Historical contingency and entrenchment in protein evolution under purifying selection

The fitness contribution of an allele at one genetic site may depend on alleles at other sites, a phenomenon known as epistasis. Epistasis can profoundly influence the process of evolution in populations under selection, and can shape the course of protein evolution across divergent species. Whereas epistasis between adaptive substitutions has been the subject of extensive study, relatively little is known about epistasis under purifying selection. Here we use mechanistic models of thermodynamic stability in a ligand-binding protein to explore the structure of epistatic interactions between substitutions that fix in protein sequences under purifying selection. We find that the selection coefficients of mutations that are nearly-neutral when they fix are highly contingent on the presence of preceding mutations. Conversely, mutations that are nearly-neutral when they fix are subsequently entrenched due to epistasis with later substitutions. Our evolutionary model includes insertions and deletions, as well as point mutations, and so it allows us to quantify epistasis within each of these classes of mutations, and also to study the evolution of protein length. We find that protein length remains largely constant over time, because indels are more deleterious than point mutations. Our results imply that, even under purifying selection, protein sequence evolution is highly contingent on history and so it cannot be predicted by the phenotypic effects of mutations assayed in the wild-type sequence.Comment: 42 pages, 13 figure

The inevitability of unconditionally deleterious substitutions during adaptation

Studies on the genetics of adaptation typically neglect the possibility that a deleterious mutation might fix. Nonetheless, here we show that, in many regimes, the first substitution is most often deleterious, even when fitness is expected to increase in the long term. In particular, we prove that this phenomenon occurs under weak mutation for any house-of-cards model with an equilibrium distribution. We find that the same qualitative results hold under Fisher's geometric model. We also provide a simple intuition for the surprising prevalence of unconditionally deleterious substitutions during early adaptation. Importantly, the phenomenon we describe occurs on fitness landscapes without any local maxima and is therefore distinct from "valley-crossing". Our results imply that the common practice of ignoring deleterious substitutions leads to qualitatively incorrect predictions in many regimes. Our results also have implications for the substitution process at equilibrium and for the response to a sudden decrease in population size.Comment: Corrected typos and minor errors in Supporting Informatio

Digital Commonwealth: Handbook of Digital Storytelling

Developed by the Digital Commonwealth project team at the University of the West of Scotland, funded by The Big Lottery, University of the West of Scotland and The Media Trust. The handbook is structured around exploring a theme (in this case the Commonwealth) and then ideas for using blogging, audio, social media and video for digital storytelling. Each section contains: ● An overview of the aims and learning for each skill ● An introduction to the skill ● Suggestions for how to use this skill for digital storytelling ● Examples of the skill in action (including examples from the Digital Commonwealth project

Digital Commonwealth: Handbook of Digital Storytelling

Developed by the Digital Commonwealth project team at the University of the West of Scotland, funded by The Big Lottery, University of the West of Scotland and The Media Trust. The handbook is structured around exploring a theme (in this case the Commonwealth) and then ideas for using blogging, audio, social media and video for digital storytelling. Each section contains: ● An overview of the aims and learning for each skill ● An introduction to the skill ● Suggestions for how to use this skill for digital storytelling ● Examples of the skill in action (including examples from the Digital Commonwealth project

Digital Commonwealth:Handbook of Digital Storytelling

Developed by the Digital Commonwealth project team at the University of the West of Scotland, funded by The Big Lottery, University of the West of Scotland and The Media Trust. The handbook is structured around exploring a theme (in this case the Commonwealth) and then ideas for using blogging, audio, social media and video for digital storytelling. Each section contains: ● An overview of the aims and learning for each skill ● An introduction to the skill ● Suggestions for how to use this skill for digital storytelling ● Examples of the skill in action (including examples from the Digital Commonwealth project

