Empirical Fitness Landscapes Research Articles

Evolutionary druggability for low-dimensional fitness landscapes toward new metrics for antimicrobial applications

The term ‘druggability’ describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant’s sensitivity across a breadth of drugs in a panel, or a given drug’s range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and 7 β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel (‘variant vulnerability’), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target (‘drug applicability’). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G x G x E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

Evolutionary druggability for low-dimensional fitness landscapes toward new metrics for antimicrobial applications.

The term 'druggability' describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant's sensitivity across a breadth of drugs in a panel, or a given drug's range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and 7 β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel ('variant vulnerability'), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target ('drug applicability'). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G x G x E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

Increased Positive Selection in Highly Recombining Genes Does not Necessarily Reflect an Evolutionary Advantage of Recombination.

It is commonly thought that the long-term advantage of meiotic recombination is to dissipate genetic linkage, allowing natural selection to act independently on different loci. It is thus theoretically expected that genes with higher recombination rates evolve under more effective selection. On the other hand, recombination is often associated with GC-biased gene conversion (gBGC), which theoretically interferes with selection by promoting the fixation of deleterious GC alleles. To test these predictions, several studies assessed whether selection was more effective in highly recombining genes (due to dissipation of genetic linkage) or less effective (due to gBGC), assuming a fixed distribution of fitness effects (DFE) for all genes. In this study, I directly derive the DFE from a gene's evolutionary history (shaped by mutation, selection, drift, and gBGC) under empirical fitness landscapes. I show that genes that have experienced high levels of gBGC are less fit and thus have more opportunities for beneficial mutations. Only a small decrease in the genome-wide intensity of gBGC leads to the fixation of these beneficial mutations, particularly in highly recombining genes. This results in increased positive selection in highly recombining genes that is not caused by more effective selection. Additionally, I show that the death of a recombination hotspot can lead to a higher dN/dS than its birth, but with substitution patterns biased towards AT, and only at selected positions. This shows that controlling for a substitution bias towards GC is therefore not sufficient to rule out the contribution of gBGC to signatures of accelerated evolution. Finally, although gBGC does not affect the fixation probability of GC-conservative mutations, I show that by altering the DFE, gBGC can also significantly affect nonsynonymous GC-conservative substitution patterns.

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.

Alphabet cardinality and adaptive evolution

One of the most fundamental characteristics of a fitness landscape is its dimensionality, which is defined by genotype length and alphabet cardinality—the number of alleles per locus. Prior work has shown that increasing landscape dimensionality can promote adaptation by forming new ‘uphill’ mutational paths to the global fitness peak, but can also frustrate adaptation by increasing landscape ruggedness. How these two topographical changes interact to influence adaptation is an open question. Here, we address this question in the context of alphabet cardinality, using theoretical fitness landscapes with tuneable fitness correlations, as well as three empirical fitness landscapes for proteins. We find that the primary effect of increasing alphabet cardinality is the introduction of a new global fitness peak. Controlling for this effect, we find that increasing alphabet cardinality promotes adaptation on uncorrelated fitness landscapes, but frustrates adaptation on correlated fitness landscapes. The primary explanation is that the increased ruggedness that accompanies alphabet expansion is characterized by an increase in mean peak height on uncorrelated fitness landscapes, but a decrease in mean peak height in correlated fitness landscapes. Moreover, in two of the empirical fitness landscapes we observe no effect of increasing alphabet cardinality on adaptation, despite an increase in the number of peaks and a decrease in mean peak height, calling into question the utility of these common measures of landscape ruggedness as indicators of evolutionary outcomes.

A fitness trade-off explains the early fate of yeast aneuploids with chromosome gains

The early development of aneuploidy from an accidental chromosome missegregation shows contrasting effects. On the one hand, it is associated with significant cellular stress and decreased fitness. On the other hand, it often carries a beneficial effect and provides a quick (but typically transient) solution to external stress. These apparently controversial trends emerge in several experimental contexts, particularly in the presence of duplicated chromosomes. However, we lack a mathematical evolutionary modeling framework that comprehensively captures these trends from the mutational dynamics and the trade-offs involved in the early stages of aneuploidy. Here, focusing on chromosome gains, we address this point by introducing a fitness model where a fitness cost of chromosome duplications is contrasted by a fitness advantage from the dosage of specific genes. The model successfully captures the experimentally measured probability of emergence of extra chromosomes in a laboratory evolution setup. Additionally, using phenotypic data collected in rich media, we explored the fitness landscape, finding evidence supporting the existence of a per-gene cost of extra chromosomes. Finally, we show that the substitution dynamics of our model, evaluated in the empirical fitness landscape, explains the relative abundance of duplicated chromosomes observed in yeast population genomics data. These findings lay a firm framework for the understanding of the establishment of newly duplicated chromosomes, providing testable quantitative predictions for future observations.

