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First, I am not a biologist, so this question might be naive:

Computer information processing and storage is based on 2-digit system of bits with values 0 and 1. Now, DNA stores the information in a 4-digit system: A, C, G, T. Three base pairs form a codon and can encode 43 amino acids.

Is there a good reason why a 4-level system (which can store 2 bits per encoding entity) evolved rather than a 2-level or a system with a larger number of symbols in the alphabet?

Put differently: Why was a binary system not preferred for storage and processing of data? In computing, binary is much easier, and the very few tests of exotic higher-level data processing have not really been successful.

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    $\begingroup$ At an abstract level, both systems perform information storage and processing. My question was not whether living organisms are computers, but why - on the abstract level of information, why a 4-level encoding system has been favoured. Your comment seems to be not constructive - but maybe I misunderstood something? $\endgroup$ – NicoDean Aug 31 '15 at 16:43
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    $\begingroup$ Why not? There is no inherent drawback in a base 4 system instead of a base 2. In the absence of selection pressure, the precise system evolution ended up with may just be a coincidence. $\endgroup$ – Roland Aug 31 '15 at 22:23
  • $\begingroup$ It's an interesting question but I doubt that it has an answer, only hypotheses. This paper may interest you. $\endgroup$ – canadianer Aug 31 '15 at 23:56
  • $\begingroup$ @Roland how do you know there was no selection pressure; i can't imagine that this was the first and only system that was developed - Looking at the complexity, I can't believe that there were no prior steps of more primitive information encoding systems, and not more than one of such systems competing. $\endgroup$ – NicoDean Sep 1 '15 at 10:44
  • $\begingroup$ @canadianer thanks for this paper, that looks pretty cool! as far as i see, they start already with 4-nary logic. but the structure of the info-encoding, using two nb per codon is great! $\endgroup$ – NicoDean Sep 1 '15 at 10:45
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The current hypothesis is that RNA came first, DNA and proteins came later. So the reason that four bases are used might be related to the initial RNA world, and then DNA just reused the already existing RNA bases in a slightly modified form. In the RNA world, all functions had to be performed by RNA. Having more bases available than two would likely be important to be able to adopt various structures and create binding pockets or active sites for ribozymes.

You can't really think of the genetic code as an abstract data storage device. There are physical and chemical consequences to the choice of encoding. For example, proteins have to be able to bind to DNA and recognize particular patterns. With your binary code, the recognition sequence would have to be longer, because each basepair contains less information. The tRNA anticodons would have to be larger for protein biosynthesis to work with the binary code. Another issue that plays a role in some processes is that GC base pairs are more stable than AU/AT base pairs.

These are all just hypotheses. Evolution doesn't necessarily choose the best option, sometimes it is just the most convenient one that still works well.

I also found a review titled "Why are there four letters in the genetic alphabet?" that makes a similar point as my first one.

All present models to explain the fact that we have four base types in our genetic alphabet hinge, in covert or overt form, on the assumption that the genetic alphabet evolved in an RNA world

Another factor I didn't think of that is mentioned there is that while more bases make better ribozymes, more bases also decrease the accuracy of replication.

In summary, two-dimensional RNA-like structures (and, presumably also the three-dimensional structures) become better defined as alphabet size increases, whereas the accuracy of replication decreases.

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  • $\begingroup$ that is a wonderful answere, thank you! there are some insights I haven't thought of - especially the RNA world hypothesis. great! And thanks for the link to the paper! $\endgroup$ – NicoDean Sep 2 '15 at 16:54
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Why does nature use a 4-level system (DNA) to encode information?

Short answer: Ease of manufacture, simplicity of matching, sufficiency for requirements. Fewer simple bases take less effort to create, provide fewer possible matches, yet is complex enough to code what is required while retaining sufficient degeneracy for success. Also it was the coincidence of replicase–alphabet co-evolution, both occurring in the same place at the same time.

