scholarly journals Effective potential reveals evolutionary trajectories in complex fitness landscapes

2019 ◽  
Author(s):  
Matteo Smerlak
Keyword(s):  
Effective Potential ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Coarse Graining ◽  
Fitness Landscapes ◽  
Coarse Grained ◽  
Mutational Robustness ◽  
Sequencing Technologies ◽  
Wide Range ◽  
Evolutionary Trajectories

AbstractGrowing efforts to measure fitness landscapes in molecular and microbial systems are premised on a tight relationship between landscape topography and evolutionary trajectories. This relationship, however, is far from being straightforward: depending on their mutation rate, Darwinian populations can climb the closest fitness peak (survival of the fittest), settle in lower regions with higher mutational robustness (survival of the flattest), or fail to adapt altogether (error catastrophes). These bifurcations highlight that evolution does not necessarily drive populations “from lower peak to higher peak”, as Wright imagined. The problem therefore remains: how exactly does a complex landscape topography constrain evolution, and can we predict where it will go next? Here I introduce a generalization of quasispecies theory which identifies metastable evolutionary states as minima of an effective potential. From this representation I derive a coarse-grained, Markov state model of evolution, which in turn forms a basis for evolutionary predictions across a wide range of mutation rates. Because the effective potential is related to the ground state of a quantum Hamiltonian, my approach could stimulate fruitful interactions between evolutionary dynamics and quantum many-body theory.SIGNIFICANCE STATEMENTThe course of evolution is determined by the relationship between heritable types and their adaptive values, the fitness landscape. Thanks to the explosive development of sequencing technologies, fitness landscapes have now been measured in a diversity of systems from molecules to micro-organisms. How can we turn these data into evolutionary predictions? I show that preferred evolutionary trajectories are revealed when the effects of selection and mutations are blended in a single effective evolutionary force. With this reformulation, the dynamics of selection and mutation becomes Markovian, bringing a wealth of classical visualization and analysis tools to bear on evolutionary dynamics. Among these is a coarse-graining of evolutionary dynamics along its metastable states which greatly reduces the complexity of the prediction problem.

scholarly journals On the deformability of an empirical fitness landscape by microbial evolution

2018 ◽  
Vol 115 (44) ◽  
pp. 11286-11291 ◽  
Author(s):  
Djordje Bajić ◽  
Jean C. C. Vila ◽  
Zachary D. Blount ◽  
Alvaro Sánchez
Keyword(s):  
Environmental Effects ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Adaptive Dynamics ◽  
Microbial Evolution ◽  
Fitness Landscapes ◽  
Complex Genetics ◽  
Evolutionary Innovation ◽  
Genotype Space ◽  
Evolutionary Trajectories

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.

scholarly journals On the deformability of an empirical fitness landscape by microbial evolution

2018 ◽  
Author(s):  
Djordje Bajić ◽  
Jean C.C. Vila ◽  
Zachary D. Blount ◽  
Alvaro Sánchez
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Adaptive Dynamics ◽  
Microbial Evolution ◽  
Fitness Landscapes ◽  
Complex Genetics ◽  
Evolutionary Innovation ◽  
Genome Wide ◽  
Genotype Space ◽  
Evolutionary Trajectories

AbstractA 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. In spite of 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 E. coli. Deformability is quantified by the non-commutativity 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 leave these as a “legacy”, producing long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our methods and results provide the basis for an integration between adaptive and eco-evolutionary dynamics with complex genetics and genomics.

scholarly journals The distribution of epistasis on simple fitness landscapes

2018 ◽  
Author(s):  
Christelle Fraïsse ◽  
John J. Welch
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Null Model ◽  
Large Data ◽  
Fitness Landscapes ◽  
Mutational Bias ◽  
Data Set ◽  
Epistatic Interactions ◽  
Standing Variation ◽  
Mean And Variance

