Physical Constraints on Epistasis

Design principles of multi-map variation in biological systems

Complexity in biology is often described using a multi-map hierarchical architecture, where the genotype, representing the encoded information, is mapped to the functional level, known as the phenotype, which is then connected to a latent phenotype we refer to as fitness. This underlying architecture governs the processes driving evolution. Furthermore, natural selection, along with other neutral forces, can, in turn, modify these maps. At each level, variation is observed. Here, I propose the need to establish principles that can aid in understanding the transformation of variation within this multi-map architecture. Specifically, I will introduce three, related to the presence of modulators, constraints, and the modular channeling of variation. By comprehending these design principles in various biological systems, we can gain better insights into the mechanisms underlying these maps and how they ultimately contribute to evolutionary dynamics.

Evolutionary rewiring of the dynamic network underpinning allosteric epistasis in NS1 of influenza A virus

Viral proteins frequently mutate to evade or antagonize host innate immune responses, yet the impact of these mutations on the molecular energy landscape remains unclear. Epistasis, the intramolecular communications between mutations, often renders the combined mutational effects unpredictable. Nonstructural protein 1 (NS1) is a major virulence factor of the influenza A virus (IAV) that activates host PI3K by binding to its p85β subunit. Here, we present the deep analysis for the impact of evolutionary mutations in NS1 that emerged between the 1918 pandemic IAV strain and its descendant PR8 strain. Our analysis reveal how the mutations rewired inter-residue communications which underlies long-range allosteric and epistatic networks in NS1. Our findings show that PR8 NS1 binds to p85β with approximately 10-fold greater affinity than 1918 NS1 due to allosteric mutational effects. Notably, these mutations also exhibited long-range epistatic effects. NMR chemical shift perturbation and methyl-axis order parameter analyses revealed that the mutations induced long-range structural and dynamic changes in PR8 NS1, enhancing its affinity to p85β. Complementary MD simulations and graph-based network analysis uncover how these mutations rewire dynamic residue interaction networks, which underlies the long-range epistasis and allosteric effects on p85β-binding affinity. Significantly, we find that conformational dynamics of residues with high betweenness centrality play a crucial role in communications between network communities and are highly conserved across influenza A virus evolution. These findings advance our mechanistic understanding of the allosteric and epistatic communications between distant residues and provides insight into their role in the molecular evolution of NS1.

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.

Physical effects of learning

Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks. This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience. Here, we show that learning in linear physical networks with weak input signals leaves architectural imprints on the Hessian of a physical system. Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system "susceptibility") increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task. Overall, these effects embody the typical scenario for learning processes in physical systems in the weak input regime, suggesting ways of discovering whether a physical network may have been trained.

Canalisation and plasticity on the developmental manifold of Caenorhabditis elegans

How do the same mechanisms that faithfully regenerate complex developmental programmes in spite of environmental and genetic perturbations also allow responsiveness to environmental signals, adaptation and genetic evolution? Using the nematode Caenorhabditis elegans as a model, we explore the phenotypic space of growth and development in various genetic and environmental contexts. Our data are growth curves and developmental parameters obtained by automated microscopy. Using these, we show that among the traits that make up the developmental space, correlations within a particular context are predictive of correlations among different contexts. Furthermore, we find that the developmental variability of this animal can be captured on a relatively low-dimensional phenotypic manifold and that on this manifold, genetic and environmental contributions to plasticity can be deconvolved independently. Our perspective offers a new way of understanding the relationship between robustness and flexibility in complex systems, suggesting that projection and concentration of dimension can naturally align these forces as complementary rather than competing.

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.

Global epistasis on fitness landscapes

Epistatic interactions between mutations add substantial complexity to adaptive landscapes and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a mutation is well-predicted by the fitness of its genetic background, may actually be of help in our efforts to reconstruct fitness landscapes and infer adaptive trajectories. Microscopic interactions between mutations, or inherent nonlinearities in the fitness landscape, may cause global epistasis patterns to emerge. In this brief review, we provide a succinct overview of recent work about global epistasis, with an emphasis on building intuition about why it is often observed. To this end, we reconcile simple geometric reasoning with recent mathematical analyses, using these to explain why different mutations in an empirical landscape may exhibit different global epistasis patterns—ranging from diminishing to increasing returns. Finally, we highlight open questions and research directions.

This article is part of the theme issue ‘Interdisciplinary approaches to predicting evolutionary biology’.

The community-function landscape of microbial consortia

Quantitatively linking the composition and function of microbial communities is a major aspiration of microbial ecology. Microbial community functions emerge from a complex web of molecular interactions between cells, which give rise to population-level interactions among strains and species. Incorporating this complexity into predictive models is highly challenging. Inspired by a similar problem in genetics of predicting quantitative phenotypes from genotypes, an ecological community-function (or structure-function) landscape could be defined that maps community composition and function. In this piece, we present an overview of our current understanding of these community landscapes, their uses, limitations, and open questions. We argue that exploiting the parallels between both landscapes could bring powerful predictive methodologies from evolution and genetics into ecology, providing a boost to our ability to engineer and optimize microbial consortia.

