Pairwise and higher-order genetic interactions during the evolution of a tRNA

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%.

Sampling Strategies for Experimentally Mapping Molecular Fitness Landscapes Using High-Throughput Methods

Empirical studies of genotype-phenotype-fitness maps of proteins are fundamental to understanding the evolutionary process, in elucidating the space of possible genotypes accessible through mutations in a landscape of phenotypes and fitness effects. Yet, comprehensively mapping molecular fitness landscapes remains challenging since all possible combinations of amino acid substitutions for even a few protein sites are encoded by an enormous genotype space. High-throughput mapping of genotype space can be achieved using large-scale screening experiments known as multiplexed assays of variant effect (MAVEs). However, to accommodate such multi-mutational studies, the size of MAVEs has grown to the point where a priori determination of sampling requirements is needed. To address this problem, we propose calculations and simulation methods to approximate minimum sampling requirements for multi-mutational MAVEs, which we combine with a new library construction protocol to experimentally validate our approximation approaches. Analysis of our simulated data reveals how sampling trajectories differ between simulations of nucleotide versus amino acid variants and among mutagenesis schemes. For this, we show quantitatively that marginal gains in sampling efficiency demand increasingly greater sampling effort when sampling for nucleotide sequences over their encoded amino acid equivalents. We present a new library construction protocol that efficiently maximizes sequence variation, and demonstrate using ultradeep sequencing that the library encodes virtually all possible combinations of mutations within the experimental design. Insights learned from our analyses together with the methodological advances reported herein are immediately applicable toward pooled experimental screens of arbitrary design, enabling further assay upscaling and expanded testing of genotype space.

The Emergence of Non-Linear Evolutionary Trade-offs and the Maintenance of Genetic Polymorphisms

Evolutionary models of quantitative traits often assume trade-offs between beneficial and detrimental traits, requiring modelers to specify a function linking costs to benefits. The choice of trade-off function is often consequential; functions that assume diminishing returns (accelerating costs) typically lead to single equilibrium genotypes, while decelerating costs often lead to evolutionary branching. Despite their importance, we still lack a strong theoretical foundation to base the choice of trade-off function. To address this gap, we explore how trade-off functions can emerge from the genetic architecture of a quantitative trait. We developed a multi-locus model of disease resistance, assuming each locus had random antagonistic pleiotropic effects on resistance and fecundity. We used this model to generate genotype landscapes and explored how additive versus epistatic genetic architectures influenced the shape of the trade-off function. Regardless of epistasis, our model consistently led to accelerating costs. We then used our genotype landscapes to build an evolutionary model of disease resistance. Unlike other models with accelerating costs, our approach often led to genetic polymorphisms at equilibrium. Our results suggest that accelerating costs are a strong null model for evolutionary trade-offs and that the eco-evolutionary conditions required for polymorphism may be more nuanced than previously believed.

Engineered CRISPR-Cas12a for higher-order combinatorial chromatin perturbations

Multiplexed genetic perturbations are critical for testing functional interactions among coding or non-coding genetic elements. Compared to double-stranded DNA cutting, repressive chromatin formation using CRISPR interference (CRISPRi) avoids genotoxicity and is more effective for perturbing non-coding regulatory elements in pooled assays. However, current CRISPRi pooled screening approaches are limited to targeting one to three genomic sites per cell. We engineer an Acidaminococcus Cas12a (AsCas12a) variant, multiplexed transcriptional interference AsCas12a (multiAsCas12a), that incorporates R1226A, a mutation that stabilizes the ribonucleoprotein-DNA complex via DNA nicking. The multiAsCas12a-KRAB fusion improves CRISPRi activity over DNase-dead AsCas12a-KRAB fusions, often rescuing the activities of lentivirally delivered CRISPR RNAs (crRNA) that are inactive when used with the latter. multiAsCas12a-KRAB supports CRISPRi using 6-plex crRNA arrays in high-throughput pooled screens. Using multiAsCas12a-KRAB, we discover enhancer elements and dissect the combinatorial function of cis-regulatory elements in human cells. These results instantiate a group testing framework for efficiently surveying numerous combinations of chromatin perturbations for biological discovery and engineering.

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.

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.

Higher-order combinatorial chromatin perturbations by engineered CRISPR-Cas12a for functional genomics

Multiplexed genetic perturbations are critical for testing functional interactions among coding or non-coding genetic elements. Compared to double-stranded DNA cutting, repressive chromatin formation using CRISPR interference (CRISPRi) avoids genotoxicity and is more effective for perturbing non-coding regulatory elements in pooled assays. However, current CRISPRi pooled screening approaches are limited to targeting 1-3 genomic sites per cell. To develop a tool for higher-order ( > 3) combinatorial targeting of genomic sites with CRISPRi in functional genomics screens, we engineered an Acidaminococcus Cas12a variant -- referred to as mul tiplexed transcriptional interference AsCas12a (multiAsCas12a). multiAsCas12a incorporates a key mutation, R1226A, motivated by the hypothesis of nicking-induced stabilization of the ribonucleoprotein:DNA complex for improving CRISPRi activity. multiAsCas12a significantly outperforms prior state-of-the-art Cas12a variants in combinatorial CRISPRi targeting using high-order multiplexed arrays of lentivirally transduced CRISPR RNAs (crRNA), including in high-throughput pooled screens using 6-plex crRNA array libraries. Using multiAsCas12a CRISPRi, we discover new enhancer elements and dissect the combinatorial function of cis-regulatory elements. These results instantiate a group testing framework for efficiently surveying potentially numerous combinations of chromatin perturbations for biological discovery and engineering.