Epistasis and Adaptation on Fitness Landscapes

Epistasis occurs when the effect of a mutation depends on its carrier's genetic background. Despite increasing evidence that epistasis for fitness is common, its role during evolution is contentious. Fitness landscapes, which are mappings of genotype or phenotype to fitness, capture the full extent and complexity of epistasis. Fitness landscape theory has shown how epistasis affects the course and the outcome of evolution. Moreover, by measuring the competitive fitness of sets of tens to thousands of connected genotypes, empirical fitness landscapes have shown that epistasis is frequent and depends on the fitness measure, the choice of mutations for the landscape, and the environment in which it was measured. In this article, I review fitness landscape theory and experiments and their implications for the role of epistasis in adaptation. I discuss theoretical expectations in the light of empirical fitness landscapes and highlight open challenges and future directions toward integrating theory and data and incorporating ecological factors.

Host-parasite coevolution promotes innovation through deformations in fitness landscapes.

During the struggle for survival, populations occasionally evolve new functions that give them access to untapped ecological opportunities. Theory suggests that coevolution between species can promote the evolution of such innovations by deforming fitness landscapes in ways that open new adaptive pathways. We directly tested this idea by using high-throughput gene editing-phenotyping technology (MAGE-Seq) to measure the fitness landscape of a virus, bacteriophage λ, as it coevolved with its host, the bacterium Escherichia coli. An analysis of the empirical fitness landscape revealed mutation-by-mutation-by-host-genotype interactions that demonstrate coevolution modified the contours of λ's landscape. Computer simulations of λ's evolution on a static versus shifting fitness landscape showed that the changes in contours increased λ's chances of evolving the ability to use a new host receptor. By coupling sequencing and pairwise competition experiments, we demonstrated that the first mutation λ evolved en route to the innovation would only evolve in the presence of the ancestral host, whereas later steps in λ's evolution required the shift to a resistant host. When time-shift replays of the coevolution experiment were run where host evolution was artificially accelerated, λ did not innovate to use the new receptor. This study provides direct evidence for the role of coevolution in driving evolutionary novelty and provides a quantitative framework for predicting evolution in coevolving ecological communities.

An Analysis of Corporate Sustainability Behaviour Through the Lens of Empirical Fitness Landscapes

An Analysis of Corporate Sustainability Behaviour Through the Lens of Empirical Fitness Landscapes

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.

Reflections on the Predictability of Evolution: Toward a Conceptual Framework.

SummaryEvolution is generally considered to be unpredictable because genetic variations are known to occur randomly. However, remarkable patterns of repeated convergent evolution are observed, for instance, loss of pigments by organisms living in caves. Analogous phenotypes appear in similar environments, sometimes in response to similar constraints. Alongside randomness, a certain evolutionary determinism also exists, for instance, the selection of particular phenotypes subjected to particular environmental constraints in the “evolutionary funnel.” We pursue the idea that eco-evolutionary specialization is in some way determinist. The conceptual framework of phenotypic changes entailing specialization presented in this essay explains how evolution can be predicted. We also discuss how the predictability of evolution could be tested using the case of metabolic specialization through gene losses. We also put forward that microorganisms could be key models to test and possibly make headway evolutionary predictions and knowledge about evolution.

Human Search in a Fitness Landscape: How to Assess the Difficulty of a Search Problem

Computational modeling is widely used to study how humans and organizations search and solve problems in fields such as economics, management, cultural evolution, and computer science. We argue that current computational modeling research on human problem-solving needs to address several fundamental issues in order to generate more meaningful and falsifiable contributions. Based on comparative simulations and a new type of visualization of how to assess the nature of the fitness landscape, we address two key assumptions that approaches such as the NK framework rely on: that the NK captures the continuum of the complexity of empirical fitness landscapes and that search behavior is a distinct component, independent from the topology of the fitness landscape. We show the limitations of the most common approach to conceptualize how complex, or rugged, a landscape is, as well as how the nature of the fitness landscape is fundamentally intertwined with search behavior. Finally, we outline broader implications for how to simulate problem-solving.

