Beyond the (geometric) mean: stochastic models undermine deterministic predictions of bet hedger evolution.

Bet hedging is a ubiquitous strategy for risk reduction in the face of unpredictable environmental change where a lineage lowers its variance in fitness across environments at the expense of also lowering its arithmetic mean fitness. Classically, the benefit of bet hedging has been quantified using geometric mean fitness (GMF); bet hedging is expected to evolve if and only if it has a higher GMF than the wild-type. We build upon previous research on the effect of incorporating stochasticity in phenotypic distribution, environment, and reproduction to investigate the extent to which these sources of stochasticity will impact the evolution of real-world bet hedging traits. We utilize both individual-based simulations and Markov chain numerics to demonstrate that modeling stochasticity can alter the sign of selection for the bet hedger compared to deterministic predictions. We find that bet hedging can be deleterious at small population sizes and beneficial at larger population sizes. This non-monotonic dependence of the sign of selection on population size, known as sign inversion, exists across parameter space for both conservative and diversified bet hedgers. We apply our model to published data of bet hedging strategies to show that sign inversion exists for biologically relevant parameters in two study systems: Papaver dubium, an annual poppy with variable germination phenology, and Salmonella typhimurium, a pathogenic bacteria that exhibits antibiotic persistence. Taken together, our results suggest that GMF is not enough to predict when bet hedging is adaptive.

Developing evolution-resistant drugs for COVID-19.

Analyzing how mutations affect the main protease of SARS-CoV-2 may help researchers develop drugs that are effective against current and future variants of the virus.

Covalent docking and molecular dynamics simulations reveal the specificity-shifting mutations Ala237Arg and Ala237Lys in TEM beta-lactamase.

The rate of modern drug discovery using experimental screening methods still lags behind the rate at which pathogens mutate, underscoring the need for fast and accurate predictive simulations of protein evolution. Multidrug-resistant bacteria evade our defenses by expressing a series of proteins, the most famous of which is the 29-kilodalton enzyme, TEM ß-lactamase. Considering these challenges, we applied a covalent docking heuristic to measure the effects of all possible alanine 237 substitutions in TEM due to this codon's importance for catalysis and effects on the binding affinities of commercially-available ß-lactam compounds. In addition to the usual mutations that reduce substrate binding due to steric hindrance, we identified two distinctive specificity-shifting TEM mutations, Ala237Arg and Ala237Lys, and their respective modes of action. Notably, we discovered and verified through minimum inhibitory concentration assays that, while these mutations and their bulkier side chains lead to steric clashes that curtail ampicillin binding, these same groups foster salt bridges with the negatively-charged side-chain of the cephalosporin cefixime, widely used in the clinic to treat multi-resistant bacterial infections. To measure the stability of these unexpected interactions, we used molecular dynamics simulations and found the binding modes to be stable despite the application of biasing forces. Finally, we found that both TEM mutants also bind strongly to other drugs containing negatively-charged R-groups, such as carumonam and ceftibuten. As with cefixime, this increased binding affinity stems from a salt bridge between the compounds' negative moieties and the positively-charged side chain of the arginine or lysine, suggesting a shared mechanism. In addition to reaffirming the power of using simulations as molecular microscopes, our results can guide the rational design of next-generation ß-lactam antibiotics and bring the community closer to retaking the lead against the recurrent threat of multidrug-resistant pathogens.

Density fluctuations, homeostasis, and reproduction effects in bacteria.

Single-cells grow by increasing their biomass and size. Here, we report that while mass and size accumulation rates of single Escherichia coli cells are exponential, their density and, thus, the levels of macromolecular crowding fluctuate during growth. As such, the average rates of mass and size accumulation of a single cell are generally not the same, but rather cells differentiate into increasing one rate with respect to the other. This differentiation yields a density homeostasis mechanism that we support mathematically. Further, we observe that density fluctuations can affect the reproduction rates of single cells, suggesting a link between the levels of macromolecular crowding with metabolism and overall population fitness. We detail our experimental approach and the "invisible" microfluidic arrays that enabled increased precision and throughput. Infections and natural communities start from a few cells, thus, emphasizing the significance of density-fluctuations when taking non-genetic variability into consideration.

Predicting the viability of beta-lactamase: How folding and binding free energies correlate with beta-lactamase fitness.

