Rate of sequence divergence under constant selection

Senescence and entrenchment in evolution of amino acid sites

Amino acid propensities at a site change in the course of protein evolution. This may happen for two reasons. Changes may be triggered by substitutions at epistatically interacting sites elsewhere in the genome. Alternatively, they may arise due to environmental changes that are external to the genome. Here, we design a framework for distinguishing between these alternatives. Using analytical modelling and simulations, we show that they cause opposite dynamics of the fitness of the allele currently occupying the site: it tends to increase with the time since its origin due to epistasis ("entrenchment"), but to decrease due to random environmental fluctuations ("senescence"). By analysing the genomes of vertebrates and insects, we show that the amino acids originating at negatively selected sites experience strong entrenchment. By contrast, the amino acids originating at positively selected sites experience senescence. We propose that senescence of the current allele is a cause of adaptive evolution.

Neutral Theory and Rapidly Evolving Viral Pathogens

The evolution of viral pathogens is shaped by strong selective forces that are exerted during jumps to new hosts, confrontations with host immune responses and antiviral drugs, and numerous other processes. However, while undeniably strong and frequent, adaptive evolution is largely confined to small parts of information-packed viral genomes, and the majority of observed variation is effectively neutral. The predictions and implications of the neutral theory have proven immensely useful in this context, with applications spanning understanding within-host population structure, tracing the origins and spread of viral pathogens, predicting evolutionary dynamics, and modeling the emergence of drug resistance. We highlight the multiple ways in which the neutral theory has had an impact, which has been accelerated in the age of high-throughput, high-resolution genomics.

Changing preferences: deformation of single position amino acid fitness landscapes and evolution of proteins

The fitness landscape-the function that relates genotypes to fitness-and its role in directing evolution are a central object of evolutionary biology. However, its huge dimensionality precludes understanding of even the basic aspects of its shape. One way to approach it is to ask a simpler question: what are the properties of a function that assigns fitness to each possible variant at just one particular site-a single position fitness landscape-and how does it change in the course of evolution? Analyses of genomic data from multiple species and multiple individuals within a species have proved beyond reasonable doubt that fitness functions of positions throughout the genome do themselves change with time, thus shaping protein evolution. Here, I will briefly review the literature that addresses these dynamics, focusing on recent genome-scale analyses of fitness functions of amino acid sites, i.e. vectors of fitnesses of 20 individual amino acid variants at a given position of a protein. The set of amino acids that confer high fitness at a particular position changes with time, and the rate of this change is comparable with the rate at which a position evolves, implying that this process plays a major role in evolutionary dynamics. However, the causes of these changes remain largely unclear.

Epistasis and the Dynamics of Reversion in Molecular Evolution

Recent studies of protein evolution contend that the longer an amino acid substitution is present at a site, the less likely it is to revert to the amino acid previously occupying that site. Here we study this phenomenon of decreasing reversion rates rigorously and in a much more general context. We show that, under weak mutation and for arbitrary fitness landscapes, reversion rates decrease with time for any site that is involved in at least one epistatic interaction. Specifically, we prove that, at stationarity, the hazard function of the distribution of waiting times until reversion is strictly decreasing for any such site. Thus, in the presence of epistasis, the longer a particular character has been absent from a site, the less likely the site will revert to its prior state. We also explore several examples of this general result, which share a common pattern whereby the probability of having reverted increases rapidly at short times to some substantial value before becoming almost flat after a few substitutions at other sites. This pattern indicates a characteristic tendency for reversion to occur either almost immediately after the initial substitution or only after a very long time.

A model of substitution trajectories in sequence space and long-term protein evolution

The nature of factors governing the tempo and mode of protein evolution is a fundamental issue in evolutionary biology. Specifically, whether or not interactions between different sites, or epistasis, are important in directing the course of evolution became one of the central questions. Several recent reports have scrutinized patterns of long-term protein evolution claiming them to be compatible only with an epistatic fitness landscape. However, these claims have not yet been substantiated with a formal model of protein evolution. Here, we formulate a simple covarion-like model of protein evolution focusing on the rate at which the fitness impact of amino acids at a site changes with time. We then apply the model to the data on convergent and divergent protein evolution to test whether or not the incorporation of epistatic interactions is necessary to explain the data. We find that convergent evolution cannot be explained without the incorporation of epistasis and the rate at which an amino acid state switches from being acceptable at a site to being deleterious is faster than the rate of amino acid substitution. Specifically, for proteins that have persisted in modern prokaryotic organisms since the last universal common ancestor for one amino acid substitution approximately ten amino acid states switch from being accessible to being deleterious, or vice versa. Thus, molecular evolution can only be perceived in the context of rapid turnover of which amino acids are available for evolution.

