Block structure and stability of the genetic code

A binary representation of the genetic code

This article introduces a novel binary representation of the canonical genetic code based on both the structural similarities of the nucleotides, as well as the physicochemical properties of the encoded amino acids. Each of the four mRNA bases is assigned a unique 2-bit identifier, so that the 64 triplet codons are each indexed by a 6-bit label. The ordering of the bits reflects the hierarchical organization manifested by the DNA replication/repair and tRNA translation systems. In this system, transition and transversion mutations are naturally expressed as binary operations, and the severities of the different point mutations can be analyzed. Using a principal component analysis, it is shown that the physicochemical properties of amino acids related to protein folding also correlate with certain bit positions of their respective labels. Thus, the likelihood for a point mutation to be conservative, and less likely to cause a change in protein functionality, can be estimated.

Analysis of the optimality of the standard genetic code

Many theories have been proposed attempting to explain the origin of the genetic code. In this work, we compare performance of the standard genetic code against millions of randomly generated codes. On left, ability of genetic codes to encode additional information and their robustness to frameshift mutations.

An analysis of single amino acid repeats as use case for application specific background models

Background

Sequence analysis aims to identify biologically relevant signals against a backdrop of functionally meaningless variation. Increasingly, it is recognized that the quality of the background model directly affects the performance of analyses. State-of-the-art approaches rely on classical sequence models that are adapted to the studied dataset. Although performing well in the analysis of globular protein domains, these models break down in regions of stronger compositional bias or low complexity. While these regions are typically filtered, there is increasing anecdotal evidence of functional roles. This motivates an exploration of more complex sequence models and application-specific approaches for the investigation of biased regions.

Results

Traditional Markov-chains and application-specific regression models are compared using the example of predicting runs of single amino acids, a particularly simple class of biased regions. Cross-fold validation experiments reveal that the alternative regression models capture the multi-variate trends well, despite their low dimensionality and in contrast even to higher-order Markov-predictors. We show how the significance of unusual observations can be computed for such empirical models. The power of a dedicated model in the detection of biologically interesting signals is then demonstrated in an analysis identifying the unexpected enrichment of contiguous leucine-repeats in signal-peptides. Considering different reference sets, we show how the question examined actually defines what constitutes the 'background'. Results can thus be highly sensitive to the choice of appropriate model training sets. Conversely, the choice of reference data determines the questions that can be investigated in an analysis.

Conclusions

Using a specific case of studying biased regions as an example, we have demonstrated that the construction of application-specific background models is both necessary and feasible in a challenging sequence analysis situation.

Stability of the genetic code and optimal parameters of amino acids

The standard genetic code is known to be much more efficient in minimizing adverse effects of misreading errors and one-point mutations in comparison with a random code having the same structure, i.e. the same number of codons coding for each particular amino acid. We study the inverse problem, how the code structure affects the optimal physico-chemical parameters of amino acids ensuring the highest stability of the genetic code. It is shown that the choice of two or more amino acids with given properties determines unambiguously all the others. In this sense the code structure determines strictly the optimal parameters of amino acids or the corresponding scales may be derived directly from the genetic code. In the code with the structure of the standard genetic code the resulting values for hydrophobicity obtained in the scheme "leave one out" and in the scheme with fixed maximum and minimum parameters correlate significantly with the natural scale. The comparison of the optimal and natural parameters allows assessing relative impact of physico-chemical and error-minimization factors during evolution of the genetic code. As the resulting optimal scale depends on the choice of amino acids with given parameters, the technique can also be applied to testing various scenarios of the code evolution with increasing number of codified amino acids. Our results indicate the co-evolution of the genetic code and physico-chemical properties of recruited amino acids.