Analysis of the evolution of resistance to multiple antibiotics enables prediction of the Escherichia coli phenotype-based fitness landscape

The fitness landscape represents the complex relationship between genotype or phenotype and fitness under a given environment, the structure of which allows the explanation and prediction of evolutionary trajectories. Although previous studies have constructed fitness landscapes by comprehensively studying the mutations in specific genes, the high dimensionality of genotypic changes prevents us from developing a fitness landscape capable of predicting evolution for the whole cell. Herein, we address this problem by inferring the phenotype-based fitness landscape for antibiotic resistance evolution by quantifying the multidimensional phenotypic changes, i.e., time-series data of resistance for eight different drugs. We show that different peaks of the landscape correspond to different drug resistance mechanisms, thus supporting the validity of the inferred phenotype-fitness landscape. We further discuss how inferred phenotype-fitness landscapes could contribute to the prediction and control of evolution. This approach bridges the gap between phenotypic/genotypic changes and fitness while contributing to a better understanding of drug resistance evolution.

Experimental and In Silico Analysis of TEM β-Lactamase Adaptive Evolution

Multiple mutations often have non-additive (epistatic) phenotypic effects. Epistasis is of fundamental biological relevance but is not well understood mechanistically. Adaptive evolution, i.e., the evolution of new biochemical activities, is rich in epistatic interactions. To better understand the principles underlying epistasis during genetic adaptation, we studied the evolution of TEM-1 β-lactamase variants exhibiting cefotaxime resistance. We report the collection of a library of 487 observed evolutionary trajectories for TEM-1 and determine the epistasis status based on cefotaxime resistance phenotype for 206 combinations of 2-3 TEM-1 mutations involving 17 positions under adaptive selective pressure. Gain-of-function (GOF) mutations are gatekeepers for adaptation. To see if GOF phenotypes can be inferred based solely on sequence data, we calculated the enrichment of GOF mutations in the different categories of epistatic pairs. Our results suggest that this is possible because GOF mutations are particularly enriched in sign and reciprocal sign epistasis, which leave a major imprint on the sequence space accessible to evolution. We also used FoldX to explore the relationship between thermodynamic stability and epistasis. We found that mutations in observed evolutionary trajectories tend to destabilize the folded structure of the protein, albeit their cumulative effects are consistently below the protein's free energy of folding. The destabilizing effect is stronger for epistatic pairs, suggesting that modest or local alterations in folding stability can modulate catalysis. Finally, we report a significant relationship between epistasis and the degree to which two protein positions are structurally and dynamically coupled, even in the absence of ligand.

Interpretable modeling of genotype-phenotype landscapes with state-of-the-art predictive power

Large-scale measurements linking genetic background to biological function have driven a need for models that can incorporate these data for reliable predictions and insight into the underlying biophysical system. Recent modeling efforts, however, prioritize predictive accuracy at the expense of model interpretability. Here, we present LANTERN (landscape interpretable nonparametric model, https://github.com/usnistgov/lantern), a hierarchical Bayesian model that distills genotype-phenotype landscape (GPL) measurements into a low-dimensional feature space that represents the fundamental biological mechanisms of the system while also enabling straightforward, explainable predictions. Across a benchmark of large-scale datasets, LANTERN equals or outperforms all alternative approaches, including deep neural networks. LANTERN furthermore extracts useful insights of the landscape, including its inherent dimensionality, a latent space of additive mutational effects, and metrics of landscape structure. LANTERN facilitates straightforward discovery of fundamental mechanisms in GPLs, while also reliably extrapolating to unexplored regions of genotypic space.

Extremophile enzyme optimization for low temperature and high salinity are fundamentally incompatible

The evolutionary mechanisms behind cold and high-saline co-adaptation of proteins are not thoroughly understood. To explore how enzymes evolve in response to multiple environmental pressures we developed a novel in silico method to model the directed evolution of proteins, the Protein Evolution Parameter Calculator (PEPC). PEPC carries out single amino acid substitutions that lead to improvements in the selected user-defined parameters. To investigate the evolutionary relationship between increased flexibility and decreased isoelectric point, which are presumed indicators of cold and saline adaptation in proteins, we applied PEPC to a subset of core haloarchaea orthologous group (cHOG) proteins from the mesophilic Halobacterium salinarum NRC-1 and cold-tolerant Halorubrum lacusprofundi strain ATCC 49239. The results suggest that mutations that increase flexibility will also generally increase isoelectric point. These findings suggest that enzyme adaptation to low temperature and high salinity might be evolutionarily counterposed based on the structural characteristics of probable amino acid mutations. This may help to explain the apparent lack of truly psychrophilic halophiles in nature, and why microbes adapted to polar hypersaline environments typically have mesophilic temperature optima. A better understanding of protein evolution to extremely cold and salty conditions will aid in our understanding of where and how life is distributed on Earth and in our solar system.

