Maximal Genetic Code Symmetry Is a Physicochemical Purine–Pyrimidine Symmetry Language for Transcription and Translation in the Flow of Genetic Information from DNA to Proteins

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article describes the maximal genetic code symmetry as a physicochemical purine-pyrimidine symmetry language for transcription and translation in the flow of genetic information from DNA to protein.

To improve the manuscript, the authors should take the following considerations:

(1) The authors should provide and discuss genetic code modeling, specifically highlighting the p-adic approach, which can describe many properties of the genetic code. The primary mathematical tool is a p-adic distance, which adequately describes similarities within the genetic code. The authors should discuss applying the mathematical method to other sequences with a bioinformatic content.

(2) The authors should provide and discuss error-tolerant coding, specifically error-detecting and error-correcting codes, from a theoretical biology point of view.

The submitted manuscript has significant scientific insights and the conclusions are soundly supported by the fundamental comprehension of the genetic code structure. However, the manuscript requires major revisions before being accepted in the well-circulated International Journal of Molecular Sciences.

Author Response

This article describes the maximal genetic code symmetry as a physicochemical purine-pyrimidine symmetry language for transcription and translation in the flow of genetic information from DNA to protein.

To improve the manuscript, the authors should take the following considerations:

(1) The authors should provide and discuss genetic code modeling, specifically highlighting the p-adic approach, which can describe many properties of the genetic code. The primary mathematical tool is a p-adic distance, which adequately describes similarities within the genetic code. The authors should discuss applying the mathematical method to other sequences with a bioinformatic content.

(2) The authors should provide and discuss error-tolerant coding, specifically error-detecting and error-correcting codes, from a theoretical biology point of view.

The submitted manuscript has significant scientific insights and the conclusions are soundly supported by the fundamental comprehension of the genetic code structure. However, the manuscript requires major revisions before being accepted in the well-circulated International Journal of Molecular Sciences.

A comprehensive answer was given to both questions from the reviewer in the Discussion section of the manuscript, rows:               554-609:

The genetic code regulates how the translation system decodes the 61 genetic codons into 20 natural amino acids along with 3 termination signals in process of proteinogenesis. The genetic code is degenerate because more than one type of codon encodes a single amino acid. In general, degeneracy is associated with mathematical group theoretical structure [16-21]. The algebraic approach to the SGC was proposed with the aim of explaining the degeneracies encountered resulting by a sequence of symmetry breaking. However, the evolution of the genetic code through the progressive symmetry breaking by using the group theoretical structure proposes that, in the beginning, it was not possible to distinguish the function of codons which therefore all encoded the same information. With the consecutive creation of amino acids during such proposed evolution, the number of codons within the degeneracy groups gradually decreased into two singlets (Methionine/start signal and Tryptophane), nine doubles, two triplets (Isoleucine and 3 stop signals), five quadruplets, and three sextets. 

The degeneracy distribution considers only the number of codons for each amino acid according to Nirenberg’s empirical result, without including any physicochemical affinity between bases and codons [7]. However, the degeneracy of amino acids coding takes place of the most crucial and enigmatic aspects to this day. For example, some authors created also a new theory based on symmetry principles of code degeneracy and hypothesized that the primitive pre-early code had codons of four bases. Only 32 codons of 256 possible combinations (44) had some symmetries with amino acids degeneracy 2, and the rest asymmetric codons with amino acids degeneracy 4 [22].  This mathematical model based also on number theory starting from extant variants of the last universal common ancestor (LUCA) which was the first to have the universal genetic code with three-nucleotides codons [22-25] like the present Standard genetic code.

Despite of genetic code degeneracy all symmetries including double mirror symmetry and purine-pyrimidine symmetry net of the SSyGC table remain unchanged for all RNA and DNA living species (Subsect. 2.7, Figs. 4 and 7.2.). 

