Learning the pattern of epistasis linking genotype and phenotype in a protein

Emergent time scales of epistasis in protein evolution

We introduce a data-driven epistatic model of protein evolution, capable of generating evolutionary trajectories spanning very different time scales reaching from individual mutations to diverged homologs. Our in silico evolution encompasses random nucleotide mutations, insertions and deletions, and models selection using a fitness landscape, which is inferred via a generative probabilistic model for protein families. We show that the proposed framework accurately reproduces the sequence statistics of both short-time (experimental) and long-time (natural) protein evolution, suggesting applicability also to relatively data-poor intermediate evolutionary time scales, which are currently inaccessible to evolution experiments. Our model uncovers a highly collective nature of epistasis, gradually changing the fitness effect of mutations in a diverging sequence context, rather than acting via strong interactions between individual mutations. This collective nature triggers the emergence of a long evolutionary time scale, separating fast mutational processes inside a given sequence context, from the slow evolution of the context itself. The model quantitatively reproduces epistatic phenomena such as contingency and entrenchment, as well as the loss of predictability in protein evolution observed in deep mutational scanning experiments of distant homologs. It thereby deepens our understanding of the interplay between mutation and selection in shaping protein diversity and functions, allows one to statistically forecast evolution, and challenges the prevailing independent-site models of protein evolution, which are unable to capture the fundamental importance of epistasis.

The genetic architecture of protein stability

There are more ways to synthesize a 100-amino acid (aa) protein (20100) than there are atoms in the universe. Only a very small fraction of such a vast sequence space can ever be experimentally or computationally surveyed. Deep neural networks are increasingly being used to navigate high-dimensional sequence spaces1. However, these models are extremely complicated. Here, by experimentally sampling from sequence spaces larger than 1010, we show that the genetic architecture of at least some proteins is remarkably simple, allowing accurate genetic prediction in high-dimensional sequence spaces with fully interpretable energy models. These models capture the nonlinear relationships between free energies and phenotypes but otherwise consist of additive free energy changes with a small contribution from pairwise energetic couplings. These energetic couplings are sparse and associated with structural contacts and backbone proximity. Our results indicate that protein genetics is actually both rather simple and intelligible.

The simplicity of protein sequence-function relationships

How complex are the rules by which a protein's sequence determines its function? High-order epistatic interactions among residues are thought to be pervasive, suggesting an idiosyncratic and unpredictable sequence-function relationship. But many prior studies may have overestimated epistasis, because they analyzed sequence-function relationships relative to a single reference sequence-which causes measurement noise and local idiosyncrasies to snowball into high-order epistasis-or they did not fully account for global nonlinearities. Here we present a reference-free method that jointly infers specific epistatic interactions and global nonlinearity using a bird's-eye view of sequence space. This technique yields the simplest explanation of sequence-function relationships and is more robust than existing methods to measurement noise, missing data, and model misspecification. We reanalyze 20 experimental datasets and find that context-independent amino acid effects and pairwise interactions, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of phenotypic variance and over 92% in every case. Only a tiny fraction of genotypes are strongly affected by higher-order epistasis. Sequence-function relationships are also sparse: a miniscule fraction of amino acids and interactions account for 90% of phenotypic variance. Sequence-function causality across these datasets is therefore simple, opening the way for tractable approaches to characterize proteins' genetic architecture.

Addressing epistasis in the design of protein function

Mutations in protein active sites can dramatically improve function. The active site, however, is densely packed and extremely sensitive to mutations. Therefore, some mutations may only be tolerated in combination with others in a phenomenon known as epistasis. Epistasis reduces the likelihood of obtaining improved functional variants and dramatically slows natural and lab evolutionary processes. Research has shed light on the molecular origins of epistasis and its role in shaping evolutionary trajectories and outcomes. In addition, sequence- and AI-based strategies that infer epistatic relationships from mutational patterns in natural or experimental evolution data have been used to design functional protein variants. In recent years, combinations of such approaches and atomistic design calculations have successfully predicted highly functional combinatorial mutations in active sites. These were used to design thousands of functional active-site variants, demonstrating that, while our understanding of epistasis remains incomplete, some of the determinants that are critical for accurate design are now sufficiently understood. We conclude that the space of active-site variants that has been explored by evolution may be expanded dramatically to enhance natural activities or discover new ones. Furthermore, design opens the way to systematically exploring sequence and structure space and mutational impacts on function, deepening our understanding and control over protein activity.

Mechanistic conformational and substrate selectivity profiles emerging in the evolution of enzymes via parallel trajectories

Laboratory evolution studies have demonstrated that parallel evolutionary trajectories can lead to genetically distinct enzymes with high activity towards a non-preferred substrate. However, it is unknown whether such enzymes have convergent conformational dynamics and mechanistic features. To address this question, we use as a model the wild-type Homo sapiens kynureninase (HsKYNase), which is of great interest for cancer immunotherapy. Earlier, we isolated HsKYNase_66 through an unusual evolutionary trajectory, having a 410-fold increase in the kcat/KM for kynurenine (KYN) and reverse substrate selectivity relative to HsKYNase. Here, by following a different evolutionary trajectory we generate a genetically distinct variant, HsKYNase_93D9, that exhibits KYN catalytic activity comparable to that of HsKYNase_66, but instead it is a "generalist" that accepts 3'-hydroxykynurenine (OH-KYN) with the same proficiency. Pre-steady-state kinetic analysis reveals that while the evolution of HsKYNase_66 is accompanied by a change in the rate-determining step of the reactions, HsKYNase_93D9 retains the same catalytic mechanism as HsKYNase. HDX-MS shows that the conformational dynamics of the two enzymes are markedly different and distinct from ortholog prokaryotic enzymes with high KYN activity. Our work provides a mechanistic framework for understanding the relationship between evolutionary mechanisms and phenotypic traits of evolved generalist and specialist enzyme species.

