Evolutionary accessibility of mutational pathways

Functional effects of different mutations are known to combine to the total effect in highly nontrivial ways. For the trait under evolutionary selection ('fitness'), measured values over all possible combinations of a set of mutations yield a fitness landscape that determines which mutational states can be reached from a given initial genotype. Understanding the accessibility properties of fitness landscapes is conceptually important in answering questions about the predictability and repeatability of evolutionary adaptation. Here we theoretically investigate accessibility of the globally optimal state on a wide variety of model landscapes, including landscapes with tunable ruggedness as well as neutral 'holey' landscapes. We define a mutational pathway to be accessible if it contains the minimal number of mutations required to reach the target genotype, and if fitness increases in each mutational step. Under this definition accessibility is high, in the sense that at least one accessible pathway exists with a substantial probability that approaches unity as the dimensionality of the fitness landscape (set by the number of mutational loci) becomes large. At the same time the number of alternative accessible pathways grows without bounds. We test the model predictions against an empirical 8-locus fitness landscape obtained for the filamentous fungus Aspergillus niger. By analyzing subgraphs of the full landscape containing different subsets of mutations, we are able to probe the mutational distance scale in the empirical data. The predicted effect of high accessibility is supported by the empirical data and is very robust, which we argue reflects the generic topology of sequence spaces. Together with the restrictive assumptions that lie in our definition of accessibility, this implies that the globally optimal configuration should be accessible to genome wide evolution, but the repeatability of evolutionary trajectories is limited owing to the presence of a large number of alternative mutational pathways.     

Environment changes epistasis to alter trade‐offs along alternative evolutionary paths

The fitness effect of a mutation can depend on both its genetic background, known as epistasis, and the prevailing external environment. Many examples of these dependencies are known, but few studies consider both aspects in combination, especially as they affect mutations that have been selected together. We examine interactions between five coevolved mutations in eight diverse environments. We find that mutations are, on average, beneficial across environments, but that there is high variation in their fitness effects, including many examples of mutations conferring a cost in some, but not other, genetic background‐environment combinations. Indeed, even when global interaction trends are accounted for, specific local mutation interactions are common and differed across environments. One consequence of this dependence is that the range of trade‐offs in genotype fitness across selected and alternative environments are contingent on the particular evolutionary path followed over the mutation landscape. Finally, although specific interactions were common, there was a consistent pattern of diminishing returns epistasis whereby mutation effects were less beneficial when added to genotypes of higher fitness. Our results underline that specific mutation effects are highly dependent on the combination of genetic and external environments, and support a general relationship between a genotype's current fitness and its potential to increase in fitness.     

Properties of selected mutations and genotypic landscapes under Fisher's geometric model

The fitness landscape—the mapping between genotypes and fitness—determines properties of the process of adaptation. Several small genotypic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here, we generate several testable predictions for the properties of these small genotypic landscapes under Fisher's geometric model of adaptation. When the ancestral strain is far from the fitness optimum, we analytically compute the fitness effect of selected mutations and their epistatic interactions. Epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected, or coselected in an adaptive walk. Simulations show that genotypic landscapes built from Fisher's model are very close to an additive landscape when the ancestral strain is far from the optimum. However, when it is close to the optimum, a large diversity of landscape with substantial roughness and sign epistasis emerged. Strikingly, small genotypic landscapes built from several replicate adaptive walks on the same underlying landscape were highly variable, suggesting that several realizations of small genotypic landscapes are needed to gain information about the underlying architecture of the fitness landscape.     

Evolutionary dynamics, epistatic interactions, and biological information

We investigate a definition of biological information that connects population genetics with the tools of information theory by focusing on the distribution of genotypes found in a population. Previous research has treated loci as non-interacting by making specific approximations in the calculation of information-theoretic quantities. We expand earlier mathematical forms to include epistasis, or interactions between mutations at all pairs of loci. Application of our improved measure of biological information to evolution on two-locus, two-allele fitness landscapes demonstrates that mutual information between loci reflects epistatic interaction of mutations. Finally, we consider four-locus, two-allele fitness landscapes with modular structure. As modular interactions are inherently epistatic, we demonstrate that our refined approximation provides insight into the underlying structure of these non-trivial fitness landscapes.     

Exploiting the Adaptation Dynamics to Predict the Distribution of Beneficial Fitness Effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depends on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remains nearly a constant for exponentially decaying distributions and increases when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold good for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.     