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.

ACIDES: on-line monitoring of forward genetic screens for protein engineering

Forward genetic screens of mutated variants are a versatile strategy for protein engineering and investigation, which has been successfully applied to various studies like directed evolution (DE) and deep mutational scanning (DMS). While next-generation sequencing can track millions of variants during the screening rounds, the vast and noisy nature of the sequencing data impedes the estimation of the performance of individual variants. Here, we propose ACIDES that combines statistical inference and in-silico simulations to improve performance estimation in the library selection process by attributing accurate statistical scores to individual variants. We tested ACIDES first on a random-peptide-insertion experiment and then on multiple public datasets from DE and DMS studies. ACIDES allows experimentalists to reliably estimate variant performance on the fly and can aid protein engineering and research pipelines in a range of applications, including gene therapy.

Pervasive epistasis exposes intramolecular networks in adaptive enzyme evolution

Enzyme evolution is characterized by constant alterations of the intramolecular residue networks supporting their functions. The rewiring of these network interactions can give rise to epistasis. As mutations accumulate, the epistasis observed across diverse genotypes may appear idiosyncratic, that is, exhibit unique effects in different genetic backgrounds. Here, we unveil a quantitative picture of the prevalence and patterns of epistasis in enzyme evolution by analyzing 41 fitness landscapes generated from seven enzymes. We show that >94% of all mutational and epistatic effects appear highly idiosyncratic, which greatly distorted the functional prediction of the evolved enzymes. By examining seemingly idiosyncratic changes in epistasis along adaptive trajectories, we expose several instances of higher-order, intramolecular rewiring. Using complementary structural data, we outline putative molecular mechanisms explaining higher-order epistasis along two enzyme trajectories. Our work emphasizes the prevalence of epistasis and provides an approach to exploring this phenomenon through a molecular lens.

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.

Learning protein fitness landscapes with deep mutational scanning data from multiple sources

One of the key points of machine learning-assisted directed evolution (MLDE) is the accurate learning of the fitness landscape, a conceptual mapping from sequence variants to the desired function. Here, we describe a multi-protein training scheme that leverages the existing deep mutational scanning data from diverse proteins to aid in understanding the fitness landscape of a new protein. Proof-of-concept trials are designed to validate this training scheme in three aspects: random and positional extrapolation for single-variant effects, zero-shot fitness predictions for new proteins, and extrapolation for higher-order variant effects from single-variant effects. Moreover, our study identified previously overlooked strong baselines, and their unexpectedly good performance brings our attention to the pitfalls of MLDE. Overall, these results may improve our understanding of the association between different protein fitness profiles and shed light on developing better machine learning-assisted approaches to the directed evolution of proteins. A record of this paper's transparent peer review process is included in the supplemental information.

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.

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.

Deep mutational scanning: A versatile tool in systematically mapping genotypes to phenotypes

Unveiling how genetic variations lead to phenotypic variations is one of the key questions in evolutionary biology, genetics, and biomedical research. Deep mutational scanning (DMS) technology has allowed the mapping of tens of thousands of genetic variations to phenotypic variations efficiently and economically. Since its first systematic introduction about a decade ago, we have witnessed the use of deep mutational scanning in many research areas leading to scientific breakthroughs. Also, the methods in each step of deep mutational scanning have become much more versatile thanks to the oligo-synthesizing technology, high-throughput phenotyping methods and deep sequencing technology. However, each specific possible step of deep mutational scanning has its pros and cons, and some limitations still await further technological development. Here, we discuss recent scientific accomplishments achieved through the deep mutational scanning and describe widely used methods in each step of deep mutational scanning. We also compare these different methods and analyze their advantages and disadvantages, providing insight into how to design a deep mutational scanning study that best suits the aims of the readers' projects.

High-throughput approaches to functional characterization of genetic variation in yeast

Expansion of sequencing efforts to include thousands of genomes is providing a fundamental resource for determining the genetic diversity that exists in a population. Now, high-throughput approaches are necessary to begin to understand the role these genotypic changes play in affecting phenotypic variation. Saccharomyces cerevisiae maintains its position as an excellent model system to determine the function of unknown variants with its exceptional genetic diversity, phenotypic diversity, and reliable genetic manipulation tools. Here, we review strategies and techniques developed in yeast that scale classic approaches of assessing variant function. These approaches improve our ability to better map quantitative trait loci at a higher resolution, even for rare variants, and are already providing greater insight into the role that different types of mutations play in phenotypic variation and evolution not just in yeast but across taxa.

The structure of genotype-phenotype maps makes fitness landscapes navigable

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution.

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.

Understanding and evolving prions by yeast multiplexed assays

Yeast genetics made it possible to derive the first fundamental insights into prion composition, conformation, and propagation. Fast-forward 30 years and the same model organism is now proving an extremely powerful tool to comprehensively explore the impact of mutations in prion sequences on their function, toxicity, and physical properties. Here, we provide an overview of novel multiplexed strategies where deep mutagenesis is combined to a range of tailored selection assays in yeast, which are particularly amenable for investigating prions and prion-like sequences. By mimicking evolution in a flask, these multiplexed approaches are revealing mechanistic insights on the consequences of prion self-assembly, while also reporting on the structure prion sequences adopt in vivo.