Epistasis not needed to explain low dN/dS

An important question in molecular evolution is whether an amino acid that occurs at a given position makes an independent contribution to fitness, or whether its effect depends on the state of other loci in the organism's genome, a phenomenon known as epistasis. In a recent letter to Nature, Breen et al. (2012) argued that epistasis must be "pervasive throughout protein evolution" because the observed ratio between the per-site rates of non-synonymous and synonymous substitutions (dN/dS) is much lower than would be expected in the absence of epistasis. However, when calculating the expected dN/dS ratio in the absence of epistasis, Breen et al. assumed that all amino acids observed in a protein alignment at any particular position have equal fitness. Here, we relax this unrealistic assumption and show that any dN/dS value can in principle be achieved at a site, without epistasis. Furthermore, for all nuclear and chloroplast genes in the Breen et al. dataset, we show that the observed dN/dS values and the observed patterns of amino acid diversity at each site are jointly consistent with a non-epistatic model of protein evolution.Comment: This manuscript is in response to "Epistasis as the primary factor in molecular evolution" by Breen et al. Nature 490, 535-538 (2012

Mutation bias shapes the spectrum of adaptive substitutions

Evolutionary adaptation often occurs by the fixation of beneficial mutations. This mode of adaptation can be characterized quantitatively by a spectrum of adaptive substitutions, i.e., a distribution for types of changes fixed in adaptation. Recent work establishes that the changes involved in adaptation reflect common types of mutations, raising the question of how strongly the mutation spectrum shapes the spectrum of adaptive substitutions. We address this question with a codon-based model for the spectrum of adaptive amino acid substitutions, applied to three large datasets covering thousands of amino acid changes identified in natural and experimental adaptation in Saccharomyces cerevisiae, Escherichia coli, and Mycobacterium tuberculosis Using species-specific mutation spectra based on prior knowledge, we find that the mutation spectrum has a proportional influence on the spectrum of adaptive substitutions in all three species. Indeed, we find that by inferring the mutation rates that best explain the spectrum of adaptive substitutions, we can accurately recover the species-specific mutation spectra. However, we also find that the predictive power of the model differs substantially between the three species. To better understand these differences, we use population simulations to explore the factors that influence how closely the spectrum of adaptive substitutions mirrors the mutation spectrum. The results show that the influence of the mutation spectrum decreases with increasing mutational supply ([Formula: see text]) and that predictive power is strongly affected by the number and diversity of beneficial mutations

MAVE-NN: learning genotype-phenotype maps from multiplex assays of variant effect

Multiplex assays of variant effect (MAVEs) are a family of methods that includes deep mutational scanning experiments on proteins and massively parallel reporter assays on gene regulatory sequences. Despite their increasing popularity, a general strategy for inferring quantitative models of genotype-phenotype maps from MAVE data is lacking. Here we introduce MAVE-NN, a neural-network-based Python package that implements a broadly applicable information-theoretic framework for learning genotype-phenotype maps-including biophysically interpretable models-from MAVE datasets. We demonstrate MAVE-NN in multiple biological contexts, and highlight the ability of our approach to deconvolve mutational effects from otherwise confounding experimental nonlinearities and noise

Higher-order epistasis and phenotypic prediction

Contemporary high-throughput mutagenesis experiments are providing an increasingly detailed view of the complex patterns of genetic interaction that occur between multiple mutations within a single protein or regulatory element. By simultaneously measuring the effects of thousands of combinations of mutations, these experiments have revealed that the genotype-phenotype relationship typically reflects not only genetic interactions between pairs of sites but also higher-order interactions among larger numbers of sites. However, modeling and understanding these higher-order interactions remains challenging. Here we present a method for reconstructing sequence-to-function mappings from partially observed data that can accommodate all orders of genetic interaction. The main idea is to make predictions for unobserved genotypes that match the type and extent of epistasis found in the observed data. This information on the type and extent of epistasis can be extracted by considering how phenotypic correlations change as a function of mutational distance, which is equivalent to estimating the fraction of phenotypic variance due to each order of genetic interaction (additive, pairwise, three-way, etc.). Using these estimated variance components, we then define an empirical Bayes prior that in expectation matches the observed pattern of epistasis and reconstruct the genotype-phenotype mapping by conducting Gaussian process regression under this prior. To demonstrate the power of this approach, we present an application to the antibody-binding domain GB1 and also provide a detailed exploration of a dataset consisting of high-throughput measurements for the splicing efficiency of human pre-mRNA [Formula: see text] splice sites, for which we also validate our model predictions via additional low-throughput experiments