Adaptive Walks Research Articles

Biomolecular information gained through in vitro evolution.

An in vitro evolution is a simplified Darwinian evolution in well-controlled surroundings. This evolution process can be modeled as a hill-climbing or adaptive walk on a fitness landscape in sequence space. The evolving molecular system gains at least two kinds of information originating from the converged sequences and the fitness increment of the evolving biopolymer as the adaptive walker. These two represent two aspects of the biomolecular information, its extent and its content, respectively. Here, we review studies related to formulation of the "content" and "extent" of biomolecular information. The two aspects are interconnected through physicochemical properties of the biopolymer, contrary to the case of conventional information, which seems to be independent of matter. The interconnection was analyzed based on the analogy between the evolution process and thermodynamics. The linear combination of the two by a temperature-like fluctuation factor resulted in a free-energy-like monotonically increasing function during the evolution process.

Exploring protein fitness landscapes by directed evolution

Directed evolution circumvents our profound ignorance of how a protein's sequence encodes its function by using iterative rounds of random mutation and artificial selection to discover new and useful proteins. Proteins can be tuned to adapt to new functions or environments by simple adaptive walks involving small numbers of mutations. Directed evolution studies have shown how rapidly some proteins can evolve under strong selection pressures and, because the entire 'fossil record' of evolutionary intermediates is available for detailed study, they have provided new insight into the relationship between sequence and function. Directed evolution has also shown how mutations that are functionally neutral can set the stage for further adaptation.

The Properties of Adaptive Walks in Evolving Populations of Fungus

Author SummaryAdaptation is one of the least understood processes in biology because it relies on beneficial mutations, which are often too rare to study. We developed a method to infer the number and size of beneficial mutations substituted during adaptation, a process called an adaptive walk, and used this to test predictions about the properties of adaptive walks in experimental populations of fungus. Our work shows that, in contrast to the gradualist view of adaptation dominant since the 1930s, adaptive walks tend to be fast and short, with beneficial mutations of large effect substituted first, followed by those of smaller effect.

AN ADAPTIVE WALK BY HUMAN IMMUNODEFICIENCY VIRUS TYPE 1 THROUGH A FLUCTUATING FITNESS LANDSCAPE

The mutational landscape model of adaptive sequence evolution has been used to explain an unexpected strong positive linear relationship between marginal fitness and mean site-specific amino acid frequency in the functionally important HIV-1 gp120 V3 protein region. The model predicts a positive linear relationship between the probability that a particular beneficial allele, among several, is the next to spread to fixation during an adaptive walk, its transition probability, and the allele's selection coefficient. Here, stochastic simulation is used to confirm the intuition that the linear relationship between transition probabilities and selection coefficients, predicted by the model, should, under fluctuating selection, produce a linear relationship between allele frequency, averaged across populations, and fitness. In addition, these relationships hold for the effective population size and mutation rate of HIV-1 and for the moderately strong selection observed for V3. A survey of the strength of mutation for diverse organisms suggests that these relationships may be widely applicable.

Grapham: Graphical models with adaptive random walk Metropolis algorithms

Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on graphical models for directed acyclic graphs. The implemented algorithms include the seminal Adaptive Metropolis algorithm adjusting the proposal covariance according to the history of the chain and a Metropolis algorithm adjusting the proposal scale based on the observed acceptance probability. Different variants of the algorithms allow one, for example, to use these two algorithms together, employ delayed rejection and adjust several parameters of the algorithms. The implemented Metropolis-within-Gibbs update allows arbitrary sampling blocks. The software is written in C and uses a simple extension language Lua in configuration.

The Genetics of Adaptation for Eight Microvirid Bacteriophages

Theories of adaptive molecular evolution have recently experienced significant expansion, and their predictions and assumptions have begun to be subjected to rigorous empirical testing. However, these theories focus largely on predicting the first event in adaptive evolution, the fixation of a single beneficial mutation. To address long-term adaptation it is necessary to include new assumptions, but empirical data are needed for guidance. To empirically characterize the general properties of adaptive walks, eight recently isolated relatives of the single-stranded DNA (ssDNA) bacteriophage φX174 (family Microviridae) were adapted to identical selective conditions. Three of the eight genotypes were adapted in replicate, for a total of 11 adaptive walks. We measured fitness improvement and identified the genetic changes underlying the observed adaptation. Nearly all phages were evolvable; nine of the 11 lineages showed a significant increase in fitness. However, fitness plateaued quickly, and adaptation was achieved through only three substitutions on average. Parallel evolution was rampant, both across replicates of the same genotype as well as across different genotypes, yet adaptation of replicates never proceeded through the exact same set of mutations. Despite this, final fitnesses did not vary significantly among replicates. Final fitnesses did vary significantly across genotypes but not across phylogenetic groupings of genotypes. A positive correlation was found between the number of substitutions in an adaptive walk and the magnitude of fitness improvement, but no correlation was found between starting and ending fitness. These results provide an empirical framework for future adaptation theory.