Idiosyncratic epistasis leads to global fitness-correlated trends

Epistasis can markedly affect evolutionary trajectories. In recent decades, protein-level fitness landscapes have revealed extensive idiosyncratic epistasis among specific mutations. By contrast, other work has found ubiquitous and apparently nonspecific patterns of global diminishing-returns and increasing-costs epistasis among mutations across the genome. Here, we used a hierarchical CRISPR gene drive system to construct all combinations of 10 missense mutations from across the genome in budding yeast and measured their fitness in six environments. We show that the resulting fitness landscapes exhibit global fitness-correlated trends but that these trends emerge from specific idiosyncratic interactions. We thus provide experimental validation of recent theoretical work arguing that fitness-correlated trends can emerge as the generic consequence of idiosyncratic epistasis.

Higher order genetic interactions switch cancer genes from two-hit to one-hit drivers

The classic two-hit model posits that both alleles of a tumor suppressor gene (TSG) must be inactivated to cause cancer. In contrast, for some oncogenes and haploinsufficient TSGs, a single genetic alteration can suffice to increase tumor fitness. Here, by quantifying the interactions between mutations and copy number alterations (CNAs) across 10,000 tumors, we show that many cancer genes actually switch between acting as one-hit or two-hit drivers. Third order genetic interactions identify the causes of some of these switches in dominance and dosage sensitivity as mutations in other genes in the same biological pathway. The correct genetic model for a gene thus depends on the other mutations in a genome, with a second hit in the same gene or an alteration in a different gene in the same pathway sometimes representing alternative evolutionary paths to cancer.

Decoding 'Unnecessary Complexity': A Law of Complexity and a Concept of Hidden Variation Behind "Missing Heritability" in Precision Medicine

The high hopes for the Human Genome Project and personalized medicine were not met because the relationship between genotypes and phenotypes turned out to be more complex than expected. In a previous study we laid the foundation of a theory of complexity and showed that because of the blind nature of evolution, and molecular and historical contingency, cells have accumulated unnecessary complexity, complexity beyond what is necessary and sufficient to describe an organism. Here we provide empirical evidence and show that unnecessary complexity has become integrated into the genome in the form of redundancy and is relevant to molecular evolution of phenotypic complexity. Unnecessary complexity creates uncertainty between molecular and phenotypic complexity, such that phenotypic complexity (CP) is higher than molecular complexity (CM), which is higher than DNA complexity (CD). The qualitative inequality in complexity is based on the following hierarchy: CP > CM > CD. This law-like relationship holds true for all complex traits, including complex diseases. We present a hypothesis of two types of variation, namely open and closed (hidden) systems, show that hidden variation provides a hitherto undiscovered "third source" of phenotypic variation, beside genotype and environment, and argue that "missing heritability" for some complex diseases is likely to be a case of "diluted heritability". There is a need for radically new ways of thinking about the principles of genotype-phenotype relationship. Understanding how cells use hidden, pathway variation to respond to stress can shed light on why two individuals who share the same risk factors may not develop the same disease, or how cancer cells escape death.

Unbiased inference of the fitness landscape ruggedness from imprecise fitness estimates

Fitness landscapes map genotypes to their corresponding fitness under given environments and allow explaining and predicting evolutionary trajectories. Of particular interest is the landscape ruggedness or the unevenness of the landscape, because it impacts many aspects of evolution such as the likelihood that a population is trapped in a local fitness peak. Although the ruggedness has been inferred from a number of empirically mapped fitness landscapes, it is unclear to what extent this inference is affected by fitness estimation error, which is inevitable in the experimental determination of fitness landscapes. Here, we address this question by simulating fitness landscapes under various theoretical models, with or without fitness estimation error. We find that all eight examined measures of landscape ruggedness are overestimated due to imprecise fitness quantification, but different measures are affected to different degrees. We devise a method to use replicate fitness measures to correct this bias and show that our method performs well under realistic conditions. We conclude that previously reported fitness landscape ruggedness is likely upward biased owing to the negligence of fitness estimation error and advise that future fitness landscape mapping should include at least three biological replicates to permit an unbiased inference of the ruggedness.

Pairwise interactions in gene expression determine a hierarchical transcriptional profile in the human brain

The orchestrated expression of thousands of genes gives rise to the complexity of the human brain. However, the structures governing these myriad gene-gene interactions remain unclear. By analyzing transcription data from more than 2000 sites in six human brains, we found that pairwise interactions between genes, without considering any higher-order interactions, are sufficient to predict the transcriptional pattern of the genome for individual brain regions and the transcriptional profile of the entire brain consisting of more than 200 areas. These findings suggest a quadratic complexity of transcriptional patterns in the human brain, which is much simpler than expected. In addition, using a pairwise interaction model, we revealed that the strength of gene-gene interactions in the human brain gives rise to the nearly maximal number of transcriptional clusters, which may account for the functional and structural richness of the brain.