The Effect of Bacterial Recombination on Adaptation on Fitness Landscapes with Limited Peak Accessibility

There is ample empirical evidence revealing that fitness landscapes are often complex: the fitness effect of a newly arisen mutation can depend strongly on the allelic state at other loci. However, little is known about the effects of recombination on adaptation on such fitness landscapes. Here, we investigate how recombination influences the rate of adaptation on a special type of complex fitness landscapes. On these landscapes, the mutational trajectories from the least to the most fit genotype are interrupted by genotypes with low relative fitness. We study the dynamics of adapting populations on landscapes with different compositions and numbers of low fitness genotypes, with and without recombination. Our results of the deterministic model (assuming an infinite population size) show that recombination generally decelerates adaptation on these landscapes. However, in finite populations, this deceleration is outweighed by the accelerating Fisher-Muller effect under certain conditions. We conclude that recombination has complex effects on adaptation that are highly dependent on the particular fitness landscape, population size and recombination rate.     

Properties of adaptive walks on uncorrelated landscapes under strong selection and weak mutation

We examine properties of adaptive walks on uncorrelated (i.e. random) fitness landscapes starting from moderately fit genotypes under strong selection weak mutation. As an extension of Orr's model for a single step in an adaptive walk under these conditions, we show that the fitness rank of the dominant genotype in a population after the fixation of a beneficial mutation is, on average, (i+6)/4, where i is the fitness rank of the starting genotype. This accounts for the change in rank due to acquiring a new set of single-mutation neighbors after fixing a new allele through natural selection. Under this scenario, adaptive walks can be modeled as a simple Markov chain on the space of possible fitness ranks with an absorbing state at i = 1, from which no beneficial mutations are accessible. We find that these walks are typically short and are often completed in a single step when starting from a moderately fit genotype. As in Orr's original model, these results are insensitive to both the distribution of fitness effects and most biological details of the system under consideration.     

Fitness landscapes emerging from pharmacodynamic functions in the evolution of multidrug resistance

Adaptive evolution often involves beneficial mutations at more than one locus. In this case, the trajectory and rate of adaptation is determined by the underlying fitness landscape, that is, the fitness values and mutational connectivity of all genotypes under consideration. Drug resistance, especially resistance to multiple drugs simultaneously, is also often conferred by mutations at several loci so that the concept of fitness landscapes becomes important. However, fitness landscapes underlying drug resistance are not static but dependent on drug concentrations, which means they are influenced by the pharmacodynamics of the drugs administered. Here, I present a mathematical framework for fitness landscapes of multidrug resistance based on Hill functions describing how drug concentrations affect fitness. I demonstrate that these ‘pharmacodynamic fitness landscapes’ are characterized by pervasive epistasis that arises through (i) fitness costs of resistance (even when these costs are additive), (ii) nonspecificity of resistance mutations to drugs, in particular cross‐resistance, and (iii) drug interactions (both synergistic and antagonistic). In the latter case, reciprocal drug suppression may even lead to reciprocal sign epistasis, so that the doubly resistant genotype occupies a local fitness peak that may be difficult to access by evolution. Simulations exploring the evolutionary dynamics on some pharmacodynamic fitness landscapes with both constant and changing drug concentrations confirm the crucial role of epistasis in determining the rate of multidrug resistance evolution.     

HIV-1 Replication Fitness of HLA-B*57/58:01 CTL Escape Variants Is Restored by the Accumulation of Compensatory Mutations in Gag