Longer answer:

First, I am not a biologist, so this question might be naive:

Beginners and experts are welcome at SE.

All of our information processing and storing is based on 2-level logic, bits with 0 and 1.

Euler's number ($e$) is defined as the sum of an infinite series $\sum_{n=0}^\infty \frac{1}{n!}$ and has the lowest radix economy, but it's not convenient to implement in logic circuits. With the radix economy of $e$ set at 1.000, ternary is 1.0046 and binary is 1.0615.

Ternary computers have been constructed using ternary logic and while they are uncommon ternary logic is used in SQL; even in binary based computers.

Most, but not all of our information processing and storing is based on 2-level logic.

Now, DNA stores the information in a 4-level system: A, C, G, T. Three basepairs form a codon and can encode 4^3 amino acids.

Most, but not all.

The five canonical, or primary, nucleobases are: adenine (A), cytosine (C), guanine (G), thymine (T), and uracil (U). DNA uses A, G, C, and T while RNA uses A, G, C, and U.

In the laboratory DNA has been created with 6 and 8 bases, it is functional.

See the (paywall) report: "Hachimoji DNA and RNA: A genetic system with eight building blocks", Feb 22 2019, by Shuichi Hoshika, Nicole A. Leal, Myong-Jung Kim, Myong-Sang Kim, Nilesh B. Karalkar, Hyo-Joong Kim, Alison M. Bates, Norman E. Watkins Jr., Holly A. SantaLucia, Adam J. Meyer, Saurja DasGupta, Joseph A. Piccirilli, Andrew D. Ellington, John SantaLucia Jr., Millie M. Georgiadis, and Steven A. Benner. (Google Cache version).

Spinach DNA modified with 8 bases

"Fig. 4 Structure and fluorescent properties of hachimoji RNA molecules.
(A) Schematic showing the full hachimoji spinach variant aptamer; additional nucleotide components of the hachimoji system are shown as black letters at positions 8, 10, 76, and 78 (B, Z, P, and S, respectively). The fluor binds in loop L12 (25). (B to E) Fluorescence of various species in equal amounts as determined by UV. Fluorescence was visualized under a blue light (470 nm) with an amber (580 nm) filter.
(B) Control with fluor only, lacking RNA.
(C) Hachimoji spinach with the sequence shown in (A).
(D) Native spinach aptamer with fluor.
(E) Fluor and spinach aptamer containing Z at position 50, replacing the A:U pair at positions 53:29 with G:C to restore the triple observed in the crystal structure. This places the quenching Z chromophore near the fluor; CD spectra suggest that this variant had the same fold as native spinach (fig. S8).".

Centrifuge tube C contains the spinach with the DNA containing eight bases.

Is there a good reason for why during early evolution, a 4-level system (which can store 2 bits per encoding entity) is favoured over a 2-level system or over larger systems?

Yes.

  • Copying fidelity decreases roughly exponentially with increasing size (N pairs) of the alphabet (keeping the length of the genome fixed). The reason for this is that as one adds more letters to the alphabet, they will resemble each other more and more, and hence the chance of mispairing and mutagenesis increases.

  • Overall metabolic efficiency and fitness are determined by the size, we have 20 amino acids to code for (smaller makes 16 or less) and 3 stop codons. So we have a space for 64, and rely on degeneracy to provide a degree of 'error correction' (synonymization) where errors are converted, usually to produce non-fatal errors. While seldom fatal translation errors can still cause rare diseases.

We are already running inefficiently, going to a larger number of pairs introduces unnecessary complexity and going smaller isn't available for the number of amino acids that must be coded for. Increasing the codon length makes DNA larger, as it is it must already be coiled to stuff it into the cells; one third larger DNA would better fit cells that are also one third larger.

