His Cys CAU UGC ————————————————————————————————— CAG UGA Stop Gln —————————————— CAA UGG Trp ————————————————————————————————— AAG GGA Lys AAA GGG ——————————————— Gly AAC GGU Asn AAU GGC ————————————————————————————————— UUC CCU Phe UUU CCC ——————————————— Pro — UUG CCA Leu UUA CCG

100 100 010 010 011 011 111 111 110 110 000 000 001 001

Italics—A + U rich codons; bold—C + G rich codons; columns I and III—predominantly A + U rich columns; columns II and IV—predominantly C + G rich columns; columns I and II—“leading” group of codons; columns III and IV — “nonleading” group of codons; purine–pyrimidine binary representation of codons (last column) — purines (G,A)/code 1, pyrimidines (C,U)/code 0. Codons in the same row have equal purine–pyrimidine representation code.

M. Rosandić, V. Paar / Gene 543 (2014) 45–52 Table 2 First step of constructing “ideal” classiﬁcation scheme of the genetic code combining 3 × 6 codons encoding Ser, Arg, and Leu amino acids.

STANDARD

PUR - PYR

“IDEAL”

SCHEME

SCHEME LG

Col. IV

Box 1

3.2. Construction of the “ideal” sextet's classiﬁcation scheme of the genetic code 3.2.1. Construction of sextet's core The key for constructing the new scheme is to combine two mutually separated codon segments of Ser: the four-codon box of Ser (denoted by Ser(4)): • • • •

UCU UCC UCA UCG

and the two-codon segment of Ser (denoted by Ser(2)), that is in the standard scheme dispersed to a distant box: • AGU • AGC.

A(4)

A(2)

Box 2

Box 3

S(2) A

S(4) L(2)

L(4)

A Box 4

Positions of codons fromSer, Arg and Leu amino acids in thematrix of “ideal” classiﬁcation scheme are shown. Codons at the remaining positionswithinmatrix are determined using this “core” of three codon sextets and the symmetry properties.

The “ideal” classification scheme is generated by combination of six codons encoding each of Ser, Arg and Leu amino acids (Table 2). The initial generator of the whole “leading” group is Ser. The initial Ser and the linearly extended Arg cover three successive boxes from below in column II, and in conjunction with four of six Leu codons at the bottom of column 1 they define the whole “leading” group of 32 codons. All codons assigned to Ser and Arg are aligned in continuous array over three boxes. The remaining two of six Leu codons provide a “seed” for constructing the “nonleading” group of 32 codons in the “ideal” scheme. In the “ideal” scheme the regions covered by all three codon sextets are mutually connected, which is not the case for standard and purine–pyrimidine classification schemes (Fig. 1). Combining the three sextets we obtain the main symmetry pattern of the “ideal” scheme. The four columns of the “ideal” scheme satisfy the following regularity: i) Box 2 = complement of box 1, and box 4 = complement of box 3. ii) Column 2 = purine–pyrimidine transform (A ↔ G, C ↔ U), and column 4 = purine–pyrimidine transform of column 3. iii) Successive pairs of each row have the same purine–pyrimidine binary codes. iv) Columns 3 and 4 are obtained by purine– pyrimidine transformation of nucleotides at the first position in codons from columns 1 and 2, respectively. We show that the sextets “transfer” these regularities to the whole scheme.

Box 1 ——————————————————————————————————————————————— Box 2 ↑ CGU Arg(4) CGC CGA CGG ——————————————————————————————————————————————— Box 3 ↑ AGA Arg(2) AGG ↑ AGU Ser(2) AGC ——————————————————————————————————————————————— Box 4 ↑ Leu(4) CUC UCU Ser(4) CUU UCC CUG UCA UUG Leu(2) CUA ← UCG → UUA

Col. III

Col. II

Col. I

NLG

“Nonleading” group

“Leading” group

Fig. 1. Comparison of positions covered by three codon sextets (encoding Ser, Arg and Leu) in three different classification schemes of the genetic code, standard (Nirenberg, 2004; Nirenberg et al., 1965), purine–pyrimidine based (Nikolajewa et al., 2005) and “ideal” scheme based on codon sextets (Table 1). LG — 16 × 2 codon positions in the “leading” group; NLG — 16 × 2 codon positions in the “nonleading” group; amino acids — S = Ser, L = Leu, A = Arg. Ser(4), Arg(4), and Leu(4) — the filled four-codon boxes of Ser, Arg, and Leu, respectively. Ser(2), Arg(2), and Leu(2) — the two-codon pairs from half-filled codon boxes of Ser, Arg, and Leu, respectively.