Nature-Inspired Intelligent Computing: A Comprehensive Survey

Nature, with its numerous surprising rules, serves as a rich source of creativity for the development of artificial intelligence, inspiring researchers to create several nature-inspired intelligent computing paradigms based on natural mechanisms. Over the past decades, these paradigms have revealed effective and flexible solutions to practical and complex problems. This paper summarizes the natural mechanisms of diverse advanced nature-inspired intelligent computing paradigms, which provide valuable lessons for building general-purpose machines capable of adapting to the environment autonomously. According to the natural mechanisms, we classify nature-inspired intelligent computing paradigms into 4 types: evolutionary-based, biological-based, social-cultural-based, and science-based. Moreover, this paper also illustrates the interrelationship between these paradigms and natural mechanisms, as well as their real-world applications, offering a comprehensive algorithmic foundation for mitigating unreasonable metaphors. Finally, based on the detailed analysis of natural mechanisms, the challenges of current nature-inspired paradigms and promising future research directions are presented.

Quantifying higher-order epistasis: beware the chimera

Epistasis, or interactions in which alleles at one locus modify the fitness effects of alleles at other loci, plays a fundamental role in genetics, protein evolution, and many other areas of biology. Epistasis is typically quantified by computing the deviation from the expected fitness under an additive or multiplicative model using one of several formulae. However, these formulae are not all equivalent. Importantly, one widely used formula - which we call the chimeric formula - measures deviations from a multiplicative fitness model on an additive scale, thus mixing two measurement scales. We show that for pairwise interactions, the chimeric formula yields a different magnitude, but the same sign (synergistic vs. antagonistic) of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula - thus confusing negative epistatic interactions with positive interactions, and vice versa. We resolve these inconsistencies by deriving fundamental connections between the different epistasis formulae and the parameters of the multivariate Bernoulli distribution . Our results demonstrate that the additive and multiplicative epistasis formulae are more mathematically sound than the chimeric formula. Moreover, we demonstrate that the mathematical issues with the chimeric epistasis formula lead to markedly different biological interpretations of real data. Analyzing multi-gene knockout data in yeast, multi-way drug interactions in E. coli , and deep mutational scanning (DMS) of several proteins, we find that 10 - 60% of higher-order interactions have a change in sign with the multiplicative or additive epistasis formula. These sign changes result in qualitatively different findings on functional divergence in the yeast genome, synergistic vs. antagonistic drug interactions, and and epistasis between protein mutations. In particular, in the yeast data, the more appropriate multiplicative formula identifies nearly 500 additional negative three-way interactions, thus extending the trigenic interaction network by 25%.

Gauge fixing for sequence-function relationships

Quantitative models of sequence-function relationships are ubiquitous in computational biology, e.g., for modeling the DNA binding of transcription factors or the fitness landscapes of proteins. Interpreting these models, however, is complicated by the fact that the values of model parameters can often be changed without affecting model predictions. Before the values of model parameters can be meaningfully interpreted, one must remove these degrees of freedom (called "gauge freedoms" in physics) by imposing additional constraints (a process called "fixing the gauge"). However, strategies for fixing the gauge of sequence-function relationships have received little attention. Here we derive an analytically tractable family of gauges for a large class of sequence-function relationships. These gauges are derived in the context of models with all-order interactions, but an important subset of these gauges can be applied to diverse types of models, including additive models, pairwise-interaction models, and models with higher-order interactions. Many commonly used gauges are special cases of gauges within this family. We demonstrate the utility of this family of gauges by showing how different choices of gauge can be used both to explore complex activity landscapes and to reveal simplified models that are approximately correct within localized regions of sequence space. The results provide practical gauge-fixing strategies and demonstrate the utility of gauge-fixing for model exploration and interpretation.

Epistasis facilitates functional evolution in an ancient transcription factor

A protein's genetic architecture - the set of causal rules by which its sequence produces its functions - also determines its possible evolutionary trajectories. Prior research has proposed that the genetic architecture of proteins is very complex, with pervasive epistatic interactions that constrain evolution and make function difficult to predict from sequence. Most of this work has analyzed only the direct paths between two proteins of interest - excluding the vast majority of possible genotypes and evolutionary trajectories - and has considered only a single protein function, leaving unaddressed the genetic architecture of functional specificity and its impact on the evolution of new functions. Here, we develop a new method based on ordinal logistic regression to directly characterize the global genetic determinants of multiple protein functions from 20-state combinatorial deep mutational scanning (DMS) experiments. We use it to dissect the genetic architecture and evolution of a transcription factor's specificity for DNA, using data from a combinatorial DMS of an ancient steroid hormone receptor's capacity to activate transcription from two biologically relevant DNA elements. We show that the genetic architecture of DNA recognition consists of a dense set of main and pairwise effects that involve virtually every possible amino acid state in the protein-DNA interface, but higher-order epistasis plays only a tiny role. Pairwise interactions enlarge the set of functional sequences and are the primary determinants of specificity for different DNA elements. They also massively expand the number of opportunities for single-residue mutations to switch specificity from one DNA target to another. By bringing variants with different functions close together in sequence space, pairwise epistasis therefore facilitates rather than constrains the evolution of new functions.

An integrated technology for quantitative wide mutational scanning of human antibody Fab libraries

Antibodies are engineerable quantities in medicine. Learning antibody molecular recognition would enable the in silico design of high affinity binders against nearly any proteinaceous surface. Yet, publicly available experiment antibody sequence-binding datasets may not contain the mutagenic, antigenic, or antibody sequence diversity necessary for deep learning approaches to capture molecular recognition. In part, this is because limited experimental platforms exist for assessing quantitative and simultaneous sequence-function relationships for multiple antibodies. Here we present MAGMA-seq, an integrated technology that combines multiple antigens and multiple antibodies and determines quantitative biophysical parameters using deep sequencing. We demonstrate MAGMA-seq on two pooled libraries comprising mutants of nine different human antibodies spanning light chain gene usage, CDR H3 length, and antigenic targets. We demonstrate the comprehensive mapping of potential antibody development pathways, sequence-binding relationships for multiple antibodies simultaneously, and identification of paratope sequence determinants for binding recognition for broadly neutralizing antibodies (bnAbs). MAGMA-seq enables rapid and scalable antibody engineering of multiple lead candidates because it can measure binding for mutants of many given parental antibodies in a single experiment.