One of the long-standing holy grails of molecular evolution has been the ability to predict an organism's fitness directly from its genotype. With such predictive abilities in hand, researchers would be able to more accurately forecast how organisms will evolve and how proteins with novel functions could be engineered, leading to revolutionary advances in medicine and biotechnology. In this work, we assemble the largest reported set of experimental TEM-1 ß-lactamase folding free energies and use this data in conjunction with previously acquired fitness data and computational free energy predictions to determine how much of the fitness of ß-lactamase can be directly predicted by thermodynamic folding and binding free energies. We focus upon ß-lactamase because of its long history as a model enzyme and its central role in antibiotic resistance. Based upon a set of 21 ß-lactamase single and double mutants expressly designed to influence protein folding, we first demonstrate that modeling software designed to compute folding free energies such as FoldX and PyRosetta can meaningfully, although not perfectly, predict the experimental folding free energies of single mutants. Interestingly, while these techniques also yield sensible double mutant free energies, we show that they do so for the wrong physical reasons. We then go on to assess how well both experimental and computational folding free energies explain single mutant fitness. We find that folding free energies account for, at most, 24% of the variance in ß-lactamase fitness values according to linear models and, somewhat surprisingly, complementing folding free energies with computationally-predicted binding free energies of residues near the active site only increases the folding-only figure by a few percent. This strongly suggests that the majority of ß-lactamase's fitness is controlled by factors other than free energies. Overall, our results shed a bright light on to what extent the community is justified in using thermodynamic measures to infer protein fitness as well as how applicable modern computational techniques for predicting free energies will be to the large data sets of multiply-mutated proteins forthcoming.

Genomic clustering of fitness-affecting mutations favors the evolution of chromosomal instability.

Most solid cancers are characterized by chromosomal instability (CIN)-an elevated rate of large-scale chromosomal aberrations and ploidy changes. Chromosomal instability may arise through mutations in a range of genomic integrity loci and is commonly associated with fast disease progression, poor prognosis, and multidrug resistance. However, the evolutionary forces promoting CIN-inducing alleles (hereafter, CIN mutators) during carcinogenesis remain poorly understood. Here, we develop a stochastic, individual-based model of indirect selection experienced by CIN mutators via genomic associations with fitness-affecting mutations. Because mutations associated with CIN affect large swaths of the genome and have the potential to simultaneously comprise many individual loci, we show that indirect selection on CIN mutators is critically influenced by genome organization. In particular, we find strong support for a key role played by the spatial clustering of loci with either beneficial or deleterious mutational effects. Genomic clustering of selected loci allows CIN mutators to generate favorable chromosomal changes that facilitate their rapid expansion within a neoplasm and, in turn, accelerate carcinogenesis. We then examine the distribution of oncogenic and tumor-suppressing loci in the human genome and find both to be potentially more clustered along the chromosome than expected, leading us to speculate that human genome may be susceptible to CIN hitchhiking. More quantitative data on fitness effects of individual mutations will be necessary, though, to assess the true levels of clustering in the human genome and the effectiveness of indirect selection for CIN. Finally, we use our model to examine how therapeutic strategies that increase the deleterious burden of genetically unstable cells by raising either the rate of CIN or the cost of deleterious mutations affect CIN evolution. We find that both can inhibit CIN hitchhiking and delay carcinogenesis in some circumstances, yet, in line with earlier work, we find the latter to be considerably more effective.

Migration promotes mutator alleles in subdivided populations.

Mutator alleles that elevate the genomic mutation rate may invade nonrecombining populations by hitchhiking with beneficial mutations. Mutators have been repeatedly observed to take over adapting laboratory populations and have been found at high frequencies in both microbial pathogen and cancer populations in nature. Recently, we have shown that mutators are only favored by selection in sufficiently large populations and transition to being disfavored as population size decreases. This population size-dependent sign inversion in selective effect suggests that population structure may also be an important determinant of mutation rate evolution. Although large populations may favor mutators, subdividing such populations into sufficiently small subpopulations (demes) might effectively inhibit them. On the other hand, migration between small demes that otherwise inhibit hitchhiking may promote mutator fixation in the whole metapopulation. Here, we use stochastic, agent-based simulations and evolution experiments with the yeast Saccharomyces cerevisiae to show that mutators can, indeed, be favored by selection in subdivided metapopulations composed of small demes connected by sufficient migration. In fact, we show that population structure plays a previously unsuspected role in promoting mutator success in subdivided metapopulations when migration is rare.