A study of entropy/clarity of genetic sequences using metric spaces and fuzzy sets

The study of genetic sequences is of great importance in biology and medicine. Sequence analysis and taxonomy are two major fields of application of bioinformatics. In the present paper we extend the notion of entropy and clarity to the use of different metrics and apply them in the case of the Fuzzy Polynuclotide Space (FPS). Applications of these notions on selected polynucleotides and complete genomes both in the I(12×k) space, but also using their representation in FPS are presented. Our results show that the values of fuzzy entropy/clarity are indicative of the degree of complexity necessary for the description of the polynucleotides in the FPS, although in the latter case the interpretation is slightly different than in the case of the I(12×k) hypercube. Fuzzy entropy/clarity along with the use of appropriate metrics can contribute to sequence analysis and taxonomy.

A model-independent approach to infer hierarchical codon substitution dynamics

Background

Codon substitution constitutes a fundamental process in molecular biology that has been studied extensively. However, prior studies rely on various assumptions, e.g. regarding the relevance of specific biochemical properties, or on conservation criteria for defining substitution groups. Ideally, one would instead like to analyze the substitution process in terms of raw dynamics, independently of underlying system specifics. In this paper we propose a method for doing this by identifying groups of codons and amino acids such that these groups imply closed dynamics. The approach relies on recently developed spectral and agglomerative techniques for identifying hierarchical organization in dynamical systems.

Results

We have applied the techniques on an empirically derived Markov model of the codon substitution process that is provided in the literature. Without system specific knowledge of the substitution process, the techniques manage to "blindly" identify multiple levels of dynamics; from amino acid substitutions (via the standard genetic code) to higher order dynamics on the level of amino acid groups. We hypothesize that the acquired groups reflect earlier versions of the genetic code.

Conclusions

The results demonstrate the applicability of the techniques. Due to their generality, we believe that they can be used to coarse grain and identify hierarchical organization in a broad range of other biological systems and processes, such as protein interaction networks, genetic regulatory networks and food webs.

Origin and evolution of the genetic code: the universal enigma

The genetic code is nearly universal, and the arrangement of the codons in the standard codon table is highly nonrandom. The three main concepts on the origin and evolution of the code are the stereochemical theory, according to which codon assignments are dictated by physicochemical affinity between amino acids and the cognate codons (anticodons); the coevolution theory, which posits that the code structure coevolved with amino acid biosynthesis pathways; and the error minimization theory under which selection to minimize the adverse effect of point mutations and translation errors was the principal factor of the code's evolution. These theories are not mutually exclusive and are also compatible with the frozen accident hypothesis, that is, the notion that the standard code might have no special properties but was fixed simply because all extant life forms share a common ancestor, with subsequent changes to the code, mostly, precluded by the deleterious effect of codon reassignment. Mathematical analysis of the structure and possible evolutionary trajectories of the code shows that it is highly robust to translational misreading but there are numerous more robust codes, so the standard code potentially could evolve from a random code via a short sequence of codon series reassignments. Thus, much of the evolution that led to the standard code could be a combination of frozen accident with selection for error minimization although contributions from coevolution of the code with metabolic pathways and weak affinities between amino acids and nucleotide triplets cannot be ruled out. However, such scenarios for the code evolution are based on formal schemes whose relevance to the actual primordial evolution is uncertain. A real understanding of the code origin and evolution is likely to be attainable only in conjunction with a credible scenario for the evolution of the coding principle itself and the translation system.

Mutational robustness and geometrical form in protein structures

Theoretical studies of RNA and lattice protein models suggest that mutationally robust or the so-called designable phenotypes tend to have special geometric features such as being more compact and more geometrically regular. Such geometrical forms have been also linked to speed of folding and stability properties that may also assist in promoting mutational robustness. Here we test these theoretical predictions on a non-redundant collection of 2,660 experimentally determined structures from the PDB (Protein Data Bank) and CATH (Class Architecture Topology Homologous superfamily) database. We first developed an index summarizing the geometrical regularity of the structures and then used this index to show that the statistical pattern of empirical data is consistent with the theoretical predictions relating geometry to mutational robustness. Mutationally robust proteins tend to be more symmetric and compact. But, the relationship between compactness and robustness cannot be explained simply by the geometrical packing of individual amino acids in proteins; rather, it is the property of the whole system that is related to the statistical characteristics of the folding landscape. Finally, we hypothesize that a triplet relationship between mutational robustness, stability and form is a general properties of objects that optimize real-valued relationships between sequences and discrete structures.

