Drift on holey landscapes as a dominant evolutionary process.

An organism's phenotype has been shaped by evolution but the specific processes have to be indirectly inferred for most species. For example, correlations among traits imply the historical action of correlated selection and, more generally, the expression and distribution of traits is expected to be reflective of the adaptive landscapes that have shaped a population. However, our expectations about how quantitative traits-like most behaviors, physiological processes, and life-history traits-should be distributed under different evolutionary processes are not clear. Here, we show that genetic variation in quantitative traits is not distributed as would be expected under dominant evolutionary models. Instead, we found that genetic variation in quantitative traits across six phyla and 60 species (including both Plantae and Animalia) is consistent with evolution across high-dimensional "holey landscapes." This suggests that the leading conceptualizations and modeling of the evolution of trait integration fail to capture how phenotypes are shaped and that traits are integrated in a manner contrary to predictions of dominant evolutionary theory. Our results demonstrate that our understanding of how evolution has shaped phenotypes remains incomplete and these results provide a starting point for reassessing the relevance of existing evolutionary models.

Fully accessible fitness landscape of oncogene-negative lung adenocarcinoma.

Cancer genomes are almost invariably complex with genomic alterations cooperating during each step of carcinogenesis. In cancers that lack a single dominant oncogene mutation, cooperation between the inactivation of multiple tumor suppressor genes can drive tumor initiation and growth. Here, we shed light on how the sequential acquisition of genomic alterations generates oncogene-negative lung tumors. We couple tumor barcoding with combinatorial and multiplexed somatic genome editing to characterize the fitness landscapes of three tumor suppressor genes NF1, RASA1, and PTEN, the inactivation of which jointly drives oncogene-negative lung adenocarcinoma initiation and growth. The fitness landscape was surprisingly accessible, with each additional mutation leading to growth advantage. Furthermore, the fitness landscapes remained fully accessible across backgrounds with the inactivation of additional tumor suppressor genes. These results suggest that while predicting cancer evolution will be challenging, acquiring the multiple alterations that drive the growth of oncogene-negative tumors can be facilitated by the lack of constraints on mutational order.

Unpredictability of the Fitness Effects of Antimicrobial Resistance Mutations Across Environments in Escherichia coli.

The evolution of antimicrobial resistance (AMR) in bacteria is a major public health concern, and antibiotic restriction is often implemented to reduce the spread of resistance. These measures rely on the existence of deleterious fitness effects (i.e. costs) imposed by AMR mutations during growth in the absence of antibiotics. According to this assumption, resistant strains will be outcompeted by susceptible strains that do not pay the cost during the period of restriction. The fitness effects of AMR mutations are generally studied in laboratory reference strains grown in standard growth environments; however, the genetic and environmental context can influence the magnitude and direction of a mutation's fitness effects. In this study, we measure how three sources of variation impact the fitness effects of Escherichia coli AMR mutations: the type of resistance mutation, the genetic background of the host, and the growth environment. We demonstrate that while AMR mutations are generally costly in antibiotic-free environments, their fitness effects vary widely and depend on complex interactions between the mutation, genetic background, and environment. We test the ability of the Rough Mount Fuji fitness landscape model to reproduce the empirical data in simulation. We identify model parameters that reasonably capture the variation in fitness effects due to genetic variation. However, the model fails to accommodate the observed variation when considering multiple growth environments. Overall, this study reveals a wealth of variation in the fitness effects of resistance mutations owing to genetic background and environmental conditions, which will ultimately impact their persistence in natural populations.

Viral Fitness Landscapes Based on Self-organizing Maps.

The creation of fitness maps from viral populations especially in the case of RNA viruses, with high mutation rates producing quasispecies, is complex since the mutant spectrum is in a very high-dimensional space. In this work, a new approach is presented using a class of neural networks, Self-Organized Maps (SOM), to represent realistic fitness landscapes in two RNA viruses: Human Immunodeficiency Virus type 1 (HIV-1) and Hepatitis C Virus (HCV). This methodology has proven to be very effective in the classification of viral quasispecies, using as criterium the mutant sequences in the population. With HIV-1, the fitness landscapes are constructed by representing the experimentally determined fitness on the sequence map. This approach permitted the depiction of the evolutionary paths of the variants subjected to processes of fitness loss and gain in cell culture. In the case of HCV, the efficiency was measured as a function of the frequency of each haplotype in the population by ultra-deep sequencing. The fitness landscapes obtained provided information on the efficiency of each variant in the quasispecies environment, that is, in relation to the entire spectrum of mutants. With the SOM maps, it is possible to determine the evolutionary dynamics of the different haplotypes.

Virus Evolution on Fitness Landscapes.