A two-step PCR assembly for construction of gene variants across large mutational distances

Construction of empirical fitness landscapes has transformed our understanding of genotype–phenotype relationships across genes. However, most empirical fitness landscapes have been constrained to the local genotype neighbourhood of a gene primarily due to our limited ability to systematically construct genotypes that differ by a large number of mutations. Although a few methods have been proposed in the literature, these techniques are complex owing to several steps of construction or contain a large number of amplification cycles that increase chances of non-specific mutations. A few other described methods require amplification of the whole vector, thereby increasing the chances of vector backbone mutations that can have unintended consequences for study of fitness landscapes. Thus, this has substantially constrained us from traversing large mutational distances in the genotype network, thereby limiting our understanding of the interactions between multiple mutations and the role these interactions play in evolution of novel phenotypes. In the current work, we present a simple but powerful approach that allows us to systematically and accurately construct gene variants at large mutational distances. Our approach relies on building-up small fragments containing targeted mutations in the first step followed by assembly of these fragments into the complete gene fragment by polymerase chain reaction (PCR). We demonstrate the utility of our approach by constructing variants that differ by up to 11 mutations in a model gene. Our work thus provides an accurate method for construction of multi-mutant variants of genes and therefore will transform the studies of empirical fitness landscapes by enabling exploration of genotypes that are far away from a starting genotype.

Disentangling the Contribution of Each Descriptive Characteristic of Every Single Mutation to Its Functional Effects

Mutational effects predictions continue to improve in accuracy as advanced artificial intelligence (AI) algorithms are trained on exhaustive experimental data. The next natural questions to ask are if it is possible to gain insights into which attribute of the mutation contributes how much to the mutational effects and if one can develop universal rules for mapping the descriptors to mutational effects. In this work, we mainly address the former aspect using a framework of interpretable AI. Relations between the physicochemical descriptors and their contributions to the mutational effects are extracted by analyzing the data on 29,832 variants from eight systematic deep mutational scan studies. An opposite trend in the dependence of fitness and solubility on the distance of the amino acid from the catalytic sites could be extracted and quantified. The dependence of the mutational effect contributions on the position-specific scoring matrix (PSSM) score for the amino acid after mutation or the BLOSUM score of the substitution showed universal trends. Our attempts in the present work to explain the quantitative differences in the dependence on conservation and SASA across proteins were not successful. The work nevertheless brings transparency into the predictions and development of rules, and will hopefully lead to empirically uncovering the universalities among these rules.

The genotype-phenotype landscape of an allosteric protein

Allostery is a fundamental biophysical mechanism that underlies cellular sensing, signaling, and metabolism. Yet a quantitative understanding of allosteric genotype-phenotype relationships remains elusive. Here, we report the large-scale measurement of the genotype-phenotype landscape for an allosteric protein: the lac repressor from Escherichia coli, LacI. Using a method that combines long-read and short-read DNA sequencing, we quantitatively measure the dose-response curves for nearly 105 variants of the LacI genetic sensor. The resulting data provide a quantitative map of the effect of amino acid substitutions on LacI allostery and reveal systematic sequence-structure-function relationships. We find that in many cases, allosteric phenotypes can be quantitatively predicted with additive or neural-network models, but unpredictable changes also occur. For example, we were surprised to discover a new band-stop phenotype that challenges conventional models of allostery and that emerges from combinations of nearly silent amino acid substitutions.

Fitness landscape of a dynamic RNA structure

RNA structures are dynamic. As a consequence, mutational effects can be hard to rationalize with reference to a single static native structure. We reasoned that deep mutational scanning experiments, which couple molecular function to fitness, should capture mutational effects across multiple conformational states simultaneously. Here, we provide a proof-of-principle that this is indeed the case, using the self-splicing group I intron from Tetrahymena thermophila as a model system. We comprehensively mutagenized two 4-bp segments of the intron. These segments first come together to form the P1 extension (P1ex) helix at the 5' splice site. Following cleavage at the 5' splice site, the two halves of the helix dissociate to allow formation of an alternative helix (P10) at the 3' splice site. Using an in vivo reporter system that couples splicing activity to fitness in E. coli, we demonstrate that fitness is driven jointly by constraints on P1ex and P10 formation. We further show that patterns of epistasis can be used to infer the presence of intramolecular pleiotropy. Using a machine learning approach that allows quantification of mutational effects in a genotype-specific manner, we demonstrate that the fitness landscape can be deconvoluted to implicate P1ex or P10 as the effective genetic background in which molecular fitness is compromised or enhanced. Our results highlight deep mutational scanning as a tool to study alternative conformational states, with the capacity to provide critical insights into the structure, evolution and evolvability of RNAs as dynamic ensembles. Our findings also suggest that, in the future, deep mutational scanning approaches might help reverse-engineer multiple alternative or successive conformations from a single fitness landscape.

Multiple mutations within individual oncogenes

Recent studies of the cancer genome have identified numerous patients harboring multiple mutations (MM) within individual oncogenes. These MM (de novo MM) in cis synergistically activate the mutated oncogene and promote tumorigenesis, indicating a positive epistatic interaction between mutations. The relatively frequent de novo MM suggest that intramolecular positive epistasis is widespread in oncogenes. Studies also suggest that negative and higher-order epistasis affects de novo MM. Comparison of de novo MM and MM associated with drug-resistant secondary mutations (secondary MM) revealed several similarities with respect to allelic configuration, mutational selection and functionality of individual mutations. Conversely, they have several differences, most notably the difference in drug sensitivities. Secondary MM usually confer resistance to molecularly targeted therapies, whereas several de novo MM are associated with increased sensitivity, implying that both can be useful as therapeutic biomarkers. Unlike secondary MM in which specific secondary resistant mutations are selected, minor (infrequent) functionally weak mutations are convergently selected in de novo MM, which may provide an explanation as to why such mutations accumulate in cancer. The third type of MM is MM from different subclones. This type of MM is associated with parallel evolution, which may contribute to relapse and treatment failure. Collectively, MM within individual oncogenes are diverse, but all types of MM are associated with cancer evolution and therapeutic response. Further evaluation of oncogenic MM is warranted to gain a deeper understanding of cancer genetics and evolution.