For Leu there are two codon segments: the four-codon box of Leu (to be denoted by Leu(4)): • • • •

CUC CUU CUG CUA

and the two-codon pair of Leu (to be denoted by Leu(2)): • UUG • UUA that is in the standard scheme dispersed to a distant box. With respect to the standard scheme of genetic code, the ordering of codons is reversed within Leu(2) and within both codon pairs in Leu(4), which has no effect on the genetic code. It is seen that Leu(4) is equal to the (A ↔ G + C ↔ U) purine–pyrimidine transform of Ser(4): Leuð4Þ ¼ ƒ ðA↔G þ C↔UÞ Serð4Þ where ƒ(A ↔ G + C ↔ U) stands for the A ↔ G + C ↔ U transformation of all nucleotides within codons to the right of it, i.e., within codons in Ser(4). Also, Leu(2) can be expressed as: Leuð2Þ ¼ ƒ 23 ðA↔G þ C↔UÞ Serð4Þlp where ƒ23(A ↔ G + C ↔ U) stands for the A ↔ G + C ↔ U transformation of nucleotides at the second and third positions within the lower pair of codons in Ser(4), that are denoted by Ser(4) lp. This

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positions Leu(2) to the bottom of column 3, i.e., to the lower half of box 4 in column 3. It should be pointed out that the symmetry transformations employed in construction of the “ideal” scheme, like f(A ↔ G + C ↔ U), are not an external input into the scheme, but they arise automatically due to the structure of codons encoding the sextets. The Leu(4) and Ser(4) are positioned as box 4 in columns I and II, respectively (Table 2). The transformation between box 4 in column I and box 4 in column II is generalized to all corresponding boxes in columns I and II, and referred to as Rule 1: Rule 1: ðcolumn IÞ ¼ ƒðA↔G þ C↔UÞ ðcolumn IIÞ: Next, Ser(2) represents anticodons of the lower pair of codons in Ser(4), i.e., of Ser(4)lp: Serð2Þ ¼ g ðA↔U þ C↔GÞ Serð4Þlp where g(A ↔ U + C ↔ G) stands for the A ↔ U + C ↔ G transformation of all nucleotides within codons to the right of it. Now we extend linearly Ser(2) above Ser(4) (Table 2). Then, Ser(2) represents the lower codon pair in box 3 (from above) in column II. Together, Ser(4) and Ser(2) represent the compact 6-codon array encoding Ser. Let us now combine into the “ideal” scheme the third sextet, Arg. In the standard genetic code Arg consists of two distinct codon segments: the four-codon box (denoted by Arg(4)): • • • •

CGU CGC CGA CGG

and a two-codon segment that is from another distinct box from the standard scheme (denoted by Arg(2)): • AGA • AGG. It is seen that Arg(2) contains anticodons of the upper pair of codons from Ser(4) (denoted by Ser(4)up): Argð2Þ ¼ g ðA↔U þ C↔GÞ Serð4Þup : In this way we obtain in column II the combined 4-codon box • Arg(2) • Ser(2) forming the box 3 in column II. It is seen that this box is a complement of box 4 from column II. This gives rise to Rule 2a: Rule 2a: ðbox 3 in column IIÞ ¼ g ðA↔U þ C↔GÞ ðbox 4 in column IIÞ: Above box 3 we align the remaining 4-codon segment of Arg, i.e., Arg(4), that becomes box 2 in column II. 3.2.2. Construction of complete “leading” group (columns I and II) From Table 2 it is seen that the construction of sextet's core provides box 4 in column I and boxes 2–4 in column II of the “leading” group. The remaining four boxes belonging to the “leading” group are constructed by using symmetry transformations as follows. Rule 2a, relating box 4 and box 3 in column II, is extended to Rule 2b that relates box 1 and box 2:

Rule 2b: ðbox 1 in column IIÞ ¼ g ðA↔U þ C↔GÞ ðbox 2 in column IIÞ: Therefore, box 1 in column 2 is obtained as complement of box 2 (i.e., of Arg(4)): • • • •

GCA GCG GCU GCC.