In the opinion piece "Why are there four letters in the genetic alphabet?", Nature Reviews Genetics volume 4, pages 995–1001 (2003), by Eörs Szathmáry there are the following observations:

Page 995:

"There are four main constraints on the successful incorporation of a new base pair$^{[6–8]}$:

  • chemical stability (the base should not readily decompose);

  • thermodynamic stability (new base pairs should not destabilize nucleic-acid structures);

  • enzymatic processability (polymerases should accept the base pairs as substrates, catalyse addition to the primer and be able to carry on the process); and

  • kinetic selectivity (orthogonality to other base pairs).

All four criteria are important but the combination of the last two, which we might call replicability, has received particular attention because it is the main obstacle to adding to the genetic alphabet.".

Page 997:

"Theoretical arguments
The feasibility of alternative base pairs raises the question: why are there four bases in the natural genetic alphabet? As Orgel pointed out, there are two types of answer: either evolution has never experimented with alternative base pairs or four bases ‘were enough’$^{[20]}$. The first option might hold for the hydrophobic base pairs discussed above (an adequate early synthesis might be lacking), but it is unlikely to be true for all of the hydrogen-bonding bases in a prebiotic ‘chemical mayhem’. At any rate, it does not explain why we do not have only two bases$^{[21–24]}$. It therefore seems worthwhile to pursue the second option: why might four bases be enough? If ‘enough’ is understood in terms of evolutionary stability, it means optimality within the frame of the structural constraints that are afforded by natural selection. Here, I describe attempts to show that four bases are optimal under STABILIZING SELECTION, especially when we consider MUTATION–SELECTION EQUILIBRIUM. I then discuss evidence for the optimal size of the genetic code obtained from in silico DIRECTIONAL SELECTION and finally analyse a more abstract contribution from so-called ERROR-CODING THEORY.".

Page 1000:

"Theoretical investigations based on structural, energetic and information-theoretic studies confirm the view that increased alphabet size decreases copying fidelity while increasing information density. This indicates that there must be an optimum alphabet size in terms of fitness, whether we assume that the genetic.alphabet was fixed in an RNA world or not.

...

According to the RNA-world-based view, the genetic alphabet became fixed more than 3 billion years ago$^{[31]}$, and the origin of the genetic code and translation happened subsequently$^{[42]}$. This line of reasoning indicates that the informational/operational division of labour between nucleic acids and proteins$^{[43}]$ has uncoupled the genetic alphabet from enzymatic functionality constraints. As the genetic code evolved in the context of a certain genetic alphabet, any further change of the alphabet would have been unnecessary and/or extremely unlikely.

If, however, the genetic code originated by the simultaneous co-evolution of nucleic acids and proteins (a much more complicated model), then the fixation of the genetic alphabet must be considered in this complex context. Here, the general insight of Mac Dónaill$^{[38]}$ helps: the information density of the alphabet is a useful concept, whether the exercised function is ribozymic or a messenger function in protein synthesis. In this case, the problem of the size of the ‘catalytic alphabet’ (the number of encoded amino acids) readily arises: why do we have 20 rather than, for example, 16 or 25 different amino acids? It has been pointed out that some of the considerations discussed in this article (effects on catalytic efficiency and translation fidelity) apply to this related problem$^{[32}]$. However, another crucial factor is likely to be involved: the metabolic cost of producing amino acids. An amino acid that belongs to the same biosynthetic family$^{[43]}$ is expected to increase catalytic efficiency only modestly and its metabolic cost is likely to be small. By contrast, an amino acid from a new biosynthetic family is likely to confer a high enzymatic advantage, but is expected to incur high metabolic costs (for instance, many new ATP-requiring steps).".

References:

$[6.]$ Mathis, G. & Hunziker, J. Towards a DNA-like duplex without hydrogen-bonded base pairs. Angew. Chem. Int. Ed. 41, 3203–3205 (2002).

$[7.]$ Ogawa, A. K., Wu, Y., Berger, M., Schultz, P. G. & Romesberg, F. E. Rational design of an unnatural base pair with increased kinetic selectivity. J. Am. Chem. Soc. 122, 8803–8804 (2000).

