A colorful origin for the genetic code: Information theory, statistical mechanics and the emergence of molecular codes

Phase transitions in evolutionary dynamics

Sharp changes in state, such as transitions from survival to extinction, are hallmarks of evolutionary dynamics in biological systems. These transitions can be explored using the techniques of statistical physics and the physics of nonlinear and complex systems. For example, a survival-to-extinction transition can be characterized as a non-equilibrium phase transition to an absorbing state. Here, we review the literature on phase transitions in evolutionary dynamics. We discuss directed percolation transitions in cellular automata and evolutionary models, and models that diverge from the directed percolation universality class. We explore in detail an example of an absorbing phase transition in an agent-based model of evolutionary dynamics, including previously unpublished data demonstrating similarity to, but also divergence from, directed percolation, as well as evidence for phase transition behavior at multiple levels of the model system's evolutionary structure. We discuss phase transition models of the error catastrophe in RNA virus dynamics and phase transition models for transition from chemistry to biochemistry, i.e., the origin of life. We conclude with a review of phase transition dynamics in models of natural selection, discuss the possible role of phase transitions in unraveling fundamental unresolved questions regarding multilevel selection and the major evolutionary transitions, and assess the future outlook for phase transitions in the investigation of evolutionary dynamics.

The structure of the genetic code as an optimal graph clustering problem

The standard genetic code (SGC) is the set of rules by which genetic information is translated into proteins, from codons, i.e. triplets of nucleotides, to amino acids. The questions about the origin and the main factor responsible for the present structure of the code are still under a hot debate. Various methodologies have been used to study the features of the code and assess the level of its potential optimality. Here, we introduced a new general approach to evaluate the quality of the genetic code structure. This methodology comes from graph theory and allows us to describe new properties of the genetic code in terms of conductance. This parameter measures the robustness of codon groups against the potential changes in translation of the protein-coding sequences generated by single nucleotide substitutions. We described the genetic code as a partition of an undirected and unweighted graph, which makes the model general and universal. Using this approach, we showed that the structure of the genetic code is a solution to the graph clustering problem. We presented and discussed the structure of the codes that are optimal according to the conductance. Despite the fact that the standard genetic code is far from being optimal according to the conductance, its structure is characterised by many codon groups reaching the minimum conductance for their size. The SGC represents most likely a local minimum in terms of errors occurring in protein-coding sequences and their translation.

Dimensional reduction in complex living systems: Where, why, and how

The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data-by distilling underlying principles and mechanisms-necessitates dimensional reduction. We propose that living systems achieve exquisite dimensional reduction, originating from their capacity to learn, through evolution and phenotypic plasticity, the relevant aspects of a non-random, smooth physical reality. We explain how geometric insights by mathematicians allow one to identify these genuine hallmarks of life and distinguish them from universal properties of generic data sets. We illustrate these principles in a concrete example of protein evolution, suggesting a simple general recipe that can be applied to understand other biological systems.

Genetic codes optimized as a traveling salesman problem

The Standard Genetic Code (SGC) is robust to mutational errors such that frequently occurring mutations minimally alter the physio-chemistry of amino acids. The apparent correlation between the evolutionary distances among codons and the physio-chemical distances among their cognate amino acids suggests an early co-diversification between the codons and amino acids. Here we formulated the co-minimization of evolutionary distances between codons and physio-chemical distances between amino acids as a Traveling Salesman Problem (TSP) and solved it with a Hopfield neural network. In this unsupervised learning algorithm, macromolecules (e.g., tRNAs and aminoacyl-tRNA synthetases) associating codons with amino acids were considered biological analogs of Hopfield neurons associating "tour cities" with "tour positions". The Hopfield network efficiently yielded an abundance of genetic codes that were more error-minimizing than SGC and could thus be used to design artificial genetic codes. We further argue that as a self-optimization algorithm, the Hopfield neural network provides a model of origin of SGC and other adaptive molecular systems through evolutionary learning.