A Scalable Unbiased Sampling Method Based on Multi-Peer Adaptive Random Walk

PDF HTML阅读 XML下载 导出引用 引用提醒 基于自适应随机行走的可扩展无偏抽样方法 DOI: 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: Supported by the National Natural Science Foundation of China under Grant Nos.60873215, 60621003 (国家自然科学基金); theNational Basic Research Program of China under Grant No.2005CB321801 (国家重点基础研究发展计划(973)); the SpecializedResearch Fund for the Doctoral Program of Higher Education of China No.200899980003 (高等学校博士学科点专项科研基金); theFoundation for the Author of National Excellent Doctoral Dissertation of China under Grant No.200141 (高等学校全国优秀博士学位论文作者专项); the Graduate Research Innovation Fund of NUDT of China under Grant No.B080602 (国防科学技术大学优秀研究生创新资助) A Scalable Unbiased Sampling Method Based on Multi-Peer Adaptive Random Walk Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:针对非结构化P2P 系统中可扩展的快速无偏抽样问题,提出了一种基于多个peer 自适应随机行走的抽样方法SMARW.在该方法中,基于代理随机行走选择一组临时的peer 执行抽样过程,一次产生一组可调数目的抽样节点,提高了抽样速度,选择每次产生的抽样节点作为临时peer 进行新的抽样过程,这种简单的方法可以保证系统具有近似最优的系统负载均衡程度.同时,SMARW 利用自适应的分布式随机行走修正过程提高抽样过程的收敛速度.理论分析和模拟测试表明,SMARW 方法具有较高的无偏抽样能力以及近似最优的系统负载均衡程度. Abstract:To deal with the scalable and fast unbiased sampling problems in unstructured P2P systems, a sampling method based on multi-peer adaptive random walk (SMARW) is proposed. In the method, based on the multi-peerrandom walk process, a set of provisional peers are selected as agents which start the sampling processes, by whichthe sampling process is speeded up with receiving a set of tunable number samples each time; Meanwhile, afterreceiving new samples earlier agents are replaced with these new samples which repeat the sampling process. Withthis simple replacement, it can be guaranteed with high probability that the system can reach the optimal loadbalance; furthermore, SMARW adopts an adaptive distributed random walk adjustment process to increase theconvergence rate of the sampling process. A detailed theorical analysis and performance evaluation confirm thatSMARW has a high level of unbiased sampling and near-optimal load balancing capability. 参考文献 相似文献 引证文献

How Proteins Adapt: Lessons from Directed Evolution

Applying artificial selection to create new proteins has allowed us to explore fundamental processes of molecular evolution. These "directed evolution" experiments have shown that proteins can readily adapt to new functions or environments via simple adaptive walks involving small numbers of mutations. With the entire "fossil record" available for detailed study, these experiments have provided new insight into adaptive mechanisms and the effects of mutation and recombination. Directed evolution has also shown how mutations that are functionally neutral can set the stage for further adaptation. Watching adaptation in real time helps one to appreciate the power of the evolutionary design algorithm.

Butterfly speciation and the distribution of gene effect sizes fixed during adaptation

Mimicry has had a significant historical influence as a tractable system for studying adaptation and is known to play a role in speciation. Here, we discuss recent theoretical treatment of adaptive walks to local adaptive peaks and contrast this with the adaptive landscape of mimicry. Evolution of novel Müllerian mimicry patterns almost certainly involves substitution of a major mutation to provide an initial similarity to the model, such that major gene effects are expected to an even greater degree than for other adaptive traits. The likelihood of large adaptive peak shifts in mimicry evolution may therefore promote speciation. In addition, mimicry adaptive peaks are determined by the local abundance of particular patterns and may be more fluid than the case for other traits. It will therefore be of considerable interest to test empirically the distribution of effect sizes fixed during mimicry evolution. Here, we show the feasibility of this by presenting a preliminary quantitative trait locus (QTL) analysis of Heliconius colour patterns. This shows that a number of modifier loci of different effect sizes influence forewing band morphology. We also show multiple pleiotropic effects of major Heliconius patterning loci and discuss the likelihood of multiple substitutions at the same loci in pattern evolution, which would inflate the importance of major loci in QTL analysis of the gene effect sizes. Analyses such as these have the potential to uncover the genetic architecture of both within and between species adaptive differences.