Genotype sampling for deep-learning assisted experimental mapping of a combinatorially complete fitness landscape

MOTIVATION

Experimental characterization of fitness landscapes, which map genotypes onto fitness, is important for both evolutionary biology and protein engineering. It faces a fundamental obstacle in the astronomical number of genotypes whose fitness needs to be measured for any one protein. Deep learning may help to predict the fitness of many genotypes from a smaller neural network training sample of genotypes with experimentally measured fitness. Here I use a recently published experimentally mapped fitness landscape of more than 260 000 protein genotypes to ask how such sampling is best performed.

RESULTS

I show that multilayer perceptrons, recurrent neural networks, convolutional networks, and transformers, can explain more than 90% of fitness variance in the data. In addition, 90% of this performance is reached with a training sample comprising merely ≈103 sequences. Generalization to unseen test data is best when training data is sampled randomly and uniformly, or sampled to minimize the number of synonymous sequences. In contrast, sampling to maximize sequence diversity or codon usage bias reduces performance substantially. These observations hold for more than one network architecture. Simple sampling strategies may perform best when training deep learning neural networks to map fitness landscapes from experimental data.

AVAILABILITY AND IMPLEMENTATION

The fitness landscape data analyzed here is publicly available as described previously (Papkou et al. 2023). All code used to analyze this landscape is publicly available at https://github.com/andreas-wagner-uzh/fitness_landscape_sampling.

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.

Rheostats, toggles, and neutrals, Oh my! A new framework for understanding how amino acid changes modulate protein function

Advances in personalized medicine and protein engineering require accurately predicting outcomes of amino acid substitutions. Many algorithms correctly predict that evolutionarily-conserved positions show "toggle" substitution phenotypes, which is defined when a few substitutions at that position retain function. In contrast, predictions often fail for substitutions at the less-studied "rheostat" positions, which are defined when different amino acid substitutions at a position sample at least half of the possible functional range. This review describes efforts to understand the impact and significance of rheostat positions: (1) They have been observed in globular soluble, integral membrane, and intrinsically disordered proteins; within single proteins, their prevalence can be up to 40%. (2) Substitutions at rheostat positions can have biological consequences and ∼10% of substitutions gain function. (3) Although both rheostat and "neutral" (defined when all substitutions exhibit wild-type function) positions are nonconserved, the two classes have different evolutionary signatures. (4) Some rheostat positions have pleiotropic effects on function, simultaneously modulating multiple parameters (e.g., altering both affinity and allosteric coupling). (5) In structural studies, substitutions at rheostat positions appear to cause only local perturbations; the overall conformations appear unchanged. (6) Measured functional changes show promising correlations with predicted changes in protein dynamics; the emergent properties of predicted, dynamically coupled amino acid networks might explain some of the complex functional outcomes observed when substituting rheostat positions. Overall, rheostat positions provide unique opportunities for using single substitutions to tune protein function. Future studies of these positions will yield important insights into the protein sequence/function relationship.

Protein design using structure-based residue preferences

Recent developments in protein design rely on large neural networks with up to 100s of millions of parameters, yet it is unclear which residue dependencies are critical for determining protein function. Here, we show that amino acid preferences at individual residues-without accounting for mutation interactions-explain much and sometimes virtually all of the combinatorial mutation effects across 8 datasets (R2 ~ 78-98%). Hence, few observations (~100 times the number of mutated residues) enable accurate prediction of held-out variant effects (Pearson r > 0.80). We hypothesized that the local structural contexts around a residue could be sufficient to predict mutation preferences, and develop an unsupervised approach termed CoVES (Combinatorial Variant Effects from Structure). Our results suggest that CoVES outperforms not just model-free methods but also similarly to complex models for creating functional and diverse protein variants. CoVES offers an effective alternative to complicated models for identifying functional protein mutations.

Identifying LasR Quorum Sensors with Improved Signal Specificity by Mapping the Sequence-Function Landscape

Programmable intercellular signaling using components of naturally occurring quorum sensing can allow for coordinated functions to be engineered in microbial consortia. LuxR-type transcriptional regulators are widely used for this purpose and are activated by homoserine lactone (HSL) signals. However, they often suffer from imperfect molecular discrimination of structurally similar HSLs, causing misregulation within engineered consortia containing multiple HSL signals. Here, we studied one such example, the regulator LasR from Pseudomonas aeruginosa. We elucidated its sequence-function relationship for ligand specificity using targeted protein engineering and multiplexed high-throughput biosensor screening. A pooled combinatorial saturation mutagenesis library (9,486 LasR DNA sequences) was created by mutating six residues in LasR's β5 sheet with single, double, or triple amino acid substitutions. Sort-seq assays were performed in parallel using cognate and noncognate HSLs to quantify each corresponding sensor's response to each HSL signal, which identified hundreds of highly specific variants. Sensor variants identified were individually assayed and exhibited up to 60.6-fold (p = 0.0013) improved relative activation by the cognate signal compared to the wildtype. Interestingly, we uncovered prevalent mutational epistasis and previously unidentified residues contributing to signal specificity. The resulting sensors with negligible signal crosstalk could be broadly applied to engineer bacteria consortia.

The simplicity of protein sequence-function relationships

How complicated is the genetic architecture of proteins - the set of causal effects by which sequence determines function? High-order epistatic interactions among residues are thought to be pervasive, making a protein's function difficult to predict or understand from its sequence. Most studies, however, used methods that overestimate epistasis, because they analyze genetic architecture relative to a designated reference sequence - causing measurement noise and small local idiosyncrasies to propagate into pervasive high-order interactions - or have not effectively accounted for global nonlinearity in the sequence-function relationship. Here we present a new reference-free method that jointly estimates global nonlinearity and specific epistatic interactions across a protein's entire genotype-phenotype map. This method yields a maximally efficient explanation of a protein's genetic architecture and is more robust than existing methods to measurement noise, partial sampling, and model misspecification. We reanalyze 20 combinatorial mutagenesis experiments from a diverse set of proteins and find that additive and pairwise effects, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of total variance in measured phenotypes (and >92% in every case). Only a tiny fraction of genotypes are strongly affected by third- or higher-order epistasis. Genetic architecture is also sparse: the number of terms required to explain the vast majority of variance is smaller than the number of genotypes by many orders of magnitude. The sequence-function relationship in most proteins is therefore far simpler than previously thought, opening the way for new and tractable approaches to characterize it.