Leveraging phenotypic variability to identify genetic interactions in human phenotypes

Although thousands of loci have been associated with human phenotypes, the role of gene-environment (GxE) interactions in determining individual risk of human diseases remains unclear. This is partly because of the severe erosion of statistical power resulting from the massive number of statistical tests required to detect such interactions. Here, we focus on improving the power of GxE tests by developing a statistical framework for assessing quantitative trait loci (QTLs) associated with the trait means and/or trait variances. When applying this framework to body mass index (BMI), we find that GxE discovery and replication rates are significantly higher when prioritizing genetic variants associated with the variance of the phenotype (vQTLs) compared to when assessing all genetic variants. Moreover, we find that vQTLs are enriched for associations with other non-BMI phenotypes having strong environmental influences, such as diabetes or ulcerative colitis. We show that GxE effects first identified in quantitative traits such as BMI can be used for GxE discovery in disease phenotypes such as diabetes. A clear conclusion is that strong GxE interactions mediate the genetic contribution to body weight and diabetes risk.

The complex role of genetic background in shaping the effects of spontaneous and induced mutations

Spontaneous and induced mutations frequently show different phenotypic effects across genetically distinct individuals. It is generally appreciated that these background effects mainly result from genetic interactions between the mutations and segregating loci. However, the architectures and molecular bases of these genetic interactions are not well understood. Recent work in a number of model organisms has tried to advance knowledge of background effects both by using large‐scale screens to find mutations that exhibit this phenomenon and by identifying the specific loci that are involved. Here, we review this body of research, emphasizing in particular the insights it provides into both the prevalence of background effects across different mutations and the mechanisms that cause these background effects.

A large fraction of mutations show different effects in distinct individuals.

These background effects are mainly caused by epistasis with segregating loci.

Mapping studies show a diversity of genetic architectures can be involved.

Genetically complex changes in gene expression are often, but not always, causative.

Idiosyncratic epistasis creates universals in mutational effects and evolutionary trajectories

Patterns of epistasis and shapes of fitness landscapes are of wide interest because of their bearings on a number of evolutionary theories. The common phenomena of slowing fitness increases during adaptations and diminishing returns from beneficial mutations are believed to reflect a concave fitness landscape and a preponderance of negative epistasis. Paradoxically, fitness decreases tend to decelerate and harm from deleterious mutations shrinks during the accumulation of random mutations-patterns thought to indicate a convex fitness landscape and a predominance of positive epistasis. Current theories cannot resolve this apparent contradiction. Here, we show that the phenotypic effect of a mutation varies substantially depending on the specific genetic background and that this idiosyncrasy in epistasis creates all of the above trends without requiring a biased distribution of epistasis. The idiosyncratic epistasis theory explains the universalities in mutational effects and evolutionary trajectories as emerging from randomness due to biological complexity.

Inferring a complete genotype-phenotype map from a small number of measured phenotypes

Understanding evolution requires detailed knowledge of genotype-phenotype maps; however, it can be a herculean task to measure every phenotype in a combinatorial map. We have developed a computational strategy to predict the missing phenotypes from an incomplete, combinatorial genotype-phenotype map. As a test case, we used an incomplete genotype-phenotype dataset previously generated for the malaria parasite’s ‘chloroquine resistance transporter’ (PfCRT). Wild-type PfCRT (PfCRT^3D7) lacks significant chloroquine (CQ) transport activity, but the introduction of the eight mutations present in the ‘Dd2’ isoform of PfCRT (PfCRT^Dd2) enables the protein to transport CQ away from its site of antimalarial action. This gain of a transport function imparts CQ resistance to the parasite. A combinatorial map between PfCRT^3D7 and PfCRT^Dd2 consists of 256 genotypes, of which only 52 have had their CQ transport activities measured through expression in the Xenopus laevis oocyte. We trained a statistical model with these 52 measurements to infer the CQ transport activity for the remaining 204 combinatorial genotypes between PfCRT^3D7 and PfCRT^Dd2. Our best-performing model incorporated a binary classifier, a nonlinear scale, and additive effects for each mutation. The addition of specific pairwise- and high-order-epistatic coefficients decreased the predictive power of the model. We evaluated our predictions by experimentally measuring the CQ transport activities of 24 additional PfCRT genotypes. The R² value between our predicted and newly-measured phenotypes was 0.90. We then used the model to probe the accessibility of evolutionary trajectories through the map. Approximately 1% of the possible trajectories between PfCRT^3D7 and PfCRT^Dd2 are accessible; however, none of the trajectories entailed eight successive increases in CQ transport activity. These results demonstrate that phenotypes can be inferred with known uncertainty from a partial genotype-phenotype dataset. We also validated our approach against a collection of previously published genotype-phenotype maps. The model therefore appears general and should be applicable to a large number of genotype-phenotype maps.