Analysis of statistical correlations between properties of adaptive walks in fitness landscapes.

The fitness landscape metaphor has been central in our way of thinking about adaptation. In this scenario, adaptive walks are idealized dynamics that mimic the uphill movement of an evolving population towards a fitness peak of the landscape. Recent works in experimental evolution have demonstrated that the constraints imposed by epistasis are responsible for reducing the number of accessible mutational pathways towards fitness peaks. Here, we exhaustively analyse the statistical properties of adaptive walks for two empirical fitness landscapes and theoretical NK landscapes. Some general conclusions can be drawn from our simulation study. Regardless of the dynamics, we observe that the shortest paths are more regularly used. Although the accessibility of a given fitness peak is reasonably correlated to the number of monotonic pathways towards it, the two quantities are not exactly proportional. A negative correlation between predictability and mean path divergence is established, and so the decrease of the number of effective mutational pathways ensures the convergence of the attraction basin of fitness peaks. On the other hand, other features are not conserved among fitness landscapes, such as the relationship between accessibility and predictability.

Recombination and mutational robustness in neutral fitness landscapes.

Mutational robustness quantifies the effect of random mutations on fitness. When mutational robustness is high, most mutations do not change fitness or have only a minor effect on it. From the point of view of fitness landscapes, robust genotypes form neutral networks of almost equal fitness. Using deterministic population models it has been shown that selection favors genotypes inside such networks, which results in increased mutational robustness. Here we demonstrate that this effect is massively enhanced by recombination. Our results are based on a detailed analysis of mesa-shaped fitness landscapes, where we derive precise expressions for the dependence of the robustness on the landscape parameters for recombining and non-recombining populations. In addition, we carry out numerical simulations on different types of random holey landscapes as well as on an empirical fitness landscape. We show that the mutational robustness of a genotype generally correlates with its recombination weight, a new measure that quantifies the likelihood for the genotype to arise from recombination. We argue that the favorable effect of recombination on mutational robustness is a highly universal feature that may have played an important role in the emergence and maintenance of mechanisms of genetic exchange.

Lexical Landscapes as large in silico data for examining advanced properties of fitness landscapes.

In silico approaches have served a central role in the development of evolutionary theory for generations. This especially applies to the concept of the fitness landscape, one of the most important abstractions in evolutionary genetics, and one which has benefited from the presence of large empirical data sets only in the last decade or so. In this study, we propose a method that allows us to generate enormous data sets that walk the line between in silico and empirical: word usage frequencies as catalogued by the Google ngram corpora. These data can be codified or analogized in terms of a multidimensional empirical fitness landscape towards the examination of advanced concepts—adaptive landscape by environment interactions, clonal competition, higher-order epistasis and countless others. We argue that the greater Lexical Landscapes approach can serve as a platform that offers an astronomical number of fitness landscapes for exploration (at least) or theoretical formalism (potentially) in evolutionary biology.

Empirical mean-noise fitness landscapes reveal the fitness impact of gene expression noise

The effects of cell-to-cell variation (noise) in gene expression have proven difficult to quantify because of the mechanistic coupling of noise to mean expression. To independently quantify the effects of changes in mean expression and noise we determine the fitness landscapes in mean-noise expression space for 33 genes in yeast. For most genes, short-lived (noise) deviations away from the expression optimum are nearly as detrimental as sustained (mean) deviations. Fitness landscapes can be classified by a combination of each gene’s sensitivity to protein shortage or surplus. We use this classification to explore evolutionary scenarios for gene expression and find that certain landscape topologies can break the mechanistic coupling of mean and noise, thus promoting independent optimization of both properties. These results demonstrate that noise is detrimental for many genes and reveal non-trivial consequences of mean-noise-fitness topologies for the evolution of gene expression systems.

Estimating the predictability of cancer evolution.