The Influence of Higher-Order Epistasis on Biological Fitness Landscape Topography.

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We conclude by highlighting opportunities for further theoretical and experimental work dissecting the influence that epistasis of all orders has on fitness landscape topography and on the efficiency of evolution by natural selection.

Patterns of musculoskeletal growth and dimensional changes associated with selection and developmental plasticity in domestic and wild strain turkeys.

Domestication is a type of experimental evolution in which humans have artificially selected for specific desired traits. Selected strain animals can be utilized to identify correlated responses by comparing them to the wild strain. In particular, domestic turkeys have been selected for increased body mass and high-growth rate, most significantly over the past 60 years. Yet it remains unclear how artificial selection has affected the morphology and evolution of the musculoskeletal system as a whole. Here, we compare growth rate over 21 weeks, hind limb bone scaling across ontogeny via in vivo CT scanning, and muscle proportions in wild and domestic turkeys to identify differences in structural scaling and the potential contributions of selection and developmental plasticity to whole-organism morphology. The domestic turkeys grew at a higher rate (0.14 kg/day vs. 0.05 kg/day) and reached over 3 times the body mass of wild birds. Comparing the proportional muscle masses in adult turkeys, only the trunk had a greater mass ratio in the domestic turkey, driven solely by M. pectoralis (2.8 times larger). The proportional increase in only breast meat and no other muscles highlights the surgical precision attainable with artificial selection. The domestic turkey femur and tibiotarsus displayed increases in polar moment of area, apparently maintaining torsional strength as body mass increased. The lack of dimensional change in the more vertically held tarsometatarsus is consistent with the pattern expected due to developmental plasticity. These results from the domestic turkey emphasize that there are morphological limits to preserving the balance between growth and function, and varying rates of trait evolution can further complicate this equilibrium.

Sign of selection on mutation rate modifiers depends on population size.

The influence of population size (N) on natural selection acting on alleles that affect fitness has been understood for almost a century. As N declines, genetic drift overwhelms selection and alleles with direct fitness effects are rendered neutral. Often, however, alleles experience so-called indirect selection, meaning they affect not the fitness of an individual but the fitness distribution of its offspring. Some of the best-studied examples of indirect selection include alleles that modify aspects of the genetic system such as recombination and mutation rates. Here, we use analytics, simulations, and experimental populations of Saccharomyces cerevisiae to examine the influence of N on indirect selection acting on alleles that increase the genomic mutation rate (mutators). Mutators experience indirect selection via genomic associations with beneficial and deleterious mutations they generate. We show that, as N declines, indirect selection driven by linked beneficial mutations is overpowered by drift before drift can neutralize the cost of the deleterious load. As a result, mutators transition from being favored by indirect selection in large populations to being disfavored as N declines. This surprising phenomenon of sign inversion in selective effect demonstrates that indirect selection on mutators exhibits a profound and qualitatively distinct dependence on N.

Enzyme Efficiency but Not Thermostability Drives Cefotaxime Resistance Evolution in TEM-1 ß-Lactamase.

A leading intellectual challenge in evolutionary genetics is to identify the specific phenotypes that drive adaptation. Enzymes offer a particularly promising opportunity to pursue this question, because many enzymes' contributions to organismal fitness depend on a comparatively small number of experimentally accessible properties. Moreover, on first principles the demands of enzyme thermostability stand in opposition to the demands of catalytic activity. This observation, coupled with the fact that enzymes are only marginally thermostable, motivates the widely held hypothesis that mutations conferring functional improvement require compensatory mutations to restore thermostability. Here, we explicitly test this hypothesis for the first time, using four missense mutations in TEM-1 ß-lactamase that jointly increase cefotaxime Minimum Inhibitory Concentration (MIC) ∼1500-fold. First, we report enzymatic efficiency (kcat/KM) and thermostability (Tm, and thence ΔG of folding) for all combinations of these mutations. Next, we fit a quantitative model that predicts MIC as a function of kcat/KM and ΔG. While kcat/KM explains ∼54% of the variance in cefotaxime MIC (∼92% after log transformation), ΔG does not improve explanatory power of the model. We also find that cefotaxime MIC rises more slowly in kcat/KM than predicted. Several explanations for these discrepancies are suggested. Finally, we demonstrate substantial sign epistasis in MIC and kcat/KM, and antagonistic pleiotropy between phenotypes, in spite of near numerical additivity in the system. Thus constraints on selectively accessible trajectories, as well as limitations in our ability to explain such constraints in terms of underlying mechanisms are observed in a comparatively "well-behaved" system.

