The codon usage code for co-translational folding of viral capsids

Codon bias is common to all organisms and is the result of mutation, drift, and selection. Selection for the efficiency and accuracy of translation is well recognized as a factor shaping the codon usage. In contrast, fewer studies report the control of the rate of translation as an additional selective pressure influencing the codon usage of an organism. Experimental molecular evolution using RNA virus populations is a powerful tool for the identification of mechanisms underlying the codon bias. Indeed, the role of deoptimized codons on the co-translational folding has been proven in the capsids of two fecal-orally transmitted picornaviruses, poliovirus and the hepatitis A virus, emphasizing the role of the frequency of codons in determining the phenotype. However, most studies on virus codon usage rely only on computational analyses, and experimental studies should be encouraged to clearly define the role of selection on codon evolution.

Shedding light on the underlying characteristics of genomes using Kronecker model families of codon evolution

The mechanistic models of codon evolution rely on some simplistic assumptions in order to reduce the computational complexity of estimating the high number of parameters of the models. This paper is an attempt to investigate how much these simplistic assumptions are misleading when they violate the nature of the biological dataset in hand. We particularly focus on three simplistic assumptions made by most of the current mechanistic codon models including: 1) only single substitutions between nucleotides within codons in the codon transition rate matrix are allowed. 2) mutation is homogenous across nucleotides within a codon. 3) assuming HKY nucleotide model is good enough at the nucleotide level. For this purpose, we developed a framework of mechanistic codon models, each model in the framework hold or relax some of the mentioned simplifying assumptions. Holding or relaxing the three simplistic assumptions results in total to eight different mechanistic models in the framework. Through several experiments on biological datasets and simulations we show that the three simplistic assumptions are unrealistic for most of the biological datasets and relaxing these assumptions lead to accurate estimation of evolutionary parameters such as selection pressure.

Molecular Evolution in Small Steps under Prevailing Negative Selection: A Nearly Universal Rule of Codon Substitution

The widely accepted view that evolution proceeds in small steps is based on two premises: 1) negative selection acts strongly against large differences and 2) positive selection favors small-step changes. The two premises are not biologically connected and should be evaluated separately. We now extend a previous approach to studying codon evolution in the entire genome. Codon substitution rate is a function of the physicochemical distance between amino acids (AAs), equated with the step size of evolution. Between nine pairs of closely related species of plants, invertebrates, and vertebrates, the evolutionary rate is strongly and negatively correlated with a set of AA distances (ΔU, scaled to [0, 1]). ΔU, a composite measure of evolutionary rates across diverse taxa, is influenced by almost all of the 48 physicochemical properties used here. The new analyses reveal a crucial trend hidden from previous studies: ΔU is strongly correlated with the evolutionary rate (R2 > 0.8) only when the genes are predominantly under negative selection. Because most genes in most taxa are strongly constrained by negative selection, ΔU has indeed appeared to be a nearly universal measure of codon evolution. In conclusion, molecular evolution at the codon level generally takes small steps due to the prevailing negative selection. Whether positive selection may, or may not, follow the small-step rule is addressed in a companion study.

Molecular evolution in small steps under prevailing negative selection – A nearly-universal rule of codon substitution

The widely accepted view that evolution proceeds in small steps is based on two premises: i) negative selection acts strongly against large differences (Kimura 1983); and ii) positive selection favors small-step changes (Fisher 1930). The two premises are not biologically connected and should be evaluated separately. We now extend the approach of Tang et al. (2004) to codon evolution for the entire genome. Codon substitution rate is a function of the physico-chemical distance between amino acids (AAs), equated with the step size of evolution. This step size depends on a large number of physico-chemical properties as 46 of the 48 properties examined affect the rate. Between 9 pairs of closely-related species of plants, invertebrates and vertebrates, the evolutionary rate is indeed strongly andnegativelycorrelated with the AA distance (ΔU, scaled to [0, 1]). While the analyses corroborate the published results that relied on partial genomes, there is an important difference: ΔUis strongly correlated with the evolutionary rate (R2> 0.8) only when the genes are under predominant negative selection. Nevertheless, since most genes in most taxa are strongly constrained by negative selection, ΔUwould appear to be a nearly-universal measure of codon evolution. In conclusion, the driving force of the small-step evolution at the codon level is negative selection. The unanswered question of whether positive selection may, or may not, follow the small-step rule will be addressed in a companion study (Chen, et al. 2019).

