The mutation effect reaction norm (mu-rn) highlights environmentally dependent mutation effects and epistatic interactions

Environment by environment interactions (ExE) differ across genetic backgrounds (ExExG)

While the terms "gene-by-gene interaction" (GxG) and "gene-by-environment interaction" (GxE) are widely recognized in the fields of quantitative and evolutionary genetics, "environment-byenvironment interaction" (ExE) is a term used less often. In this study, we find that environmentby-environment interactions are a meaningful driver of phenotypes, and moreover, that they differ across different genotypes (suggestive of ExExG). To support this conclusion, we analyzed a large dataset of roughly 1,000 mutant yeast strains with varying degrees of resistance to different antifungal drugs. Our findings reveal that the effectiveness of a drug combination, relative to single drugs, often differs across drug resistant mutants. Remarkably, even mutants that differ by only a single nucleotide change can have dramatically different drug × drug (ExE) interactions. We also introduce a new framework that more accurately predicts the direction and magnitude of ExE interactions for some mutants. Understanding how ExE interactions change across genotypes (ExExG) is crucial not only for modeling the evolution of pathogenic microbes, but also for enhancing our knowledge of the underlying cell biology and the sources of phenotypic variance within populations. While the significance of ExExG interactions has been overlooked in evolutionary and population genetics, these fields and others stand to benefit from understanding how these interactions shape the complex behavior of living systems.

Distinguishing mutants that resist drugs via different mechanisms by examining fitness tradeoffs

There is growing interest in designing multidrug therapies that leverage tradeoffs to combat resistance. Tradeoffs are common in evolution and occur when, for example, resistance to one drug results in sensitivity to another. Major questions remain about the extent to which tradeoffs are reliable, specifically, whether the mutants that provide resistance to a given drug all suffer similar tradeoffs. This question is difficult because the drug-resistant mutants observed in the clinic, and even those evolved in controlled laboratory settings, are often biased towards those that provide large fitness benefits. Thus, the mutations (and mechanisms) that provide drug resistance may be more diverse than current data suggests. Here, we perform evolution experiments utilizing lineage-tracking to capture a fuller spectrum of mutations that give yeast cells a fitness advantage in fluconazole, a common antifungal drug. We then quantify fitness tradeoffs for each of 774 evolved mutants across 12 environments, finding these mutants group into classes with characteristically different tradeoffs. Their unique tradeoffs may imply that each group of mutants affects fitness through different underlying mechanisms. Some of the groupings we find are surprising. For example, we find some mutants that resist single drugs do not resist their combination, while others do. And some mutants to the same gene have different tradeoffs than others. These findings, on one hand, demonstrate the difficulty in relying on consistent or intuitive tradeoffs when designing multidrug treatments. On the other hand, by demonstrating that hundreds of adaptive mutations can be reduced to a few groups with characteristic tradeoffs, our findings may yet empower multidrug strategies that leverage tradeoffs to combat resistance. More generally speaking, by grouping mutants that likely affect fitness through similar underlying mechanisms, our work guides efforts to map the phenotypic effects of mutation.

The role of epistasis in evolutionary rescue

The process by which adaptive evolution preserves a population threatened with extinction due to environmental changes is known as evolutionary rescue. Several factors determine the fate of those populations, including demography and genetic factors, such as standing genetic variation, gene flow, availability of de novo mutations, and so on. Despite the extensive debate about evolutionary rescue in the current literature, a study about the role of epistasis and the topography of the fitness landscape on the fate of dwindling populations is missing. In the current work, we aim to fill this gap and study the influence of epistasis on the probability of extinction of populations. We present simulation results, and analytical approximations are derived. Counterintuitively, we show that the likelihood of extinction is smaller when the degree of epistasis is higher. The reason underneath is twofold: first, higher epistasis can promote mutations of more significant phenotypic effects, but also, the incongruence between the maps genotype-phenotype and phenotype-fitness turns the fitness landscape at low epistasis more rugged, thus curbing some of its advantages.

Distinguishing mutants that resist drugs via different mechanisms by examining fitness tradeoffs

There is growing interest in designing multidrug therapies that leverage tradeoffs to combat resistance. Tradeoffs are common in evolution and occur when, for example, resistance to one drug results in sensitivity to another. Major questions remain about the extent to which tradeoffs are reliable, specifically, whether the mutants that provide resistance to a given drug all suffer similar tradeoffs. This question is difficult because the drug-resistant mutants observed in the clinic, and even those evolved in controlled laboratory settings, are often biased towards those that provide large fitness benefits. Thus, the mutations (and mechanisms) that provide drug resistance may be more diverse than current data suggests. Here, we perform evolution experiments utilizing lineage-tracking to capture a fuller spectrum of mutations that give yeast cells a fitness advantage in fluconazole, a common antifungal drug. We then quantify fitness tradeoffs for each of 774 evolved mutants across 12 environments, finding these mutants group into 6 classes with characteristically different tradeoffs. Their unique tradeoffs may imply that each group of mutants affects fitness through different underlying mechanisms. Some of the groupings we find are surprising. For example, we find some mutants that resist single drugs do not resist their combination, while others do. And some mutants to the same gene have different tradeoffs than others. These findings, on one hand, demonstrate the difficulty in relying on consistent or intuitive tradeoffs when designing multidrug treatments. On the other hand, by demonstrating that hundreds of adaptive mutations can be reduced to a few groups with characteristic tradeoffs, our findings may yet empower multidrug strategies that leverage tradeoffs to combat resistance. More generally speaking, by grouping mutants that likely affect fitness through similar underlying mechanisms, our work guides efforts to map the phenotypic effects of mutation.