$[8.]$ Kool, E. T. Synthetically modified DNAs as substrates for polymerases. Curr. Opin. Chem. Biol. 4, 602–608 (2000).

$[20.]$ Orgel, L. E. Nucleic acids — adding to the genetic alphabet. Nature 343, 18–20 (1990).

$[21.]$ Orgel, L. E. Evolution of the genetic apparatus. J. Mol. Bio . 38, 381–393 (1968).

$[22.]$ Crick, F. H. C. The origin of the genetic code. J. Mol. Biol. 38, 367–379 (1968).

$[23.]$ Wächtershäuser, G. An all-purine precursor of nucleic acids. Proc. Natl Acad. Sci. USA 85, 1134–1135 (1988).

$[24.]$ Zubay, G. An all-purine precursor of nucleic acids. Chemtracts 2, 439–442 (1991).

$[31.]$ Szathmáry, E. Four letters in the genetic alphabet: a frozen evolutionary optimum? Proc. R. Soc. Lond. B 245, 91–99 (1991).

$[32.]$ Szathmáry, E. What is the optimum size for the genetic alphabet? Proc. Natl Acad. Sci. USA 89, 2614–2618 (1992).

$[38.]$ Mac Dónaill, D. A. Why nature chose A, C, G and U/T: an error-coding perspective of nucleotide alphabet composition. Orig. Life Evol. Biosphere 33, 433–455 (2003).

$[42.]$ Szathmáry, E. The origin of the genetic code: amino acids as cofactors in an RNA world. Trends Genet. 15, 223–229 (1999).

$[43.]$ Wong, J. T. A coevolution theory of the genetic code. Proc. Natl Acad. Sci. USA 72, 1909–1912 (1975).

Further Information:

Eörs Szathmáry’s Wikipedia web page
http://www.colbud.hu/fellows/szathmary.shtml - The Collegium Budapest is closed.

Scripps Research Institute

Steven Benner’s web page
http://www.chem.ufl.edu/benner.html - Dr. Benner left UoF in 2005.

Asked differently: Why did evolution not prefer to have a binary system to store and process data? For us, binary is much easier, and the very few tests of exotic higher-level data processing were not really successful.

Binary has nothing to do with evolution. Few of us can count to 255 in binary, we prefer decimal. Both ternary computers and SQL are "really successful", people prefer the alternatives.

This is intended to be an answer suitable for a layperson. Eörs Szathmáry’s article and it's associated references can be consulted for more details.

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  • $\begingroup$ Thank you for this very interesting answer, after 3.5years. it gives a quite broader perspective. $\endgroup$ – NicoDean Mar 6 at 18:11
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    $\begingroup$ @NicoDean You are most welcome. I referred to the newest information available and used it for my answer but ultimately an old opinion article offered a simpler explanation. There exists many theories, not all of them are disproved. $\endgroup$ – Rob Mar 6 at 21:06
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General answer

The use of binary in computers arose primarily from practical considerations of how to represent digits using electric current or voltage (i.e. either ‘on’ or ‘off’ is the least equivocal). Such representation was not only — or even primarily — for storing information of different numerical types, but for programming logic using Boolean algebra. Physical storage of data can be in various different formats (magnetic, optical, electrical) but these are functionally equivalent and the retrieval and conversion of binary data into integers real numbers, text or images is predominantly a mathematical rather than a physical concern.

DNA has various functions, but these do not include a concern with programming logic. In storage of data of different types, there is no problem representing different bases or radixes — sufficient different nucleic acid bases are available to represent base-4 digits. The most pertinent question in storage is one that does not arise in computer memory, that is the physical transformation of the information into other molecules. This can take the form of inverse copying of a genomic nucleic acid (DNA or, perhaps originally, RNA) in replication, the copying of one strand of information in a DNA duplex into a single strand of a related but not identical nucleic acid in the transcription to mRNA (messenger RNA), and ‘reading’ (translation) of the information in the chemical bases of the mRNA to produce a protein composed of amino acids — quite different chemical molecules.

