The population genetics of adaptation: the adaptation of DNA sequences

I describe several patterns characterizing the genetics of adaptation at the DNA level. Following Gillespie (1983, 1984, 1991), I consider a population presently fixed for the ith best allele at a locus and study the sequential substitution of favorable mutations that results in fixation of the fittest DNA sequence locally available. Given a wild type sequence that is less than optimal, I derive the fitness rank of the next allele typically fixed by natural selection as well as the mean and variance of the jump in fitness that results when natural selection drives a substitution. Looking over the whole series of substitutions required to reach the best allele, I show that the mean fitness jumps occurring throughout an adaptive walk are constrained to a twofold window of values, assuming only that adaptation begins from a reasonably fit allele. I also show that the first substitution and the substitution of largest effect account for a large share of the total fitness increase during adaptation. I further show that the distribution of selection coefficients fixed throughout such an adaptive walk is exponential (ignoring mutations of small effect), a finding reminiscent of that seen in Fisher's geometric model of adaptation. Last, I show that adaptation by natural selection behaves in several respects as the average of two idealized forms of adaptation, perfect and random.     

A sharp minimum on the mean number of steps taken in adaptive walks

It was recently conjectured by H.A. Orr that from a random initial point on a random fitness landscape of alphabetic sequences with one-mutation adjacency, chosen from a larger class of landscapes, no adaptive algorithm can arrive at a local optimum in fewer than on average e-1 steps. Here, using an example in which the mean number of steps to a local optimum equals (A-1)/A, where A is the number of distinct "letters" in the "alphabet" from which sequences are constructed, it is shown that as originally stated, the conjecture does not hold. It is also demonstrated that (A-1)/A is a sharp minimum on the mean number of steps taken in adaptive walks on fitness landscapes of alphabetic sequences with one-mutation adjacency. As the example that achieves the new lower bound has properties that are not often considered as potential attributes for fitness landscapes-non-identically distributed fitnesses and negative fitness correlations for adjacent points-a weaker set of conditions characteristic of more commonly studied fitness landscapes is proposed under which the lower bound on the mean length of adaptive walks is conjectured to equal e-1.     

The distribution of fitness effects among beneficial mutations in Fisher's geometric model of adaptation

Recent models of adaptation at the DNA sequence level assume that the fitness effects of new mutations show certain statistical properties. In particular, these models assume that the distribution of fitness effects among new mutations is in the domain of attraction of the so-called Gumbel-type extreme value distribution. This assumption has not, however, been justified on any biological or theoretical grounds. In this note, I study random mutation in one of the simplest models of mutation and adaptation-Fisher's geometric model. I show that random mutation in this model yields a distribution of mutational effects that belongs to the Gumbel type. I also show that the distribution of fitness effects among rare beneficial mutations in Fisher's model is asymptotically exponential. I confirm these analytic findings with exact computer simulations. These results provide some support for the use of Gumbel-type extreme value theory in studies of adaptation and point to a surprising connection between recent phenotypic- and sequence-based models of adaptation: in both, the distribution of fitness effects among rare beneficial mutations is approximately exponential.     

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.     

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 square root of 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.     

Random oligonucleotide mutagenesis: application to a large protein coding sequence of a major histocompatibility complex class I gene, H-2DP.

We have used random oligonucleotide mutagenesis (or saturation mutagenesis) to create a library of point mutations in the alpha 1 protein domain of a Major Histocompatibility Complex (MHC) molecule. This protein domain is critical for T cell and B cell recognition. We altered the MHC class I H-2DP gene sequence such that synthetic mutant alpha 1 exons (270 bp of coding sequence), which contain mutations identified by sequence analysis, can replace the wild type alpha 1 exon. The synthetic exons were constructed from twelve overlapping oligonucleotides which contained an average of 1.3 random point mutations per intact exon. DNA sequence analysis of mutant alpha 1 exons has shown a point mutant distribution that fits a Poisson distribution, and thus emphasizes the utility of this mutagenesis technique to "scan" a large protein sequence for important mutations. We report our use of saturation mutagenesis to scan an entire exon of the H-2DP gene, a cassette strategy to replace the wild type alpha 1 exon with individual mutant alpha 1 exons, and analysis of mutant molecules expressed on the surface of transfected mouse L cells.     