AbstractFitness interactions between mutations can influence a population’s evolution in many different ways. While epistatic effects are difficult to measure precisely, important information about the overall distribution is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effects sizes, mutational bias, and maladaptation of the wild-type. We illustrate our approach by reanalysing a large data set of mutant effects in a yeast snoRNA. Though characterized by some strong epistatic interactions, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have little effect 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 it is expected to vary in consistent ways between new mutations, standing variation, and fixed mutations.

scholarly journals A scaled MP-PIC method for bubbling fluidization

2021 ◽  
Author(s):  
Xing Zhao ◽  
Yong Jiang ◽  
Fei Li ◽  
Wei Wang
Keyword(s):  
Fluidized Beds ◽  
Volume Fraction ◽  
Phase Particle ◽  
Scaling Law ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Particle In Cell ◽  
Wide Range ◽  
Pic Method ◽  
Multi Phase

Coarse-grained methods have been widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method, and validated in the simulation of two bubbling fluidized beds. The simulation result shows this scaled MP-PIC can reduce the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios. In future, we expect that a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will further improve the performance of coarse-grained modeling in simulation of fluidized beds.

scholarly journals The distribution of epistasis on simple fitness landscapes

2019 ◽  
Vol 15 (4) ◽  
pp. 20180881 ◽  
Author(s):  
Christelle Fraïsse ◽  
John J. Welch
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Null Model ◽  
Fitness Landscapes ◽  
Mutational Bias ◽  
Variable Effect ◽  
Epistatic Effects ◽  
Standing Variation ◽  
Mean And Variance ◽  
Nucleolar Rna

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 determinants of mutational robustness in a viral molecular fitness landscape

2017 ◽  
Author(s):  
Manasi A. Pethe ◽  
Aliza B. Rubenstein ◽  
Dmitri Zorine ◽  
Sagar D. Khare
Keyword(s):  
Fitness Landscape ◽  
Rna Virus ◽  
Fitness Landscapes ◽  
Viral Fitness ◽  
Mutational Robustness ◽  
Hcv Protease ◽  
Viral Polyprotein ◽  
Biophysical Interactions ◽  
Proteins And Peptides

Biophysical interactions between proteins and peptides are key determinants of genotype-fitness landscapes, but an understanding of how molecular structure and residue-level energetics at protein-peptide interfaces shape functional landscapes remains elusive. Combining information from yeast-based library screening, next-generation sequencing and structure-based modeling, we report comprehensive sequence-energetics-function mapping of the specificity landscape of the Hepatitis C Virus (HCV) NS3/4A protease, whose function — site-specific cleavages of the viral polyprotein — is a key determinant of viral fitness. We elucidate the cleavability of 3.2 million substrate variants by the HCV protease and find extensive clustering of cleavable and uncleavable motifs in sequence space indicating mutational robustness, and thereby providing a plausible molecular mechanism to buffer the effects of low replicative fidelity of this RNA virus. Specificity landscapes of known drug-resistant variants are similarly clustered. Our results highlight the key and constraining role of molecular-level energetics in shaping plateau-like fitness landscapes from quasispecies theory.

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

2018 ◽  
Author(s):  
Atish Agarwala ◽  
Daniel S. Fisher
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Broad Class ◽  
Fitness Landscapes ◽  
High Dimensional ◽  
General Function ◽  
Long Distance ◽  
Future Evolution ◽  
Adaptive Mutations ◽  
Adaptive Walks

AbstractThe 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.

scholarly journals The fitness landscape of the codon space across environments

2018 ◽  
Author(s):  
Inès Fragata ◽  
Sebastian Matuszewski ◽  
Mark A. Schmitz ◽  
Thomas Bataillon ◽  
Jeffrey D. Jensen ◽  
...  
Keyword(s):  
Amino Acid ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Fitness Landscapes ◽  
Synonymous Mutations ◽  
Landscape Studies ◽  
Fitness Effects ◽  
Bayesian Monte Carlo ◽  
The Relationship