Negadi 2023 [26] presented a novel approach to studying the genetic code’s mathematical and chemical structure revealing the genetic code symmetries through computations involving Fibonacci-like sequences. He found a full mathematical and chemical connection with the “ideal sextet’s classification scheme” of our Ideal Genetic Code table [27]. He examined the total number of hydrogen in side of chains of all amino acids 61 sense codons from Ideal Genetic Code table and “the hydrogen and atoms numbers as “seeds” of three sextets (Serine, Arginine and Leucine), which will create the entire hydrogen atom and even nucleon content of the whole set of amino acids and will also play a prominent role mathematical and (chemically inspired) “seeds” in computing the chemical content of the twenty amino acids, including degeneracy”. The same author in 2024 [28] presented also Fibonacci-like sequences to examine the symmetries of our Supersymmetry Genetic Code table which derived from the Ideal Genetic Code table [6], in a charged physiological state of amino acids in a pH environment around 7.4 testing the efficiency of his method of atom content in unraveling relationships with the genetic code with vertical and horizontal mirror symmetry axis between all purines and pyrimidines of the whole code. 

Breslauer et al. 1986 [29.] and Klump et al 2020 [30] measured free energy of codons using spectroscopic and calorimetric techniques and concluded that free energy of each codon is equal to the free energy of its reverse complement. Inserted these values in mitochondrial human genetic code table they were randomly scattered. The authors analyzed the free energy of codons in the SGC table. We show that the mirror symmetry of the SSyGC table, DNA quadruplets and our classification of codons and trinucleotides are perfectly imbedded in the mirror symmetry energy code as well as identical mirror symmetry from free energy values for all four members of DNA quadruplets and codons/trinucleotide quadruplets of their classification [31].

Reviewer 2 Report

Comments and Suggestions for Authors

*1. The authors aimed to discover the role of genetic code symmetries in the flow of genetic information from DNA to protein in the transcription and translation processes.

 

*2. The manuscript is novel and interesting and fills a gap in the current literature.

 

*3. The Introduction is too short and does not adequately show the background of the study. Please expand.

 

*4. Results are relevant and well presented. Good tables and figures.

 

*5. Discussion section is too short and superficial. It needs to be expanded citing and commenting other similar studies in the current literature. The main topics of your study need to be better highlighted.

 

*6. Methods are adequate and well described.

Author Response

*1. The authors aimed to discover the role of genetic code symmetries in the flow of genetic information from DNA to protein in the transcription and translation processes.

*2. The manuscript is novel and interesting and fills a gap in the current literature.

*3. The Introduction is too short and does not adequately show the background of the study. Please expand.

*4. Results are relevant and well presented. Good tables and figures.

*5. Discussion section is too short and superficial. It needs to be expanded citing and commenting other similar studies in the current literature. The main topics of your study need to be better highlighted.

*6. Methods are adequate and well described.

 

       Reply to reviewer:

Rows: 68-76

1. Introduction

Our “symmetry-based theory of the genetic code” with the SSyGC table also supports the role of the quadruplet symmetries in DNA molecule of each living species as well of our trinucleotides/codon’s classification. One reviewer of our review article with this problematic [7] commented our discovery of the SSyGC table as very interesting but related only to the genetic code representing a kind of puzzle without broader significance.  His comment was encouragement to prove whether these symmetries having any role in processes of transcription and translation during proteinogenesis. This was a challenge for us, and the result is this paper.

Rows: 486-488

2.6. The differentiation between all start/stop signals

Stop signals UAG and UAA have the first two weak bases U and A and stop signal UGA has mix bases with the second base purine (G) (Fig. 2). Due to that, tRNA can recognize them that they are from split boxes.

