Codon evolution is governed by linear formulas

Equalizing the information amounts of protein and mRNA by information theory

Based on the Shannon's information communication theory, information amount of the entire length of a polymeric macromolecule can be calculated in bits through adding the entropies of each building block. Proteins, DNA and RNA are such macromolecules. When only the building blocks' variation is considered as the source of entropy, there is seemingly lower information in case of the protein if this approach is applied directly on a protein of specific size and the coding sequence size of the mRNA corresponding to the particular length of the protein. This decrease in the information amount seems contradictory but this apparent conflict is resolved by considering the conformational variations in proteins as a new variable in the calculation and balancing the approximated entropy of the coding part of the mRNA and the protein. Probabilities can change therefore we also assigned hypothetical probabilities to the conformational states, which represent the uneven distribution as the time spent in one conformation, providing the probability of the presence in either or one of the possible conformations. Results that are obtained by using hypothetical probabilities are in line with the experimental values of variations in the conformational-state of protein populations. This equalization approach has further biological relevance that it compensates for the degeneracy in the codon usage during protein translation and it leads to the conclusion that the alphabet size for the protein is rather optimal for the proper protein functioning within the thermodynamic milieu of the cell. The findings were also discussed in relation to the codon bias and have implications in relation to the codon evolution concept. Eventually, this work brings the fields of protein structural studies and molecular protein translation processes together with a novel approach.

A novel skew analysis reveals substitution asymmetries linked to genetic code GC-biases and PolIII a-subunit isoforms

Strand biases reflect deviations from a null expectation of DNA evolution that assumes strand-symmetric substitution rates. Here, we present strong evidence that nearest-neighbour preferences are a strand-biased feature of bacterial genomes, indicating neighbour-dependent substitution asymmetries. To detect such asymmetries we introduce an alignment free index (relative abundance skews). The profiles of relative abundance skews along coding sequences can trace the phylogenetic relations of bacteria, suggesting that the patterns of neighbour-dependent substitution strand-biases are not common among different lineages, but are rather species-specific. Analysis of neighbour-dependent and codon-site skews sheds light on the origins of substitution asymmetries. Via a simple model we argue that the structure of the genetic code imposes position-dependent substitution strand-biases along coding sequences, as a response to GC mutation pressure. Thus, the organization of the genetic code per se can lead to an uneven distribution of nucleotides among different codon sites, even when requirements for specific codons and amino-acids are not accounted for. Moreover, our results suggest that strand-biases in replication fidelity of PolIII α-subunit induce substitution asymmetries, both neighbour-dependent and independent, on a genome scale. The role of DNA repair systems, such as transcription-coupled repair, is also considered.

Normalization of Complete Genome Characteristics: Application to Evolution from Primitive Organisms to Homo sapiens

Normalized nucleotide and amino acid contents of complete genome sequences can be visualized as radar charts. The shapes of these charts depict the characteristics of an organism's genome. The normalized values calculated from the genome sequence theoretically exclude experimental errors. Further, because normalization is independent of both target size and kind, this procedure is applicable not only to single genes but also to whole genomes, which consist of a huge number of different genes. In this review, we discuss the applications of the normalization of the nucleotide and predicted amino acid contents of complete genomes to the investigation of genome structure and to evolutionary research from primitive organisms to Homo sapiens. Some of the results could never have been obtained from the analysis of individual nucleotide or amino acid sequences but were revealed only after the normalization of nucleotide and amino acid contents was applied to genome research. The discovery that genome structure was homogeneous was obtained only after normalization methods were applied to the nucleotide or predicted amino acid contents of genome sequences. Normalization procedures are also applicable to evolutionary research. Thus, normalization of the contents of whole genomes is a useful procedure that can help to characterize organisms.

Evidence for Natural Selection in Nucleotide Content Relationships Based on Complete Mitochondrial Genomes: Strong Effect of Guanine Content on Separation between Terrestrial and Aquatic Vertebrates

The complete vertebrate mitochondrial genome consists of 13 coding genes. We used this genome to investigate the existence of natural selection in vertebrate evolution. From the complete mitochondrial genomes, we predicted nucleotide contents and then separated these values into coding and non-coding regions. When nucleotide contents of a coding or non-coding region were plotted against the nucleotide content of the complete mitochondrial genomes, we obtained linear regression lines only between homonucleotides and their analogs. On every plot using G or A content purine, G content in aquatic vertebrates was higher than that in terrestrial vertebrates, while A content in aquatic vertebrates was lower than that in terrestrial vertebrates. Based on these relationships, vertebrates were separated into two groups, terrestrial and aquatic. However, using C or T content pyrimidine, clear separation between these two groups was not obtained. The hagfish (Eptatretus burgeri) was further separated from both terrestrial and aquatic vertebrates. Based on these results, nucleotide content relationships predicted from the complete vertebrate mitochondrial genomes reveal the existence of natural selection based on evolutionary separation between terrestrial and aquatic vertebrate groups. In addition, we propose that separation of the two groups might be linked to ammonia detoxification based on high G and low A contents, which encode Glu rich and Lys poor proteins.

Self-similarity analysis of eubacteria genome based on weighted graph

We introduce a weighted graph model to investigate the self-similarity characteristics of eubacteria genomes. The regular treating in similarity comparison about genome is to discover the evolution distance among different genomes. Few people focus their attention on the overall statistical characteristics of each gene compared with other genes in the same genome. In our model, each genome is attributed to a weighted graph, whose topology describes the similarity relationship among genes in the same genome. Based on the related weighted graph theory, we extract some quantified statistical variables from the topology, and give the distribution of some variables derived from the largest social structure in the topology. The 23 eubacteria recently studied by Sorimachi and Okayasu are markedly classified into two different groups by their double logarithmic point-plots describing the similarity relationship among genes of the largest social structure in genome. The results show that the proposed model may provide us with some new sights to understand the structures and evolution patterns determined from the complete genomes.

