Entropy of the genetic information and evolution.

The entropy of the amino acid sequences coded by DNA is considered as a measure of diversity of variety of proteins, and is taken as a measure of evolution. The DNA or m-RNA sequence is considered as a stationary second-order Markov chain composed of four kinds of bases. Because of the biased nature of the genetic code table, increase of entropy of amino acid sequences is possible with biased nucleotide sequence. Thus the biased DNA base composition and the extreme rarity of the base doublet CpG of higher organisms are explained. It is expected that the amino acid composition was highly biased at the days of the origin of the genetic code table, and the more frequent amino acids have tended to get rarer, and the rarer ones more frequent. This tendency is observed in the evolution of hemoglobin, cytochrome C, fibrinopeptide, immunoglobulin and lysozyme, and protein as a whole.     

Entropy increase and information loss in Markov models of evolution

Markov models of evolution describe changes in the probability distribution of the trait values a population might exhibit. In consequence, they also describe how entropy and conditional entropy values evolve, and how the mutual information that characterizes the relation between an earlier and a later moment in a lineage’s history depends on how much time separates them. These models therefore provide an interesting perspective on questions that usually are considered in the foundations of physics—when and why does entropy increase and at what rates do changes in entropy take place? They also throw light on an important epistemological question: are there limits on what your observations of the present can tell you about the evolutionary past?     

A model of evolution for accumulating genetic information

By taking into account recent knowledge of multigene families and other repetitive DNA sequences, a model of evolution by gene duplication for accumulating genetic information is studied. Genetic information is defined as the sum of distinct functions that the gene family can perform. A coefficient, "genetic diversity" is defined and used in this study, that is highly correlated with genetic information. Initially, a multigene family with a few gene copies is assumed, and natural selection starts to work on this gene family to increase genetic diversity contained in the gene family. As an important mechanism, unequal crossing-over is incorporated. Together with mutation, it is responsible for supplying genetic variability among individuals for selection to work. A specific model, in which individuals with less genetic diversity are selectively disadvantageous, has been studied in detail. Through approximate theoretical analysis and extensive Monte Carlo studies, it has been shown that the system is an extremely efficient way to accumulate genetic information. For attaining one gene, the genetic load is much smaller under this model than under the traditional model of natural selection. The model may be applied to the process of origin of multigene families with diverse copy members such as those of immunoglobulin or cytochrome P450. In general, the process of creating new genes by duplication might be somewhere between the present and the traditional models.     

An engineer's view on genetic information and biological evolution

We develop ideas on genome replication introduced in Battail [Europhys. Lett. 40 (1997) 343]. Starting with the hypothesis that the genome replication process uses error-correcting means, and the auxiliary one that nested codes are used to this end, we first review the concepts of redundancy and error-correcting codes. Then we show that these hypotheses imply that: distinct species exist with a hierarchical taxonomy, there is a trend of evolution towards complexity, and evolution proceeds by discrete jumps. At least the first two features above may be considered as biological facts so, in the absence of direct evidence, they provide an indirect proof in favour of the hypothesized error-correction system. The very high redundancy of genomes makes it possible. In order to explain how it is implemented, we suggest that soft codes and replication decoding, to be briefly described, are plausible candidates. Experimentally proven properties of long-range correlation of the DNA message substantiate this claim.     

A recombination-based model for the origin and early evolution of genetic information

Recombination is the exchange of groups of subunits between two entities. It is argued here that this process was central to the origin of life, because it allowed for the creation of useful information from a random pool of linear polymers. The length distribution of such a pool could be broadened if these polymers, such as RNA strands, have the capability of interacting and performing a cross-strand nucleophilic attack of a hydroxy group on a phosphate. Both the formation of stable secondary structures such as stem-loops and selection for self-replication can operate to push the equilibrium length distribution of the pool to longer and more catalytically proficient oligomers. There is empirical and theoretical support for these operations. Finally, in a collection of recombining linear oligomers, the advent of short recognition sequences that favor certain interactions over others, the property of a genotypic 'self' could develop, which later can shed its collective nature and be subject to Darwinian evolution. This could have given rise to true replicase enzymes, for example.     