Rows:495-498

……from split box. Its neighbour is also A+U rich weak symmetric codon AUA with third base purine as well as AUG start signal (or codon for Methionine) from the same split box. Therefore, it is possible that in rare cases AUA transforms in second codon for Methionine

 

Rows: 504-551

2.7. The universality of genetic code

It is necessary to explain very important aspect of the SSyGC table – the universality. It means that each codon has a strictly determined position in the genetic code, which cannot be exchanged with any other codon. In 2019 J. Fredens and coworkers made an important experiment [15]. They created Escherichia coli as a laboratory “synthetic” species with the entire synthetic DNA genome that utilized 59 codons and two stop signals to encode 20 amino acids for protein synthesis compared to 61 codons and three stop signals in natural living organisms. E. coli had the evolution path which started by itself in early beginning of the origin of life of living species on the Earth. The number of bases in the genome of E. coli is about 5 million as for example only in a centromere of human chromosome, but it has also all 20 natural amino acids. Performing “synonymous codon compression” authors recompiled the E. coli genome omitting two (UCG, UCA) out of six codons encoding Serine, and UAG stop signal.  They concluded that E. coli with “synthetic DNA” displayed only minor changes with a slower growth rate, slightly elongated cells, and enabled deletion of previously essential tRNA. The attempts with changing other amino acids were not successful and E. coli has not survived.  

 Here we show the important role of Serine. One should note that the experiment succeeded – E. coli survived – if the two codons UCG and UCA were removed just from Serine, which have their complements AGC and AGU in the remaining 4 codons. The replication of DNA molecule enables that each strand can be reconstructed on the principle of Watson-Crick pairing (A↔U, C↔G) from opposite non mutilated strand. It means that E. coli could be reconstructed successfully with AGC and AGU complements for Serine its complete genome. This experiment showed that of crucial importance is a balanced need for all 6 codons of Serin, which is vitally responsible for energy demand.

The removed codons and stop signal from E. coli could not be replaced in the purine-pyrimidine symmetry net by some other codons, and because of that partially reconstructed genome resulted in mutant with changed phenotype and a slower growth rate. In this way, the experiment with E. coli has not proved that the new synthetic species with an unnatural genetic code was created. On the contrary, it has proved an important fact that, for normal development of species, a complete genetic code with 20 natural amino acids is needed, structured on basis of purine-pyrimidine physicochemical symmetries. Violation of symmetries endangers species and creates mutants, while the omission of codons for an individual amino acid endangers the life of species.

     According to the experiment with E. coli it can be concluded that diferent number of codons for each amino acid depends on methabolic neccesity of the individual species. At the same time the codons for the individual amino acid in mRNA are mutually equivalent. However, during translation there is a diferetiation between codons with canonical tRNA anticodon pairing and wobble pairing. Namely, because of unequal number of codons and tRNA anticodons wobble pairing is activated. We show that in this process of mRNA-tRNA translation helps the purine-pyrimidine symmetries of genetic code how to recognize codon-anticodon pairing as well as which codon belongs to amino acid with two codons and which to amino acid with four codons to realize optimal wobble pairing (Fig. 4). Because of that,  missreading during process of translation in proteinogenesis is exceptionally rare, reduced to only 10^-4. 

Rows:    554-609

3. Discussion

The genetic code regulates how the translation system decodes the 61 genetic codons into 20 natural amino acids along with 3 termination signals in process of proteinogenesis. The genetic code is degenerate because more than one type of codon encodes a single amino acid. In general, degeneracy is associated with mathematical group theoretical structure [16-21]. The algebraic approach to the SGC was proposed with the aim of explaining the degeneracies encountered resulting by a sequence of symmetry breaking. However, the evolution of the genetic code through the progressive symmetry breaking by using the group theoretical structure proposes that, in the beginning, it was not possible to distinguish the function of codons which therefore all encoded the same information. With the consecutive creation of amino acids during such proposed evolution, the number of codons within the degeneracy groups gradually decreased into two singlets (Methionine/start signal and Tryptophane), nine doubles, two triplets (Isoleucine and 3 stop signals), five quadruplets, and three sextets. 

The degeneracy distribution considers only the number of codons for each amino acid according to Nirenberg’s empirical result, without including any physicochemical affinity between bases and codons [7]. However, the degeneracy of amino acids coding takes place of the most crucial and enigmatic aspects to this day. For example, some authors created also a new theory based on symmetry principles of code degeneracy and hypothesized that the primitive pre-early code had codons of four bases. Only 32 codons of 256 possible combinations (4⁴) had some symmetries with amino acids degeneracy 2, and the rest asymmetric codons with amino acids degeneracy 4 [22].  This mathematical model based also on number theory starting from extant variants of the last universal common ancestor (LUCA) which was the first to have the universal genetic code with three-nucleotides codons [22-25] like the present Standard genetic code.