Is Novelty Predictable?

Machine learning-based design has gained traction in the sciences, most notably in the design of small molecules, materials, and proteins, with societal applications ranging from drug development and plastic degradation to carbon sequestration. When designing objects to achieve novel property values with machine learning, one faces a fundamental challenge: how to push past the frontier of current knowledge, distilled from the training data into the model, in a manner that rationally controls the risk of failure. If one trusts learned models too much in extrapolation, one is likely to design rubbish. In contrast, if one does not extrapolate, one cannot find novelty. Herein, we ponder how one might strike a useful balance between these two extremes. We focus in particular on designing proteins with novel property values, although much of our discussion is relevant to machine learning-based design more broadly.

Protein sequence landscapes are not so simple: on reference-free versus reference-based inference

In a recent preprint, Park, Metzger, and Thornton reanalyze 20 empirical protein sequence-function landscapes using a "reference-free analysis" (RFA) method they recently developed. They argue that these empirical landscapes are simpler and less epistatic than earlier work suggested, and attribute the difference to limitations of the methods used in the original analyses of these landscapes, which they claim are more sensitive to measurement noise, missing data, and other artifacts. Here, we show that these claims are incorrect. Instead, we find that the RFA method introduced by Park et al. is exactly equivalent to the reference-based least-squares methods used in the original analysis of many of these empirical landscapes (and also equivalent to a Hadamard-based approach they implement). Because the reanalyzed and original landscapes are in fact identical, the different conclusions drawn by Park et al. instead reflect different interpretations of the parameters describing the inferred landscapes; we argue that these do not support the conclusion that epistasis plays only a small role in protein sequence-function landscapes.

Evolution shapes interaction patterns for epistasis and specific protein binding in a two-component signaling system

The elegant design of protein sequence/structure/function relationships arises from the interaction patterns between amino acid positions. A central question is how evolutionary forces shape the interaction patterns that encode long-range epistasis and binding specificity. Here, we combined family-wide evolutionary analysis of natural homologous sequences and structure-oriented evolution simulation for two-component signaling (TCS) system. The magnitude-frequency relationship of coupling conservation between positions manifests a power-law-like distribution and the positions with highly coupling conservation are sparse but distributed intensely on the binding surfaces and hydrophobic core. The structure-specific interaction pattern involves further optimization of local frustrations at or near the binding surface to adapt the binding partner. The construction of family-wide conserved interaction patterns and structure-specific ones demonstrates that binding specificity is modulated by both direct intermolecular interactions and long-range epistasis across the binding complex. Evolution sculpts the interaction patterns via sequence variations at both family-wide and structure-specific levels for TCS system.

Evolutionary paths that link orthogonal pairs of binding proteins

Some protein binding pairs exhibit extreme specificities that functionally insulate them from homologs. Such pairs evolve mostly by accumulating single-point mutations, and mutants are selected if their affinity exceeds the threshold required for function1-4. Thus, homologous and high-specificity binding pairs bring to light an evolutionary conundrum: how does a new specificity evolve while maintaining the required affinity in each intermediate5,6? Until now, a fully functional single-mutation path that connects two orthogonal pairs has only been described where the pairs were mutationally close thus enabling experimental enumeration of all intermediates2. We present an atomistic and graph-theoretical framework for discovering low molecular strain single-mutation paths that connect two extant pairs, enabling enumeration beyond experimental capability. We apply it to two orthogonal bacterial colicin endonuclease-immunity pairs separated by 17 interface mutations7. We were not able to find a strain-free and functional path in the sequence space defined by the two extant pairs. But including mutations that bridge amino acids that cannot be exchanged through single-nucleotide mutations led us to a strain-free 19-mutation trajectory that is completely viable in vivo. Our experiments show that the specificity switch is remarkably abrupt, resulting from only one radical mutation on each partner. Furthermore, each of the critical specificity-switch mutations increases fitness, demonstrating that functional divergence could be driven by positive Darwinian selection. These results reveal how even radical functional changes in an epistatic fitness landscape may evolve.

Sparsity of higher-order landscape interactions enables learning and prediction for microbiomes

Microbiome engineering offers the potential to leverage microbial communities to improve outcomes in human health, agriculture, and climate. To translate this potential into reality, it is crucial to reliably predict community composition and function. But a brute force approach to cataloging community function is hindered by the combinatorial explosion in the number of ways we can combine microbial species. An alternative is to parameterize microbial community outcomes using simplified, mechanistic models, and then extrapolate these models beyond where we have sampled. But these approaches remain data-hungry, as well as requiring an a priori specification of what kinds of mechanisms are included and which are omitted. Here, we resolve both issues by introducing a mechanism-agnostic approach to predicting microbial community compositions and functions using limited data. The critical step is the identification of a sparse representation of the community landscape. We then leverage this sparsity to predict community compositions and functions, drawing from techniques in compressive sensing. We validate this approach on in silico community data, generated from a theoretical model. By sampling just [Formula: see text]1% of all possible communities, we accurately predict community compositions out of sample. We then demonstrate the real-world application of our approach by applying it to four experimental datasets and showing that we can recover interpretable, accurate predictions on composition and community function from highly limited data.

A rugged yet easily navigable fitness landscape

Fitness landscape theory predicts that rugged landscapes with multiple peaks impair Darwinian evolution, but experimental evidence is limited. In this study, we used genome editing to map the fitness of >260,000 genotypes of the key metabolic enzyme dihydrofolate reductase in the presence of the antibiotic trimethoprim, which targets this enzyme. The resulting landscape is highly rugged and harbors 514 fitness peaks. However, its highest peaks are accessible to evolving populations via abundant fitness-increasing paths. Different peaks share large basins of attraction that render the outcome of adaptive evolution highly contingent on chance events. Our work shows that ruggedness need not be an obstacle to Darwinian evolution but can reduce its predictability. If true in general, the complexity of optimization problems on realistic landscapes may require reappraisal.