These are just four codons encoding Ala. In this way, column 2 from the “ideal” scheme is completed. In the next step, we complete column 1 by applying Rule 1. In this way we construct box 1, box 2 and box 3 from column 1 by transforming box 1, box 2 and box 3 from column 2, respectively. Comparing so constructed boxes 1–3 from column 1 to the codon–amino acid catalogue, we see that the ensuing box 1 contains Start/Met codon (AUG) and three codons encoding Ile; box 2 contains two codons encoding Tyr and two stop codons (UAG, UAA); and box 3 contains two codons encoding Glu and two encoding Asp. Thus we construct the “leading” group of 32 codons (columns I and II) in the “ideal” scheme from Table 1. 3.2.3. Construction of “nonleading” group (columns III and IV) The construction of the remaining 32 codons forming the “nonleading” group is straightforward. The key link that enables transformation of the “leading” group into the “nonleading” group is provided by the Leu(2) pair of codons in the lower half of box 4 in column 3. Extending Rule 1 to columns 3 and 4, the codons from Leu(2) are mapped into the pair of codons CCA and CCG in the lower half of box 4 in column IV. These codons represent two out of four codons encoding Pro in the standard codon–amino acid catalogue. Adding on top of CCA and CCG the remaining two codons encoding Pro (CCU and CCC), box 4 is constructed in column 4. By transforming this box using purine– pyrimidine transformation (i.e., extending Rule 1 to columns III and IV), the two Phe codons (UUC, UUU) are obtained in column III above Leu(2). Thus, box 4 in column 3 is completed. Analogously as for columns 1 and 2, extending mapping Rule 2a to columns III and IV, box 4 from columns III and IV is mapped into its respective box 3 complements. By comparison to the codon–amino acid catalogue, we see that in column III the upper half of box 3 corresponds to codons encoding Lys, and the lower half to codons encoding Asn, while the four codons in box 3 from column IV encode Gly. In this way, the lower half of all four columns is constructed. Inspecting these results, a simple rule emerges for mapping of the lower half of columns I and II into the lower half of columns III and IV: the ﬁrst nucleotide in every codon from columns I and II is mapped according to the purine–pyrimidine transformation A ↔ G + C ↔ U, while the second and third nucleotides remain unchanged. Using the same transformation, the upper half of columns I and II is transformed into the upper half of columns III and IV. Thus we obtain codons encoding Val in box 1 from column III, and in box 1 from column IV codons encoding Thr. In box 2 from column III we obtain codons encoding His in the upper and encoding Gln in the lower half, and in box 2 from column IV codons encoding Cys (in upper half), and codons Stop (UGA) and Trp (UGG) (in lower half). As seen, the “ideal” scheme has a simple relation between “leading” codon group (columns I and II) and the “nonleading” group (columns III and IV): Rule 3: ð“Nonleading”groupÞ ¼ f 1 ðA↔G þ C↔UÞ ð“Leading”groupÞ where f1(A ↔ G + C ↔ U) is the purine–pyrimidine transformation

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that acts only on the first nucleotide in codons from the “leading” group, leaving the second and third nucleotides unchanged. In this way, the 18-nucleotide codon sextet's “core” from Table 2 is extended to the complete 64-nucleotide “ideal” classification scheme from Table 1 by using two transformations based on purine–pyrimidine symmetry (Rule 1 — column I to column II mapping, and rule 3 — columns I and II to columns III and IV mapping); and the weak–strong/codon–anticodon symmetry (Rules 2a and 2b — box 3 to box 4 and box 1 to box 2 mappings, respectively, within each column). 3.3. Intra-purine (A ↔ G) and intra-pyrimidine (C ↔ U) symmetry Symmetry between columns in Table 1: Column II is the A ↔ G + C ↔ U transform of column I. Analogously, column IV is the A ↔ G + C ↔ U transform of column III. Furthermore, column III can be obtained from column I by performing the A ↔ G + C ↔ U transformation of the first nucleotide in each codon. All four columns in the “ideal” scheme have mutually identical purine–pyrimidine binary code representation (A,G → 1 and U,C → 0) of the “ideal” classification scheme. Symmetries in the purine/pyrimidine binary representation: row 1 = row 2, row 3 = row 4, … row 15 = row 16 (Table 1, last column). The upper half (rows 1–8) of binary representation = lower half (rows 9–16) for the first and third nucleotides, while the binary representation of the middle nucleotide is changed by 1 ↔ 0 exchange. 3.4. Construction of complete “leading” group (columns I and II) Binary representation of rows 1–4 (box 1) = (1 ↔ 0) map of rows 5–8 (box 2), and of rows 9–12 (box 3) = (1 ↔ 0) map of rows 13–16 (box 4). A purine–pyrimidine symmetry and codon–anticodon symmetry were found previously in the purine–pyrimidine classification scheme, which differs from the “ideal” scheme due to different organization of boxes in columns and of codons within boxes (Nikolajewa et al., 2005). It should be noted that in the “ideal” scheme the symmetries are automatically generated by amino acid sextets.