Thus, the electronic or mathematical considerations that lead to the statement “In computing, binary is much easier” have no relevance for DNA and the genetic code, where chemical and structural molecular considerations are paramount. The supposition that there is a need to explain why information in DNA is not specifically binary is therefore false.

Speculation on the structural chemistry of the evolution of genetic information

The question of why 4-digit system (rather than 2- or 6- etc.) is still valid, but cannot be answered definitively. However, it is worth discussing to illustrate to numerical scientists the ways in which structural considerations might have determined the choice of information system. I shall consider two early stages in biochemical evolution at which the 4-digit system may have been selected for, after which — one should recognize — there might have been severe barriers to further change. Giving up Java and moving to Python (or even just changing from Java I to Java II) was probably not an option.

THE CHEMISTRY OF THE SELF-REPLICATING GENOME

I shall assume one of the main tenets of the RNA World Hypothesis — that RNA preceded DNA as the cellular genome. Even if the original genome were DNA, the question is the same — why four nucleic acid bases rather than two or six etc. — and the requirements of its chemical constitution are similar: to allow self-replication (hence the need to consider even numbers).

One might consider that an RNA with two bases arose first — let us assume adenine (A) and uracil (U) for the sake of argument. Later the cell acquired the catalytic ability to synthesize guanine (G) and cytosine (C), so that development from a self-replicating AU genome to an AUGC genome became possible. Assuming that this occurred before the amino acid-coding potential of the RNA had arisen, what might have favoured the more complex genome? It might have been something to do with the fact that there are three, rather than two, hydrogen bonds in a GC base-pair, perhaps producing a different RNA:RNA structure which was either more stable or easier to replicate for some reason. Alternatively it may have had nothing to do with the structure of the RNA:RNA helix, but was a side-effect of the acquisition of additional bases the greater chemical versatility of which enhanced the enzymic functions (ribozyme activity) of primaeval RNA.

If more meant better, why not six bases, rather than four? There might be specific chemical reasons like the slower development of the enzyme activities to produce other nucleic acid bases, or that with more bases the possibility of mispairing of bases was higher. (The ‘Goldilocks principle’ takes one a long way.) Or it may have been that the system worked well enough, was followed by the development of a triplet code, at which stage the system was frozen.

THE STRUCTURAL CHEMISTRY OF TRANSLATION

The die may have already been cast in the genome, above, but it would be a shame not to look at the chemistry of the decoding of the genetic information, as it is hardly a consideration for computer systems. So let us consider a competition between closely related organisms, one with a two-base genome and another with a four-base genome (and even a six-base genome). The requirement is to encode the information for a number of amino acids that can give proteins functional versatility — somewhere about the 20 (plus termination signals) we have today. The size of the codon (the word size), is 3 in a 4-bit system, accommodating 64 (43) possible codons in a (the standard) genetic code. If a 2-bit system of data storage were used then a word-size of 5 would be required to generate 32 (25) possible codons, whereas a 6-bit system could reduce the word-size to 2 with 36 (62) possible codons.

The physical consequences of such different systems would be seen in the decoding process where an adaptor molecule — transfer RNA (tRNA) — delivers amino acids to the peptidyl transferase centre of the ribosome (at one end) while interacting with the messenger RNA (mRNA) at the other end through codon–anticodon base-pairing. One might argue that the tRNA anticodon of three bases fits into the loop at the end of the helical anticodon stem in a manner that allows it adopt a relatively precise position (yes, I know about wobble) where it can make appropriate contact with the mRNA codon bases (see diagram below).