AlphaFold2 Can Predict Single-Mutation Effects

AlphaFold2 (AF) is a promising tool, but is it accurate enough to predict single mutation effects? Here, we report that the localized structural deformation between protein pairs differing by only 1-3 mutations-as measured by the effective strain-is correlated across 3901 experimental and AF-predicted structures. Furthermore, analysis of ∼11 000 proteins shows that the local structural change correlates with various phenotypic changes. These findings suggest that AF can predict the range and magnitude of single-mutation effects on average, and we propose a method to improve precision of AF predictions and to indicate when predictions are unreliable.

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.

MBE: model-based enrichment estimation and prediction for differential sequencing data

Characterizing differences in sequences between two conditions, such as with and without drug exposure, using high-throughput sequencing data is a prevalent problem involving quantifying changes in sequence abundances, and predicting such differences for unobserved sequences. A key shortcoming of current approaches is their extremely limited ability to share information across related but non-identical reads. Consequently, they cannot use sequencing data effectively, nor be directly applied in many settings of interest. We introduce model-based enrichment (MBE) to overcome this shortcoming. We evaluate MBE using both simulated and real data. Overall, MBE improves accuracy compared to current differential analysis methods.

Protein engineering via sequence-performance mapping

Discovery and evolution of new and improved proteins has empowered molecular therapeutics, diagnostics, and industrial biotechnology. Discovery and evolution both require efficient screens and effective libraries, although they differ in their challenges because of the absence or presence, respectively, of an initial protein variant with the desired function. A host of high-throughput technologies-experimental and computational-enable efficient screens to identify performant protein variants. In partnership, an informed search of sequence space is needed to overcome the immensity, sparsity, and complexity of the sequence-performance landscape. Early in the historical trajectory of protein engineering, these elements aligned with distinct approaches to identify the most performant sequence: selection from large, randomized combinatorial libraries versus rational computational design. Substantial advances have now emerged from the synergy of these perspectives. Rational design of combinatorial libraries aids the experimental search of sequence space, and high-throughput, high-integrity experimental data inform computational design. At the core of the collaborative interface, efficient protein characterization (rather than mere selection of optimal variants) maps sequence-performance landscapes. Such quantitative maps elucidate the complex relationships between protein sequence and performance-e.g., binding, catalytic efficiency, biological activity, and developability-thereby advancing fundamental protein science and facilitating protein discovery and evolution.

Transition paths in Potts-like energy landscapes: General properties and application to protein sequence models

We study transition paths in energy landscapes over multicategorical Potts configurations using the mean-field approach introduced by Mauri et al. [Phys. Rev. Lett. 130, 158402 (2023)0031-900710.1103/PhysRevLett.130.158402]. Paths interpolate between two fixed configurations or are anchored at one extremity only. We characterize the properties of "good" transition paths realizing a trade-off between exploring low-energy regions in the landscape and being not too long, such as their entropy or the probability of escape from a region of the landscape. We unveil the existence of a phase transition separating a regime in which paths are stretched in between their anchors from another regime where paths can explore the energy landscape more globally to minimize the energy. This phase transition is first illustrated and studied in detail on a mathematically tractable Hopfield-Potts toy model, then studied in energy landscapes inferred from protein sequence data.

Evolvability-enhancing mutations in the fitness landscapes of an RNA and a protein

Can evolvability-the ability to produce adaptive heritable variation-itself evolve through adaptive Darwinian evolution? If so, then Darwinian evolution may help create the conditions that enable Darwinian evolution. Here I propose a framework that is suitable to address this question with available experimental data on adaptive landscapes. I introduce the notion of an evolvability-enhancing mutation, which increases the likelihood that subsequent mutations in an evolving organism, protein, or RNA molecule are adaptive. I search for such mutations in the experimentally characterized and combinatorially complete fitness landscapes of a protein and an RNA molecule. I find that such evolvability-enhancing mutations indeed exist. They constitute a small fraction of all mutations, which shift the distribution of fitness effects of subsequent mutations towards less deleterious mutations, and increase the incidence of beneficial mutations. Evolving populations which experience such mutations can evolve significantly higher fitness. The study of evolvability-enhancing mutations opens many avenues of investigation into the evolution of evolvability.

Machine Learning for Protein Engineering

Directed evolution of proteins has been the most effective method for protein engineering. However, a new paradigm is emerging, fusing the library generation and screening approaches of traditional directed evolution with computation through the training of machine learning models on protein sequence fitness data. This chapter highlights successful applications of machine learning to protein engineering and directed evolution, organized by the improvements that have been made with respect to each step of the directed evolution cycle. Additionally, we provide an outlook for the future based on the current direction of the field, namely in the development of calibrated models and in incorporating other modalities, such as protein structure.

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.

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'.

Designed active-site library reveals thousands of functional GFP variants

Mutations in a protein active site can lead to dramatic and useful changes in protein activity. The active site, however, is sensitive to mutations due to a high density of molecular interactions, substantially reducing the likelihood of obtaining functional multipoint mutants. We introduce an atomistic and machine-learning-based approach, called high-throughput Functional Libraries (htFuncLib), that designs a sequence space in which mutations form low-energy combinations that mitigate the risk of incompatible interactions. We apply htFuncLib to the GFP chromophore-binding pocket, and, using fluorescence readout, recover >16,000 unique designs encoding as many as eight active-site mutations. Many designs exhibit substantial and useful diversity in functional thermostability (up to 96 °C), fluorescence lifetime, and quantum yield. By eliminating incompatible active-site mutations, htFuncLib generates a large diversity of functional sequences. We envision that htFuncLib will be used in one-shot optimization of activity in enzymes, binders, and other proteins.