Biological macromolecules are built from chains of building blocks. The function of a macromolecule depends on the specific chemical properties of the building blocks that make it up. Macromolecules evolve through mutations that swap one building block for another. Understanding how biomolecules work and evolve therefore requires knowledge of the effects of mutations. The effects of mutations can be measured experimentally; however, because there are a vast number of possible combinations of mutations, it is often difficult to make enough measurements to understand biomolecular function and evolution. In this paper, we describe a simple method to predict the effects of mutations on biomolecules from a small number of measurements. This method works by appropriately averaging the effects of mutations seen in different contexts. We test the method by predicting the effects of mutations on a PfCRT—a macromolecule from the malarial parasite that confers drug resistance. We find that our method is fast and effective. Using a small number of measurements, we were able to gain insight into the evolutionary steps by which this macromolecule conferred drug resistance. To make this method accessible to other researchers, we have released it as an open-source software package: https://gpseer.readthedocs.io.

DiMSum: an error model and pipeline for analyzing deep mutational scanning data and diagnosing common experimental pathologies

Deep mutational scanning (DMS) enables multiplexed measurement of the effects of thousands of variants of proteins, RNAs, and regulatory elements. Here, we present a customizable pipeline, DiMSum, that represents an end-to-end solution for obtaining variant fitness and error estimates from raw sequencing data. A key innovation of DiMSum is the use of an interpretable error model that captures the main sources of variability arising in DMS workflows, outperforming previous methods. DiMSum is available as an R/Bioconda package and provides summary reports to help researchers diagnose common DMS pathologies and take remedial steps in their analyses.

Genotype networks of 80 quantitative Arabidopsis thaliana phenotypes reveal phenotypic evolvability despite pervasive epistasis

We study the genotype-phenotype maps of 80 quantitative phenotypes in the model plant Arabidopsis thaliana, by representing the genotypes affecting each phenotype as a genotype network. In such a network, each vertex or node corresponds to an individual's genotype at all those genomic loci that affect a given phenotype. Two vertices are connected by an edge if the associated genotypes differ in exactly one nucleotide. The 80 genotype networks we analyze are based on data from genome-wide association studies of 199 A. thaliana accessions. They form connected graphs whose topography differs substantially among phenotypes. We focus our analysis on the incidence of epistasis (non-additive interactions among mutations) because a high incidence of epistasis can reduce the accessibility of evolutionary paths towards high or low phenotypic values. We find epistatic interactions in 67 phenotypes, and in 51 phenotypes every pairwise mutant interaction is epistatic. Moreover, we find phenotype-specific differences in the fraction of accessible mutational paths to maximum phenotypic values. However, even though epistasis affects the accessibility of maximum phenotypic values, the relationships between genotypic and phenotypic change of our analyzed phenotypes are sufficiently smooth that some evolutionary paths remain accessible for most phenotypes, even where epistasis is pervasive. The genotype network representation we use can complement existing approaches to understand the genetic architecture of polygenic traits in many different organisms.

Allostery and Epistasis: Emergent Properties of Anisotropic Networks

Understanding the underlying mechanisms behind protein allostery and non-additivity of substitution outcomes (i.e., epistasis) is critical when attempting to predict the functional impact of mutations, particularly at non-conserved sites. In an effort to model these two biological properties, we extend the framework of our metric to calculate dynamic coupling between residues, the Dynamic Coupling Index (DCI) to two new metrics: (i) EpiScore, which quantifies the difference between the residue fluctuation response of a functional site when two other positions are perturbed with random Brownian kicks simultaneously versus individually to capture the degree of cooperativity of these two other positions in modulating the dynamics of the functional site and (ii) DCI_asym, which measures the degree of asymmetry between the residue fluctuation response of two sites when one or the other is perturbed with a random force. Applied to four independent systems, we successfully show that EpiScore and DCI_asym can capture important biophysical properties in dual mutant substitution outcomes. We propose that allosteric regulation and the mechanisms underlying non-additive amino acid substitution outcomes (i.e., epistasis) can be understood as emergent properties of an anisotropic network of interactions where the inclusion of the full network of interactions is critical for accurate modeling. Consequently, mutations which drive towards a new function may require a fine balance between functional site asymmetry and strength of dynamic coupling with the functional sites. These two tools will provide mechanistic insight into both understanding and predicting the outcome of dual mutations.

Predictable properties of fitness landscapes induced by adaptational tradeoffs

Fitness effects of mutations depend on environmental parameters. For example, mutations that increase fitness of bacteria at high antibiotic concentration often decrease fitness in the absence of antibiotic, exemplifying a tradeoff between adaptation to environmental extremes. We develop a mathematical model for fitness landscapes generated by such tradeoffs, based on experiments that determine the antibiotic dose-response curves of Escherichia coli strains, and previous observations on antibiotic resistance mutations. Our model generates a succession of landscapes with predictable properties as antibiotic concentration is varied. The landscape is nearly smooth at low and high concentrations, but the tradeoff induces a high ruggedness at intermediate antibiotic concentrations. Despite this high ruggedness, however, all the fitness maxima in the landscapes are evolutionarily accessible from the wild type. This implies that selection for antibiotic resistance in multiple mutational steps is relatively facile despite the complexity of the underlying landscape.