Entropy in evolution

Daniel R. Brooks and E. O. Wiley have proposed a theory of evolution in which fitness is merely a rate determining factor. Evolution is driven by non-equilibrium processes which increase the entropy and information content of species together. Evolution can occur without environmental selection, since increased complexity and organization result from the likely capture at the species level of random variations produced at the chemical level. Speciation can occur as the result of variation within the species which decreases the probability of sharing genetic information. Critics of the Brooks-Wiley theory argue that they have abused terminology from information theory and t thermodynamics. In this paper I review the essentials of the theory, and give an account of hierarchical physical information systems within which the theory can be interpreted. I then show how the major conceptual objections can be answered.     

Entropy and information in evolving biological systems

Integrating concepts of maintenance and of origins is essential to explaining biological diversity. The unified theory of evolution attempts to find a common theme linking production rules inherent in biological systems, explaining the origin of biological order as a manifestation of the flow of energy and the flow of information on various spatial and temporal scales, with the recognition that natural selection is an evolutionarily relevant process. Biological systems persist in space and time by transfor ming energy from one state to another in a manner that generates structures which allows the system to continue to persist. Two classes of energetic transformations allow this; heat-generating transformations, resulting in a net loss of energy from the system, and conservative transformations, changing unusable energy into states that can be stored and used subsequently. All conservative transformations in biological systems are coupled with heat-generating transformations; hence, inherent biological production, or genealogical proesses, is positively entropic. There is a self-organizing phenomenology common to genealogical phenomena, which imparts an arrow of time to biological systems. Natural selection, which by itself is time-reversible, contributes to the organization of the self-organized genealogical trajectories. The interplay of genealogical (diversity-promoting) and selective (diversity-limiting) processes produces biological order to which the primary contribution is genealogical history. Dynamic changes occuring on times scales shorter than speciation rates are microevolutionary; those occuring on time scales longer than speciation rates are macroevolutionary. Macroevolutionary processes are neither redicible to, nor autonomous from, microevolutionary processes.Authorship alphabetical     

Ambiguity and the evolution of the genetic code

The evolution of the genetic code is an extremely complex problem. The addition of a new method by which the code could evolve, however, allows much to be explained about the way in which the present codes (₃ and ₃ ) originated. The idea that ambiguity would allow the length of the codon to change is very useful, since it predicts the distribution of the 4-blocs and 2-blocs in the code, determines where variations in the code are probable, and presents a scenario for the evolution of the code.     

Protein evolution drives the evolution of the genetic code and vice versa

A model for the developmental pathway of the genetic code, grounded on group theory and the thermodynamics of codon-anticodon interaction is presented. At variance with previous models, it takes into account not only the optimization with respect to amino acid attributes but, also physicochemical constraints and initial conditions. A 'simple-first' rule is introduced after ranking the amino acids with respect to two current measures of chemical complexity. It is shown that a primeval code of only seven amino acids is enough to build functional proteins. It is assumed that these proteins drive the further expansion of the code. The proposed primeval code is compared with surrogate codes randomly generated and with another proposal for primeval code found in the literature. The departures from the 'universal' code, observed in many organisms and cellular compartments, fit naturally in the proposed evolutionary scheme. A strong correlation is found between, on one side, the two classes of aminoacyl-tRNA synthetases, and on the other, the amino acids grouped by end-atom-type and by codon type. An inverse of Davydov's rules, to associate the amino acid end atoms (O/N and non-O/non-N) of 18 amino acids with codons containing a weak base (A/U), extended to the 20 amino acids, is derived.     