Deep Mutational Scanning of an Oxygen-Independent Fluorescent Protein CreiLOV for Comprehensive Profiling of Mutational and Epistatic Effects

Oxygen-independent, flavin mononucleotide-based fluorescent proteins (FbFPs) are promising alternatives to green fluorescent protein in anaerobic contexts. Deep mutational scanning performs systematic profiling of protein sequence-function relationships but has not been applied to FbFPs. Focusing on CreiLOV from Chlamydomonas reinhardtii, we created and analyzed two comprehensive mutant collections: (1) single-residue, site-saturation mutagenesis libraries covering all 118 residues; and (2) a full combinatorial metagenesis library among 20 mutations at 15 residues, where mutation and residue selection was based on single-site mutagenesis results. Notably, the second type of library is indispensable to study higher-order epistasis but underrepresented in the literature. Using optimized FACS-seq assays, 2,185 (>92.5%) out of 2,360 possible single-site mutants and 165,428 (>89.7%) out of 184,320 possible combinatorial mutants were reliably assigned with fitness values. We constructed statistical and machine-learning models to analyze the CreiLOV data set, enabling accurate fitness prediction of higher-order mutants using lower-order mutagenesis data. In addition, we successfully isolated CreiLOV variants with improved fluorescence quantum yield and thermostability. This work provides new empirical data and design rules to engineer combinatorial protein variants.

Genotype-phenotype landscapes for immune-pathogen coevolution

Our immune systems constantly coevolve with the pathogens that challenge them, as pathogens adapt to evade our defense responses, with our immune repertoires shifting in turn. These coevolutionary dynamics take place across a vast and high-dimensional landscape of potential pathogen and immune receptor sequence variants. Mapping the relationship between these genotypes and the phenotypes that determine immune-pathogen interactions is crucial for understanding, predicting, and controlling disease. Here, we review recent developments applying high-throughput methods to create large libraries of immune receptor and pathogen protein sequence variants and measure relevant phenotypes. We describe several approaches that probe different regions of the high-dimensional sequence space and comment on how combinations of these methods may offer novel insight into immune-pathogen coevolution.

DeMAG predicts the effects of variants in clinically actionable genes by integrating structural and evolutionary epistatic features

Despite the increasing use of genomic sequencing in clinical practice, the interpretation of rare genetic variants remains challenging even in well-studied disease genes, resulting in many patients with Variants of Uncertain Significance (VUSs). Computational Variant Effect Predictors (VEPs) provide valuable evidence in variant assessment, but they are prone to misclassifying benign variants, contributing to false positives. Here, we develop Deciphering Mutations in Actionable Genes (DeMAG), a supervised classifier for missense variants trained using extensive diagnostic data available in 59 actionable disease genes (American College of Medical Genetics and Genomics Secondary Findings v2.0, ACMG SF v2.0). DeMAG improves performance over existing VEPs by reaching balanced specificity (82%) and sensitivity (94%) on clinical data, and includes a novel epistatic feature, the 'partners score', which leverages evolutionary and structural partnerships of residues. The 'partners score' provides a general framework for modeling epistatic interactions, integrating both clinical and functional information. We provide our tool and predictions for all missense variants in 316 clinically actionable disease genes (demag.org) to facilitate the interpretation of variants and improve clinical decision-making.

Synonymous and Nonsynonymous Substitutions in Dictyostelium discoideum Ammonium Transporter amtA Are Necessary for Functional Complementation in Saccharomyces cerevisiae

Ammonium transporters are present in all three domains of life. They have undergone extensive horizontal gene transfer (HGT), gene duplication, and functional diversification and therefore offer an excellent paradigm to study protein evolution. We attempted to complement a mep1Δmep2Δmep3Δ strain of Saccharomyces cerevisiae (triple-deletion strain), which otherwise cannot grow on ammonium as a sole nitrogen source at concentrations of <3 mM, with amtA of Dictyostelium discoideum, an orthologue of S. cerevisiae MEP2. We observed that amtA did not complement the triple-deletion strain of S. cerevisiae for growth on low-ammonium medium. We isolated two mutant derivatives of amtA (amtA M1 and amtA M2) from a PCR-generated mutant plasmid library that complemented the triple-deletion strain of S. cerevisiae. amtA M1 bears three nonsynonymous and two synonymous substitutions, which are necessary for its functionality. amtA M2 bears two nonsynonymous substitutions and one synonymous substitution, all of which are necessary for functionality. Interestingly, AmtA M1 transports ammonium but does not confer methylamine toxicity, while AmtA M2 transports ammonium and confers methylamine toxicity, demonstrating functional diversification. Preliminary biochemical analyses indicated that the mutants differ in their conformations as well as their mechanisms of ammonium transport. These intriguing results clearly point out that protein evolution cannot be fathomed by studying nonsynonymous and synonymous substitutions in isolation. The above-described observations have significant implications for various facets of biological processes and are discussed in detail. IMPORTANCE Functional diversification following gene duplication is one of the major driving forces of protein evolution. While the role of nonsynonymous substitutions in the functional diversification of proteins is well recognized, knowledge of the role of synonymous substitutions in protein evolution is in its infancy. Using functional complementation, we isolated two functional alleles of the D. discoideum ammonium transporter gene (amtA), which otherwise does not function in S. cerevisiae as an ammonium transporters. One of them is an ammonium transporter, while the other is an ammonium transporter that also confers methylammonium (ammonium analogue) toxicity, suggesting functional diversification. Surprisingly, both alleles require a combination of synonymous and nonsynonymous substitutions for their functionality. These results bring out a hitherto-unknown pathway of protein evolution and pave the way for not only understanding protein evolution but also interpreting single nucleotide polymorphisms (SNPs).

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.

Hierarchical sequence-affinity landscapes shape the evolution of breadth in an anti-influenza receptor binding site antibody

Broadly neutralizing antibodies (bnAbs) that neutralize diverse variants of a particular virus are of considerable therapeutic interest. Recent advances have enabled us to isolate and engineer these antibodies as therapeutics, but eliciting them through vaccination remains challenging, in part due to our limited understanding of how antibodies evolve breadth. Here, we analyze the landscape by which an anti-influenza receptor binding site (RBS) bnAb, CH65, evolved broad affinity to diverse H1 influenza strains. We do this by generating an antibody library of all possible evolutionary intermediates between the unmutated common ancestor (UCA) and the affinity-matured CH65 antibody and measure the affinity of each intermediate to three distinct H1 antigens. We find that affinity to each antigen requires a specific set of mutations - distributed across the variable light and heavy chains - that interact non-additively (i.e., epistatically). These sets of mutations form a hierarchical pattern across the antigens, with increasingly divergent antigens requiring additional epistatic mutations beyond those required to bind less divergent antigens. We investigate the underlying biochemical and structural basis for these hierarchical sets of epistatic mutations and find that epistasis between heavy chain mutations and a mutation in the light chain at the V_H-V_L interface is essential for binding a divergent H1. Collectively, this is the first work to comprehensively characterize epistasis between heavy and light chain mutations and shows that such interactions are both strong and widespread. Together with our previous study analyzing a different class of anti-influenza antibodies, our results implicate epistasis as a general feature of antibody sequence-affinity landscapes that can potentiate and constrain the evolution of breadth.