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.     

King''s Formula for the Mutation Load with Epistasis

A formula by J. L. King gives the equilibrium mutation load as L = 2 sigma ui(1 - qi)/z - x) in which ui is the mutation rate to deleterious alleles at the ith locus, qi is the frequency of mutant alleles at this locus, x is the mean number of such mutant genes per individual before selection, z is the mean number in individuals eliminated by selection, and the summation is over all relevant loci. We show that this rule is inaccurate for intense selection and that a correct formula is L = 2 sigma ui(1 - qi) w/(z - x) = 2U w/(z - x) = 2U/(z - x + 2U) in which U is the mean number of new mutations per haploid genome in the population and w is the mean relative fitness before selection. If w/(z - x) less than 1/2, the mutation load is less than the Haldane value (U less than or equal to L less than or equal to 2U) and can be considerably less. In a diploid asexual population, however, with independent occurrence of mutations, L = 1 - e-2U regardless of the mode of selection.     

Stability and morphology comparisons of self-assembled virus-like particles from wild-type and mutant human hepatitis B virus capsid proteins

Instead of displaying the wild-type selective export of virions containing mature genomes, human hepatitis B virus (HBV) mutant I97L, changing from an isoleucine to a leucine at amino acid 97 of HBV core antigen (HBcAg), lost the high stringency of selectivity in genome maturity during virion export. To understand the structural basis of this so-called "immature secretion" phenomenon, we compared the stability and morphology of self-assembled capsid particles from the wild-type and mutant I97L HBV, in either full-length (HBcAg1-183) or truncated core protein contexts (HBcAg1-149 and HBcAg1-140). Using negative staining and electron microscopy, full-length particles appear as "thick-walled" spherical particles with little interior space, whereas truncated particles appear as "thin-walled" spherical particles with a much larger inner space. We found no significant differences in capsid stability between wild-type and mutant I97L particles under denaturing pH and temperature in either full-length or truncated core protein contexts. In general, HBV capsid particles (HBcAg1-183, HBcAg1-149, and HBcAg1-140) are very robust but will dissociate at pH 2 or 14, at temperatures higher than 75 degrees C, or in 0.1% sodium dodecyl sulfate (SDS). An unexpected upshift banding pattern of the SDS-treated full-length particles during agarose gel electrophoresis is most likely caused by disulfide bonding of the last cysteine of HBcAg. HBV capsids are known to exist in natural infection as dimorphic T=3 or T=4 icosahedral particles. No difference in the ratio between T=3 (78%) and T=4 particles (20.3%) are found between wild-type HBV and mutant I97L in the context of HBcAg1-140. In addition, we found no difference in capsid stability between T=3 and T=4 particles successfully separated by using a novel agarose gel electrophoresis procedure.     

Adaptation in the env gene of HIV-1 and evolutionary theories of disease progression

The exact mechanisms by which HIV overwhelms the immune system remain poorly understood. Among the several explanations of HIV disease progression, most include adaptation of the viral genome to the host environment as a causal factor. Therefore, quantifying the rate and pattern of adaptive evolution within infected patients is critical to understanding the development of AIDS. Using sequence data from infected individuals sampled at multiple time points, I estimate the within-host adaptation rate of the HIV-1 env gene for viral populations from 50 different patients. I find that, averaging across patients, one adaptive substitution occurs every 3.3 months. Also, one adaptive mutation is driven to a high frequency (>50% but <100%) every 2.5 months. Taken together, such adaptive events occur once every 25 viral generations, which is the fastest adaptation rate ever recorded for a single protein-coding gene. Within the entire env gene, I estimate that a majority ( approximately 55%) of both nonsynonymous substitutions and high-frequency polymorphisms are adaptive. Further, in the C2-V5 region of env, I find that patients with longer asymptomatic periods have virus populations with higher adaptation rates, corroborating the notion that a broad, strong immune response against epitopes in the env gene product leads to longer asymptomatic periods. I conclude by discussing the distribution of nonsynonymous changes over the env gene.     