MotivationHow predictable is the evolution of cancer? This fundamental question is of immense relevance for the diagnosis, prognosis and treatment of cancer. Evolutionary biologists have approached the question of predictability based on the underlying fitness landscape. However, empirical fitness landscapes of tumor cells are impossible to determine in vivo. Thus, in order to quantify the predictability of cancer evolution, alternative approaches are required that circumvent the need for fitness landscapes.ResultsWe developed a computational method based on conjunctive Bayesian networks (CBNs) to quantify the predictability of cancer evolution directly from mutational data, without the need for measuring or estimating fitness. Using simulated data derived from >200 different fitness landscapes, we show that our CBN-based notion of evolutionary predictability strongly correlates with the classical notion of predictability based on fitness landscapes under the strong selection weak mutation assumption. The statistical framework enables robust and scalable quantification of evolutionary predictability. We applied our approach to driver mutation data from the TCGA and the MSK-IMPACT clinical cohorts to systematically compare the predictability of 15 different cancer types. We found that cancer evolution is remarkably predictable as only a small fraction of evolutionary trajectories are feasible during cancer progression.Availability and implementation https://github.com/cbg-ethz/predictability\\_of\\_cancer\\_evolution Supplementary information Supplementary data are available at Bioinformatics online.

DISSEQT-DIStribution-based modeling of SEQuence space Time dynamics.

Rapidly evolving microbes are a challenge to model because of the volatile, complex, and dynamic nature of their populations. We developed the DISSEQT pipeline (DIStribution-based SEQuence space Time dynamics) for analyzing, visualizing, and predicting the evolution of heterogeneous biological populations in multidimensional genetic space, suited for population-based modeling of deep sequencing and high-throughput data. The pipeline is openly available on GitHub (https://github.com/rasmushenningsson/DISSEQT.jl, accessed 23 June 2019) and Synapse (https://www.synapse.org/#!Synapse: syn11425758, accessed 23 June 2019), covering the entire workflow from read alignment to visualization of results. Our pipeline is centered around robust dimension and model reduction algorithms for analysis of genotypic data with additional capabilities for including phenotypic features to explore dynamic genotype–phenotype maps. We illustrate its utility and capacity with examples from evolving RNA virus populations, which present one of the highest degrees of genetic heterogeneity within a given population found in nature. Using our pipeline, we empirically reconstruct the evolutionary trajectories of evolving populations in sequence space and genotype–phenotype fitness landscapes. We show that while sequence space is vastly multidimensional, the relevant genetic space of evolving microbial populations is of intrinsically low dimension. In addition, evolutionary trajectories of these populations can be faithfully monitored to identify the key minority genotypes contributing most to evolution. Finally, we show that empirical fitness landscapes, when reconstructed to include minority variants, can predict phenotype from genotype with high accuracy.

Machine learning-assisted directed protein evolution with combinatorial libraries

To reduce experimental effort associated with directed protein evolution and to explore the sequence space encoded by mutating multiple positions simultaneously, we incorporate machine learning into the directed evolution workflow. Combinatorial sequence space can be quite expensive to sample experimentally, but machine-learning models trained on tested variants provide a fast method for testing sequence space computationally. We validated this approach on a large published empirical fitness landscape for human GB1 binding protein, demonstrating that machine learning-guided directed evolution finds variants with higher fitness than those found by other directed evolution approaches. We then provide an example application in evolving an enzyme to produce each of the two possible product enantiomers (i.e., stereodivergence) of a new-to-nature carbene Si-H insertion reaction. The approach predicted libraries enriched in functional enzymes and fixed seven mutations in two rounds of evolution to identify variants for selective catalysis with 93% and 79% ee (enantiomeric excess). By greatly increasing throughput with in silico modeling, machine learning enhances the quality and diversity of sequence solutions for a protein engineering problem.

Genetic Background Modifies the Topography of a Fitness Landscape, Influencing the Dynamics of Adaptive Evolution

Understanding the forces that drive the dynamics of adaptive evolution is a goal of many sub-fields and applications of evolutionary biology, including in evolutionary computation. The fitness landscape analogy has served as a useful abstraction for addressing these topics across many systems, and recent treatments have revealed how different environments can frame the particulars of adaptive evolution by changing the topography of fitness landscapes. In this study, we examine how the larger, ambient genetic context in which a protein is embedded affects fitness landscape topography and subsequent evolution. Using simulations on empirical fitness landscapes, we discover that the genetic background - genetic variability in regions outside of the locus under study (in this case, an essential bacterial enzyme target of antibiotics) - influences the speed and direction of evolution in several surprising ways. These findings have implications for how we study the evolution of drug resistance in nature, and for presumptions about how biological evolution might be expected to occur in genetically-modified organisms. More generally, the findings speak to theory surrounding how “difference can beget difference” in adaptive evolution (whether biological, computational, or technological): that small differences in environmental or genetic background can greatly alter the specifics of how evolution occurs, which can rapidly drive even slightly diverged populations further apart.