The population genetics of collateral resistance and sensitivity

Resistance mutations against one drug can elicit collateral sensitivity against other drugs. Multi-drug treatments exploiting such trade-offs can help slow down the evolution of resistance. However, if mutations with diverse collateral effects are available, a treated population may evolve either collateral sensitivity or collateral resistance. How to design treatments robust to such uncertainty is unclear. We show that many resistance mutations in Escherichia coli against various antibiotics indeed have diverse collateral effects. We propose to characterize such diversity with a joint distribution of fitness effects (JDFE) and develop a theory for describing and predicting collateral evolution based on simple statistics of the JDFE. We show how to robustly rank drug pairs to minimize the risk of collateral resistance and how to estimate JDFEs. In addition to practical applications, these results have implications for our understanding of evolution in variable environments.

Drugs known as antibiotics are the main treatment for most serious infections caused by bacteria. However, many bacteria are acquiring genetic mutations that make them resistant to the effects of one or more types of antibiotics, making them harder to eliminate.

One way to tackle drug-resistant bacteria is to develop new types of antibiotics; however, in recent years, the rate at which new antibiotics have become available has been dwindling. Using two or more existing drugs, one after another, can also be an effective way to eliminate resistant bacteria. The success of any such ‘multi-drug’ treatment lies in being able to predict whether mutations that make the bacteria resistant to one drug simultaneously make it sensitive to another, a phenomenon known as collateral sensitivity.

Different resistance mutations may have different collateral effects: some may increase the bacteria’s sensitivity to the second drug, while others might make the bacteria more resistant. However, it is currently unclear how to design robust multi-drug treatments that take this diversity of collateral effects into account.

Here, Ardell and Kryazhimskiy used a concept called JDFE (short for the joint distribution of fitness effects) to describe the diversity of collateral effects in a population of bacteria exposed to a single drug. This information was then used to mathematically model how collateral effects evolved in the population over time.

Ardell and Kryazhimskiy showed that this approach can predict how likely a population is to become collaterally sensitive or collaterally resistant to a second antibiotic. Drug pairs can then be ranked according to the risk of collateral resistance emerging, so long as information on the variety of resistance mutations available to the bacteria are included in the model.

Each year, more than 700,000 people die from infections caused by bacteria that are resistant to one or more antibiotics. The findings of Ardell and Kryazhimskiy may eventually help clinicians design multi-drug treatments that effectively eliminate bacterial infections and help to prevent more bacteria from evolving resistance to antibiotics. However, to achieve this goal, more research is needed to fully understand the range collateral effects caused by resistance mutations.

Dynamics-Evolution Correspondence in Protein Structures

The genotype-phenotype mapping of proteins is a fundamental question in structural biology. In this Letter, with the analysis of a large dataset of proteins from hundreds of protein families, we quantitatively demonstrate the correlations between the noise-induced protein dynamics and mutation-induced variations of native structures, indicating the dynamics-evolution correspondence of proteins. Based on the investigations of the linear responses of native proteins, the origin of such a correspondence is elucidated. It is essential that the noise- and mutation-induced deformations of the proteins are restricted on a common low-dimensional subspace, as confirmed from the data. These results suggest an evolutionary mechanism of the proteins gaining both dynamical flexibility and evolutionary structural variability.

Global epistasis emerges from a generic model of a complex trait

Epistasis between mutations can make adaptation contingent on evolutionary history. Yet despite widespread ‘microscopic’ epistasis between the mutations involved, microbial evolution experiments show consistent patterns of fitness increase between replicate lines. Recent work shows that this consistency is driven in part by global patterns of diminishing-returns and increasing-costs epistasis, which make mutations systematically less beneficial (or more deleterious) on fitter genetic backgrounds. However, the origin of this ‘global’ epistasis remains unknown. Here, we show that diminishing-returns and increasing-costs epistasis emerge generically as a consequence of pervasive microscopic epistasis. Our model predicts a specific quantitative relationship between the magnitude of global epistasis and the stochastic effects of microscopic epistasis, which we confirm by reanalyzing existing data. We further show that the distribution of fitness effects takes on a universal form when epistasis is widespread and introduce a novel fitness landscape model to show how phenotypic evolution can be repeatable despite sequence-level stochasticity.

Emergence and propagation of epistasis in metabolic networks

Epistasis is often used to probe functional relationships between genes, and it plays an important role in evolution. However, we lack theory to understand how functional relationships at the molecular level translate into epistasis at the level of whole-organism phenotypes, such as fitness. Here, I derive two rules for how epistasis between mutations with small effects propagates from lower- to higher-level phenotypes in a hierarchical metabolic network with first-order kinetics and how such epistasis depends on topology. Most importantly, weak epistasis at a lower level may be distorted as it propagates to higher levels. Computational analyses show that epistasis in more realistic models likely follows similar, albeit more complex, patterns. These results suggest that pairwise inter-gene epistasis should be common, and it should generically depend on the genetic background and environment. Furthermore, the epistasis coefficients measured for high-level phenotypes may not be sufficient to fully infer the underlying functional relationships.