Global fitness landscapes of the Shine-Dalgarno sequence

Shine-Dalgarno sequences (SD) in prokaryotic mRNA facilitate protein translation by pairing with rRNA in ribosomes. Although conventionally defined as AG-rich motifs, recent genomic surveys reveal great sequence diversity, questioning how SD functions. Here, we determined the molecular fitness (i.e., translation efficiency) of 4⁹ synthetic 9-nt SD genotypes in three distinct mRNA contexts in Escherichia coli. We uncovered generic principles governing the SD fitness landscapes: (1) Guanine contents, rather than canonical SD motifs, best predict the fitness of both synthetic and endogenous SD; (2) the genotype-fitness correlation of SD promotes its evolvability by steadily supplying beneficial mutations across fitness landscapes; and (3) the frequency and magnitude of deleterious mutations increase with background fitness, and adjacent nucleotides in SD show stronger epistasis. Epistasis results from disruption of the continuous base pairing between SD and rRNA. This “chain-breaking” epistasis creates sinkholes in SD fitness landscapes and may profoundly impact the evolution and function of prokaryotic translation initiation and other RNA-mediated processes. Collectively, our work yields functional insights into the SD sequence variation in prokaryotic genomes, identifies a simple design principle to guide bioengineering and bioinformatic analysis of SD, and illuminates the fundamentals of fitness landscapes and molecular evolution.

Minimum epistasis interpolation for sequence-function relationships

Massively parallel phenotyping assays have provided unprecedented insight into how multiple mutations combine to determine biological function. While such assays can measure phenotypes for thousands to millions of genotypes in a single experiment, in practice these measurements are not exhaustive, so that there is a need for techniques to impute values for genotypes whose phenotypes have not been directly assayed. Here, we present an imputation method based on inferring the least epistatic possible sequence-function relationship compatible with the data. In particular, we infer the reconstruction where mutational effects change as little as possible across adjacent genetic backgrounds. The resulting models can capture complex higher-order genetic interactions near the data, but approach additivity where data is sparse or absent. We apply the method to high-throughput transcription factor binding assays and use it to explore a fitness landscape for protein G.

A Reflection on 50 Years of John Maynard Smith’s “Protein Space”

In this Perspectives article, Ogbunugafor revisits a famous and influential analogy introduced by renowned evolutionary biologist John Maynard Smith in a 1970 manuscript entitled “Natural selection and the concept of protein space (Smith 1970)...

In 1970, John Maynard Smith published a letter, entitled “Natural Selection and the Concept of a Protein Space,” that proposed a simple analogy for the incremental process of adaptive evolution. His “Protein Space” analogy contains the substrate for many central ideas in evolutionary genetics, and has motivated important discoveries within several subdisciplines of evolutionary science. In this Perspectives article, I commemorate the 50th anniversary of this seminal work by discussing its unique legacy and by describing its intriguing historical context. I propose that the Protein Space analogy is not only important because of its scientific richness, but also because of what it can teach us about the art of constructing useful and subversive analogies.

Highly Combinatorial Genetic Interaction Analysis Reveals a Multi-Drug Transporter Influence Network

Many traits are complex, depending non-additively on variant combinations. Even in model systems, such as the yeast S. cerevisiae, carrying out the high-order variant-combination testing needed to dissect complex traits remains a daunting challenge. Here, we describe “X-gene” genetic analysis (XGA), a strategy for engineering and profiling highly combinatorial gene perturbations. We demonstrate XGA on yeast ABC transporters by engineering 5,353 strains, each deleted for a random subset of 16 transporters, and profiling each strain’s resistance to 16 compounds. XGA yielded 85,648 genotype-to-resistance observations, revealing high-order genetic interactions for 13 of the 16 transporters studied. Neural networks yielded intuitive functional models and guided exploration of fluconazole resistance, which was influenced non-additively by five genes. Together, our results showed that highly combinatorial genetic perturbation can functionally dissect complex traits, supporting pursuit of analogous strategies in human cells and other model systems.

Celaj et al. introduce “X-gene” genetic analysis (XGA), a strategy for modeling complex systems by engineering and profiling highly combinatorial genetic perturbations. They apply XGA to 16 yeast ABC transporters, revealing many high-order genetic interactions. Neural network models yielded intuitive functional models and illuminated an ABC transporter influence network, supporting application of XGA to other organisms and processes.

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

The dynamics of evolution is intimately shaped by epistasis - interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past evolution on future evolution. In this work, we introduce a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance. Their Gaussian character allows for tractable computational as well as analytic understanding. We study the properties of these landscapes focusing on the simplest evolutionary process: random adaptive (uphill) walks. Conventional measures of "ruggedness" are shown to not much affect such adaptive walks. Instead, the long-distance statistics of epistasis cause all properties to be highly conditional on past evolution, determining the statistics of the local landscape (the distribution of fitness-effects of available mutations and combinations of these), as well as the global geometry of evolutionary trajectories. In order to further explore the effects of conditioning on past evolution, we model the effects of slowly changing environments. At long times, such fitness "seascapes" cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods in which adaptive mutations are rare and the population waits for more new directions to be opened up by changes in the environment. Finally, we discuss prospects for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.

