Higher-order epistasis and phenotypic prediction

Developing the 'omic toolkit of comparative physiologists

Typical 'omic analyses reduce complex biological systems to simple lists of supposedly independent variables, failing to account for changes in the wider transcriptional landscape. In this commentary, we discuss the utility of network approaches for incorporating this wider context into the study of physiological phenomena. We highlight opportunities to build on traditional network tools by utilising cutting-edge techniques to account for higher order interactions (i.e. beyond pairwise associations) within datasets, allowing for more accurate models of complex 'omic systems. Finally, we show examples of previous works utilising network approaches to gain additional insight into their organisms of interest. As 'omics grow in both their popularity and breadth of application, so does the requirement for flexible analytical tools capable of interpreting and synthesising complex datasets.

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 commonplace within the fields of quantitative and evolutionary genetics, "environment-by-environment interaction" (ExE) is a term used less often. In this study, we find that environment-by-environment interactions are a meaningful driver of phenotypes, and that they differ across different genotypes (suggestive of ExExG). To reach this conclusion, we analyzed a large dataset of roughly 1,000 mutant yeast strains with varying degrees of resistance to different antifungal drugs. We show that the effectiveness of a drug combination, relative to single drugs, often varies across different drug resistant mutants. Even mutants that differ by only a single nucleotide change can have dramatically different drug x drug (ExE) interactions. We also introduce a new framework that better predicts the direction and magnitude of ExE interactions for some mutants. Studying how ExE interactions change across genotypes (ExExG) is not only important when modeling the evolution of pathogenic microbes, but also for broader efforts to understand the cell biology underlying these interactions and to resolve the source of phenotypic variance across populations. The relevance of ExExG interactions have been largely omitted from canon in evolutionary and population genetics, but these fields and others stand to benefit from perspectives that highlight how interactions between external forces craft the complex behavior of living systems.

Robust genetic codes enhance protein evolvability

The standard genetic code defines the rules of translation for nearly every life form on Earth. It also determines the amino acid changes accessible via single-nucleotide mutations, thus influencing protein evolvability-the ability of mutation to bring forth adaptive variation in protein function. One of the most striking features of the standard genetic code is its robustness to mutation, yet it remains an open question whether such robustness facilitates or frustrates protein evolvability. To answer this question, we use data from massively parallel sequence-to-function assays to construct and analyze 6 empirical adaptive landscapes under hundreds of thousands of rewired genetic codes, including those of codon compression schemes relevant to protein engineering and synthetic biology. We find that robust genetic codes tend to enhance protein evolvability by rendering smooth adaptive landscapes with few peaks, which are readily accessible from throughout sequence space. However, the standard genetic code is rarely exceptional in this regard, because many alternative codes render smoother landscapes than the standard code. By constructing low-dimensional visualizations of these landscapes, which each comprise more than 16 million mRNA sequences, we show that such alternative codes radically alter the topological features of the network of high-fitness genotypes. Whereas the genetic codes that optimize evolvability depend to some extent on the detailed relationship between amino acid sequence and protein function, we also uncover general design principles for engineering nonstandard genetic codes for enhanced and diminished evolvability, which may facilitate directed protein evolution experiments and the bio-containment of synthetic organisms, respectively.

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.

Rugged fitness landscapes minimize promiscuity in the evolution of transcriptional repressors

How a protein's function influences the shape of its fitness landscape, smooth or rugged, is a fundamental question in evolutionary biochemistry. Smooth landscapes arise when incremental mutational steps lead to a progressive change in function, as commonly seen in enzymes and binding proteins. On the other hand, rugged landscapes are poorly understood because of the inherent unpredictability of how sequence changes affect function. Here, we experimentally characterize the entire sequence phylogeny, comprising 1,158 extant and ancestral sequences, of the DNA-binding domain (DBD) of the LacI/GalR transcriptional repressor family. Our analysis revealed an extremely rugged landscape with rapid switching of specificity, even between adjacent nodes. Further, the ruggedness arises due to the necessity of the repressor to simultaneously evolve specificity for asymmetric operators and disfavors potentially adverse regulatory crosstalk. Our study provides fundamental insight into evolutionary, molecular, and biophysical rules of genetic regulation through the lens of fitness landscapes.

Empowering Protein Engineering through Recombination of Beneficial Substitutions

Directed evolution stands as a seminal technology for generating novel protein functionalities, a cornerstone in biocatalysis, metabolic engineering, and synthetic biology. Today, with the development of various mutagenesis methods and advanced analytical machines, the challenge of diversity generation and high-throughput screening platforms is largely solved, and one of the remaining challenges is: how to empower the potential of single beneficial substitutions with recombination to achieve the epistatic effect. This review overviews experimental and computer-assisted recombination methods in protein engineering campaigns. In addition, integrated and machine learning-guided strategies were highlighted to discuss how these recombination approaches contribute to generating the screening library with better diversity, coverage, and size. A decision tree was finally summarized to guide the further selection of proper recombination strategies in practice, which was beneficial for accelerating protein engineering.