Local stability and evolution of the genetic code

The standard genetic code is known to be robust to translation errors and point mutations. We studied how small modifications of the standard code affect its robustness. The robustness was assessed in terms of a proper stability function, the negative variations of which correspond to a more robust code. The fraction of more robust codes obtained under small modifications appeared to be unexpectedly high, about 0.1-0.4 depending on the choice of stability function and code modifications, yet significantly lower than the corresponding fraction in the random codes (about a half). In this sense the standard code ought to be considered distinctly non-random in accordance with previous observations. The distribution of the negative variations of stability function revealed very abrupt drop beyond one standard deviation, much sharper than for Gaussian distribution or for the random codes with the same number of codons in the sets coding for amino acids or stop-codons. This behavior holds for both the standard code as a whole and its binary NRN-NYN, NWN-NSN, and NMN-NKN blocks. Previously, it has been proved that such binary block structure is necessary for the robustness of a code and is inherent to the standard genetic code. The modifications of the standard code corresponding to more robust coding may be related to the different variants of the code. These effects may also contribute to the rates of replacements of amino acids. The observed features demonstrate the joint impact of random factors and natural selection during evolution of the genetic code.     

Language evolution and information theory

This paper places models of language evolution within the framework of information theory. We study how signals become associated with meaning. If there is a probability of mistaking signals for each other, then evolution leads to an error limit: increasing the number of signals does not increase the fitness of a language beyond a certain limit. This error limit can be overcome by word formation: a linear increase of the word length leads to an exponential increase of the maximum fitness. We develop a general model of word formation and demonstrate the connection between the error limit and Shannon's noisy coding theorem.     

Characterizing the evolution of genetic variance using genetic covariance tensors

Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection in natural populations will require ascertaining how genetic variance–covariance (G) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in genetic covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata, we show that much of the divergence in genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of genetic variance within populations, suggesting that genetic drift may be a major cause of divergence in genetic variance among these populations.     

RNA minihelices and the decoding of genetic information

The rules of the genetic code are determined by the specific aminoacylation of transfer RNAs by aminoacyl transfer RNA synthetase. A straightforward analysis shows that a system of synthetase-tRNA interactions that relies on anticodons for specificity could, in principle, enable most synthetases to distinguish their cognate tRNA isoacceptors from all others. Although the anticodons of some tRNAs are recognition sites for the cognate aminoacyl tRNA synthetases, for other synthetases the anticodon is dispensable for specific aminoacylation. In particular, alanine and histidine tRNA synthetases aminoacylate small RNA minihelices that reconstruct the part of their cognate tRNAs that is proximate to the amino acid attachment site. Helices with as few as six base pairs can be efficiently aminoacylated. The specificity of aminoacylation is determined by a few nucleotides and can be converted from one amino acid to another by the change of only a few nucleotides. These findings suggest that, for a subgroup of the synthetases, there is a distinct code in the acceptor helix of transfer RNAs that determines aminoacylation specificity.     

On the origin and evolution of the genetic code

Two ideas have essentially been used to explain the origin of the genetic code: Crick's frozen accident and Woese's amino acid-codon specific chemical interaction. Whatever the origin and codon-amino acid correlation, it is difficult to imagine the sudden appearance of the genetic code in its present form of 64 codons coding for 20 amino acids without appealing to some evolutionary process. On the contrary, it is more reasonable to assume that it evolved from a much simpler initial state in which a few triplets were coding for each of a small number of amino acids. Analysis of genetic code through information theory and the metabolism of pyrimidine biosynthesis provide evidence that suggests that the genetic code could have begun in an RNA world with the two letters A and U grouped in eight triplets coding for seven amino acids and one stop signal. This code could have progressively evolved by making gradual use of letters G and C to end with 64 triplets coding for 20 amino acids and three stop signals. According to proposed evidence, DNA could have appeared after the four-letter structure was already achieved. In the newborn DNA world, T substituted U to get higher physicochemical and genetic stability.