Recent insights into the genotype-phenotype relationship from massively parallel genetic assays

With the molecular revolution in Biology, a mechanistic understanding of the genotype-phenotype relationship became possible. Recently, advances in DNA synthesis and sequencing have enabled the development of deep mutational scanning assays, capable of scoring comprehensive libraries of genotypes for fitness and a variety of phenotypes in massively parallel fashion. The resulting empirical genotype-fitness maps pave the way to predictive models, potentially accelerating our ability to anticipate the behaviour of pathogen and cancerous cell populations from sequencing data. Besides from cellular fitness, phenotypes of direct application in industry (e.g. enzyme activity) and medicine (e.g. antibody binding) can be quantified and even selected directly by these assays. This review discusses the technological basis of and recent developments in massively parallel genetics, along with the trends it is uncovering in the genotype-phenotype relationship (distribution of mutation effects, epistasis), their possible mechanistic bases and future directions for advancing towards the goal of predictive genetics.

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

Understanding the pattern of epistasis-the non-independence of mutations-is critical for relating genotype and phenotype. However, the combinatorial complexity of potential epistatic interactions has severely limited the analysis of this problem. Using new mutational approaches, we report a comprehensive experimental study of all 2¹³ mutants that link two phenotypically distinct variants of the Entacmaea quadricolor fluorescent protein-an opportunity to examine epistasis up to the 13^th order. The data show the existence of many high-order epistatic interactions between mutations, but also reveal extraordinary sparsity, enabling novel experimental and computational strategies for learning the relevant epistasis. We demonstrate that such information, in turn, can be used to accurately predict phenotypes in practical situations where the number of measurements is limited. Finally, we show how the observed epistasis shapes the solution space of single-mutation trajectories between the parental fluorescent proteins, informative about the protein's evolutionary potential. This work provides conceptual and experimental strategies to profoundly characterize epistasis in a protein, relevant to both natural and laboratory evolution.

Changes in gene expression predictably shift and switch genetic interactions

Non-additive interactions between mutations occur extensively and also change across conditions, making genetic prediction a difficult challenge. To better understand the plasticity of genetic interactions (epistasis), we combine mutations in a single protein performing a single function (a transcriptional repressor inhibiting a target gene). Even in this minimal system, genetic interactions switch from positive (suppressive) to negative (enhancing) as the expression of the gene changes. These seemingly complicated changes can be predicted using a mathematical model that propagates the effects of mutations on protein folding to the cellular phenotype. More generally, changes in gene expression should be expected to alter the effects of mutations and how they interact whenever the relationship between expression and a phenotype is nonlinear, which is the case for most genes. These results have important implications for understanding genotype-phenotype maps and illustrate how changes in genetic interactions can often—but not always—be predicted by hierarchical mechanistic models.

Non-additive genetic interactions are plastic and can complicate genetic prediction. Here, using deep mutagenesis of the lambda repressor, Li et al. reveal that changes in gene expression can alter the strength and direction of genetic interactions between mutations in many genes and develop mathematical models for predicting them.

Pairwise Interactions among Brain Regions Organize Large-Scale Functional Connectivity during Execution of Various Tasks

Spatially separated brain areas interact with each other to form networks with coordinated activities, supporting various brain functions. Interaction structures among brain areas have been widely investigated through pairwise measures. However, interactions among multiple (e.g., triple and quadruple) areas cannot be reduced to pairwise interactions. Such higher order interactions (HOIs), e.g., exclusive-or (XOR) operation, are widely implemented in computation systems and are crucial for effective information processing. However, it is currently unclear whether any HOIs are present in large-scale brain functional networks when subjects are executing specific tasks. Here we analyzed functional magnetic resonance imaging (fMRI) data collected from human subjects executing various perceptual, motor, and cognitive tasks. We found that HOI strength in the macroscopic functional networks was very weak for all tasks, suggesting that major brain activities do not rely on HOIs on the macroscopic level at the timescale of hundreds of milliseconds. These weak HOIs during tasks were further investigated with a neural network model activated by external inputs, which suggested that weak pairwise interactions among brain areas organized the system without involving HOIs. Taken together, these results demonstrated the dominance of pairwise interactions in organizing coordinated activities among different brain areas to support various brain functions.

Cryptic genetic variation accelerates evolution by opening access to diverse adaptive peaks

Cryptic genetic variation can facilitate adaptation in evolving populations. To elucidate the underlying genetic mechanisms, we used directed evolution in Escherichia coli to accumulate variation in populations of yellow fluorescent proteins and then evolved these proteins toward the new phenotype of green fluorescence. Populations with cryptic variation evolved adaptive genotypes with greater diversity and higher fitness than populations without cryptic variation, which converged on similar genotypes. Populations with cryptic variation accumulated neutral or deleterious mutations that break the constraints on the order in which adaptive mutations arise. In doing so, cryptic variation opens paths to adaptive genotypes, creates historical contingency, and reduces the predictability of evolution by allowing different replicate populations to climb different adaptive peaks and explore otherwise-inaccessible regions of an adaptive landscape.

The causes of evolvability and their evolution

Evolvability is the ability of a biological system to produce phenotypic variation that is both heritable and adaptive. It has long been the subject of anecdotal observations and theoretical work. In recent years, however, the molecular causes of evolvability have been an increasing focus of experimental work. Here, we review recent experimental progress in areas as different as the evolution of drug resistance in cancer cells and the rewiring of transcriptional regulation circuits in vertebrates. This research reveals the importance of three major themes: multiple genetic and non-genetic mechanisms to generate phenotypic diversity, robustness in genetic systems, and adaptive landscape topography. We also discuss the mounting evidence that evolvability can evolve and the question of whether it evolves adaptively.