Transfer RNA and anticodon loop interactions

A quintuplet anticodon and five-base interaction (although not impossible) would appear less naturally adapted to the structural chemistry of RNA. Similar objections would not apply to a two-base interaction, although one might argue that total energy of interaction between two base-pairs was insufficient to prevent errors. The error consideration also applies to a binary system where the difference in energy between a five-base interaction and a four-base interaction (i.e. a simple mismatch) would be low. Indeed, if the hypothetical competition between 2-bit and 4-bit organisms had occurred, the 2-bit system would also have been more prone to error frequency through slippage during replication.

The Last Word…

…goes to Steven Benner, whose group has constructed 8-base DNA in the laboratory:

“The ability to store information is not very interesting for evolution. You have to be able to transfer that information into a molecule that does something.”

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Actually, I never saw nature information is stored by binary system, binary number is invented by human. I think it may be several reason that 4-level system is better.

1. Storage space. If DNA is stored using a 2-level system, what would happen? For example, let's use 00 for A, 01 for C, 10 for G, 11 for T, a three base pairs codon "AGT" would be "001011", that would be a six base pair codon , so it is longer. Even if you want to use a condon to directly represent one kind of amino acid, there would be 22 amino acids and one start codon and one stop codon, so that need at least 24 different kind of codons. So how many base pairs would be in one codon? 2^5=32, so that would be five base pairs in one codon. For example, "00101" would be directly represent glycine. That would occupy much more storage space than 4-level system, which means our chromosome would be 40% longer than a 4-level system. Do you think it is not a big deal? That means we would need much more energy to replicate DNA, metabolism, etc. Creatures evolved from a very strict environment, wasteful organisms may not survive.

2. Too much error. The goal of genetic code it to inherent their information efficiently and accurately. Longer DNA strand than 4-level make it costs much more time in replication, transcription and translation, and also make it is very fragile and easier to break down. DNA replication is not like a computer. In a computer, you can select "01010000101", ctrl+c, and click someone else, ctrl+v, that would be a exactly same codon "01010000101", but it does not happen in DNA replication. The mispair rate of Eukaryota DNA replication is 10^(-8), but in Prokaryota, it is 10^(-5). So for original creatures, the possibility of error in a three-basepair-codon would be 2.99997*10^(-5), and the possibility of error in a five-basepair-codon would be 4.99999*10^(-5). Its error rate is almost twice that three-basepair-codon! As I said before, the goal of genetic code is to inherent their information efficiently and accurately. Too many errors cannot survive either. Actually, some biologist proposed that maybe three-basepair-codon is evolved from much longer codon, and longer size codon die out because much more error.

Codon Size Reduction as the Origin of the Triplet Genetic Code

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    $\begingroup$ Your reasoning is entirely teleological, and therefore wrong. It was most probably due to chemical possibility at the time and not much more. $\endgroup$ – Athe Sep 1 '15 at 10:28
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The genetic code has to be able to specify 20 different amino acids, plus a termination codon, so a 21-word lexicon, where all the words are the same length. That is the coding problem.

Q: What is the smallest alphabet that can accomplish this?

A: an alphabet with 4 different letters.

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    $\begingroup$ You can represent 21 values with a binary system as well, I don't understand this answer. $\endgroup$ – Mad Scientist Sep 2 '15 at 13:23
  • $\begingroup$ I may be out of my depth, or just confused. As @sunboyharry alludes to, you can save computer storage space if you encode each nucleotide as binary digits, 00, 01, 10, 11, instead of using the ascii or utf-8 encodings. This is a classical bioinformatics homework problem at the introductory level. So with this logic all of the 3 nt codons in the current code and be specified as a bit-vector, or as a binary digit (64 different numbers). $\endgroup$ – mdperry Sep 2 '15 at 13:45
  • $\begingroup$ You can represent the value 21 in a binary system (10101, where you need 5 letters), or in an alphabet that has 21 or more letters. Consider the latin alphabet with 26 levels. You need one letter to represent that information. So what you said does not really make sense to me. $\endgroup$ – NicoDean Sep 2 '15 at 16:51

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