Expression of HLA-B*57 and the closely related HLA-B*58:01 are associated with prolonged survival after HIV-1 infection. However, large differences in disease course are observed among HLA-B*57/58:01 patients. Escape mutations in CTL epitopes restricted by these HLA alleles come at a fitness cost and particularly the T242N mutation in the TW10 CTL epitope in Gag has been demonstrated to decrease the viral replication capacity. Additional mutations within or flanking this CTL epitope can partially restore replication fitness of CTL escape variants. Five HLA-B*57/58:01 progressors and 5 HLA-B*57/58:01 long-term nonprogressors (LTNPs) were followed longitudinally and we studied which compensatory mutations were involved in the restoration of the viral fitness of variants that escaped from HLA-B*57/58:01-restricted CTL pressure. The Sequence Harmony algorithm was used to detect homology in amino acid composition by comparing longitudinal Gag sequences obtained from HIV-1 patients positive and negative for HLA-B*57/58:01 and from HLA-B*57/58:01 progressors and LTNPs. Although virus isolates from HLA-B*57/58:01 individuals contained multiple CTL escape mutations, these escape mutations were not associated with disease progression. In sequences from HLA-B*57/58:01 progressors, 5 additional mutations in Gag were observed: S126N, L215T, H219Q, M228I and N252H. The combination of these mutations restored the replication fitness of CTL escape HIV-1 variants. Furthermore, we observed a positive correlation between the number of escape and compensatory mutations in Gag and the replication fitness of biological HIV-1 variants isolated from HLA-B*57/58:01 patients, suggesting that the replication fitness of HLA-B*57/58:01 escape variants is restored by accumulation of compensatory mutations.     

Environmental change exposes beneficial epistatic interactions in a catalytic RNA

Natural selection drives populations of individuals towards local peaks in a fitness landscape. These peaks are created by the interactions between individual mutations. Fitness landscapes may change as an environment changes. In a previous contribution, we discovered a variant of the Azoarcus group I ribozyme that represents a local peak in the RNA fitness landscape. The genotype at this peak is distinguished from the wild-type by four point mutations. We here report ribozyme fitness data derived from constructing all possible combinations of these point mutations. We find that these mutations interact epistatically. Importantly, we show that these epistatic interactions change qualitatively in the three different environments that we studied. We find examples where the relative fitness of a ribozyme can change from neutral or negative in one environment, to positive in another. We also show that the fitness effect of a specific GC-AU base pair switch is dependent on both the environment and the genetic context. Moreover, the mutations that we study improve activity at the cost of decreased structural stability. Environmental change is ubiquitous in nature. Our results suggest that such change can facilitate adaptive evolution by exposing new peaks of a fitness landscape. They highlight a prominent role for genotype-environment interactions in doing so.     

Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage t7

Understanding how interactions among deleterious mutations affect fitness may shed light on a variety of fundamental biological phenomena, including the evolution of sex, the buffering of genetic variations, and the topography of fitness landscapes. It remains an open question under what conditions and to what extent such interactions may be synergistic or antagonistic. To address this question, we employed a computer model for the intracellular growth of bacteriophage T7. We created in silico 90,000 mutants of phage T7, each carrying from 1 to 30 mutations, and evaluated the fitness of each by simulating its growth cycle. The simulations sought to account for the severity of single deleterious mutations on T7 growth, as well as the effect of the resource environment on our fitness measures. We found that mildly deleterious mutations interacted synergistically in poor-resource environments but antagonistically in rich-resource environments. However, severely deleterious mutations always interacted antagonistically, irrespective of environment. These results suggest that synergistic epistasis may be difficult to experimentally distinguish from nonepistasis because its effects appear to be most pronounced when the effects of mutations on fitness are most challenging to measure. Our approach demonstrates how computer simulations of developmental processes can be used to quantitatively study genetic interactions at the population level.     

Defining the landscape of adaptive genetic diversity

Whether they are used to describe fitness, genome architecture or the spatial distribution of environmental variables, the concept of a landscape has figured prominently in our collective reasoning. The tradition of landscapes in evolutionary biology is one of fitness mapped onto axes defined by phenotypes or molecular sequence states. The characteristics of these landscapes depend on natural selection, which is structured across both genomic and environmental landscapes, and thus, the bridge among differing uses of the landscape concept (i.e. metaphorically or literally) is that of an adaptive phenotype and its distribution across geographical landscapes in relation to selective pressures. One of the ultimate goals of evolutionary biology should thus be to construct fitness landscapes in geographical space. Natural plant populations are ideal systems with which to explore the feasibility of attaining this goal, because much is known about the quantitative genetic architecture of complex traits for many different plant species. What is less known are the molecular components of this architecture. In this issue of Molecular Ecology, Parchman et al. (2012) pioneer one of the first truly genome-wide association studies in a tree that moves us closer to this form of mechanistic understanding for an adaptive phenotype in natural populations of lodgepole pine (Pinus contorta Dougl. ex Loud.).     