In vivo molecular evolution reveals biophysical origins of organismal fitness

In nature, evolution occurs through the continuous adaptation of a population to its environment. At the molecular level, adaptive changes in protein sequence and expression impact organismal fitness and, consequently, dictate population dynamics. Here, we have used a "weak link" method to favor variations in one gene, allowing adaptation to thermostability to be studied in molecular detail as bacteria were grown continuously for approximately 1500 generations. Surprisingly, only six mutant alleles, representing less than 1% of the possible missense mutations, were observed, suggesting a highly constrained molecular landscape during protein evolution. The changes in organismal fitness were linked directly to incremental increases in enzyme stability and activity maxima and corresponded to the narrow temperature ranges where each mutant enjoyed success within the overall population. Thus, continuous evolution of a single gene permits a quantitative approach that extends from the phenotypes of the microbial populations to their underlying biophysical basis.     

The rate of adaptation in asexuals

I study the population genetics of adaptation in asexuals. I show that the rate of adaptive substitution in an asexual species or nonrecombining chromosome region is a bell-shaped function of the mutation rate: at some point, increasing the mutation rate decreases the rate of substitution. Curiously, the mutation rate that maximizes the rate of adaptation depends solely on the strength of selection against deleterious mutations. In particular, adaptation is fastest when the genomic rate of mutation, U, equals the harmonic mean of selection coefficients against deleterious mutations, where we assume that selection for favorable alleles is milder than that against deleterious ones. This simple result is independent of the shape of the distribution of effects among favorable and deleterious mutations, population size, and the action of clonal interference. In the course of this work, I derive an approximation to the probability of fixation of a favorable mutation in an asexual genome or nonrecombining chromosome region in which both favorable and deleterious mutations occur.     

Cerebellar complex spike firing is suitable to induce as well as to stabilize motor learning

BACKGROUND: Cerebellar Purkinje cells (PC) generate two responses: the simple spike (SS), with high firing rates (>100 Hz), and the complex spike (CS), characterized by conspicuously low discharge rates (1-2 Hz). Contemporary theories of cerebellar learning suggest that the CS discharge pattern encodes an error signal that drives changes in SS activity, ultimately related to motor behavior. This then predicts that CS will discharge in relation to the error and at random once the error has been nulled by the new behavior. RESULTS: We tested this hypothesis with saccadic adaptation in macaque monkeys as a model of cerebellar-dependent motor learning. During saccadic adaptation, error information unconsciously changes the endpoint of a saccade prompted by a visual target that shifts its final position during the saccade. We recorded CS from PC of the posterior vermis before, during, and after saccadic adaptation. In clear contradiction to the "error signal" concept, we found that CS occurred at random before adaptation onset, i.e., when the error was maximal, and built up to a specific saccade-related discharge profile during the course of adaptation. This profile became most pronounced at the end of adaptation, i.e., when the error had been nulled. CONCLUSIONS: We suggest that CS firing may underlie the stabilization of a learned motor behavior, rather than serving as an electrophysiological correlate of an error.     

Changes in human immunodeficiency virus type 1 Gag at positions L449 and P453 are linked to I50V protease mutants in vivo and cause reduction of sensitivity to amprenavir and improved viral fitness in vitro