Positive selection on human gamete-recognition genes

Coevolution of genes that encode interacting proteins expressed on the surfaces of sperm and eggs can lead to variation in reproductive compatibility between mates and reproductive isolation between members of different species. Previous studies in mice and other mammals have focused in particular on evidence for positive or diversifying selection that shapes the evolution of genes that encode sperm-binding proteins expressed in the egg coat or zona pellucida (ZP). By fitting phylogenetic models of codon evolution to data from the 1000 Genomes Project, we identified candidate sites evolving under diversifying selection in the human genes ZP3 and ZP2. We also identified one candidate site under positive selection in C4BPA, which encodes a repetitive protein similar to the mouse protein ZP3R that is expressed in the sperm head and binds to the ZP at fertilization. Results from several additional analyses that applied population genetic models to the same data were consistent with the hypothesis of selection on those candidate sites leading to coevolution of sperm- and egg-expressed genes. By contrast, we found no candidate sites under selection in a fourth gene (ZP1) that encodes an egg coat structural protein not directly involved in sperm binding. Finally, we found that two of the candidate sites (in C4BPA and ZP2) were correlated with variation in family size and birth rate among Hutterite couples, and those two candidate sites were also in linkage disequilibrium in the same Hutterite study population. All of these lines of evidence are consistent with predictions from a previously proposed hypothesis of balancing selection on epistatic interactions between C4BPA and ZP3 at fertilization that lead to the evolution of co-adapted allele pairs. Such patterns also suggest specific molecular traits that may be associated with both natural reproductive variation and clinical infertility.

Unbiased estimate of synonymous and non-synonymous substitution rates with non-stationary base composition

The measure of synonymous and non-synonymous substitution rates (dS and dN) is useful for assessing selection operating on protein sequences or for investigating mutational processes affecting genomes. In particular, the ratio is expected to be a good proxy of ω, the probability of fixation of non-synonymous mutations relative to that of neutral mutations. Standard methods for estimating dN, dS or ω rely on the assumption that the base composition of sequences is at the equilibrium of the evolutionary process. In many clades, this assumption of stationarity is in fact incorrect, and we show here through simulations and through analyses of empirical data that non-stationarity biases the estimate of dN, dS and ω. We show that the bias in the estimate of ω can be fixed by explicitly considering non-stationarity in the modeling of codon evolution, in a maximum likelihood framework. Moreover, we propose an exact method of estimate of dN and dS on branches, based on stochastic mapping, that can take into account non-stationarity. This method can be directly applied to any kind of model of evolution of codons, as long as neutrality is clearly parameterized.

On the interpretation of results returned by branch-site models

In a recent study, Murrell et al. (2015) compared the performance of several branch-site models of codon evolution. Their interpretation of results published by Lu & Guindon (2014) suggests that the stochastic branch-site model implemented in the software fitmodel is anti-conservative altogether, i.e., positive selection is detected more often than expected when analyzing sequences evolving under a mixture of neutrality and negative selection. I argue here that this presentation of the performance of fitmodel is misleading and should not deter evolutionary biologists from using this approach in exploratory analyses of selection patterns at the molecular level.

On the interpretation of results returned by branch-site models

In a recent study, Murrell et al. (2015) compared the performance of several branch-site models of codon evolution. Their interpretation of results published by Lu & Guindon (2014) suggests that the stochastic branch-site model implemented in the software fitmodel is anti-conservative altogether, i.e., positive selection is detected more often than expected when analyzing sequences evolving under a mixture of neutrality and negative selection. I argue here that this presentation of the performance of fitmodel is misleading and should not deter evolutionary biologists from using this approach in exploratory analyses of selection patterns at the molecular level.