Table 3 Transformation of codons from “ideal” scheme of genetic code into the A + T rich/C + G rich trinucleotide classiﬁcation. A E

BRC

Codons

1 2 3 4 5 6 7 8

(101: AUG, AUA, GCA, GCG, GUG, GUA, ACA, ACG) (100: AUC, AUU, GCU, GCC, GUC, GUU, ACU, ACC) (010: UAC, UAU, CGU, CGC, CAC, CAU, UGU, UGC) (011: UAG, UAA, CGA, CGG, CAG, CAA, UGA, UGG) (111: GAG, GAA, AGA, AGG, AAG, AAA, GGA, GGG) (110: GAC, GAU, AGU, AGC, AAC, AAU, GGU, GGC) (000: CUC, CUU, UCU, UCC,UUC, UUU, CCU, CCC) (001: CUG, CUA, UCA, UCG, UUG, UUA, CCA, CCG)

B A + U rich trinucleotides

C + G rich trinucleotides

Subgroup Ia

Subgroup IIa

1 AUG 4 UGA 4 UAG

3 CAU 8 UCA 8 CUA

3 UAC 2 ACU 2 AUC

1 GUA 6 AGU 6 GAU

3 CGU 2 GUC 2 GCU

1 ACG 6 GAC 6 AGC

1 GCA 4 CAG 4 CGA

3 UGC 8 UCG 8 UCG

Subgroup Ib

Subgroup Ic

Subgroup Ib

Subgroup Ic

UAA 4 AAU 6 AUA 1 ACA 1 AAC 6 CAA 4 AAG 5 GAA 5 AGA 5 AAA 5

8 UUA 2 AUU 3 UAU 3 UGU 2 GUU 8 UUG 7 CUU 7 UUC 7 UCU 7 UUU

GCC 2 CCG 8 CGC 3 CAC 3 CCA 8 ACC 2 CCU 7 UCC 7 CUC 7 CCC 7

6 GGC 4 CGG 1 GCG 1 GUG 4 UGG 6 GGU 5 AGG 5 GGA 5 GAG 5 GGG

(A) Purine–pyrimidine enumeration (E = 1 to 8) assigned to trinucleotides from A + U rich/C + G rich classiﬁcation scheme. Enumerations 1 to 8 correspond to eight possible binary representation codes (BRC). Italics: A + U rich codons; bold, C + G rich codons. (B) A + T rich/C + G rich trinucleotide classiﬁcation (Rosandić et al., 2013a, 2013b) and the corresponding purine–pyrimidine binary representation according to panel A.

