Expected frequencies of codon use as a function of mutation rates and codon fitnesses

Codon usage and selection on proteins

Selection pressures on proteins are usually measured by comparing homologous nucleotide sequences (Zuckerkandl and Pauling 1965). Recently we introduced a novel method, termed volatility, to estimate selection pressures on proteins on the basis of their synonymous codon usage (Plotkin and Dushoff 2003; Plotkin et al. 2004). Here we provide a theoretical foundation for this approach. Under the Fisher-Wright model, we derive the expected frequencies of synonymous codons as a function of the strength of selection on amino acids, the mutation rate, and the effective population size. We analyze the conditions under which we can expect to draw inferences from biased codon usage, and we estimate the time scales required to establish and maintain such a signal. We find that synonymous codon usage can reliably distinguish between negative selection and neutrality only for organisms, such as some microbes, that experience large effective population sizes or periods of elevated mutation rates. The power of volatility to detect positive selection is also modest--requiring approximately 100 selected sites--but it depends less strongly on population size. We show that phenomena such as transient hyper-mutators can improve the power of volatility to detect selection, even when the neutral site heterozygosity is low. We also discuss several confounding factors, neglected by the Fisher-Wright model, that may limit the applicability of volatility in practice.

Estimating selection pressures from limited comparative data

We recently introduced a novel method for estimating selection pressures on proteins, termed "volatility," which requires only a single genome sequence. Some criticisms that have been levied against this approach are valid, but many others are based on misconceptions of volatility, or they apply equally to comparative methods of estimating selection. Here, we introduce a simple regression technique for estimating selection pressures on all proteins in a genome, on the basis of limited comparative data. The regression technique does not depend on an underlying population-genetic mechanism. This new approach to estimating selection across a genome should be more powerful and more widely applicable than volatility itself.

Complete DNA sequence analyses of the first two varicella-zoster virus glycoprotein E (D150N) mutant viruses found in North America: evolution of genotypes with an accelerated cell spread phenotype

Varicella-zoster virus (VZV) is considered to be one of the most genetically stable of all the herpesviruses. Yet two VZV strains with a D150N missense mutation within the gE glycoprotein were isolated in North America in 1998 and 2002. The mutant strains have an accelerated cell spread phenotype, which distinguishes them from all wild-type and laboratory viruses. Since the VZV genome contains 70 additional open reading frames (ORFs), the possibility existed that the phenotypic change was actually due to an as-yet-undiscovered mutation or deletion elsewhere in the genome. To exclude this hypothesis, the entire genomes of the two mutant viruses were sequenced and found to contain 124,883 (VZV-MSP) and 125,459 (VZV-BC) nucleotides. Coding single-nucleotide polymorphisms (SNPs) were identified in 14 ORFs. One missense mutation was discovered in gH, but none was found in gB, gI, gL, or gK. There were no coding SNPs in the major regulatory protein ORF 62. One polymorphism was discovered which could never have been anticipated based on current knowledge of herpesvirus genomics, namely, the origins of replication differed from those in the prototype strain but not in a manner expected to affect cell spread. When the two complete mutant VZV sequences were surveyed in their entirety, the most reasonable conclusion was that the increased cell spread phenotype was dependent substantially or solely on the single D150N polymorphism in glycoprotein gE. The genomic results also expanded the evolutionary database by identifying which VZV ORFs were more likely to mutate over time.

Theoretical molecular biology: prospectives and perspectives

I briefly discuss some aspects of theoretical molecular biology. Specifically, I include the issues of searches for homologies via string matchings, for patterns of specific nucleotide groupings and of sequence-structure relationship. The various approaches developed in order to achieve this end are described, attempting to convey some of the excitement in this quickly growing field.

The missense errors in protein can be controlled by selective synonymous codon usage at the level of transcription

In the cases of the 6-fold degenerate residues and the stop signal, selective codon usage at the level of transcription can account for a 10-20% variation in their mistranslation rate. For all other residues, the mistranslation rate is dependent upon the degree of degeneracy only, but not upon the pattern of synonymous codon usage.

An estimate on the effect of point mutation and natural selection on the rate of amino acid replacement in proteins

We outline a method for estimating quantitatively the influence of point mutations and selection on the frequencies of codons and amino acids. We show how the mutation rate, i.e., the rate of amino acid replacement due to point mutation, can be affected by the codon usage as well as by the rates of the involved base exchanges. A comparison of the mutation rates calculated from reliable values of codon usage and base exchange probabilities with those that would be expected on the basis of chance reveals a notable suppression of replacements leading to tryptophan, glutamate, lysine, and methionine, and particularly of those leading to the termination codons. If selection constraints are neglected and only mutations are taken into account, the best agreement between expected and observed frequencies of both codons and amino acids is obtained for alpha = 1.13-1.15, where (Formula: see text). The "selection values" of codons and amino acids derived by our method show a pattern that partially deviates from others in the literature. For example, the selection pressure on methionine and cysteine turns out to be much more pronounced than expected if only the discrepancies between their observed and expected occurrences in proteins are considered. To estimate to what extent randomly occurring amino acid replacements are accepted by selection, we constructed an "acceptability matrix" from the well-established matrix of accepted point mutations. On the basis of this matrix "acceptability values" of the amino acids can be defined that correlate with their selection values. We also examine the significance of mutations and selection of amino acids with respect to their physicochemical properties and functions in proteins. The conservatism of amino acid replacements with respect to certain properties such as polarity can be brought about by the mutational process alone, whereas the conservatism with respect to other relevant properties--among them all measures of bulkiness--obviously is the result of additional selectional constraints on the evolution of protein structures.

Does the 'non-coding' strand code?

The hypothesis that DNA strands complementary to the coding strand contain in phase coding sequences has been investigated. Statistical analysis of the 50 genes of bacteriophage T7 shows no significant correlation between patterns of codon usage on the coding and non-coding strands. In Bacillus and yeast genes the correlation observed is not different from that expected with random synonymous codon usage, while a high correlation seen in 52 E. coli genes can be explained in terms of an excess of RNY codons. A deficiency of UUA, CUA and UCA codons (complementary to termination) seems to be restricted to the E. coli genes, and may be due to low abundance of the relevant cognate tRNA species. Thus the analysis shows that the non-coding strand has the properties expected of a sequence complementary to a coding strand, with no indications that it encodes, or may have encoded, proteins.

Selection pressures on codon usage in the complete genome of bacteriophage T7

We searched the complete 39,936 base DNA sequence of bacteriophage T7 for nonrandomness that might be attributed to natural selection. Codon usage in the 50 genes of T7 is nonrandom, both over the whole code and among groups of synonymous codons. There is a great excess of purine- any base-pyrimidine (RNY) codons. Codon usage varies between genes, but from the pooled data for the whole genome (12,145 codons) certain putative selective constraints can be identified. Codon usage appears to be influenced by host tRNA abundance (particularly in highly expressed genes), tRNA-mRNA (one such interaction being perhaps responsible for maintaining the excess of RNY codons) and a lack of short palindromes. This last constraint is probably due to selection against host restriction enzyme recognition sites; this is the first report of an effect of this kind on codon usage. Selection against susceptibility to mutational damage does not appear to have been involved.