On the origin of degeneracy in the genetic code

The degeneracy of amino acid coding is one of the most crucial and enigmatic aspects of the genetic code. Different theories about the origin of the genetic code have been developed. However, to date, there is no comprehensive hypothesis on the mechanism that might have generated the degeneracy as we observe it. Here, we provide a new theory that explains the origin of the degeneracy based only on symmetry principles. The approach allows one to describe exactly the degeneracy of the early code (progenitor of the genetic code of LUCA, the last universal common ancestor) which is hypothesized to have the same degeneracy as the present vertebrate mitochondrial genetic code. The theory is based upon the tessera code, that fits as the progenitor of the early code. Moreover, we describe in detail the possible evolutionary transitions implied by our theory. The approach is supported by a unified mathematical framework that accounts for the degeneracy properties of both nuclear and mitochondrial genetic codes. Our work provides a new perspective to the understanding of the origin of the genetic code and the roles of symmetry principles in the organization of genetic information.

The influence of different types of translational inaccuracies on the genetic code structure

BACKGROUND

The standard genetic code is a recipe for assigning unambiguously 21 labels, i.e. amino acids and stop translation signal, to 64 codons. However, at early stages of the translational machinery development, the codons did not have to be read unambiguously and the early genetic codes could have contained some ambiguous assignments of codons to amino acids. Therefore, the goal of this work was to obtain the genetic code structures which could have evolved assuming different types of inaccuracy of the translational machinery starting from unambiguous assignments of codons to amino acids.

RESULTS

We developed a theoretical model assuming that the level of uncertainty of codon assignments can gradually decrease during the simulations. Since it is postulated that the standard code has evolved to be robust against point mutations and mistranslations, we developed three simulation scenarios assuming that such errors can influence one, two or three codon positions. The simulated codes were selected using the evolutionary algorithm methodology to decrease coding ambiguity and increase their robustness against mistranslation.

CONCLUSIONS

The results indicate that the typical codon block structure of the genetic code could have evolved to decrease the ambiguity of amino acid to codon assignments and to increase the fidelity of reading the genetic information. However, the robustness to errors was not the decisive factor that influenced the genetic code evolution because it is possible to find theoretical codes that minimize the reading errors better than the standard genetic code.

Green function of correlated genes in a minimal mechanical model of protein evolution

The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly coupled amino acid network with interactions and motions that are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids and thereby, the transmission of forces. Mutations introduce localized perturbations to the propagator that scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis-the interaction among mutations in the gene-is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution and observe long-range epistasis, which facilitates collective functional modes.

Genetic Code Optimization for Cotranslational Protein Folding: Codon Directional Asymmetry Correlates with Antiparallel Betasheets, tRNA Synthetase Classes

A new codon property, codon directional asymmetry in nucleotide content (CDA), reveals a biologically meaningful genetic code dimension: palindromic codons (first and last nucleotides identical, codon structure XZX) are symmetric (CDA = 0), codons with structures ZXX/XXZ are 5'/3' asymmetric (CDA = - 1/1; CDA = - 0.5/0.5 if Z and X are both purines or both pyrimidines, assigning negative/positive (-/+) signs is an arbitrary convention). Negative/positive CDAs associate with (a) Fujimoto's tetrahedral codon stereo-table; (b) tRNA synthetase class I/II (aminoacylate the 2'/3' hydroxyl group of the tRNA's last ribose, respectively); and (c) high/low antiparallel (not parallel) betasheet conformation parameters. Preliminary results suggest CDA-whole organism associations (body temperature, developmental stability, lifespan). Presumably, CDA impacts spatial kinetics of codon-anticodon interactions, affecting cotranslational protein folding. Some synonymous codons have opposite CDA sign (alanine, leucine, serine, and valine), putatively explaining how synonymous mutations sometimes affect protein function. Correlations between CDA and tRNA synthetase classes are weaker than between CDA and antiparallel betasheet conformation parameters. This effect is stronger for mitochondrial genetic codes, and potentially drives mitochondrial codon-amino acid reassignments. CDA reveals information ruling nucleotide-protein relations embedded in reversed (not reverse-complement) sequences (5'-ZXX-3'/5'-XXZ-3').

The information capacity of the genetic code: Is the natural code optimal?