The landscape paradigm is revisited in the light of evolution in simple systems. A brief overview of different classes of fitness landscapes is followed by a more detailed discussion of the RNA model, which is currently the only evolutionary model that allows for a comprehensive molecular analysis of a fitness landscape. Neutral networks of genotypes are indispensable for the success of evolution. Important insights into the evolutionary mechanism are gained by considering the topology of sequence and shape spaces. The dynamic concept of molecular quasispecies is viewed in the light of the landscape paradigm. The distribution of fitness values in state space is mirrored by the population structures of mutant distributions. Two classes of thresholds for replication error or mutations are important: (i) the-conventional-genotypic error threshold, which separates ordered replication from random drift on neutral networks, and (ii) a phenotypic error threshold above which the molecular phenotype is lost. Empirical landscapes are reviewed and finally, the implications of the landscape concept for virus evolution are discussed.

Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape.

A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnNe/s time (Ne , effective population size; s, selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially. Theoretically, PE has been linked to self-organized criticality (SOC), a model in which the size of "avalanches" in an evolving system is power-law-distributed, resulting in increasing rarity of major events. Here we show, however, that a PE-like evolutionary regime is the default for a very simple model of an evolving population that does not rely on SOC or any other special conditions.

Fitness Landscape Analysis of a tRNA Gene Reveals that the Wild Type Allele is Sub-optimal, Yet Mutationally Robust.

Fitness landscape mapping and the prediction of evolutionary trajectories on these landscapes are major tasks in evolutionary biology research. Evolutionary dynamics is tightly linked to the landscape topography, but this relation is not straightforward. Here, we analyze a fitness landscape of a yeast tRNA gene, previously measured under four different conditions. We find that the wild type allele is sub-optimal, and 8-10% of its variants are fitter. We rule out the possibilities that the wild type is fittest on average on these four conditions or located on a local fitness maximum. Notwithstanding, we cannot exclude the possibility that the wild type might be fittest in some of the many conditions in the complex ecology that yeast lives at. Instead, we find that the wild type is mutationally robust ("flat"), while more fit variants are typically mutationally fragile. Similar observations of mutational robustness or flatness have been so far made in very few cases, predominantly in viral genomes.

Modeling Sequence-Space Exploration and Emergence of Epistatic Signals in Protein Evolution.

During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here, we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous proteins, to propose stochastic models of experimental protein evolution. These models predict quantitatively important features of experimentally evolved sequence libraries, like fitness distributions and position-specific mutational spectra. They also allow us to efficiently simulate sequence libraries for a vast array of combinations of experimental parameters like sequence divergence, selection strength, and library size. We showcase the potential of the approach in reanalyzing two recent experiments to determine protein structure from signals of epistasis emerging in experimental sequence libraries. To be detectable, these signals require sufficiently large and sufficiently diverged libraries. Our modeling framework offers a quantitative explanation for different outcomes of recently published experiments. Furthermore, we can forecast the outcome of time- and resource-intensive evolution experiments, opening thereby a way to computationally optimize experimental protocols.

Rapid adaptation of recombining populations on tunable fitness landscapes.

How does standing genetic variation affect polygenic adaptation in recombining populations? Despite a large body of work in quantitative genetics, epistatic and weak additive fitness effects among simultaneously segregating genetic variants are difficult to capture experimentally or to predict theoretically. In this study, we simulated adaptation on fitness landscapes with tunable ruggedness driven by standing genetic variation in recombining populations. We confirmed that recombination hinders the movement of a population through a rugged fitness landscape. When surveying the effect of epistasis on the fixation of alleles, we found that the combined effects of high ruggedness and high recombination probabilities lead to preferential fixation of alleles that had a high initial frequency. This indicates that positive epistatic alleles escape from being broken down by recombination when they start at high frequency. We further extract direct selection coefficients and pairwise epistasis along the adaptive path. When taking the final fixed genotype as the reference genetic background, we observe that, along the adaptive path, beneficial direct selection appears stronger and pairwise epistasis weaker than in the underlying fitness landscape. Quantitatively, the ratio of epistasis and direct selection is smaller along the adaptive path ( ≈ 1 $$ \approx 1 $$ ) than expected. Thus, adaptation on a rugged fitness landscape may lead to spurious signals of direct selection generated through epistasis. Our study highlights how the interplay of epistasis and recombination constrains the adaptation of a diverse population to a new environment.

Relation Between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.

Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141-144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141-144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks.

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks.

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and "ruggedness". As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population's evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.

Molecular Biology and Evolution of Cancer: From Discovery to Action.