Distributions of beneficial fitness effects in RNA

Beneficial mutations are the driving force of evolution by natural selection. Yet, relatively little is known about the distribution of the fitness effects of beneficial mutations in populations. Recent work of Gillespie and Orr suggested some of the first generalizations for the distributions of beneficial fitness effects and, surprisingly, they depend only weakly on biological details. In particular, the theory suggests that beneficial mutations obey an exponential distribution of fitness effects, with the same exponential parameter across different regions of genotype space, provided only that few possible beneficial mutations are available to that genotype. Here we tested this hypothesis with a quasi-empirical model of RNA evolution in which fitness is based on the secondary structures of molecules and their thermodynamic stabilities. The fitnesses of randomly selected genotypes appeared to follow a Gumbel-type distribution and thus conform to a basic assumption of adaptation theory. However, the observed distributions of beneficial fitness effects conflict with specific predictions of the theory. In particular, the distributions of beneficial fitness effects appeared exponential only when the vast majority of small-effect beneficial mutations were ignored. Additionally, the distribution of beneficial fitness effects varied with the fitness of the parent genotype. We believe that correlation of the fitness values among similar genotypes is likely the cause of the departure from the predictions of recent adaptation theory. Although in conflict with the current theory, these results suggest that more complex statistical generalizations about beneficial mutations may be possible.     

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.     

Extreme Genetic Fragility of the HIV-1 Capsid

Genetic robustness, or fragility, is defined as the ability, or lack thereof, of a biological entity to maintain function in the face of mutations. Viruses that replicate via RNA intermediates exhibit high mutation rates, and robustness should be particularly advantageous to them. The capsid (CA) domain of the HIV-1 Gag protein is under strong pressure to conserve functional roles in viral assembly, maturation, uncoating, and nuclear import. However, CA is also under strong immunological pressure to diversify. Therefore, it would be particularly advantageous for CA to evolve genetic robustness. To measure the genetic robustness of HIV-1 CA, we generated a library of single amino acid substitution mutants, encompassing almost half the residues in CA. Strikingly, we found HIV-1 CA to be the most genetically fragile protein that has been analyzed using such an approach, with 70% of mutations yielding replication-defective viruses. Although CA participates in several steps in HIV-1 replication, analysis of conditionally (temperature sensitive) and constitutively non-viable mutants revealed that the biological basis for its genetic fragility was primarily the need to coordinate the accurate and efficient assembly of mature virions. All mutations that exist in naturally occurring HIV-1 subtype B populations at a frequency >3%, and were also present in the mutant library, had fitness levels that were >40% of WT. However, a substantial fraction of mutations with high fitness did not occur in natural populations, suggesting another form of selection pressure limiting variation in vivo. Additionally, known protective CTL epitopes occurred preferentially in domains of the HIV-1 CA that were even more genetically fragile than HIV-1 CA as a whole. The extreme genetic fragility of HIV-1 CA may be one reason why cell-mediated immune responses to Gag correlate with better prognosis in HIV-1 infection, and suggests that CA is a good target for therapy and vaccination strategies.     

Epistasis among Deleterious Mutations in the HIV-1 Protease

A central goal in molecular evolution is to understand how genetic interactions between protein mutations shape protein function and fitness. While intergenic epistasis has been extensively explored in eukaryotes, bacteria, and viruses, intragenic epistatic interactions have been insufficiently studied. Here, we employ a model system in which lambda phage fitness correlates with the enzymatic activity of human immunodeficiency virus type 1 (HIV-1) protease to systematically determine the epistatic interactions between intragenic pairs of deleterious protein substitutions. We generated 114 genotypes of the HIV-1 protease, each carrying pairs of nucleotide substitution mutations whose separated and combined deleterious effects on fitness were then determined. A high proportion (39%) of pairs displayed lethality. Several pairs exhibited significant interactions for fitness, including positive and negative epistasis. Significant negative epistatic interactions predominated (15%) over positive interactions (2%). However, the average ± SD epistatic effect, ē = 0.0025 ± 0.1334, was not significantly different from zero (p = 0.8368). Notably, epistatic interactions, regardless of epistatic direction, tend to be more frequent in the context of less deleterious mutations. In the present study, the high frequencies of lethality and negative epistasis indicate that the HIV-1 protease is highly sensitive to the effects of deleterious mutations. Therefore, proteins may not be as robust to mutational change as is usually expected.     