GCAT: A network model of mutational influences between amino acid positions in PSD95pdz3

Proteins exist for more than 3 billion years: proof of a sustainable design. They have mechanisms coping with internal perturbations (e.g., amino acid mutations), which tie genetic backgrounds to diseases or drug therapy failure. One difficulty to grasp these mechanisms is the asymmetry of amino acid mutational impact: a mutation at position i in the sequence, which impact a position j does not imply that the mutation at position j impacts the position i. Thus, to distinguish the influence of the mutation of i on j from the influence of the mutation of j on i, position mutational influences must be represented with directions. Using the X ray structure of the third PDZ domain of PDS-95 (Protein Data Bank 1BE9) and in silico mutations, we build a directed network called GCAT that models position mutational influences. In the GCAT, a position is a node with edges that leave the node (out-edges) for the influences of the mutation of the position on other positions and edges that enter the position (in-edges) for the influences of the mutation of other positions on the position. 1BE9 positions split into four influence categories called G, C, A and T going from positions influencing on average less other positions and influenced on average by less other positions (category C) to positions influencing on average more others positions and influenced on average by more other positions (category T). The four categories depict position neighborhoods in the protein structure with different tolerance to mutations.

Conformal prediction under feedback covariate shift for biomolecular design

Many applications of machine-learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, a data-driven approach for designing proteins is to train a regression model to predict the fitness of protein sequences and then use it to propose new sequences believed to exhibit greater fitness than observed in the training data. Since validating designed sequences in the wet laboratory is typically costly, it is important to quantify the uncertainty in the model's predictions. This is challenging because of a characteristic type of distribution shift between the training and test data that arises in the design setting-one in which the training and test data are statistically dependent, as the latter is chosen based on the former. Consequently, the model's error on the test data-that is, the designed sequences-has an unknown and possibly complex relationship with its error on the training data. We introduce a method to construct confidence sets for predictions in such settings, which account for the dependence between the training and test data. The confidence sets we construct have finite-sample guarantees that hold for any regression model, even when it is used to choose the test-time input distribution. As a motivating use case, we use real datasets to demonstrate how our method quantifies uncertainty for the predicted fitness of designed proteins and can therefore be used to select design algorithms that achieve acceptable tradeoffs between high predicted fitness and low predictive uncertainty.

Intragenic compensation through the lens of deep mutational scanning

A significant fraction of mutations in proteins are deleterious and result in adverse consequences for protein function, stability, or interaction with other molecules. Intragenic compensation is a specific case of positive epistasis when a neutral missense mutation cancels effect of a deleterious mutation in the same protein. Permissive compensatory mutations facilitate protein evolution, since without them all sequences would be extremely conserved. Understanding compensatory mechanisms is an important scientific challenge at the intersection of protein biophysics and evolution. In human genetics, intragenic compensatory interactions are important since they may result in variable penetrance of pathogenic mutations or fixation of pathogenic human alleles in orthologous proteins from related species. The latter phenomenon complicates computational and clinical inference of an allele's pathogenicity. Deep mutational scanning is a relatively new technique that enables experimental studies of functional effects of thousands of mutations in proteins. We review the important aspects of the field and discuss existing limitations of current datasets. We reviewed ten published DMS datasets with quantified functional effects of single and double mutations and described rates and patterns of intragenic compensation in eight of them.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12551-022-01005-w.

Higher-order epistasis and phenotypic prediction

One core goal of genetics is to systematically understand the mapping between the DNA sequence of an organism (genotype) and its measurable characteristics (phenotype). Understanding this mapping is often challenging because of interactions between mutations, where the result of combining several different mutations can be very different than the sum of their individual effects. Here we provide a statistical framework for modeling complex genetic interactions of this type. The key idea is to ask how fast the effects of mutations change when introducing the same mutation in increasingly distant genetic backgrounds. We then propose a model for phenotypic prediction that takes into account this tendency for the effects of mutations to be more similar in nearby genetic backgrounds.

Contemporary high-throughput mutagenesis experiments are providing an increasingly detailed view of the complex patterns of genetic interaction that occur between multiple mutations within a single protein or regulatory element. By simultaneously measuring the effects of thousands of combinations of mutations, these experiments have revealed that the genotype–phenotype relationship typically reflects not only genetic interactions between pairs of sites but also higher-order interactions among larger numbers of sites. However, modeling and understanding these higher-order interactions remains challenging. Here we present a method for reconstructing sequence-to-function mappings from partially observed data that can accommodate all orders of genetic interaction. The main idea is to make predictions for unobserved genotypes that match the type and extent of epistasis found in the observed data. This information on the type and extent of epistasis can be extracted by considering how phenotypic correlations change as a function of mutational distance, which is equivalent to estimating the fraction of phenotypic variance due to each order of genetic interaction (additive, pairwise, three-way, etc.). Using these estimated variance components, we then define an empirical Bayes prior that in expectation matches the observed pattern of epistasis and reconstruct the genotype–phenotype mapping by conducting Gaussian process regression under this prior. To demonstrate the power of this approach, we present an application to the antibody-binding domain GB1 and also provide a detailed exploration of a dataset consisting of high-throughput measurements for the splicing efficiency of human pre-mRNA 5′ splice sites, for which we also validate our model predictions via additional low-throughput experiments.