A combination dimensionality reduction approach to codon position patterns of eubacteria based on their complete genomes

Graphical techniques have become powerful tools for the visualization and analysis of complicated biological systems. However, we cannot give such a graphical representation in a 2D/3D space when the dimensions of the represented data are more than three dimensions. The proposed method, a combination dimensionality reduction approach (CDR), consists of two parts: (i) principal component analysis (PCA) with a newly defined parameter ρ and (ii) locally linear embedding (LLE) with a proposed graphical selection for its optional parameter k. The CDR approach with ρ and k not only avoids loss of principal information, but also sufficiently well preserves the global high-dimensional structures in low-dimensional space such as 2D or 3D. The applications of the CDR on characteristic analysis at different codon positions in genome show that the method is a useful tool by which biologists could find useful biological knowledge.

Modeling compositional dynamics based on GC and purine contents of protein-coding sequences

Background

Understanding the compositional dynamics of genomes and their coding sequences is of great significance in gaining clues into molecular evolution and a large number of publically-available genome sequences have allowed us to quantitatively predict deviations of empirical data from their theoretical counterparts. However, the quantification of theoretical compositional variations for a wide diversity of genomes remains a major challenge.

Results

To model the compositional dynamics of protein-coding sequences, we propose two simple models that take into account both mutation and selection effects, which act differently at the three codon positions, and use both GC and purine contents as compositional parameters. The two models concern the theoretical composition of nucleotides, codons, and amino acids, with no prerequisite of homologous sequences or their alignments. We evaluated the two models by quantifying theoretical compositions of a large collection of protein-coding sequences (including 46 of Archaea, 686 of Bacteria, and 826 of Eukarya), yielding consistent theoretical compositions across all the collected sequences.

Conclusions

We show that the compositions of nucleotides, codons, and amino acids are largely determined by both GC and purine contents and suggest that deviations of the observed from the expected compositions may reflect compositional signatures that arise from a complex interplay between mutation and selection via DNA replication and repair mechanisms.

Reviewers

This article was reviewed by Zhaolei Zhang (nominated by Mark Gerstein), Guruprasad Ananda (nominated by Kateryna Makova), and Daniel Haft.

Distinguishable codon usage and amino acid composition patterns among substrates of leaderless secretory pathways from proteobacteria

The combined set of codon usage frequencies (61 sense codons) from the 111 annotated sequences of leaderless secreted type I, type III, type IV, and type VI proteins from proteobacteria were subjected to the forward and backward selection to obtain a combination of most effective predictor variables for classification/prediction purposes. The group of 24 codon frequencies displayed a strong discriminatory power with an accuracy of 100% for originally grouped and 97.3 +/- 1.6% for cross-validated (LOOCV) cases and an acceptable error rate (0.062 +/- 0.012) in k-fold (k = 6) cross-validation (KCV). The summary frequencies of synonymous codons for ten amino acids as the alternative predictor variables revealed a comparable discriminatory power (92.8 +/- 2.5% for LOOCV), however at somewhat lower levels of prediction accuracy (0.106 +/- 0.015 of KCV). A number of significant (p < 0.001) differences were found among indices of codon usage and amino acid composition depending on a definite secretion type. About 60% of secretion substrates were characterized as apparently originated from horizontal gene transfer events or putative alien genes and found to be unequally allocated in respect of groups. The proposed prediction approaches could be used to specify secretome proteins from genomic sequences as well as to assess the compatibility between bacterial secretion pathways and secretion substrates.

Classification analysis of dual nucleotides using dimension reduction

We introduce a new approach to investigate the dual nucleotides compositions of 11 Gram-positive and 12 Gram-negative eubacteria recently studied by Sorimachi and Okayasu. The approach firstly obtains a 16-dimension vector set of dual nucleotides by PN-curve from the complete genome of organism. Each vector of the set corresponds to a single gene of genome. Then we reduce the 16-dimension vector set to 2-dimension by principal components analysis (PCA). The reduction avoids possible loss of information averaging all 16-dimension vectors. Then we suggest a 2D graphical representation based on the 2-dimension vector to investigate the classification patters among different organisms.

Organisms can essentially be classified according to two codon patterns

We recently classified 23 bacteria into two types based on their complete genomes; "S-type" as represented by Staphylococcus aureus and "E-type" as represented by Escherichia coli. Classification was characterized by concentrations of Arg, Ala or Lys in the amino acid composition calculated from the complete genome. Based on these previous classifications, not only prokaryotic but also eukaryotic genome structures were investigated by amino acid compositions and nucleotide contents. Organisms consisting of 112 bacteria, 15 archaea and 18 eukaryotes were classified into two major groups by cluster analysis using GC contents at the three codon positions calculated from complete genomes. The 145 organisms were classified into "AT-type" and "GC-type" represented by high A or T (low G or C) and high G or C (low A or T) contents, respectively, at every third codon position. Reciprocal changes between G or C and A or T contents at the third codon position occurred almost synchronously in every codon among the organisms. Correlations between amino acid concentrations (Ala, Ile and Lys) and the nucleotide contents at the codon position were obtained in both "AT-type" and "GC-type" organisms, but with different regression coefficients. In certain correlations of amino acid concentrations with GC contents, eukaryotes, archaea and bacteria showed different behaviors; thus these kingdoms evolved differently. All organisms are basically classifiable into two groups having characteristic codon patterns; organisms with low GC and high AT contents at the third codon position and their derivatives, and organisms with an inverse relationship.