AbstractFitness landscapes map the relationship between genotypes and fitness. However, most fitness landscape studies ignore the genetic architecture imposed by the codon table and thereby neglect the potential role of synonymous mutations. To quantify the fitness effects of synonymous mutations and their potential impact on adaptation on a fitness landscape, we use a new software based on Bayesian Monte Carlo Markov Chain methods and reestimate selection coefficients of all possible codon mutations across 9 amino-acid positions in Saccharomyces cerevisiae Hsp90 across 6 environments. We quantify the distribution of fitness effects of synonymous mutations and show that it is dominated by many mutations of small or no effect and few mutations of larger effect. We then compare the shape of the codon fitness landscape across amino-acid positions and environments, and quantify how the consideration of synonymous fitness effects changes the evolutionary dynamics on these fitness landscapes. Together these results highlight a possible role of synonymous mutations in adaptation and indicate the potential mis-inference when they are neglected in fitness landscape studies.

scholarly journals Fitness landscape analysis reveals that the wild type allele is sub-optimal and mutationally robust

2021 ◽  
Author(s):  
Tzahi Gabzi ◽  
Yitzhak Tzachi Pilpel ◽  
Tamar Friedlander
Keyword(s):  
Mutation Rate ◽  
Evolutionary Biology ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Mutation Rates ◽  
Wild Type Allele ◽  
Wild Type ◽  
Type Allele ◽  
Landscape Mapping ◽  
Evolutionary Trajectories

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. Models predict different evolutionary outcomes depending on mutation rates: high-fitness genotypes should dominate the population under low mutation rates and lower-fitness, mutationally robust (also called 'flat') genotypes - at higher mutation rates. Yet, so far, flat genotypes have been demonstrated in very few cases, particularly in viruses. The quantitative conditions for their emergence were studied only in simplified single-locus, two-peak landscapes. In particular, it is unclear whether within the same genome some genes can be flat while the remaining ones are fit. Here, we analyze a previously measured fitness landscape of a yeast tRNA gene. We found that the wild type allele is sub-optimal, but is mutationally robust ('flat'). Using computer simulations, we estimated the critical mutation rate in which transition from fit to flat allele should occur for a gene with such characteristics. We then used a scaling argument to extrapolate this critical mutation rate for a full genome, assuming the same mutation rate for all genes. Finally, we propose that while the majority of genes are still selected to be fittest, there are a few mutation hot-spots like the tRNA, for which the mutationally robust flat allele is favored by selection.

scholarly journals High-order epistasis in catalytic power of dihydrofolate reductase gives rise to a rugged fitness landscape in the presence of trimethoprim selection

2018 ◽  
Author(s):  
Yusuf Talha Tamer ◽  
Ilona K. Gaszek ◽  
Haleh Abdizadeh ◽  
Tugce Altinusak Batur ◽  
Kimberly Reynolds ◽  
...  
Keyword(s):  
Dihydrofolate Reductase ◽  
Biochemical Parameters ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Computational Study ◽  
Binding Pocket ◽  
Resistance Mechanisms ◽  
Fitness Landscapes ◽  
High Order ◽  
Catalytic Power

ABSTRACTEvolutionary fitness landscapes of certain antibiotic target enzymes have been comprehensively mapped showing strong high order epistasis between mutations, but understanding these effects at the biochemical and molecular levels remained open. Here, we carried out an extensive experimental and computational study to quantitatively understand the evolutionary dynamics of Escherichia coli dihydrofolate reductase (DHFR) enzyme in the presence of trimethoprim induced selection. Biochemical and structural characterization of resistance-conferring mutations targeting a total of ten residues spanning the substrate binding pocket of DHFR revealed distinct resistance mechanisms. Next, we experimentally measured biochemical parameters (Km, Ki, and kcat) for a mutant library carrying all possible combinations of six resistance-conferring DHFR mutations and quantified epistatic interactions between them. We found that the epistasis between DHFR mutations is high-order for catalytic power of DHFR (kcat and Km), but less prevalent for trimethoprim affinity (Ki). Taken together our data provide a concrete illustration of how epistatic coupling at the level of biochemical parameters can give rise to complex fitness landscapes, and suggest new strategies for developing mutant specific inhibitors.

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