Cancer progression is an evolutionary process. During this process, evolving cancer cell populations encounter restrictive ecological niches within the body, such as the primary tumor, circulatory system, and diverse metastatic sites. Efforts to prevent or delay cancer evolution-and progression-require a deep understanding of the underlying molecular evolutionary processes. Herein we discuss a suite of concepts and tools from evolutionary and ecological theory that can inform cancer biology in new and meaningful ways. We also highlight current challenges to applying these concepts, and propose ways in which incorporating these concepts could identify new therapeutic modes and vulnerabilities in cancer.

On the deformability of an empirical fitness landscape by microbial evolution.

A fitness landscape is a map between the genotype and its reproductive success in a given environment. The topography of fitness landscapes largely governs adaptive dynamics, constraining evolutionary trajectories and the predictability of evolution. Theory suggests that this topography can be deformed by mutations that produce substantial changes to the environment. Despite its importance, the deformability of fitness landscapes has not been systematically studied beyond abstract models, and little is known about its reach and consequences in empirical systems. Here we have systematically characterized the deformability of the genome-wide metabolic fitness landscape of the bacterium Escherichia coli Deformability is quantified by the noncommutativity of epistatic interactions, which we experimentally demonstrate in mutant strains on the path to an evolutionary innovation. Our analysis shows that the deformation of fitness landscapes by metabolic mutations rarely affects evolutionary trajectories in the short range. However, mutations with large environmental effects produce long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our results therefore suggest that, even in situations in which mutations have strong environmental effects, fitness landscapes may retain their power to forecast evolution over small mutational distances despite the potential attenuation of that power over longer evolutionary trajectories. Our methods and results provide an avenue for integrating adaptive and eco-evolutionary dynamics with complex genetics and genomics.

Impact of In Vivo Protein Folding Probability on Local Fitness Landscapes.

It is incompletely understood how biophysical properties like protein stability impact molecular evolution and epistasis. Epistasis is defined as specific when a mutation exclusively influences the phenotypic effect of another mutation, often at physically interacting residues. In contrast, nonspecific epistasis results when a mutation is influenced by a large number of nonlocal mutations. As most mutations are pleiotropic, the in vivo folding probability-governed by basal protein stability-is thought to determine activity-enhancing mutational tolerance, implying that nonspecific epistasis is dominant. However, evidence exists for both specific and nonspecific epistasis as the prevalent factor, with limited comprehensive data sets to support either claim. Here, we use deep mutational scanning to probe how in vivo enzyme folding probability impacts local fitness landscapes. We computationally designed two different variants of the amidase AmiE with statistically indistinguishable catalytic efficiencies but lower probabilities of folding in vivo compared with wild-type. Local fitness landscapes show slight alterations among variants, with essentially the same global distribution of fitness effects. However, specific epistasis was predominant for the subset of mutations exhibiting positive sign epistasis. These mutations mapped to spatially distinct locations on AmiE near the initial mutation or proximal to the active site. Intriguingly, the majority of specific epistatic mutations were codon dependent, with different synonymous codons resulting in fitness sign reversals. Together, these results offer a nuanced view of how protein folding probability impacts local fitness landscapes and suggest that transcriptional-translational effects are as important as stability in determining evolutionary outcomes.

An uncertainty law for microbial evolution.

Medical practice would benefit from a thorough understanding of constraints and uncertainty in microbial evolution. Higher order epistasis refers to unexpected effects of multiple mutations even if both single mutations and pairwise effects have been accounted for. Recent studies show that higher order epistasis is abundant in nature, for bacteria as well as higher organisms. However, the importance of higher order effects has been debated. It has been suggested that such effects cannot be interpreted, and should not be considered. Here, we show conclusively that higher order epistasis changes the adaptive prospects for a population. The conclusion is based on an exhaustive search of 193,270,310 hyper-cube graphs and applications of graph theory. Our results are more precise, yet more universal, than related research since they depend on mathematical theory, rather than sampling or simulations. Moreover, the uncertainty we establish for microbial evolution, due to higher order epistasis is not sensitive for detailed model assumptions, such as the baseline being additive or log-additive fitness.

Changing mutational and adaptive landscapes and the genesis of cancer.