Modeling evolution using the probability of fixation: history and implications

Many models of evolution calculate the rate of evolution by multiplying the rate at which new mutations originate within a population by a probability of fixation. Here we review the historical origins, contemporary applications, and evolutionary implications of these "origin-fixation" models, which are widely used in evolutionary genetics, molecular evolution, and phylogenetics. Origin-fixation models were first introduced in 1969, in association with an emerging view of "molecular" evolution. Early origin-fixation models were used to calculate an instantaneous rate of evolution across a large number of independently evolving loci; in the 1980s and 1990s, a second wave of origin-fixation models emerged to address a sequence of fixation events at a single locus. Although origin fixation models have been applied to a broad array of problems in contemporary evolutionary research, their rise in popularity has not been accompanied by an increased appreciation of their restrictive assumptions or their distinctive implications. We argue that origin-fixation models constitute a coherent theory of mutation-limited evolution that contrasts sharply with theories of evolution that rely on the presence of standing genetic variation. A major unsolved question in evolutionary biology is the degree to which these models provide an accurate approximation of evolution in natural populations.

The use of orthologous sequences to predict the impact of amino acid substitutions on protein function

Computational predictions of the functional impact of genetic variation play a critical role in human genetics research. For nonsynonymous coding variants, most prediction algorithms make use of patterns of amino acid substitutions observed among homologous proteins at a given site. In particular, substitutions observed in orthologous proteins from other species are often assumed to be tolerated in the human protein as well. We examined this assumption by evaluating a panel of nonsynonymous mutants of a prototypical human enzyme, methylenetetrahydrofolate reductase (MTHFR), in a yeast cell-based functional assay. As expected, substitutions in human MTHFR at sites that are well-conserved across distant orthologs result in an impaired enzyme, while substitutions present in recently diverged sequences (including a 9-site mutant that "resurrects" the human-macaque ancestor) result in a functional enzyme. We also interrogated 30 sites with varying degrees of conservation by creating substitutions in the human enzyme that are accepted in at least one ortholog of MTHFR. Quite surprisingly, most of these substitutions were deleterious to the human enzyme. The results suggest that selective constraints vary between phylogenetic lineages such that inclusion of distant orthologs to infer selective pressures on the human enzyme may be misleading. We propose that homologous proteins are best used to reconstruct ancestral sequences and infer amino acid conservation among only direct lineal ancestors of a particular protein. We show that such an "ancestral site preservation" measure outperforms other prediction methods, not only in our selected set for MTHFR, but also in an exhaustive set of E. coli LacI mutants.

Sequence space and the ongoing expansion of the protein universe

The need to maintain the structural and functional integrity of an evolving protein severely restricts the repertoire of acceptable amino-acid substitutions. However, it is not known whether these restrictions impose a global limit on how far homologous protein sequences can diverge from each other. Here we explore the limits of protein evolution using sequence divergence data. We formulate a computational approach to study the rate of divergence of distant protein sequences and measure this rate for ancient proteins, those that were present in the last universal common ancestor. We show that ancient proteins are still diverging from each other, indicating an ongoing expansion of the protein sequence universe. The slow rate of this divergence is imposed by the sparseness of functional protein sequences in sequence space and the ruggedness of the protein fitness landscape: approximately 98 per cent of sites cannot accept an amino-acid substitution at any given moment but a vast majority of all sites may eventually be permitted to evolve when other, compensatory, changes occur. Thus, approximately 3.5 x 10(9) yr has not been enough to reach the limit of divergent evolution of proteins, and for most proteins the limit of sequence similarity imposed by common function may not exceed that of random sequences.