Human immunodeficiency virus type 1 (HIV-1) Gag protease cleavage sites (CS) undergo sequence changes during the development of resistance to several protease inhibitors (PIs). We have analyzed the association of sequence variation at the p7/p1 and p1/p6 CS in conjunction with amprenavir (APV)-specific protease mutations following PI combination therapy with APV. Querying a central resistance data repository resulted in the detection of significant associations (P < 0.001) between the presence of APV protease signature mutations and Gag L449F (p1/p6 LP1'F) and P453L (p1/p6 PP5'L) CS changes. In population-based sequence analyses the I50V mutant was invariably linked to either L449F or P453L. Clonal analysis revealed that both CS mutations were never present in the same genome. Sequential plasma samples from one patient revealed a transition from I50V M46L P453L viruses at early time points to I50V M46I L449F viruses in later samples. Various combinations of the protease and Gag mutations were introduced into the HXB2 laboratory strain of HIV-1. In both single- and multiple-cycle assay systems and in the context of I50V, the L449F and P453L changes consistently increased the 50% inhibitory concentration of APV, while the CS changes alone had no measurable effect on inhibitor sensitivity. The decreased in vitro fitness of the I50V mutant was only partially improved by addition of either CS change (I50V M46I L449F mutant replicative capacity approximately 16% of that of wild-type virus). Western blot analysis of Pr55 Gag precursor cleavage products from infected-cell cultures indicated accumulation of uncleaved Gag p1-p6 in all I50V viruses without coexisting CS changes. Purified I50V protease catalyzed cleavage of decapeptides incorporating the L449F or P453L change 10-fold and 22-fold more efficiently than cleavage of the wild-type substrate, respectively. HIV-1 protease CS changes are selected during PI therapy and can have effects on both viral fitness and phenotypic resistance to PIs.     

Energy landscape of k-point mutants of an RNA molecule

MOTIVATION: A k-point mutant of a given RNA sequence s = s(1), ..., s(n) is an RNA sequence s' = s'(1),..., s'(n) obtained by mutating exactly k-positions in s; i.e. Hamming distance between s and s' equals k. To understand the effect of pointwise mutation in RNA, we consider the distribution of energies of all secondary structures of k-point mutants of a given RNA sequence. RESULTS: Here we describe a novel algorithm to compute the mean and standard deviation of energies of all secondary structures of k-point mutants of a given RNA sequence. We then focus on the tail of the energy distribution and compute, using the algorithm AMSAG, the k-superoptimal structure; i.e. the secondary structure of a < or =k-point mutant having least free energy over all secondary structures of all k'-point mutants of a given RNA sequence, for k' < or = k. Evidence is presented that the k-superoptimal secondary structure is often closer, as measured by base pair distance and two additional distance measures, to the secondary structure derived by comparative sequence analysis than that derived by the Zuker minimum free energy structure of the original (wild type or unmutated) RNA.     

Side‐chain interactions in the regulatory domain of human glutamate dehydrogenase determine basal activity and regulation

Glutamate Dehydrogenase (GDH) is central to the metabolism of glutamate, a major excitatory transmitter in mammalian central nervous system (CNS). hGDH1 is activated by ADP and L‐leucine and powerfully inhibited by GTP. Besides this housekeeping hGDH1, duplication led to an hGDH2 isoform that is expressed in the human brain dissociating its function from GTP control. The novel enzyme has reduced basal activity (4–6% of capacity) while remaining remarkably responsive to ADP/L‐leucine activation. While the molecular basis of this evolutionary adaptation remains unclear, substitution of Ser for Arg443 in hGDH1 is shown to diminish basal activity (< 2% of capacity) and abrogate L‐leucine activation. To explore whether the Arg443Ser mutation disrupts hydrogen bonding between Arg443 and Ser409 of adjacent monomers in the regulatory domain (‘antenna’), we replaced Ser409 by Arg or Asp in hGDH1. The Ser409Arg‐1 change essentially replicated the Arg443Ser‐1 mutation effects. Molecular dynamics simulation predicted that Ser409 and Arg443 of neighboring monomers come in close proximity in the open conformation and that introduction of Ser443‐1 or Arg409‐1 causes them to separate with the swap mutation (Arg409/Ser443) reinstating their proximity. A swapped Ser409Arg/Arg443Ser‐1 mutant protein, obtained in recombinant form, regained most of the wild‐type hGDH1 properties. Also, when Ser443 was replaced by Arg443 in hGDH2 (as occurs in hGDH1), the Ser443Arg‐2 mutant acquired most of the hGDH1 properties. Hence, side‐chain interactions between 409 and 443 positions in the ‘antenna’ region of hGDHs are crucial for basal catalytic activity, allosteric regulation, and relative resistance to thermal inactivation.