By the time the process of oncogenesis has produced an advanced cancer, tumor cells have undergone extensive evolution. The cellular phenotypes resulting from this evolution have been well studied, and include accelerated growth rates, apoptosis resistance, immortality, invasiveness, and immune evasion. Yet with all of our current knowledge of tumor biology, the details of early oncogenesis have been difficult to observe and understand. Where different oncogenic mutations may work together to enhance the survival of a tumor cell, in isolation they are often pro-apoptotic, pro-differentiative or pro-senescent, and therefore often, somewhat paradoxically, disadvantageous to a cell. It is also becoming clear that somatic mutations, including those in known oncogenic drivers, are common in tissues starting at a young age. These observations raise the question: how do we largely avoid cancer for most of our lives? Here we propose that evolutionary forces can help explain this paradox. As humans and other organisms age or experience external insults such as radiation or smoking, the structure and function of tissues progressively degrade, resulting in altered stem cell niche microenvironments. As tissue integrity declines, it becomes less capable of supporting and maintaining resident stem cells. These stem cells then find themselves in a microenvironment to which they are poorly adapted, providing a competitive advantage to those cells that can restore their functionality and fitness through mutations or epigenetic changes. The resulting oncogenic clonal expansions then increase the odds of further cancer progression. Understanding how the causes of cancer, such as aging or smoking, affect tissue microenvironments to control the impact of mutations on somatic cell fitness can help reconcile the discrepancy between marked mutation accumulation starting early in life and the somatic evolution that leads to cancer at advanced ages or following carcinogenic insults. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

Trade-offs between enzyme fitness and solubility illuminated by deep mutational scanning.

Proteins are marginally stable, and an understanding of the sequence determinants for improved protein solubility is highly desired. For enzymes, it is well known that many mutations that increase protein solubility decrease catalytic activity. These competing effects frustrate efforts to design and engineer stable, active enzymes without laborious high-throughput activity screens. To address the trade-off between enzyme solubility and activity, we performed deep mutational scanning using two different screens/selections that purport to gauge protein solubility for two full-length enzymes. We assayed a TEM-1 beta-lactamase variant and levoglucosan kinase (LGK) using yeast surface display (YSD) screening and a twin-arginine translocation pathway selection. We then compared these scans with published experimental fitness landscapes. Results from the YSD screen could explain 37% of the variance in the fitness landscapes for one enzyme. Five percent to 10% of all single missense mutations improve solubility, matching theoretical predictions of global protein stability. For a given solubility-enhancing mutation, the probability that it would retain wild-type fitness was correlated with evolutionary conservation and distance to active site, and anticorrelated with contact number. Hybrid classification models were developed that could predict solubility-enhancing mutations that maintain wild-type fitness with an accuracy of 90%. The downside of using such classification models is the removal of rare mutations that improve both fitness and solubility. To reveal the biophysical basis of enhanced protein solubility and function, we determined the crystallographic structure of one such LGK mutant. Beyond fundamental insights into trade-offs between stability and activity, these results have potential biotechnological applications.

Inferring Future Landscapes: Sampling the Local Optima Level.

Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this article, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LON construction algorithms produce fitness landscape features which can explain almost all search variance. We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this "super-sampling": a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other.

The distribution of epistasis on simple fitness landscapes.

Fitness interactions between mutations can influence a population's evolution in many different ways. While epistatic effects are difficult to measure precisely, important information is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from a class of simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effect sizes, mutational bias and maladaptation of the wild type. We illustrate our approach by reanalysing a large dataset of mutant effects in a yeast snoRNA (small nucleolar RNA). Though characterized by some large epistatic effects, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have limited influence on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape and the distribution of mutations, and so is expected to vary in consistent ways between new mutations, standing variation and fixed mutations.

Biophysical principles predict fitness landscapes of drug resistance.

Fitness landscapes of drug resistance constitute powerful tools to elucidate mutational pathways of antibiotic escape. Here, we developed a predictive biophysics-based fitness landscape of trimethoprim (TMP) resistance for Escherichia coli dihydrofolate reductase (DHFR). We investigated the activity, binding, folding stability, and intracellular abundance for a complete set of combinatorial DHFR mutants made out of three key resistance mutations and extended this analysis to DHFR originated from Chlamydia muridarum and Listeria grayi We found that the acquisition of TMP resistance via decreased drug affinity is limited by a trade-off in catalytic efficiency. Protein stability is concurrently affected by the resistant mutants, which precludes a precise description of fitness from a single molecular trait. Application of the kinetic flux theory provided an accurate model to predict resistance phenotypes (IC50) quantitatively from a unique combination of the in vitro protein molecular properties. Further, we found that a controlled modulation of the GroEL/ES chaperonins and Lon protease levels affects the intracellular steady-state concentration of DHFR in a mutation-specific manner, whereas IC50 is changed proportionally, as indeed predicted by the model. This unveils a molecular rationale for the pleiotropic role of the protein quality control machinery on the evolution of antibiotic resistance, which, as we illustrate here, may drastically confound the evolutionary outcome. These results provide a comprehensive quantitative genotype-phenotype map for the essential enzyme that serves as an important target of antibiotic and anticancer therapies.