Hierarchical distribution of ascending slopes, nearly neutral networks, highlands, and local optima at the dth order in an NK fitness landscape

We obtained several structural features of an NK fitness landscape by analytical approach. Particularly, we focused on spatial distributions of “ascending slopes”, “highlands”, “nearly neutral networks”, and “local optima” along the fitness coordinate W , from the viewpoint of adaptive walks with step-width d , where d is the number of mutated sites (Hamming distance) after a generation. The parameter k governs the degree of the ruggedness on the NK landscape, and we handled cases where k is moderate against the sequence length. From the foot up to the middle region on the landscape, many ascending slopes exist (high evolvability) and these slopes extend up near the “highland”, which is mathematically defined as the specific region W = W d * where the expectation of the fitness increment becomes zero. Denoting the standard deviation of the fitness change at W = W d * by SD * , we considered the existence of “nearly neutral networks”, which percolate in the fitness band between W - SD * and W + SD * . Our results suggest that the highland corresponds to a phase-transition threshold of the formation of the nearly neutral networks. Near or over the highland, “local optima at the dth order” appear drastically (low evolvability), where d means the radius of their basins. The value of W d * increases with d increasing. Then, as the fitness ( = altitude ) becomes higher, the basin size of the local optima increases. This leads to a conclusion that it is very hard or impossible for walkers with step-width d to reach near the global peak when d is a realistic large value: d = 1 –6, and suggests that the region over the middle in real landscapes may be considerably smooth with small k-values to maintain high evolvability.

A simple model of co-evolutionary dynamics caused by epistatic selection

Epistasis is the dependency of the effect of a mutation on the genetic background in which it occurs. Epistasis has been widely documented and implicated in the evolution of species barriers and the evolution of genetic architecture. Here we propose a simple model to formalize the idea that epistasis can also lead to co-evolutionary patterns in molecular evolution of interacting genes. This model epistasis is represented by the influence of one gene substitution on the fitness rank of the resident allele at another locus. We assume that increasing or decreasing fitness rank occur equally likely. In simulations we show that this form of epistasis leads to co-evolution in the sense that the length of an adaptive walk between interacting loci is highly correlated. This effect is caused by episodes of elevated rate of evolution in both loci simultaneously. We find that the influence of epistasis on these measures of co-evolutionary dynamics is relatively robust to the details of the model. The main factor influencing the correlation in evolutionary rates is the probability that a substitution will have an epistatic effect, but the strength of epistasis or the asymmetry of the initial fitness ranks of the alleles have only a minor effect. We suggest that covariance in rates of evolution among loci could be used to detect epistasis among loci.

Adaptive Walks Toward a Moving Optimum

We investigate how the dynamics and outcomes of adaptation by natural selection are affected by environmental stability by simulating adaptive walks in response to an environmental change of fixed magnitude but variable speed. Here we consider monomorphic lineages that adapt by the sequential fixation of beneficial mutations. This is modeled by selecting short RNA sequences for folding stability and secondary structure conservation at increasing temperatures. Using short RNA sequences allows us to describe adaptive outcomes in terms of genotype (sequence) and phenotype (secondary structure) and to follow the dynamics of fitness increase. We find that slower rates of environmental change affect the dynamics of adaptive walks by reducing the fitness effect of fixed beneficial mutations, as well as by increasing the range of time in which the substitutions of largest effect are likely to occur. In addition, adaptation to slower rates of environmental change results in fitter endpoints with fewer possible end phenotypes relative to lineages that adapt to a sudden change. This suggests that care should be taken when experiments using sudden environmental changes are used to make predictions about adaptive responses to gradual change.

Evolution of canalizing Boolean networks

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive walk, which allows us to explore the fitness landscape. Mutations change the connections and the functions of the nodes. Our fitness criterion is the robustness of the dynamical attractors against small perturbations. We find that with this fitness criterion the global maximum is always reached and that there is a huge neutral space of 100% fitness. Furthermore, in spite of having such a high degree of robustness, the evolved networks still share many features with "chaotic" networks.

Deterministic and stochastic regimes of asexual evolution on rugged fitness landscapes.

We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length L. The population evolves in a maximally rugged fitness landscape with a large number of local optima. We find that whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance d(eff) up to which the population can spread in genotype space. For d(eff) = L, the deterministic quasi-species theory operates while for d(eff) < 1, the evolution is completely stochastic. Between these two limiting cases, the dynamics are described by a local quasi-species theory below a crossover time T(x) while above T(x) the population gets trapped at a local fitness peak and manages to find a better peak via either stochastic tunneling or double mutations. In the stochastic regime d(eff) < 1, we identify two subregimes associated with clonal interference and uphill adaptive walks, respectively. We argue that our findings are relevant to the interpretation of evolution experiments with microbial populations.

