Global epistasis on fitness landscapes

Assembly Graph as the Rosetta Stone of Ecological Assembly

Ecological assembly-the process of ecological community formation through species introductions-has recently seen exciting theoretical advancements across dynamical, informational, and probabilistic approaches. However, these theories often remain inaccessible to non-theoreticians, and they lack a unifying lens. Here, I introduce the assembly graph as an integrative tool to connect these emerging theories. The assembly graph visually represents assembly dynamics, where nodes symbolise species combinations and edges represent transitions driven by species introductions. Through the lens of assembly graphs, I review how ecological processes reduce uncertainty in random species arrivals (informational approach), identify graphical properties that guarantee species coexistence and examine how the class of dynamical models constrain the topology of assembly graphs (dynamical approach), and quantify transition probabilities with incomplete information (probabilistic approach). To facilitate empirical testing, I also review methods to decompose complex assembly graphs into smaller, measurable components, as well as computational tools for deriving empirical assembly graphs. In sum, this math-light review of theoretical progress aims to catalyse empirical research towards a predictive understanding of ecological assembly.

Error thresholds in the presence of epistatic interactions

Models for viral populations with high replication error rates (such as RNA viruses) rely on the quasispecies concept, in which mutational pressure beyond the so-called "error threshold" leads to a loss of essential genetic information and population collapse, an effect known as the "error catastrophe." We explain how crossing this threshold, as a result of increasing mutation rates, can be understood as a second-order phase transition, even in the presence of lethal mutations. In particular, we show that, in fitness landscapes with a single peak, this collapse is equivalent to a ferroparamagnetic transition, where the back-mutation rate plays the role of the external magnetic field. We then generalize this framework to rugged fitness landscapes, like the ones that arise from epistatic interactions, and provide numerical evidence that there is a transition from a high average fitness regime to a low average fitness one, similarly to single-peaked landscapes. The onset of the transition is heralded by a sudden change in the susceptibility to variations in the mutation rate. We use insight from replica symmetry breaking mechanisms in spin glasses, in particular by considering the fluctuations of the genotype similarity distribution as the order parameter.

Compensatory Evolution to DNA Replication Stress is Robust to Nutrient Availability

Evolutionary repair refers to the compensatory evolution that follows perturbations in cellular processes. While evolutionary trajectories are often reproducible, other studies suggest they are shaped by genotype-by-environment (GxE) interactions. Here, we test the predictability of evolutionary repair in response to DNA replication stress-a severe perturbation impairing the conserved mechanisms of DNA synthesis, resulting in genetic instability. We conducted high-throughput experimental evolution on Saccharomyces cerevisiae experiencing constitutive replication stress, grown under different glucose availabilities. We found that glucose levels impact the physiology and adaptation rate of replication stress mutants. However, the genetics of adaptation show remarkable robustness across environments. Recurrent mutations collectively recapitulated the fitness of evolved lines and are advantageous across macronutrient availability. We also identified a novel role of the mediator complex of RNA polymerase II in adaptation to replicative stress. Our results highlight the robustness and predictability of evolutionary repair mechanisms to DNA replication stress and provide new insights into the evolutionary aspects of genome stability, with potential implications for understanding cancer development.

Environment-independent distribution of mutational effects emerges from microscopic epistasis

Predicting how new mutations alter phenotypes is difficult because mutational effects vary across genotypes and environments. Recently discovered global epistasis, in which the fitness effects of mutations scale with the fitness of the background genotype, can improve predictions, but how the environment modulates this scaling is unknown. We measured the fitness effects of ~100 insertion mutations in 42 strains of Saccharomyces cerevisiae in six laboratory environments and found that the global epistasis scaling is nearly invariant across environments. Instead, the environment tunes one global parameter, the background fitness at which most mutations switch sign. As a consequence, the distribution of mutational effects is predictable across genotypes and environments. Our results suggest that the effective dimensionality of genotype-to-phenotype maps across environments is surprisingly low.

Real-time identification of epistatic interactions in SARS-CoV-2 from large genome collections

BACKGROUND

The emergence of the SARS-CoV-2 virus has highlighted the importance of genomic epidemiology in understanding the evolution of pathogens and guiding public health interventions. The Omicron variant in particular has underscored the role of epistasis in the evolution of lineages with both higher infectivity and immune escape, and therefore the necessity to update surveillance pipelines to detect them early on.

RESULTS

In this study, we apply a method based on mutual information between positions in a multiple sequence alignment, which is capable of scaling up to millions of samples. We show how it can reliably predict known experimentally validated epistatic interactions, even when using as little as 10,000 sequences, which opens the possibility of making it a near real-time prediction system. We test this possibility by modifying the method to account for the sample collection date and apply it retrospectively to multiple sequence alignments for each month between March 2020 and March 2023. We detected a cornerstone epistatic interaction in the Spike protein between codons 498 and 501 as soon as seven samples with a double mutation were present in the dataset, thus demonstrating the method's sensitivity. We test the ability of the method to make inferences about emerging interactions by testing candidates predicted after March 2023, which we validate experimentally.