3.5. A + U rich ↔ C + G rich symmetry The “ideal” classification based on serine as initial generator (Table 1) spontaneously exhibits a high degree of A + U rich ↔ C + G rich symmetry of codons, in accordance with A + T rich/C + G rich trinucleotide classification (Rosandić et al., 2013b) (with T replaced by U). The “leading” and “nonleading” codon groups are organized into two pairs of highly symmetric predominantly A + U rich and C + G rich columns (I, III and II, IV, respectively). The A + U rich columns I and III contain twelve A + U rich and four C + G rich codons each, while the C + G rich columns II and IV contain twelve C + G and four A + U rich codons. Each of the A + U rich columns I and III contains 16 A, 16 U, 8 C and 8 G nucleotides, while each of the C + G rich columns II and IV contains 16 C, 16 G, 8 A and 8 U nucleotides, reflecting a high degree of symmetry. Besides the 12 A + U rich codons, each of columns I and III contains 4 C + G rich codons that are characterized by an A or U nucleotide at the middle position (2 A and 2 U). Analogously, besides the 12 C + G rich codons, each of columns II and IV contains 4 A + U rich codons which are characterized by C or G nucleotides in the middle position (2 C and 2 G). Positions of A + U rich and C + G rich codons are diagonally symmetric, forming in the “leading” and “nonleading” groups the 2 × 2 A + U rich boxes (italics), 2 × 2 C + G rich boxes (bold) and 2 × 4 mixed blocks (alternating italics/bold), exhibiting a high degree of A + U rich/C + G rich symmetry. Deep symmetry based on intra-purine A ↔ G and intra-pyrimidine U ↔ C transformation is also reflected in the symmetry within the A + U rich/C + G rich trinucleotide classification from Rosandić

et al. (2013b). The eight purine/pyrimidine enumerations of codons (1–8) (Table 3A), are attributed to the corresponding trinucleotides in the A + U rich/C + G rich trinucleotide classification scheme (Table 3B). Codons with the same purine/pyrimidine binary code are attributed the same purine/pyrimidine enumeration (E). Purine/pyrimidine symmetry is mapped to trinucleotide classification. We find the symmetry among purine/pyrimidine enumerations in the classification scheme with respect to direct–reverse complement–complement– reverse ordering (D–RC–C–R). For example, the purine–pyrimidine enumeration of the A + U rich subgroup Ia is equal to the D ↔ RC + C ↔ R transform of enumeration corresponding to the C + G rich subgroup IIa. In this sense the genetic code can be related to the trinucleotide scheme from Rosandić et al. (2013b). Thus the purine/pyrimidine symmetry is transferred to the whole DNA, including both coding and noncoding.

3.6. Intra-weak (A ↔ U) and intra-strong (G ↔ C) codon symmetry The “ideal” scheme (Table 1) automatically exhibits a feature of intra-weak (A ↔ U) and intra-strong (G ↔ C) codon symmetry. Within each column: box 2 is a complement of box 1, and box 4 is a complement of box 3. Just this symmetry leads to the privileged position

M. Rosandić, V. Paar / Gene 543 (2014) 45–52

of six codons encoding Ser, providing its leading function in creating the “ideal” scheme. The weak–strong binary code representation (A,U → 0 and C,G → 1) of the “ideal” scheme shows additional symmetries:

Table 4 Codons (D) from A + U rich (I, III) and C + G rich columns (II, IV) in “ideal” classiﬁcation scheme of the genetic code and their complement (C), reverse (R) and reverse complement (RC) transforms. Amino acid

- within each box: row 1 = row 3, and row 2 = row 4; - between boxes: box 1 in column I = box 4 in column III, box 1 in column II = box 4 in column IV, box 1 in column III = box 3 in column I, box 1 in column IV = box 4 in column II, box 2 in column I = box 3 in column III, box 2 in column II = box 3 in column IV, box 2 in column III = box 4 in column I, box 2 in column IV = box 4 in column II. 3.7. Intra (A ↔ C) and (G ↔ U) amino–keto codon symmetry For amino–keto binary code (A,C → 0 and G,U → 1) representation of the “ideal” scheme there are several symmetries: - within each box: row 1 = row 4, and row 2 = row 3; - between boxes within each column box 1 = (1 ↔ 0) transform of box 2, box 3 = (1 ↔ 0) transform of box 4. - between boxes in different columns box 1 in column I = box 2 in column II, box 2 in column 1 = box 1 in column II, box 1 in column III = box 2 in column IV, box 2 in column III = box 1 in column IV, box 3 in column I = box 4 in column II, box 4 in column I = box 3 in column II, box 3 in column III = box 4 in column IV; box 4 in column III = box 3 in column IV. 3.8. Reverse and reverse complement symmetry Reverse and reverse complement symmetries of “ideal” scheme involve sizeable dispersions and do not preserve rows or columns. Example for reverse transform (RT): RT of AUG (box 1, row 1, column I) = GUA (box 1, row 2, column III), RT of AUC (box 1, row 3, column I) = CUA (box 4, row 4, column I), RT of AUU (box 1, row 4, column I) = UUA (box 4, row 4, column III), RT of GCA (box 1, row 1, column II) = ACG (box 1, row 2, column IV), RT of GCU (box 1, row 3, column II) = UCG (box 4, row 4, column II), RT of GCC (box 1, row 4, column II) = CCG (box 4, row 4, column IV). 3.9. Symmetry violating splitting of block pattern within the “ideal” scheme Without the “leading” group of 32 codons it is not possible to form uniquely the remaining “nonleading” group of 32 codons, even under condition of A ↔ G, U ↔ C purine–pyrimidine pairing, because of possible multiple choices. Namely, pairs of neighboring boxes from the “nonleading” group are closed entities, and there is no unique way of vertical connection. Only encompassing six-codon amino acids, each covering one and a half boxes, the two neighboring boxes linearly aligned in the same column providing a vertical connection, and the third aligning horizontally according to the “ideal” scheme, generating the unique “leading” codon group that simultaneously provides a key for creation of the “nonleading” group. This necessary condition is satisﬁed by box splitting in the sextets. Splitting of boxes is necessary to enable establishment of multiple symmetry scheme of genetic code and is an important factor to enable the coding of 20 amino acids.