Functional origins of fitness effect-sizes of compensatory mutations in the DNA bacteriophage phiX174

Abstract Epistasis is an important and poorly understood aspect of mutations and strongly influences the evolutionary impact of genetic variation on adaptation and fitness. Although recent studies have begun to characterize the distribution of epistatic effects between mutations affecting fitness, there is currently a lack of empirical information on the underlying biological causes of these epistatic interactions. What are the functional constraints that determine the effectiveness of a compensatory mutation at restoring fitness? We have measured the effect‐sizes of 52 compensatory mutations affecting nine different deleterious mutations in the major capsid and spike proteins of the DNA bacteriophage X174. On average, an experimentally detectable compensatory mutation recovers about two‐thirds of the fitness cost of the preceding deleterious mutation. Variation in fitness effect‐sizes is only weakly associated with measures of the distance separating the deleterious and compensatory mutations in the amino acid sequence or the folded protein structure. However, there is a strong association of fitness effect‐size with the correlation in the effects of the mutations on the biochemical properties of amino acids. A compensatory mutation has the largest effect‐size, on average, when both the compensatory and deleterious mutations have radical effects on the overall biochemical make‐up of the amino acids. By examining the relative contributions of specific biochemical properties to variation in fitness effect‐size, we find that the area and charge of amino acids have a major influence, which suggests that the complexity of the amino acid phenotype is simplified by selection into a reduced number of phenotypic components.     

Variation in the Fitness Effects of Mutations with Population Density and Size in Escherichia coli

The fitness effects of mutations are context specific and depend on both external (e.g., environment) and internal (e.g., cellular stress, genetic background) factors. The influence of population size and density on fitness effects are unknown, despite the central role population size plays in the supply and fixation of mutations. We addressed this issue by comparing the fitness of 92 Keio strains (Escherichia coli K12 single gene knockouts) at comparatively high (1.2×10⁷ CFUs/mL) and low (2.5×10² CFUs/mL) densities, which also differed in population size (high: 1.2×10⁸; low: 1.25×10³). Twenty-eight gene deletions (30%) exhibited a fitness difference, ranging from 5 to 174% (median: 35%), between the high and low densities. Our analyses suggest this variation among gene deletions in fitness responses reflected in part both gene orientation and function, of the gene properties we examined (genomic position, length, orientation, and function). Although we could not determine the relative effects of population density and size, our results suggest fitness effects of mutations vary with these two factors, and this variation is gene-specific. Besides being a mechanism for density-dependent selection (r-K selection), the dependence of fitness effects on population density and size has implications for any population that varies in size over time, including populations undergoing evolutionary rescue, species invasions into novel habitats, and cancer progression and metastasis. Further, combined with recent advances in understanding the roles of other context-specific factors in the fitness effects of mutations, our results will help address theoretical and applied biological questions more realistically.     

Retracing the evolutionary pathways of human immunodeficiency virus type 1 resistance to protease inhibitors: virus fitness in the absence and in the presence of drug

Human immunodeficiency virus type 1 (HIV-1) resistance to protease inhibitors (PI) is a major obstacle to the full success of combined antiretroviral therapy. High-level resistance to these compounds is the consequence of stepwise accumulation of amino acid substitutions in the HIV-1 protease (PR), following pathways that usually differ from one inhibitor to another. The selective advantage conferred by resistance mutations may depend upon several parameters: the impact of the mutation on virus infectivity in the presence or absence of drug, the nature of the drug, and its local concentration. Because drug concentrations in vivo are subject to extensive variation over time and display a markedly uneven tissue distribution, the parameters of selection for HIV-1 resistance to PI in treated patients are complex and poorly understood. In this study, we have reconstructed a large series of HIV-1 mutants that carry single or combined mutations in the PR, retracing the accumulation pathways observed in ritonavir-, indinavir-, and saquinavir-treated patients. We have then measured the phenotypic resistance and the drug-free infectivity of these mutant viruses. A deeper insight into the evolutionary value of HIV-1 PR mutants came from a novel assay system designed to measure the replicative advantage of mutant viruses as a function of drug concentration. By tracing the resultant fitness profiles, we determined the range of drug concentrations for which mutant viruses displayed a replicative advantage over the wild type and the extent of this advantage. Fitness profiles were fully consistent with the order of accumulation of resistance mutations observed in treated patients and further emphasise the key importance of local drug concentration in the patterns of selection of drug-resistant HIV-1 mutants.