Despite of genetic code degeneracy all symmetries including double mirror symmetry and purine-pyrimidine symmetry net of the SSyGC table remain unchanged for all RNA and DNA living species (Subsect. 2.7, Figs. 4 and 7.2.). 

Negadi 2023 [26] presented a novel approach to studying the genetic code’s mathematical and chemical structure revealing the genetic code symmetries through computations involving Fibonacci-like sequences. He found a full mathematical and chemical connection with the “ideal sextet’s classification scheme” of our Ideal Genetic Code table [27]. He examined the total number of hydrogen in side of chains of all amino acids 61 sense codons from Ideal Genetic Code table and “the hydrogen and atoms numbers as “seeds” of three sextets (Serine, Arginine and Leucine), which will create the entire hydrogen atom and even nucleon content of the whole set of amino acids and will also play a prominent role mathematical and (chemically inspired) “seeds” in computing the chemical content of the twenty amino acids, including degeneracy”. The same author in 2024 [28] presented also Fibonacci-like sequences to examine the symmetries of our Supersymmetry Genetic Code table which derived from the Ideal Genetic Code table [6], in a charged physiological state of amino acids in a pH environment around 7.4 testing the efficiency of his method of atom content in unraveling relationships with the genetic code with vertical and horizontal mirror symmetry axis between all purines and pyrimidines of the whole code. 

Breslauer et al. 1986 [29.] and Klump et al 2020 [30] measured free energy of codons using spectroscopic and calorimetric techniques and concluded that free energy of each codon is equal to the free energy of its reverse complement. Inserted these values in mitochondrial human genetic code table they were randomly scattered. The authors analyzed the free energy of codons in the SGC table. We show that the mirror symmetry of the SSyGC table, DNA quadruplets and our classification of codons and trinucleotides are perfectly imbedded in the mirror symmetry energy code as well as identical mirror symmetry from free energy values for all four members of DNA quadruplets and codons/trinucleotide quadruplets of their classification [31].

 

Rows: 610-615

Lei Lei  and Burton 2023 [32] observed that features of the  genetic code model include explanation for the coevolution of amino acid metabolism, amino acid chemistry, homologous aaRSs enzymes, tRNAomes and stop codons. The author stated: “wobbling at tRNA-34 evolved as the ribosome “learned” to read the anticodon”. The authors analysed the SGC without   mentioning symmetries. We showed that symmetries had important role in wobbling translation.

Rows: 678-682

Only purine-pyrimidine symmetries with a central role of the genetic code discovered the whole system and genetic information flow from DNA to protein. Recalling again the beginning of this paper with Einstein’s symmetry principle in physics as the primary feature of Nature, we extended symmetry principle on fundamental biological processes as DNA and genetic code, and origin of life.  

References:

Rows: 821-830

             

1. Findley, G.L.; Findley, A.M.; McGlynn, S.P. Symmetry characteristics of the genetic code. Natl. Acad. Sci. USA 79, 7061–7065 (1982).
2. Hornos, J.E.M. & Hornos, Y.M.M. Algebraic model for the evolution of the genetic code. Rev. Lett. 71, 4401 (1993).
3. Hornos, J.E.M.; Hornos, Y.M.M.; Forger, M. Symmetry and symmetry breaking: An algebraic approach to the genetic code. J. Mod. Phys. 13, 2795-2885 (1999).
4. Forger, M.; Hornos Y.M.M.; Hornos J.E.M. Global aspects in the algebraic approach to the genetic code. E Phys. 56, 7078-7082 (1997).
5. Antoneli, F. & Forger, N. Symmetry breaking in the genetic code: Finite groups. Comput. Model. 53, 1469–1488 (2011).
6. Lenstra, R. Evolution of the genetic code through progressive symmetry breaking. Theor. Biol. 347, 95-108 (2014).
7. Jarus, M. Crick Wobble and Superwobble in Standard Genetic Code Evolution. Mol. Evol. 89 (1): 50-61 (2021).