Column 1, A + U rich D Start/Met AUG D Ile AUA D Ile AUC D Ile AUU C Tyr UAC C Tyr UAU C Stop UAG C Stop UAA D Glu GAG D Glu GAA D Asp GAC D Asp GAU C Leu CUC C Leu CUU C Leu CUG C Leu CUA

UAC Tyr UAU Tyr UAG Stop UAA Stop AUG Start AUA Ile AUC Ile AUU Ile CUC Leu CUU Leu CUG Leu CUA Leu GAG Glu GAA Glu GAC Asp GAU Asp

GUA Val AUA Ile CUA Leu UUA Leu CAU His UAU Tyr GAU Asp AAU Asn GAG Glu AAG Lys CAG Gln UAG Stop CUC Leu UUC Phe GUC Val AUC Ile

CAU His UAU Tyr GAU Asp AAU Asn GUA Val AUA Ile CUA Leu UUA Leu CUC Leu UUC Phe GUC Val AUC Ile GAG Glu AAG Lys CAG Gln UAG Stop

Column 3, A + U rich D Val GUG D Val GUA D Val GUC D Val GUU C His CAC C His CAU C Gln CAG C Gln CAA D Lys AAG D Lys AAA D Asn AAC D Asn AAU C Phe UUC C Phe UUU C Leu UUG C Leu UUA

CAC His CAU His CAG Gln CAA Gln GUG Val GUA Val GUC Val GUU Val UUC Phe UUU Phe UUG Leu UUA Leu AAG Lys AAA Lys AAC Asn AAU Asn

GUG Val AUG Start CUG Leu UUG Leu CAC His UAC Tyr GAC Asp AAC Asn GAA Glu AAA Lys CAA Gln UAA Stop CUU Leu UUU Phe GUU Val AUU Ile

CAC His UAC Tyr GAC Asp AAC Asn GUG Val AUG Start CUG Leu UUG Leu CUU Leu UUU Phe GUU Val AUU Ile GAA Glu AAA Lys CAA Gln UAA Stop

Column 2, C + G rich D Ala GCA D Ala GCG D Ala GCU D Ala GCC C Arg CGU C Arg CGC C Arg CGA C Arg CGG D Arg AGA D Arg AGG D Ser AGU D Ser AGC C Ser UCU C Ser UCC C Ser UCA C Ser UCG

CGU Arg CGC Arg CGA Arg CGG Arg GCA Ala GCG Ala GCU Ala GCC Ala UCU Ser UCC Ser UCA Ser UCG Ser AGA Arg AGG Arg AGU Ser AGC Ser

ACG Thr GCG Ala UCG Ser CCG Pro UGC Cys CGC Arg AGC Ser GGC Gly AGA Arg GGA Gly UGA Stop CGA Arg UCU Ser CCU Pro ACU Thr GCU Ala

UGC Cys CGC Arg AGC Ser GGC Gly ACG Thr GCG Ala UCG Ser CCG Pro UCU Ser CCU Pro ACU Thr GCU Ala AGA Arg GGA Gly UGA Stop CGA Arg