Interpreting cis-regulatory mechanisms from genomic deep neural networks using surrogate models

Deep neural networks (DNNs) have greatly advanced the ability to predict genome function from sequence. Interpreting genomic DNNs in terms of biological mechanisms, however, remains difficult. Here we introduce SQUID, a genomic DNN interpretability framework based on surrogate modeling. SQUID approximates genomic DNNs in user-specified regions of sequence space using surrogate models, i.e., simpler models that are mechanistically interpretable. Importantly, SQUID removes the confounding effects that nonlinearities and heteroscedastic noise in functional genomics data can have on model interpretation. Benchmarking analysis on multiple genomic DNNs shows that SQUID, when compared to established interpretability methods, identifies motifs that are more consistent across genomic loci and yields improved single-nucleotide variant-effect predictions. SQUID also supports surrogate models that quantify epistatic interactions within and between cis-regulatory elements. SQUID thus advances the ability to mechanistically interpret genomic DNNs.

Discovering pathways through ribozyme fitness landscapes using information theoretic quantification of epistasis

The identification of catalytic RNAs is typically achieved through primarily experimental means. However, only a small fraction of sequence space can be analyzed even with high-throughput techniques. Methods to extrapolate from a limited data set to predict additional ribozyme sequences, particularly in a human-interpretable fashion, could be useful both for designing new functional RNAs and for generating greater understanding about a ribozyme fitness landscape. Using information theory, we express the effects of epistasis (i.e., deviations from additivity) on a ribozyme. This representation was incorporated into a simple model of the epistatic fitness landscape, which identified potentially exploitable combinations of mutations. We used this model to theoretically predict mutants of high activity for a self-aminoacylating ribozyme, identifying potentially active triple and quadruple mutants beyond the experimental data set of single and double mutants. The predictions were validated experimentally, with nine out of nine sequences being accurately predicted to have high activity. This set of sequences included mutants that form a previously unknown evolutionary "bridge" between two ribozyme families that share a common motif. Individual steps in the method could be examined, understood, and guided by a human, combining interpretability and performance in a simple model to predict ribozyme sequences by extrapolation.

Leveraging the genetic correlation between traits improves the detection of epistasis in genome-wide association studies

Epistasis, commonly defined as the interaction between genetic loci, is known to play an important role in the phenotypic variation of complex traits. As a result, many statistical methods have been developed to identify genetic variants that are involved in epistasis, and nearly all of these approaches carry out this task by focusing on analyzing one trait at a time. Previous studies have shown that jointly modeling multiple phenotypes can often dramatically increase statistical power for association mapping. In this study, we present the "multivariate MArginal ePIstasis Test" (mvMAPIT)-a multioutcome generalization of a recently proposed epistatic detection method which seeks to detect marginal epistasis or the combined pairwise interaction effects between a given variant and all other variants. By searching for marginal epistatic effects, one can identify genetic variants that are involved in epistasis without the need to identify the exact partners with which the variants interact-thus, potentially alleviating much of the statistical and computational burden associated with conventional explicit search-based methods. Our proposed mvMAPIT builds upon this strategy by taking advantage of correlation structure between traits to improve the identification of variants involved in epistasis. We formulate mvMAPIT as a multivariate linear mixed model and develop a multitrait variance component estimation algorithm for efficient parameter inference and P-value computation. Together with reasonable model approximations, our proposed approach is scalable to moderately sized genome-wide association studies. With simulations, we illustrate the benefits of mvMAPIT over univariate (or single-trait) epistatic mapping strategies. We also apply mvMAPIT framework to protein sequence data from two broadly neutralizing anti-influenza antibodies and approximately 2,000 heterogeneous stock of mice from the Wellcome Trust Centre for Human Genetics. The mvMAPIT R package can be downloaded at https://github.com/lcrawlab/mvMAPIT.

Enterosignatures define common bacterial guilds in the human gut microbiome

The human gut microbiome composition is generally in a stable dynamic equilibrium, but it can deteriorate into dysbiotic states detrimental to host health. To disentangle the inherent complexity and capture the ecological spectrum of microbiome variability, we used 5,230 gut metagenomes to characterize signatures of bacteria commonly co-occurring, termed enterosignatures (ESs). We find five generalizable ESs dominated by either Bacteroides, Firmicutes, Prevotella, Bifidobacterium, or Escherichia. This model confirms key ecological characteristics known from previous enterotype concepts, while enabling the detection of gradual shifts in community structures. Temporal analysis implies that the Bacteroides-associated ES is "core" in the resilience of westernized gut microbiomes, while combinations with other ESs often complement the functional spectrum. The model reliably detects atypical gut microbiomes correlated with adverse host health conditions and/or the presence of pathobionts. ESs provide an interpretable and generic model that enables an intuitive characterization of gut microbiome composition in health and disease.

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.

Environment-dependent epistasis increases phenotypic diversity in gene regulatory networks

Mutations to gene regulatory networks can be maladaptive or a source of evolutionary novelty. Epistasis confounds our understanding of how mutations affect the expression patterns of gene regulatory networks, a challenge exacerbated by the dependence of epistasis on the environment. We used the toolkit of synthetic biology to systematically assay the effects of pairwise and triplet combinations of mutant genotypes on the expression pattern of a gene regulatory network expressed in Escherichia coli that interprets an inducer gradient across a spatial domain. We uncovered a preponderance of epistasis that can switch in magnitude and sign across the inducer gradient to produce a greater diversity of expression pattern phenotypes than would be possible in the absence of such environment-dependent epistasis. We discuss our findings in the context of the evolution of hybrid incompatibilities and evolutionary novelties.