CONCLUSIONS

We show how known epistatic interaction in SARS-CoV-2 can be detected with high sensitivity, and how emerging ones can be quickly prioritized for experimental validation, an approach that could be implemented downstream of pandemic genome sequencing efforts.

Environment-independent distribution of mutational effects emerges from microscopic epistasis

Predicting how new mutations alter phenotypes is difficult because mutational effects vary across genotypes and environments. Recently discovered global epistasis, where the fitness effects of mutations scale with the fitness of the background genotype, can improve predictions, but how the environment modulates this scaling is unknown. We measured the fitness effects of ~100 insertion mutations in 42 strains of Saccharomyces cerevisiae in six laboratory environments and found that the global-epistasis scaling is nearly invariant across environments. Instead, the environment tunes one global parameter, the background fitness at which most mutations switch sign. As a consequence, the distribution of mutational effects is predictable across genotypes and environments. Our results suggest that the effective dimensionality of genotype-to-phenotype maps across environments is surprisingly low.

A simple rule for predicting function of microbial communities

Microbial communities perform many important functions, such as carbon sequestration, decomposition, pathogen resistance, etc., but quantitatively predicting functions of new communities remains a major challenge. In this issue of Cell, Diaz-Colunga et al. report a new simple statistical regularity that enables such predictions.

Global epistasis and the emergence of function in microbial consortia

The many functions of microbial communities emerge from a complex web of interactions between organisms and their environment. This poses a significant obstacle to engineering microbial consortia, hindering our ability to harness the potential of microorganisms for biotechnological applications. In this study, we demonstrate that the collective effect of ecological interactions between microbes in a community can be captured by simple statistical models that predict how adding a new species to a community will affect its function. These predictive models mirror the patterns of global epistasis reported in genetics, and they can be quantitatively interpreted in terms of pairwise interactions between community members. Our results illuminate an unexplored path to quantitatively predicting the function of microbial consortia from their composition, paving the way to optimizing desirable community properties and bringing the tasks of predicting biological function at the genetic, organismal, and ecological scales under the same quantitative formalism.

Unpredictability of the Fitness Effects of Antimicrobial Resistance Mutations Across Environments in Escherichia coli

The evolution of antimicrobial resistance (AMR) in bacteria is a major public health concern, and antibiotic restriction is often implemented to reduce the spread of resistance. These measures rely on the existence of deleterious fitness effects (i.e. costs) imposed by AMR mutations during growth in the absence of antibiotics. According to this assumption, resistant strains will be outcompeted by susceptible strains that do not pay the cost during the period of restriction. The fitness effects of AMR mutations are generally studied in laboratory reference strains grown in standard growth environments; however, the genetic and environmental context can influence the magnitude and direction of a mutation's fitness effects. In this study, we measure how three sources of variation impact the fitness effects of Escherichia coli AMR mutations: the type of resistance mutation, the genetic background of the host, and the growth environment. We demonstrate that while AMR mutations are generally costly in antibiotic-free environments, their fitness effects vary widely and depend on complex interactions between the mutation, genetic background, and environment. We test the ability of the Rough Mount Fuji fitness landscape model to reproduce the empirical data in simulation. We identify model parameters that reasonably capture the variation in fitness effects due to genetic variation. However, the model fails to accommodate the observed variation when considering multiple growth environments. Overall, this study reveals a wealth of variation in the fitness effects of resistance mutations owing to genetic background and environmental conditions, which will ultimately impact their persistence in natural populations.

Convergent genetic adaptation of Escherichia coli in minimal media leads to pleiotropic divergence

Adaptation in an environment can either be beneficial, neutral or disadvantageous in another. To test the genetic basis of pleiotropic behaviour, we evolved six lines of E. coli independently in environments where glucose and galactose were the sole carbon sources, for 300 generations. All six lines in each environment exhibit convergent adaptation in the environment in which they were evolved. However, pleiotropic behaviour was observed in several environmental contexts, including other carbon environments. Genome sequencing reveals that mutations in global regulators rpoB and rpoC cause this pleiotropy. We report three new alleles of the rpoB gene, and one new allele of the rpoC gene. The novel rpoB alleles confer resistance to Rifampicin, and alter motility. Our results show how single nucleotide changes in the process of adaptation in minimal media can lead to wide-scale pleiotropy, resulting in changes in traits that are not under direct selection.