     

An assessment of the spatial scale of local adaptation in brown trout (Salmo trutta L.): footprints of selection at microsatellite DNA loci

Local adaptation is considered a paradigm in studies of salmonid fish populations. Yet, little is known about the geographical scale of local adaptation. Is adaptive divergence primarily evident at the scale of regions or individual populations? Also, many salmonid populations are subject to spawning intrusion by farmed conspecifics that experience selection regimes fundamentally different from wild populations. This prompts the question if adaptive differences between wild populations and hatchery strains are more pronounced than between different wild populations? We addressed these issues by analyzing variation at 74 microsatellite loci (including anonymous and expressed sequence tag- and quantitative trait locus-linked markers) in 15 anadromous wild brown trout (Salmo trutta L.) populations, representing five geographical regions, along with two lake populations and two hatchery strains used for stocking some of the populations. F_ST-based outlier tests revealed more outlier loci between different geographical regions separated by 522±228 km (mean±s.d.) than between populations within regions separated by 117±79 km (mean±s.d.). A significant association between geographical distance and number of outliers between regions was evident. There was no evidence for more outliers in comparisons involving hatchery trout, but the loci under putative selection generally were not the same as those found to be outliers between wild populations. Our study supports the notion of local adaption being increasingly important at the scale of regions as compared with individual populations, and suggests that loci involved in adaptation to captive environments are not necessarily the same as those involved in adaptive divergence among wild populations.     

基于MaxEnt模型西南地区高山植被对气候变化的响应评估

采用1∶100万的中国植被类型图以及19个气候环境变量数据,基于最大熵(MaxEnt)算法和ArcGIS空间分析模块构建西南地区高山植被地理分布的气候适宜性预测模型,模拟其在基准期(1960—2000年)和不同气候情景下(A2、A1B和B1)的气候适宜性分布格局,并评价其对气候变化的适应性。结果表明:MaxEnt模型分析研究区高山植被地理分布气候适宜性的适用性非常高(AUC=0.93);最暖月均温、最湿季均温、最冷月均温等温度变量是限制其地理分布的主要气候因子;研究区高山植被地理分布的气候适宜区主要集中在西藏自治区、青海省、四川省西部及云南省西北部的部分地区;完全适宜、中度适宜、轻度适宜、不适宜的面积所占总面积比例约为1∶1∶2∶5;1960—2050年研究区高山植被潜在地理分布的气候适宜性面积有不同定程度的减少;未来3种气候变化情景下高山植被地理分布对气候变化的适应性分布格局基本一致,均为不适应区所占总面积比例较大;伴随气候变化,研究区高山植被的适应性减弱,体现在其潜在地理分布对气候变化的适应区分布范围减少;海拔5000—5500m适应性较强,适应区所占面积比例最大(53%左右);3500—4500m适应性最弱,适应区所占面积比例最小(5%左右)。     

RNA viruses as complex adaptive systems

RNA viruses have high mutation rates and so their populations exist as dynamic and complex mutant distributions. It has been consistently observed that when challenged with a new environment, viral populations adapt following hyperbolic-like kinetics: adaptation is initially very rapid, but then slows down as fitness reaches an asymptotic value. These adaptive dynamics have been explained in terms of populations moving towards the top of peaks on rugged fitness landscapes. Fitness fluctuations of varying magnitude are observed during adaptation. Often the presence of fluctuations in the evolution of physical systems indicates some form of self-organization, or where many components of the system are simultaneously involved. Here we analyze data from several in vitro evolution experiments carried out with vesicular stomatitis virus (VSV) looking for the signature of criticality and scaling. Long-range fitness correlations have been detected during the adaptive process. We also found that the magnitude of fitness fluctuations, far from being trivial, conform to a Weibull probability distribution function, suggesting that viral adaptation belongs to a broad category of phenomena previously documented in other fields and related with emergence.