Extracting characteristic properties of fitness landscape from in vitro molecular evolution: A case study on infectivity of fd phage to E.coli

We have developed a methodology for extracting characteristic properties of a fitness landscape of interest by analyzing fitness data on an in vitro molecular evolution. The in vitro evolution is required to be conducted as the following “adaptive walk”: a single parent sequence generates N mutant sequences as its offsprings, and the fittest individual among the N offsprings will become a new parent in the next generation. N is the library size of mutants to be screened in a single generation. Our theory of the adaptive walk on the “NK landscape” suggests the following: the adaptive walker starting from a random sequence climbs the landscape easily in an early stage, and then reaches a stationary phase in which the mutation-selection-random drift balance sets in. The stationary fitness value is nearly proportional to ln N . Our analysis is performed from the following points: (1) stationary fitness values, (2) time series of fitness in the transitional state, (3) mutant's fitness distribution, and (4) the strength of selection pressure. Applying our methodology, we analyzed experimental data on the in vitro evolution of a random polypeptide (139 amino acids) toward acquiring infectivity ( = ability to infect) of fd phage. As a result, we estimated that k is about 27 in this system, indicating that an arbitrary residue in a sequence is affected from other 23% residues. In this article, we demonstrated that the experimental data is consistent with our theoretical equations quantitatively, and that our methodology for extracting characteristic properties of a fitness landscape may be effective.

Experimental Rugged Fitness Landscape in Protein Sequence Space

The fitness landscape in sequence space determines the process of biomolecular evolution. To plot the fitness landscape of protein function, we carried out in vitro molecular evolution beginning with a defective fd phage carrying a random polypeptide of 139 amino acids in place of the g3p minor coat protein D2 domain, which is essential for phage infection. After 20 cycles of random substitution at sites 12–130 of the initial random polypeptide and selection for infectivity, the selected phage showed a 1.7×104-fold increase in infectivity, defined as the number of infected cells per ml of phage suspension. Fitness was defined as the logarithm of infectivity, and we analyzed (1) the dependence of stationary fitness on library size, which increased gradually, and (2) the time course of changes in fitness in transitional phases, based on an original theory regarding the evolutionary dynamics in Kauffman's n-k fitness landscape model. In the landscape model, single mutations at single sites among n sites affect the contribution of k other sites to fitness. Based on the results of these analyses, k was estimated to be 18–24. According to the estimated parameters, the landscape was plotted as a smooth surface up to a relative fitness of 0.4 of the global peak, whereas the landscape had a highly rugged surface with many local peaks above this relative fitness value. Based on the landscapes of these two different surfaces, it appears possible for adaptive walks with only random substitutions to climb with relative ease up to the middle region of the fitness landscape from any primordial or random sequence, whereas an enormous range of sequence diversity is required to climb further up the rugged surface above the middle region.

Mutation-Biased Adaptation in a Protein NK Model

Evolutionary trends responsible for systematic differences in genome and proteome composition have been attributed to GC:AT mutation bias in the context of neutral evolution or to selection acting on genome composition. A possibility that has been ignored, presumably because it is part of neither the Modern Synthesis nor the Neutral Theory, is that mutation may impose a directional bias on adaptation. This possibility is explored here with simulations of the effect of a GC:AT bias on amino acid composition during adaptive walks on an abstract protein fitness landscape called an "NK" model. The results indicate that adaptation does not preclude mutation-biased evolution. In the complete absence of neutral evolution, a modest GC:AT bias of realistic magnitude can displace the trajectory of adaptation in a mutationally favored direction, to such a degree that amino acid composition is biased substantially and persistently. Thus, mutational explanations for evolved patterns need not presuppose neutral evolution.

Properties of adaptive walks on uncorrelated landscapes under strong selection and weak mutation

We examine properties of adaptive walks on uncorrelated (i.e. random) fitness landscapes starting from moderately fit genotypes under strong selection weak mutation. As an extension of Orr's model for a single step in an adaptive walk under these conditions, we show that the fitness rank of the dominant genotype in a population after the fixation of a beneficial mutation is, on average, ( i + 6 ) / 4 , where i is the fitness rank of the starting genotype. This accounts for the change in rank due to acquiring a new set of single-mutation neighbors after fixing a new allele through natural selection. Under this scenario, adaptive walks can be modeled as a simple Markov chain on the space of possible fitness ranks with an absorbing state at i = 1 , from which no beneficial mutations are accessible. We find that these walks are typically short and are often completed in a single step when starting from a moderately fit genotype. As in Orr's original model, these results are insensitive to both the distribution of fitness effects and most biological details of the system under consideration.

THE POPULATION GENETICS OF ADAPTATION ON CORRELATED FITNESS LANDSCAPES: THE BLOCK MODEL

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.

THE POPULATION GENETICS OF ADAPTATION ON CORRELATED FITNESS LANDSCAPES: THE BLOCK MODEL

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.