Evolution of the genetic code: partial optimization of a random code for robustness to translation error in a rugged fitness landscape

Background

The standard genetic code table has a distinctly non-random structure, with similar amino acids often encoded by codons series that differ by a single nucleotide substitution, typically, in the third or the first position of the codon. It has been repeatedly argued that this structure of the code results from selective optimization for robustness to translation errors such that translational misreading has the minimal adverse effect. Indeed, it has been shown in several studies that the standard code is more robust than a substantial majority of random codes. However, it remains unclear how much evolution the standard code underwent, what is the level of optimization, and what is the likely starting point.

Results

We explored possible evolutionary trajectories of the genetic code within a limited domain of the vast space of possible codes. Only those codes were analyzed for robustness to translation error that possess the same block structure and the same degree of degeneracy as the standard code. This choice of a small part of the vast space of possible codes is based on the notion that the block structure of the standard code is a consequence of the structure of the complex between the cognate tRNA and the codon in mRNA where the third base of the codon plays a minimum role as a specificity determinant. Within this part of the fitness landscape, a simple evolutionary algorithm, with elementary evolutionary steps comprising swaps of four-codon or two-codon series, was employed to investigate the optimization of codes for the maximum attainable robustness. The properties of the standard code were compared to the properties of four sets of codes, namely, purely random codes, random codes that are more robust than the standard code, and two sets of codes that resulted from optimization of the first two sets. The comparison of these sets of codes with the standard code and its locally optimized version showed that, on average, optimization of random codes yielded evolutionary trajectories that converged at the same level of robustness to translation errors as the optimization path of the standard code; however, the standard code required considerably fewer steps to reach that level than an average random code. When evolution starts from random codes whose fitness is comparable to that of the standard code, they typically reach much higher level of optimization than the standard code, i.e., the standard code is much closer to its local minimum (fitness peak) than most of the random codes with similar levels of robustness. Thus, the standard genetic code appears to be a point on an evolutionary trajectory from a random point (code) about half the way to the summit of the local peak. The fitness landscape of code evolution appears to be extremely rugged, containing numerous peaks with a broad distribution of heights, and the standard code is relatively unremarkable, being located on the slope of a moderate-height peak.

Conclusion

The standard code appears to be the result of partial optimization of a random code for robustness to errors of translation. The reason the code is not fully optimized could be the trade-off between the beneficial effect of increasing robustness to translation errors and the deleterious effect of codon series reassignment that becomes increasingly severe with growing complexity of the evolving system. Thus, evolution of the code can be represented as a combination of adaptation and frozen accident.

Reviewers

This article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.

Open Peer Review

This article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.

Genetic code from tRNA point of view

The possible codon-anticodon pairings follow the standard genetic code, yet in a different mode. The corresponding rules for decoding sequence of the codons in mRNA with tRNA may be called "tRNA code". In this paper we analyse the mutational and translational stability of such tRNA code. Our approach is based on the model of "ambiguous intermediate" and on the study of underlying block structure and Eulerean graph technique. It is shown that the wobble rules and the reduced number of tRNA anticodons strongly affect the mutational and translational stability of the code. The selection of tRNA anticodons, besides the optimization of translation, also ensures the more reliable start and, to a lesser extent, the stop of translation. The attribution of tRNA anticodons to the groups [WWW, WWS, SWW, SWS] and [SSS, SSW, WSS, WSW] as well as [MMM, MMK, KMM, KMK] and [KKK, KKM, MKK, MKM] clearly correlates with class I and class II aminoacyl-tRNA synthetases and obeys the principle of the optimal coding in both cases. Both W-S and M-K groupings also refer to the encoding of amino acids with the large and small side-chain volumes, which may provide such an attribution. The higher variability of tRNA code agrees with the suggestions that the variations in an assignment of tRNA anticodons may serve as the driving force generating the different variants of the genetic code.