We envision the molecular evolution process as an information transfer process and provide a quantitative measure for information preservation in terms of the channel capacity according to the channel coding theorem of Shannon. We calculate Information capacities of DNA on the nucleotide (for non-coding DNA) and the amino acid (for coding DNA) level using various substitution models. We extend our results on coding DNA to a discussion about the optimality of the natural codon-amino acid code. We provide the results of an adaptive search algorithm in the code domain and demonstrate the existence of a large number of genetic codes with higher information capacity. Our results support the hypothesis of an ancient extension from a 2-nucleotide codon to the current 3-nucleotide codon code to encode the various amino acids.

Origins of tmRNA: the missing link in the birth of protein synthesis?

The RNA world hypothesis refers to the early period on earth in which RNA was central in assuring both genetic continuity and catalysis. The end of this era coincided with the development of the genetic code and protein synthesis, symbolized by the apparition of the first non-random messenger RNA (mRNA). Modern transfer-messenger RNA (tmRNA) is a unique hybrid molecule which has the properties of both mRNA and transfer RNA (tRNA). It acts as a key molecule during trans-translation, a major quality control pathway of modern bacterial protein synthesis. tmRNA shares many common characteristics with ancestral RNA. Here, we present a model in which proto-tmRNAs were the first molecules on earth to support non-random protein synthesis, explaining the emergence of early genetic code. In this way, proto-tmRNA could be the missing link between the first mRNA and tRNA molecules and modern ribosome-mediated protein synthesis.

Synthetic transitions: towards a new synthesis

The evolution of life in our biosphere has been marked by several major innovations. Such major complexity shifts include the origin of cells, genetic codes or multicellularity to the emergence of non-genetic information, language or even consciousness. Understanding the nature and conditions for their rise and success is a major challenge for evolutionary biology. Along with data analysis, phylogenetic studies and dedicated experimental work, theoretical and computational studies are an essential part of this exploration. With the rise of synthetic biology, evolutionary robotics, artificial life and advanced simulations, novel perspectives to these problems have led to a rather interesting scenario, where not only the major transitions can be studied or even reproduced, but even new ones might be potentially identified. In both cases, transitions can be understood in terms of phase transitions, as defined in physics. Such mapping (if correct) would help in defining a general framework to establish a theory of major transitions, both natural and artificial. Here, we review some advances made at the crossroads between statistical physics, artificial life, synthetic biology and evolutionary robotics.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

Self-referring DNA and protein: a remark on physical and geometrical aspects

All known life forms are based upon a hierarchy of interwoven feedback loops, operating over a cascade of space, time and energy scales. Among the most basic loops are those connecting DNA and proteins. For example, in genetic networks, DNA genes are expressed as proteins, which may bind near the same genes and thereby control their own expression. In this molecular type of self-reference, information is mapped from the DNA sequence to the protein and back to DNA. There is a variety of dynamic DNA-protein self-reference loops, and the purpose of this remark is to discuss certain geometrical and physical aspects related to the back and forth mapping between DNA and proteins. The mappings are examined as dimensional reductions and expansions between high- and low-dimensional manifolds in molecular spaces. The discussion raises basic questions regarding the nature of DNA and proteins as self-referring matter, which are examined in a simple toy model.

The non-power model of the genetic code: a paradigm for interpreting genomic information

In this article, we present a mathematical framework based on redundant (non-power) representations of integer numbers as a paradigm for the interpretation of genomic information. The core of the approach relies on modelling the degeneracy of the genetic code. The model allows one to explain many features and symmetries of the genetic code and to uncover hidden symmetries. Also, it provides us with new tools for the analysis of genomic sequences. We review briefly three main areas: (i) the Euplotid nuclear code, (ii) the vertebrate mitochondrial code, and (iii) the main coding/decoding strategies used in the three domains of life. In every case, we show how the non-power model is a natural unified framework for describing degeneracy and deriving sound biological hypotheses on protein coding. The approach is rooted on number theory and group theory; nevertheless, we have kept the technical level to a minimum by focusing on key concepts and on the biological implications.