Column 4, C + G rich D Thr ACA D Thr ACG D Thr ACU D Thr ACC C Cys UGU C Cys UGC C Stop UGA C Trp UGG D Gly GGA D Gly GGG D Gly GGU D Gly GGC C Pro CCU C Pro CCU C Pro CCA C Pro CCG

UGU Cys UGC Cys UGA Stop UGG Trp ACA Thr ACG Thr ACU Thr ACC Thr CCU Pro CCC Pro CCA Pro CCG Pro GGA Gly GGG Gly GGU Gly GGC Gly

ACA Thr GCA Ala UCA Ser CCA Pro UGU Cys CGU Arg AGU Ser GGU Gly AGG Arg GGG Gly UGG Trp CGG Arg UCC Ser CCC Pro ACC Thr GCC Ser

UGU Cys CGU Arg AGU Ser GGU Gly ACA Thr GCA Ala UCA Ser CCA Pro UCC Ser CCC Pro ACC Thr GCC Ala AGG Arg GGG Gly UGG Trp CGG Arg

Symmetrical codons (the same nucleotide at the ﬁrst and third positions, underlined), reproduce themselves in reverse mode. Arg has two symmetrical codons (CGC, AGA). Bold — C transformation reproduces codons encoding Ser four times (UCA, UCG, AGU, AGC). Italics — start/stop codons reproduced within the R,C-quartets.

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3.10. Codons and R,C-quadruplet structure Besides considering genetic code and its constituents, one should also take into account the fact that each codon is associated with four possible forms of appearance, as direct (D), complement (C), reverse (R) and reverse complement (RC), referred to as R,C-quadruplet. Such process enables that the same codon for a particular amino acid can appear as C, R or RC transform of some other codon corresponding to another amino acid, providing an increase of probability of its expression (Table 4). Each A + U rich codon generates its C, R, and RC transforms which are also A + U rich and analogously, each C + G rich codon generates C + G rich transforms. In this sense, for the same amino acid as a direct form the largest number of contributing codons is arising from the neighboring complement box acting as a balance. This means, for example, that Ser generates over C, R and RC transformations ﬁve codons for the neighboring Arg (2 × AGA, AGG, 2 × CGA). Codons from each box from A + U rich column generate through the RC and R transforms the codons distributed in both A + U rich columns. The analog situation appears for codons from the C + G rich columns generating codons distributed in both C + G rich columns. None of the boxes is excluded, revealing a strict internal symmetry of the code.

4. Discussion A fundamental question is: “What was the ordering in which the amino acids were added to the code in the evolutionary process?” Namely, the combination of three sextets accompanied by purine/ pyrimidine (A ↔ G + U ↔ C) and weak/strong (A ↔ U + C ↔ G) pairing as an important aspect of genetic code is not the result of only an interesting intellectual effort how to obtain a perfect symmetry among codons, but may also shed more light on evolutionary processes. So created code seems to exclude the “frozen accident” hypothesis (Crick, 1968) as a way of origin and contributes in favor of gradual evolutionary processes of creation. We hypothesize that the genetic code could have been developing gradually as follows. The first amino acids were generated according to the needs for those proteins that were built in the first living organisms. It could be presumed that the process took place according to the law of “supply and demand”. As we showed, the “leading” group of the “ideal” classification scheme of the genetic code is created by six-codon sets encoding Ser and Arg plus four out of six codons encoding Leu, with Ser in a privileged position. In fact, Ser is the only amino acid that simultaneously determines vertically (along the same column) the position of Arg, because of sharing a common box, and horizontally the position of Leu, positioning its four-nucleotide box through purine/pyrimidine symmetry. The priority of Ser as a “leader” in evolution of genetic code is also seen with R,C-quadruplets including C, R, and RC transforms of codons corresponding to amino acids and start/stops (Table 4). The “privileged” position of Ser arises from the fact that its six codons are extended over two neighboring boxes that are in direct ↔ complement relation (UCU, UCC, UCA, UCG/AGA, AGG, AGU, AGC). The two of its own codons (AGU, AGC) generate Ser itself by C, R, RC transformations additionally four times (UCA ↔ AGU, UCG ↔ AGC). From the other amino acids, this privilege has only once those amino acids that contain codons with the same nucleotide at the first and third positions (for example, ACA, GAG, CGC) when the direct and reverse codons are identical (Table 4, underlined codons). Such a codon encoding Ser is UCU. By self-generation over C, R, RC transformations, Ser is less dependent on transformation of codons from other amino acids and has a dominant role in the code. It should be stressed that the 64 codons are not completely autonomous: there are 16 primary codons, being transformed during crossing over in meiosis into their reverse, complement and reverse complement, and vice versa. In this sense, codons can be considered as a set of 16 quadruplets.