Variability in fitness effects can preclude selection of the fittest.

Evolutionary biologists often predict the outcome of natural selection on an allele by measuring its effects on lifetime survival and reproduction of individual carriers. However, alleles affecting traits like sex, evolvability, and cooperation can cause fitness effects that depend heavily on differences in the environmental, social, and genetic context of individuals carrying the allele. This variability makes it difficult to summarize the evolutionary fate of an allele based solely on its effects on any one individual. Attempts to average over this variability can sometimes salvage the concept of fitness. In other cases evolutionary outcomes can only be predicted by considering the entire genealogy of an allele, thus limiting the utility of individual fitness altogether. We describe a number of intriguing new evolutionary phenomena that have emerged in studies that explicitly model long-term lineage dynamics and discuss implications for the evolution of infectious diseases.

Genetically Determined Variation in Lysis Time Variance in the Bacteriophage φX174.

Researchers in evolutionary genetics recently have recognized an exciting opportunity in decomposing beneficial mutations into their proximal, mechanistic determinants. The application of methods and concepts from molecular biology and life history theory to studies of lytic bacteriophages (phages) has allowed them to understand how natural selection sees mutations influencing life history. This work motivated the research presented here, in which we explored whether, under consistent experimental conditions, small differences in the genome of bacteriophage φX174 could lead to altered life history phenotypes among a panel of eight genetically distinct clones. We assessed the clones' phenotypes by applying a novel statistical framework to the results of a serially sampled parallel infection assay, in which we simultaneously inoculated each of a large number of replicate host volumes with ∼1 phage particle. We sequentially plated the volumes over the course of infection and counted the plaques that formed after incubation. These counts served as a proxy for the number of phage particles in a single volume as a function of time. From repeated assays, we inferred significant, genetically determined heterogeneity in lysis time and burst size, including lysis time variance. These findings are interesting in light of the genetic and phenotypic constraints on the single-protein lysis mechanism of φX174. We speculate briefly on the mechanisms underlying our results, and we discuss the potential importance of lysis time variance in viral evolution.

Adaptive Landscape by Environment Interactions Dictate Evolutionary Dynamics in Models of Drug Resistance.

The adaptive landscape analogy has found practical use in recent years, as many have explored how their understanding can inform therapeutic strategies that subvert the evolution of drug resistance. A major barrier to applications of these concepts is a lack of detail concerning how the environment affects adaptive landscape topography, and consequently, the outcome of drug treatment. Here we combine empirical data, evolutionary theory, and computer simulations towards dissecting adaptive landscape by environment interactions for the evolution of drug resistance in two dimensions-drug concentration and drug type. We do so by studying the resistance mediated by Plasmodium falciparum dihydrofolate reductase (DHFR) to two related inhibitors-pyrimethamine and cycloguanil-across a breadth of drug concentrations. We first examine whether the adaptive landscapes for the two drugs are consistent with common definitions of cross-resistance. We then reconstruct all accessible pathways across the landscape, observing how their structure changes with drug environment. We offer a mechanism for non-linearity in the topography of accessible pathways by calculating of the interaction between mutation effects and drug environment, which reveals rampant patterns of epistasis. We then simulate evolution in several different drug environments to observe how these individual mutation effects (and patterns of epistasis) influence paths taken at evolutionary "forks in the road" that dictate adaptive dynamics in silico. In doing so, we reveal how classic metrics like the IC50 and minimal inhibitory concentration (MIC) are dubious proxies for understanding how evolution will occur across drug environments. We also consider how the findings reveal ambiguities in the cross-resistance concept, as subtle differences in adaptive landscape topography between otherwise equivalent drugs can drive drastically different evolutionary outcomes. Summarizing, we discuss the results with regards to their basic contribution to the study of empirical adaptive landscapes, and in terms of how they inform new models for the evolution of drug resistance.