Probable relationship between partitions of the set of codons and the origin of the genetic code

Here we study the distribution of randomly generated partitions of the set of amino acid-coding codons. Some results are an application from a previous work, about the Stirling numbers of the second kind and triplet codes, both to the cases of triplet codes having four stop codons, as in mammalian mitochondrial genetic code, and hypothetical doublet codes. Extending previous results, in this work it is found that the most probable number of blocks of synonymous codons, in a genetic code, is similar to the number of amino acids when there are four stop codons, as well as it could be for a primigenious doublet code. Also it is studied the integer partitions associated to patterns of synonymous codons and it is shown, for the canonical code, that the standard deviation inside an integer partition is one of the most probable. We think that, in some early epoch, the genetic code might have had a maximum of the disorder or entropy, independent of the assignment between codons and amino acids, reaching a state similar to "code freeze" proposed by Francis Crick. In later stages, maybe deterministic rules have reassigned codons to amino acids, forming the natural codes, such as the canonical code, but keeping the numerical features describing the set partitions and the integer partitions, like a "fossil numbers"; both kinds of partitions about the set of amino acid-coding codons.

Evolution of complete proteomes: guanine-cytosine pressure, phylogeny and environmental influences blend the proteomic architecture

Background

Guanine-cytosine (GC) composition is an important feature of genomes. Likewise, amino acid composition is a distinct, but less valued, feature of proteomes. A major concern is that it is not clear what valuable information can be acquired from amino acid composition data. To address this concern, in-depth analyses of the amino acid composition of the complete proteomes from 63 archaea, 270 bacteria, and 128 eukaryotes were performed.

Results

Principal component analysis of the amino acid matrices showed that the main contributors to proteomic architecture were genomic GC variation, phylogeny, and environmental influences. GC pressure drove positive selection on Ala, Arg, Gly, Pro, Trp, and Val, and adverse selection on Asn, Lys, Ile, Phe, and Tyr. The physico-chemical framework of the complete proteomes withstood GC pressure by frequency complementation of GC-dependent amino acid pairs with similar physico-chemical properties. Gln, His, Ser, and Val were responsible for phylogeny and their constituted components could differentiate archaea, bacteria, and eukaryotes. Environmental niche was also a significant factor in determining proteomic architecture, especially for archaea for which the main amino acids were Cys, Leu, and Thr. In archaea, hyperthermophiles, acidophiles, mesophiles, psychrophiles, and halophiles gathered successively along the environment-based principal component. Concordance between proteomic architecture and the genetic code was also related closely to genomic GC content, phylogeny, and lifestyles.

Conclusions

Large-scale analyses of the complete proteomes of a wide range of organisms suggested that amino acid composition retained the trace of GC variation, phylogeny, and environmental influences during evolution. The findings from this study will help in the development of a global understanding of proteome evolution, and even biological evolution.

What can information-asymmetric games tell us about the context of Crick's 'frozen accident'?

This paper describes a novel application of information-asymmetric (signalling) games to molecular biology in which utility is determined by the message complexity (rate) in addition to the error in information transfer (distortion). We show using a computational model how it is possible for the agents in one such game to evolve a signalling convention (separating equilibrium) that is suboptimal in terms of information transfer, but is nonetheless stable. In the context of an RNA world merging with a nascent amino acid one, such a game's equilibrium is alluded to by the genetic code, which is nearly optimal in terms of information transfer, but is also near-universal and nearly immutable. Such a framework suggests that cellularity may have emerged to encourage coordination between RNA species and sheds light on other aspects of RNA world biochemistry yet to be fully understood.

CMCpy: Genetic Code-Message Coevolution Models in Python

Code-message coevolution (CMC) models represent coevolution of a genetic code and a population of protein-coding genes (“messages”). Formally, CMC models are sets of quasispecies coupled together for fitness through a shared genetic code. Although CMC models display plausible explanations for the origin of multiple genetic code traits by natural selection, useful modern implementations of CMC models are not currently available. To meet this need we present CMCpy, an object-oriented Python API and command-line executable front-end that can reproduce all published results of CMC models. CMCpy implements multiple solvers for leading eigenpairs of quasispecies models. We also present novel analytical results that extend and generalize applications of perturbation theory to quasispecies models and pioneer the application of a homotopy method for quasispecies with non-unique maximally fit genotypes. Our results therefore facilitate the computational and analytical study of a variety of evolutionary systems. CMCpy is free open-source software available from http://pypi.python.org/pypi/CMCpy/.