It is important to stress that sextets are the only amino acids extending beyond a single box, and as such the only able to create genetic code characterized by profound symmetries and providing guidelines for primordial molecular evolution. In particular, Ser satisfies the role of “leadership” since it optimally contains needed symmetries: equal number of A + U rich (AGU, UCU, UCA) and C + G rich codons (AGC, UCC, UCG), that are present in alternating order. Two codons are extended beyond a single box, exhibiting purine–pyrimidine symmetry (AG ↔ UC at the first two nucleotide positions within codons in half filled and filled boxes, and U ↔ C at the third nucleotide position within the half filled box), direct/complement symmetry (AGU and AGC codons in half filled box are complements of UCA and UCG codons in the filled box), and simultaneously exhibiting symmetry with respect to the filled Leu box from the first column, with respect to Arg codons linearly extended in the second column to another box and with respect to the remaining two-codon Leu segment. Ser is the only amino acid satisfying all these conditions. Transformation within the same codon quadruplet is seen for Ser and its biochemically important roles and connections to other amino acids. Ser, Asp and Thr are the primary sites of linkage of sugars to proteins, forming glycoproteins. Reversible phosphorylation of peripheral serine and threonine residues of enzymes is also involved in regulation of energy metabolism and fuel storage in the body (Taniguchi, 2005). Ser, Arg and Thr in “ideal” genetic code are in direct relation because two codons encoding Arg (AGA, AGG) are complements of two codons encoding Ser (UCU, UCC), and codon ACU encoding Thr is a reverse complement of codon AGU encoding Ser. Immediately after Ser the demand for Leu during evolution was larger than four codon positions that were at disposal, while the other boxes from the “leading” group were already formed and occupied, including the box containing start AUG. Therefore the remaining two codons encoding Leu occupied two codon positions from the “nonleading” group on the opposite side. We note that just by this procedure the determination of the “nonleading” group became possible. For difference with respect to the unique “leading” group generated by sextets, the “nonleading” group consists of 4 × 2 boxes which are mutually in purine/pyrimidine correlation, but every pair of boxes makes an entity by itself. Therefore, without the two transferred A + U rich Leu codons (UUG, UUA) it would not be possible to reproduce uniquely the ordering of boxes. Higher probability for coding has also amino acids containing more of C + G rich codons, as for example Arg, Ala, Gly and Pro, more abundantly represented in C + G rich coding DNA. It is interesting how the start/stop codons are generated in the frame of “ideal” scheme. According to this scheme, the stop UAG and stop UAA are purine/pyrimidine partners of CGA and CGG encoding Arg and probably created in combination with Arg. The start AUG had an evolutionary path together with Ile and Ala and probably was generated from the very start overtaking Leu. In this way, the three start/stop codons, AUG, UAG, and UAA originated with the “leading” group. Only the stop UGA originated with the “nonleading” group, and could be generated from Ser over AGU (reversed) and UCA (reverse-complement). This is showing dynamical reversible function of start/stop codons. For example, let us take that in one generation in some gene there is a codon AGU or UCA, while in the next generation, due to crossing over, through reverse or reverse complement transformation they can transform into stop codons and thus in that locus they may interrupt the synthesis of Ser. In the next generation the process may be reversible. Such dynamical transformations of start/stop codons during generations could explain immense richness of variations within the same species (Rosandić et al., 2013b). In conclusion, it could be hypothesized that the three six-codon sets encoding Ser, Arg and Leu played a primary role in creation of “ideal” multiple symmetry genetic code, with Ser having the initiating role. Connection between codons and amino acids was established evolutionary on the basis of higher order symmetries, purine/pyrimidine, codon–anticodon and A + U rich/C + G rich that are created by three

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