Evolutionary druggability for low-dimensional fitness landscapes toward new metrics for antimicrobial applications

The term 'druggability' describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant's sensitivity across a breadth of drugs in a panel, or a given drug's range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and 7 β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel ('variant vulnerability'), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target ('drug applicability'). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G x G x E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

An extension of the Walsh-Hadamard transform to calculate and model epistasis in genetic landscapes of arbitrary shape and complexity

Accurate models describing the relationship between genotype and phenotype are necessary in order to understand and predict how mutations to biological sequences affect the fitness and evolution of living organisms. The apparent abundance of epistasis (genetic interactions), both between and within genes, complicates this task and how to build mechanistic models that incorporate epistatic coefficients (genetic interaction terms) is an open question. The Walsh-Hadamard transform represents a rigorous computational framework for calculating and modeling epistatic interactions at the level of individual genotypic values (known as genetical, biological or physiological epistasis), and can therefore be used to address fundamental questions related to sequence-to-function encodings. However, one of its main limitations is that it can only accommodate two alleles (amino acid or nucleotide states) per sequence position. In this paper we provide an extension of the Walsh-Hadamard transform that allows the calculation and modeling of background-averaged epistasis (also known as ensemble epistasis) in genetic landscapes with an arbitrary number of states per position (20 for amino acids, 4 for nucleotides, etc.). We also provide a recursive formula for the inverse matrix and then derive formulae to directly extract any element of either matrix without having to rely on the computationally intensive task of constructing or inverting large matrices. Finally, we demonstrate the utility of our theory by using it to model epistasis within both simulated and empirical multiallelic fitness landscapes, revealing that both pairwise and higher-order genetic interactions are enriched between physically interacting positions.

A computational method for predicting the most likely evolutionary trajectories in the stepwise accumulation of resistance mutations

Pathogen evolution of drug resistance often occurs in a stepwise manner via the accumulation of multiple mutations that in combination have a non-additive impact on fitness, a phenomenon known as epistasis. The evolution of resistance via the accumulation of point mutations in the DHFR genes of Plasmodium falciparum (Pf) and Plasmodium vivax (Pv) has been studied extensively and multiple studies have shown epistatic interactions between these mutations determine the accessible evolutionary trajectories to highly resistant multiple mutations. Here, we simulated these evolutionary trajectories using a model of molecular evolution, parameterised using Rosetta Flex ddG predictions, where selection acts to reduce the target-drug binding affinity. We observe strong agreement with pathways determined using experimentally measured IC50 values of pyrimethamine binding, which suggests binding affinity is strongly predictive of resistance and epistasis in binding affinity strongly influences the order of fixation of resistance mutations. We also infer pathways directly from the frequency of mutations found in isolate data, and observe remarkable agreement with the most likely pathways predicted by our mechanistic model, as well as those determined experimentally. This suggests mutation frequency data can be used to intuitively infer evolutionary pathways, provided sufficient sampling of the population.

Environmental modulation of global epistasis in a drug resistance fitness landscape

Interactions between mutations (epistasis) can add substantial complexity to genotype-phenotype maps, hampering our ability to predict evolution. Yet, recent studies have shown that the fitness effect of a mutation can often be predicted from the fitness of its genetic background using simple, linear relationships. This phenomenon, termed global epistasis, has been leveraged to reconstruct fitness landscapes and infer adaptive trajectories in a wide variety of contexts. However, little attention has been paid to how patterns of global epistasis may be affected by environmental variation, despite this variation frequently being a major driver of evolution. This is particularly relevant for the evolution of drug resistance, where antimicrobial drugs may change the environment faced by pathogens and shape their adaptive trajectories in ways that can be difficult to predict. By analyzing a fitness landscape of four mutations in a gene encoding an essential enzyme of P. falciparum (a parasite cause of malaria), here we show that patterns of global epistasis can be strongly modulated by the concentration of a drug in the environment. Expanding on previous theoretical results, we demonstrate that this modulation can be quantitatively explained by how specific gene-by-gene interactions are modified by drug dose. Importantly, our results highlight the need to incorporate potential environmental variation into the global epistasis framework in order to predict adaptation in dynamic environments.