Does the genetic code have a eukaryotic origin?

In the RNA world, RNA is assumed to be the dominant macromolecule performing most, if not all, core “house-keeping” functions. The ribo-cell hypothesis suggests that the genetic code and the translation machinery may both be born of the RNA world, and the introduction of DNA to ribo-cells may take over the informational role of RNA gradually, such as a mature set of genetic code and mechanism enabling stable inheritance of sequence and its variation. In this context, we modeled the genetic code in two content variables—GC and purine contents—of protein-coding sequences and measured the purine content sensitivities for each codon when the sensitivity (% usage) is plotted as a function of GC content variation. The analysis leads to a new pattern—the symmetric pattern—where the sensitivity of purine content variation shows diagonally symmetry in the codon table more significantly in the two GC content invariable quarters in addition to the two existing patterns where the table is divided into either four GC content sensitivity quarters or two amino acid diversity halves. The most insensitive codon sets are GUN (valine) and CAN (CAR for asparagine and CAY for aspartic acid) and the most biased amino acid is valine (always over-estimated) followed by alanine (always under-estimated). The unique position of valine and its codons suggests its key roles in the final recruitment of the complete codon set of the canonical table. The distinct choice may only be attributable to sequence signatures or signals of splice sites for spliceosomal introns shared by all extant eukaryotes.

A framework for designing and analyzing binary decision-making strategies in cellular systems

Cells make many binary (all-or-nothing) decisions based on noisy signals gathered from their environment and processed through noisy decision-making pathways. Reducing the effect of noise to improve the fidelity of decision-making comes at the expense of increased complexity, creating a tradeoff between performance and metabolic cost. We present a framework based on rate distortion theory, a branch of information theory, to quantify this tradeoff and design binary decision-making strategies that balance low cost and accuracy in optimal ways. With this framework, we show that several observed behaviors of binary decision-making systems, including random strategies, hysteresis, and irreversibility, are optimal in an information-theoretic sense for various situations. This framework can also be used to quantify the goals around which a decision-making system is optimized and to evaluate the optimality of cellular decision-making systems by a fundamental information-theoretic criterion. As proof of concept, we use the framework to quantify the goals of the externally triggered apoptosis pathway.

Communication theory and multicellular biology

In this Perspective, we propose that communication theory--a field of mathematics concerned with the problems of signal transmission, reception and processing--provides a new quantitative lens for investigating multicellular biology, ancient and modern. What underpins the cohesive organisation and collective behaviour of multicellular ecosystems such as microbial colonies and communities (microbiomes) and multicellular organisms such as plants and animals, whether built of simple tissue layers (sponges) or of complex differentiated cells arranged in tissues and organs (members of the 35 or so phyla of the subkingdom Metazoa)? How do mammalian tissues and organs develop, maintain their architecture, become subverted in disease, and decline with age? How did single-celled organisms coalesce to produce many-celled forms that evolved and diversified into the varied multicellular organisms in existence today? Some answers can be found in the blueprints or recipes encoded in (epi)genomes, yet others lie in the generic physical properties of biological matter such as the ability of cell aggregates to attain a certain complexity in size, shape, and pattern. We suggest that Lasswell's maxim "Who says what to whom in what channel with what effect" provides a foundation for understanding not only the emergence and evolution of multicellularity, but also the assembly and sculpting of multicellular ecosystems and many-celled structures, whether of natural or human-engineered origin. We explore how the abstraction of communication theory as an organising principle for multicellular biology could be realised. We highlight the inherent ability of communication theory to be blind to molecular and/or genetic mechanisms. We describe selected applications that analyse the physics of communication and use energy efficiency as a central tenet. Whilst communication theory has and could contribute to understanding a myriad of problems in biology, investigations of multicellular biology could, in turn, lead to advances in communication theory, especially in the still immature field of network information theory.