 

Rows: 836-850

 

8. Négadi, T. Revealing the Genetic Code Symmetries through Computations Involving Fibonacci-like Sequences and their Properties. Computation 11 (8) 154 (2023). http://doi.org/10.3390/computation11080154.
9. Rosandić, M; Paar, V. The novel Ideal Symmetry Genetic Code table – Common purine-pyrimidine symmetry net for all RNA and DNA species. J. Theor. Biol. 7, 524, 110748 (2021). http://doi.org/10.1016/j.jtbi.2021.110748.
10. Négadi, T. Fibonacci-like Sequences Reveal the Genetic Code Symmetries, Also When the Amino Acids Are in a Physiological Environment. Symmetry 16 (3), 293 (2024). https://doi.org/10.3390/sym16030293.
11. Breslauer, K. J.; Frank, J.; Blocker, H.; Marky, L. A. Prediction DNA duplex stability from the base sequence. Natl. Acad. Sci. USA 83, 3746-3750 (1986).
12. Klump, H. H.; Volker, J.; Breslauer, K. J. Energy Mapping of the Genetic Code and Genomic Domains: Implication for Code Evolution and Molecular Darwinism. Cambridge University Press, UK (2020)  
13. Rosandić, M.; Paar, V. The Supersymmetry Genetic Code Table and Quadruplet Symmetries of DNA Molecules Are Unchangeable and Synchronized with Codon-Free Energy Mapping during Evolution. Genes 14, 2200 (2023). https://doi.org/10.3390/genes14122200.
14. Lei Lei; Burton, Z. F. The 3 31 Nucleotide Minihelix tRNA Evolution Theorem and Origin of Life. Life 13, 2224 (2023). https://doi.org/10.3390/life13112224.

 

Rows: 872-873

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript by Rosandić et al., reported that the Maximal Genetic Code Symmetry is a Physicochemical Purine Pyrimidine Symmetry Language for Transcription and Translation in the Flow of Genetic Information from DNA to Protein. The authors demonstrated data about the Physicochemical Purine Pyrimidine Symmetry Language. This study seems to be interesting, but it is speculative and in some cases is not easy to follow and to understand. The abstract is not well written , also, the results are confusing  and the discussion is not constructive  and well written and does not provide a new information. In general I do not know, if the manuscript provides important information for the scientific community or only for a limited number of reader. Accordingly, the manuscript needs to be rephrased and simplified to make it easy to read and understand

Comments on the Quality of English Language

Needs improvement

Author Response

The manuscript by Rosandić et al., reported that the Maximal Genetic Code Symmetry is a Physicochemical Purine Pyrimidine Symmetry Language for Transcription and Translation in the Flow of Genetic Information from DNA to Protein. The authors demonstrated data about the Physicochemical Purine Pyrimidine Symmetry Language. This study seems to be interesting, but it is speculative and in some cases is not easy to follow and to understand. The abstract is not well written , also, the results are confusing  and the discussion is not constructive  and well written and does not provide a new information. In general I do not know, if the manuscript provides important information for the scientific community or only for a limited number of reader. Accordingly, the manuscript needs to be rephrased and simplified to make it easy to read and understand

 

Reply to reviewer 3:

The whole manuscript is broadened and rephrased in accordance with present knowledge and improved by our fundamental investigation of symmetries in the field of vitally important biological systems: DNA molecule, genetic code, transcription and translation in the process of proteinogenesis. Both replies to reviewers 1and 2 include also reply to reviewer 3.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors: Many thanks for your sincere efforts in improving your manuscript. The revised article is highly satisfactory and merits acceptance for publication in the International Journal of Molecular Sciences.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is now improved and can be published in the present form