Experimental exploration of a ribozyme neutral network using evolutionary algorithm and deep learning

A neutral network connects all genotypes with equivalent phenotypes in a fitness landscape and plays an important role in the mutational robustness and evolvability of biomolecules. In contrast to earlier theoretical works, evidence of large neutral networks has been lacking in recent experimental studies of fitness landscapes. This suggests that evolution could be constrained globally. Here, we demonstrate that a deep learning-guided evolutionary algorithm can efficiently identify neutral genotypes within the sequence space of an RNA ligase ribozyme. Furthermore, we measure the activities of all 2¹⁶ variants connecting two active ribozymes that differ by 16 mutations and analyze mutational interactions (epistasis) up to the 16th order. We discover an extensive network of neutral paths linking the two genotypes and reveal that these paths might be predicted using only information from lower-order interactions. Our experimental evaluation of over 120,000 ribozyme sequences provides important empirical evidence that neutral networks can increase the accessibility and predictability of the fitness landscape.

Neutral networks, which are sets of genotypes connected via single mutations that share the same phenotype, are important for evolvability. Here, the authors provide experimental evidence of a neutral network in an RNA enzyme using a high-throughput assay and deep learning.

Evolutionary action of mutations reveals antimicrobial resistance genes in Escherichia coli

Since antibiotic development lags, we search for potential drug targets through directed evolution experiments. A challenge is that many resistance genes hide in a noisy mutational background as mutator clones emerge in the adaptive population. Here, to overcome this noise, we quantify the impact of mutations through evolutionary action (EA). After sequencing ciprofloxacin or colistin resistance strains grown under different mutational regimes, we find that an elevated sum of the evolutionary action of mutations in a gene identifies known resistance drivers. This EA integration approach also suggests new antibiotic resistance genes which are then shown to provide a fitness advantage in competition experiments. Moreover, EA integration analysis of clinical and environmental isolates of antibiotic resistant of E. coli identifies gene drivers of resistance where a standard approach fails. Together these results inform the genetic basis of de novo colistin resistance and support the robust discovery of phenotype-driving genes via the evolutionary action of genetic perturbations in fitness landscapes.

Co-evolution of interacting proteins through non-contacting and non-specific mutations

Proteins often accumulate neutral mutations that do not affect current functions but can profoundly influence future mutational possibilities and functions. Understanding such hidden potential has major implications for protein design and evolutionary forecasting but has been limited by a lack of systematic efforts to identify potentiating mutations. Here, through the comprehensive analysis of a bacterial toxin-antitoxin system, we identified all possible single substitutions in the toxin that enable it to tolerate otherwise interface-disrupting mutations in its antitoxin. Strikingly, the majority of enabling mutations in the toxin do not contact and promote tolerance non-specifically to many different antitoxin mutations, despite covariation in homologues occurring primarily between specific pairs of contacting residues across the interface. In addition, the enabling mutations we identified expand future mutational paths that both maintain old toxin-antitoxin interactions and form new ones. These non-specific mutations are missed by widely used covariation and machine learning methods. Identifying such enabling mutations will be critical for ensuring continued binding of therapeutically relevant proteins, such as antibodies, aimed at evolving targets.

Droplet-based screening of phosphate transfer catalysis reveals how epistasis shapes MAP kinase interactions with substrates

The combination of ultrahigh-throughput screening and sequencing informs on function and intragenic epistasis within combinatorial protein mutant libraries. Establishing a droplet-based, in vitro compartmentalised approach for robust expression and screening of protein kinase cascades (>10⁷ variants/day) allowed us to dissect the intrinsic molecular features of the MKK-ERK signalling pathway, without interference from endogenous cellular components. In a six-residue combinatorial library of the MKK1 docking domain, we identified 29,563 sequence permutations that allow MKK1 to efficiently phosphorylate and activate its downstream target kinase ERK2. A flexibly placed hydrophobic sequence motif emerges which is defined by higher order epistatic interactions between six residues, suggesting synergy that enables high connectivity in the sequence landscape. Through positive epistasis, MKK1 maintains function during mutagenesis, establishing the importance of co-dependent residues in mammalian protein kinase-substrate interactions, and creating a scenario for the evolution of diverse human signalling networks.

Here, the authors use a droplet-based screen for phosphate transfer catalysis, testing variants of the human protein kinase MKK1 for its ability to activate its downstream target ERK2. Data reveal a flexible motif in the MKK1 docking domain that promotes efficient activation of ERK2, and suggest epistasis between the residues within that sequence.

On the sparsity of fitness functions and implications for learning

The properties of proteins and other biological molecules are encoded in large part in the sequence of amino acids or nucleotides that defines them. Increasingly, researchers estimate functions that map sequences to a particular property using machine learning and related statistical approaches. However, an important question remains unanswered: How many experimental measurements are needed in order to accurately learn these “fitness” functions? We leverage perspectives from the fields of biophysics, evolutionary biology, and signal processing to develop a theoretical framework that enables us to make progress on answering this question. We demonstrate that this framework can be used to make useful calculations on real-world data and suggest how these calculations may be used to guide experiments.

Fitness functions map biological sequences to a scalar property of interest. Accurate estimation of these functions yields biological insight and sets the foundation for model-based sequence design. However, the fitness datasets available to learn these functions are typically small relative to the large combinatorial space of sequences; characterizing how much data are needed for accurate estimation remains an open problem. There is a growing body of evidence demonstrating that empirical fitness functions display substantial sparsity when represented in terms of epistatic interactions. Moreover, the theory of Compressed Sensing provides scaling laws for the number of samples required to exactly recover a sparse function. Motivated by these results, we develop a framework to study the sparsity of fitness functions sampled from a generalization of the NK model, a widely used random field model of fitness functions. In particular, we present results that allow us to test the effect of the Generalized NK (GNK) model’s interpretable parameters—sequence length, alphabet size, and assumed interactions between sequence positions—on the sparsity of fitness functions sampled from the model and, consequently, the number of measurements required to exactly recover these functions. We validate our framework by demonstrating that GNK models with parameters set according to structural considerations can be used to accurately approximate the number of samples required to recover two empirical protein fitness functions and an RNA fitness function. In addition, we show that these GNK models identify important higher-order epistatic interactions in the empirical fitness functions using only structural information.