Quantitative Description of a Protein Fitness Landscape Based on Molecular Features.

Understanding the driving forces behind protein evolution requires the ability to correlate the molecular impact of mutations with organismal fitness. To address this issue, we employ here metallo-ß-lactamases as a model system, which are Zn(II) dependent enzymes that mediate antibiotic resistance. We present a study of all the possible evolutionary pathways leading to a metallo-ß-lactamase variant optimized by directed evolution. By studying the activity, stability and Zn(II) binding capabilities of all mutants in the preferred evolutionary pathways, we show that this local fitness landscape is strongly conditioned by epistatic interactions arising from the pleiotropic effect of mutations in the different molecular features of the enzyme. Activity and stability assays in purified enzymes do not provide explanatory power. Instead, measurement of these molecular features in an environment resembling the native one provides an accurate description of the observed antibiotic resistance profile. We report that optimization of Zn(II) binding abilities of metallo-ß-lactamases during evolution is more critical than stabilization of the protein to enhance fitness. A global analysis of these parameters allows us to connect genotype with fitness based on quantitative biochemical and biophysical parameters.

The evolution of phenotypic correlations and "developmental memory".

Development introduces structured correlations among traits that may constrain or bias the distribution of phenotypes produced. Moreover, when suitable heritable variation exists, natural selection may alter such constraints and correlations, affecting the phenotypic variation available to subsequent selection. However, exactly how the distribution of phenotypes produced by complex developmental systems can be shaped by past selective environments is poorly understood. Here we investigate the evolution of a network of recurrent nonlinear ontogenetic interactions, such as a gene regulation network, in various selective scenarios. We find that evolved networks of this type can exhibit several phenomena that are familiar in cognitive learning systems. These include formation of a distributed associative memory that can "store" and "recall" multiple phenotypes that have been selected in the past, recreate complete adult phenotypic patterns accurately from partial or corrupted embryonic phenotypes, and "generalize" (by exploiting evolved developmental modules) to produce new combinations of phenotypic features. We show that these surprising behaviors follow from an equivalence between the action of natural selection on phenotypic correlations and associative learning, well-understood in the context of neural networks. This helps to explain how development facilitates the evolution of high-fitness phenotypes and how this ability changes over evolutionary time.

Should evolutionary geneticists worry about higher-order epistasis?

Natural selection drives evolving populations up the fitness landscape, the projection from nucleotide sequence space to organismal reproductive success. While it has long been appreciated that topographic complexities on fitness landscapes can arise only as a consequence of epistatic interactions between mutations, evolutionary genetics has mainly focused on epistasis between pairs of mutations. Here we propose a generalization to the classical population genetic treatment of pairwise epistasis that yields expressions for epistasis among arbitrary subsets of mutations of all orders (pairwise, three-way, etc.). Our approach reveals substantial higher-order epistasis in almost every published fitness landscape. Furthermore we demonstrate that higher-order epistasis is critically important in two systems we know best. We conclude that higher-order epistasis deserves empirical and theoretical attention from evolutionary geneticists.

Fisher's geometric model of adaptation meets the functional synthesis: data on pairwise epistasis for fitness yields insights into the shape and size of phenotype space.

The functional synthesis uses experimental methods from molecular biology, biochemistry and structural biology to decompose evolutionarily important mutations into their more proximal mechanistic determinants. However these methods are technically challenging and expensive. Noting strong formal parallels between R.A. Fisher's geometric model of adaptation and a recent model for the phenotypic basis of protein evolution, we sought to use the former to make inferences into the latter using data on pairwise fitness epistasis between mutations. We present an analytic framework for classifying pairs of mutations with respect to similarity of underlying mechanism on this basis, and also show that these data can yield an estimate of the number of mutationally labile phenotypes underlying fitness effects. We use computer simulations to explore the robustness of our approach to violations of analytic assumptions and analyze several recently published datasets. This work provides a theoretical complement to the functional synthesis as well as a novel test of Fisher's geometric model.

The interface of protein structure, protein biophysics, and molecular evolution.

Abstract The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.