On the coevolution of genes and genetic code

The canonical genetic code acts efficiently in minimizing the effects of mistranslations and point mutations. In the work presented we have also considered the effects of single nucleotide insertions and deletions on the optimality of the genetic code. Our results suggest that the canonical genetic code compensates for the ins/del mutations as well as mistranslations and point mutations. On the other hand, we highlighted the point that ins/del mutations have a lesser impact on the selected genes of Saccharomyces cerevisiae compared to randomly generated ones. We hypothesized that the codon usage preferences in S. cerevisiae genes are responsible for the higher efficiency of translation machinery in this organism. Our results support the conjecture that codon usage preferences render the genetic code more effective in minimizing the effects of ins/del mutations.

Gene algebra from a genetic code algebraic structure

By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codons. The group obtained over the set of codons is isomorphic to the group (Z(64), +) of the integer module 64. On the Z(64)-algebra of the set of 64(N) codon sequences of length N, gene mutations are described by means of endomorphisms f:(Z(64))(N)-->(Z(64))(N). Endomorphisms and automorphisms helped us describe the gene mutation pathways. For instance, 77.7% mutations in 749 HIV protease gene sequences correspond to unique diagonal endomorphisms of the wild type strain HXB2. In particular, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to diagonal automorphisms of the wild type. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to automorphisms. Hence, in the analyses of molecular evolution process on the DNA sequence set of length N, the Z(64)-algebra will help us explain the quantitative relationships between genes.

An algorithm for the study of DNA sequence evolution based on the genetic code

Recent studies of the quantum-mechanical processes in the DNA molecule have seriously challenged the principle that mutations occur randomly. The proton tunneling mechanism causes tautomeric transitions in base pairs resulting in mutations during DNA replication. The meticulous study of the quantum-mechanical phenomena in DNA may reveal that the process of mutagenesis is not completely random. We are still far away from a complete quantum-mechanical model of DNA sequence mutagenesis because of the complexity of the processes and the complex three-dimensional structure of the molecule. In this paper we have developed a quantum-mechanical description of DNA evolution and, following its outline, we have constructed a classical model for DNA evolution assuming that some aspects of the quantum-mechanical processes have influenced the determination of the genetic code. Conversely, our model assumes that the genetic code provides information about the quantum-mechanical mechanisms of mutagenesis, as the current code is the product of an evolutionary process that tries to minimize the spurious consequences of mutagenesis. Based on this model we develop an algorithm that can be used to study the accumulation of mutations in a DNA sequence. The algorithm has a user-friendly interface and the user can change key parameters in order to study relevant hypotheses.

Rational design of DNA sequences for nanotechnology, microarrays and molecular computers using Eulerian graphs

Nucleic acids are molecules of choice for both established and emerging nanoscale technologies. These technologies benefit from large functional densities of 'DNA processing elements' that can be readily manufactured. To achieve the desired functionality, polynucleotide sequences are currently designed by a process that involves tedious and laborious filtering of potential candidates against a series of requirements and parameters. Here, we present a complete novel methodology for the rapid rational design of large sets of DNA sequences. This method allows for the direct implementation of very complex and detailed requirements for the generated sequences, thus avoiding 'brute force' filtering. At the same time, these sequences have narrow distributions of melting temperatures. The molecular part of the design process can be done without computer assistance, using an efficient 'human engineering' approach by drawing a single blueprint graph that represents all generated sequences. Moreover, the method eliminates the necessity for extensive thermodynamic calculations. Melting temperature can be calculated only once (or not at all). In addition, the isostability of the sequences is independent of the selection of a particular set of thermodynamic parameters. Applications are presented for DNA sequence designs for microarrays, universal microarray zip sequences and electron transfer experiments.