Global epistasis in plasmid-mediated antimicrobial resistance

Antimicrobial resistance (AMR) in bacteria is a major public health threat and conjugative plasmids play a key role in the dissemination of AMR genes among bacterial pathogens. Interestingly, the association between AMR plasmids and pathogens is not random and certain associations spread successfully at a global scale. The burst of genome sequencing has increased the resolution of epidemiological programs, broadening our understanding of plasmid distribution in bacterial populations. Despite the immense value of these studies, our ability to predict future plasmid-bacteria associations remains limited. Numerous empirical studies have recently reported systematic patterns in genetic interactions that enable predictability, in a phenomenon known as global epistasis. In this perspective, we argue that global epistasis patterns hold the potential to predict interactions between plasmids and bacterial genomes, thereby facilitating the prediction of future successful associations. To assess the validity of this idea, we use previously published data to identify global epistasis patterns in clinically relevant plasmid-bacteria associations. Furthermore, using simple mechanistic models of antibiotic resistance, we illustrate how global epistasis patterns may allow us to generate new hypotheses on the mechanisms associated with successful plasmid-bacteria associations. Collectively, we aim at illustrating the relevance of exploring global epistasis in the context of plasmid biology.

How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

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.

Statistically learning the functional landscape of microbial communities

Microbial consortia exhibit complex functional properties in contexts ranging from soils to bioreactors to human hosts. Understanding how community composition determines function is a major goal of microbial ecology. Here we address this challenge using the concept of community-function landscapes-analogues to fitness landscapes-that capture how changes in community composition alter collective function. Using datasets that represent a broad set of community functions, from production/degradation of specific compounds to biomass generation, we show that statistically inferred landscapes quantitatively predict community functions from knowledge of species presence or absence. Crucially, community-function landscapes allow prediction without explicit knowledge of abundance dynamics or interactions between species and can be accurately trained using measurements from a small subset of all possible community compositions. The success of our approach arises from the fact that empirical community-function landscapes appear to be not rugged, meaning that they largely lack high-order epistatic contributions that would be difficult to fit with limited data. Finally, we show that this observation holds across a wide class of ecological models, suggesting community-function landscapes can be efficiently inferred across a broad range of ecological regimes. Our results open the door to the rational design of consortia without detailed knowledge of abundance dynamics or interactions.

Evolutionary rescue on genotypic fitness landscapes

Populations facing adverse environments, novel pathogens or invasive competitors may be destined to extinction if they are unable to adapt rapidly. Quantitative predictions of the probability of survival through adaptation, evolutionary rescue, have been previously developed for one of the most natural and well-studied mappings from an organism's traits to its fitness, Fisher's geometric model (FGM). While FGM assumes that all possible trait values are accessible via mutation, in many applications only a finite set of rescue mutations will be available, such as mutations conferring resistance to a parasite, predator or toxin. We predict the probability of evolutionary rescue, via de novo mutation, when this underlying genetic structure is included. We find that rescue probability is always reduced when its genetic basis is taken into account. Unlike other known features of the genotypic FGM, however, the probability of rescue increases monotonically with the number of available mutations and approaches the behaviour of the classical FGM as the number of available mutations approaches infinity.

A polygenic explanation for Haldane's rule in butterflies

Two robust rules have been discovered about animal hybrids: Heterogametic hybrids are more unfit (Haldane's rule), and sex chromosomes are disproportionately involved in hybrid incompatibility (the large-X/Z effect). The exact mechanisms causing these rules in female heterogametic taxa such as butterflies are unknown but are suggested by theory to involve dominance on the sex chromosome. We investigate hybrid incompatibilities adhering to both rules in Papilio and Heliconius butterflies and show that dominance theory cannot explain our data. Instead, many defects coincide with unbalanced multilocus introgression between the Z chromosome and all autosomes. Our polygenic explanation predicts both rules because the imbalance is likely greater in heterogametic females, and the proportion of introgressed ancestry is more variable on the Z chromosome. We also show that mapping traits polygenic on a single chromosome in backcrosses can generate spurious large-effect QTLs. This mirage is caused by statistical linkage among polygenes that inflates estimated effect sizes. By controlling for statistical linkage, most incompatibility QTLs in our hybrid crosses are consistent with a polygenic basis. Since the two genera are very distantly related, polygenic hybrid incompatibilities are likely common in butterflies.

Epistasis and evolution: recent advances and an outlook for prediction

As organisms evolve, the effects of mutations change as a result of epistatic interactions with other mutations accumulated along the line of descent. This can lead to shifts in adaptability or robustness that ultimately shape subsequent evolution. Here, we review recent advances in measuring, modeling, and predicting epistasis along evolutionary trajectories, both in microbial cells and single proteins. We focus on simple patterns of global epistasis that emerge in this data, in which the effects of mutations can be predicted by a small number of variables. The emergence of these patterns offers promise for efforts to model epistasis and predict evolution.