Epistasis and pleiotropy shape biophysical protein subspaces associated with drug resistance

Protein space is a rich analogy for genotype-phenotype maps, where amino acid sequence is organized into a high-dimensional space that highlights the connectivity between protein variants. It is a useful abstraction for understanding the process of evolution, and for efforts to engineer proteins towards desirable phenotypes. Few mentions of protein space consider how protein phenotypes can be described in terms of their biophysical components, nor do they rigorously interrogate how forces like epistasis-describing the nonlinear interaction between mutations and their phenotypic consequences-manifest across these components. In this study, we deconstruct a low-dimensional protein space of a bacterial enzyme (dihydrofolate reductase; DHFR) into "subspaces" corresponding to a set of kinetic and thermodynamic traits [k_{cat}, K_{M}, K_{i}, and T_{m} (melting temperature)]. We then examine how combinations of three mutations (eight alleles in total) display pleiotropy, or unique effects on individual subspace traits. We examine protein spaces across three orthologous DHFR enzymes (Escherichia coli, Listeria grayi, and Chlamydia muridarum), adding a genotypic context dimension through which epistasis occurs across subspaces. In doing so, we reveal that protein space is a deceptively complex notion, and that future applications to bioengineering should consider how interactions between amino acid substitutions manifest across different phenotypic subspaces.

Deconstructing taxa x taxa xenvironment interactions in the microbiota: A theoretical examination

A major objective of microbial ecology is to identify how the composition of microbial taxa shapes host phenotypes. However, most studies focus on pairwise interactions and ignore the potentially significant effects of higher-order microbial interactions.Here, we quantify the effects of higher-order interactions among taxa on host infection risk. We apply our approach to an in silico dataset that is built to resemble a population of insect hosts with gut-associated microbial communities at risk of infection from an intestinal parasite across a breadth of nutrient environmental contexts.We find that the effect of higher-order interactions is considerable and can change appreciably across environmental contexts. Furthermore, we show that higher-order interactions can stabilize community structure thereby reducing host susceptibility to parasite invasion.Our approach illustrates how incorporating the effects of higher-order interactions among gut microbiota across environments can be essential for understanding their effects on host phenotypes.

Evolutionary druggability: leveraging low-dimensional fitness landscapes towards new metrics for antimicrobial applications

The term "druggability" describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant's sensitivity across a breadth of drugs in a panel, or a given drug's range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and seven β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel ("variant vulnerability"), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target ("drug applicability"). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G × G × E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

Epistasis meets pleiotropy in shaping biophysical protein subspaces associated with antimicrobial resistance

Protein space is a rich analogy for genotype-phenotype maps, where amino acid sequence is organized into a high-dimensional space that highlights the connectivity between protein variants. It is a useful abstraction for understanding the process of evolution, and for efforts to engineer proteins towards desirable phenotypes. Few framings of protein space consider how higher-level protein phenotypes can be described in terms of their biophysical dimensions, nor do they rigorously interrogate how forces like epistasis-describing the nonlinear interaction between mutations and their phenotypic consequences-manifest across these dimensions. In this study, we deconstruct a low-dimensional protein space of a bacterial enzyme (dihydrofolate reductase; DHFR) into "subspaces" corresponding to a set of kinetic and thermodynamic traits [(kcat, KM, Ki, and Tm (melting temperature)]. We then examine how three mutations (eight alleles in total) display pleiotropy in their interactions across these subspaces. We extend this approach to examine protein spaces across three orthologous DHFR enzymes (Escherichia coli, Listeria grayi, and Chlamydia muridarum), adding a genotypic context dimension through which epistasis occurs across subspaces. In doing so, we reveal that protein space is a deceptively complex notion, and that the process of protein evolution and engineering should consider how interactions between amino acid substitutions manifest across different phenotypic subspaces.

Reversion is most likely under high mutation supply when compensatory mutations do not fully restore fitness costs

The dynamics of adaptation, reversion, and compensation have been central topics in microbial evolution, and several studies have attempted to resolve the population genetics underlying how these dynamics occur. However, questions remain regarding how certain features-the evolution of mutators and whether compensatory mutations alleviate costs fully or partially-may influence the evolutionary dynamics of compensation and reversion. In this study, we attempt to explain findings from experimental evolution by utilizing computational and theoretical approaches toward a more refined understanding of how mutation rate and the fitness effects of compensatory mutations influence adaptive dynamics. We find that high mutation rates increase the probability of reversion toward the wild type when compensation is only partial. However, the existence of even a single fully compensatory mutation is associated with a dramatically decreased probability of reversion to the wild type. These findings help to explain specific results from experimental evolution, where compensation was observed in nonmutator strains, but reversion (sometimes with compensation) was observed in mutator strains, indicating that real-world compensatory mutations are often unable to fully alleviate the costs associated with adaptation. Our findings emphasize the potential role of the supply and quality of mutations in crafting the dynamics of adaptation and reversal, with implications for theoretical population genetics and for biomedical contexts like the evolution of antibiotic resistance.