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Claus O Wilke

Publications and source records attributed to Claus O Wilke.

At least 19 recordsLinked to original sources
PubMed2024

A computational model for bacteriophage ϕX174 gene expression.

Bacteriophage ϕX174 has been widely used as a model organism to study fundamental processes in molecular biology. However, several aspects of ϕX174 gene regulation are not fully resolved. Here we construct a computational model for ϕX174 and use the model to study gene regulation during the phage infection cycle. We estimate the relative strengths of transcription regulatory elements (promoters and terminators) by fitting the model to transcriptomics data. We show that the specific arrangement of a promoter followed immediately by a terminator, which occurs naturally in the ϕX174 genome, poses a parameter identifiability problem for the model, since the activity of one element can be partially compensated for by the other. We also simulate ϕX174 gene expression with two additional, putative transcription regulatory elements that have been proposed in prior studies. We find that the activities of these putative elements are estimated to be weak, and that variation in ϕX174 transcript abundances can be adequately explained without them. Overall, our work demonstrates that ϕX174 gene regulation is well described by the canonical set of promoters and terminators widely used in the literature.

Gene Expression Regulation, Viral↗
PubMed2006

Thermodynamics of neutral protein evolution.

Naturally evolving proteins gradually accumulate mutations while continuing to fold to stable structures. This process of neutral evolution is an important mode of genetic change and forms the basis for the molecular clock. We present a mathematical theory that predicts the number of accumulated mutations, the index of dispersion, and the distribution of stabilities in an evolving protein population from knowledge of the stability effects (delta deltaG values) for single mutations. Our theory quantitatively describes how neutral evolution leads to marginally stable proteins and provides formulas for calculating how fluctuations in stability can overdisperse the molecular clock. It also shows that the structural influences on the rate of sequence evolution observed in earlier simulations can be calculated using just the single-mutation delta deltaG values. We consider both the case when the product of the population size and mutation rate is small and the case when this product is large, and show that in the latter case the proteins evolve excess mutational robustness that is manifested by extra stability and an increase in the rate of sequence evolution. All our theoretical predictions are confirmed by simulations with lattice proteins. Our work provides a mathematical foundation for understanding how protein biophysics shapes the process of evolution.

Computer Simulation↗
PubMed2006

Selection for mutational robustness in finite populations.

We investigate the evolutionary dynamics of a finite population of RNA sequences replicating on a neutral network. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive evolution, such as increase of mean fitness over time and punctuated-equilibrium transitions, after initial mutation-selection balance has been reached. We find that a product of population size and mutation rate of approximately 30 or larger is sufficient to generate selection pressure for mutational robustness, even if the population size is orders of magnitude smaller than the neutral network on which the population resides. Our results show that quasispecies effects and neutral drift can occur concurrently, and that the relative importance of each is determined by the product of population size and mutation rate.

Animals↗
PubMed2006

Structural determinants of the rate of protein evolution in yeast.

We investigate how a protein's structure influences the rate at which its sequence evolves. Our basic hypothesis is that proteins with highly designable structures (structures that are encoded by many sequences) will evolve more rapidly. Recent theoretical advances argue that structures with a higher density of interresidue contacts are more designable, and we show that high contact density is correlated with an increased rate of sequence evolution in yeast. In addition, we investigate the correlations between the rate of sequence evolution and several other structural descriptors, carefully controlling for the strong effect of expression level on evolutionary rate. Overall, we find that the structural descriptors that we consider appear to explain roughly 10% of the variation in rates of protein evolution in yeast. We also show that despite the well-known trend for buried residues to be more conserved, proteins with a higher fraction of buried residues, nonetheless, tend to evolve their sequences more rapidly. We suggest that this effect is due to the increased designability of structures with more buried residues. Our results provide evidence that protein structure plays an important role in shaping the rate of sequence evolution and provide evidence to support recent theoretical advances linking structural designability to contact density.

Analysis of Variance↗
PubMed2006

Population genetics of translational robustness.

Recent work has shown that expression level is the main predictor of a gene's evolutionary rate and that more highly expressed genes evolve slower. A possible explanation for this observation is selection for proteins that fold properly despite mistranslation, in short selection for translational robustness. Translational robustness leads to the somewhat paradoxical prediction that highly expressed genes are extremely tolerant to missense substitutions but nevertheless evolve very slowly. Here, we study a simple theoretical model of translational robustness that allows us to gain analytic insight into how this paradoxical behavior arises.

Evolution, Molecular↗
PubMed2006

Residual human immunodeficiency virus type 1 viremia in some patients on antiretroviral therapy is dominated by a small number of invariant clones rarely found in circulating CD4+ T cells.

Antiretroviral therapy can reduce human immunodeficiency virus type 1 (HIV-1) viremia to below the detection limit of ultrasensitive clinical assays (50 copies of HIV-1 RNA/ml). However, latent HIV-1 persists in resting CD4+ T cells, and low residual levels of free virus are found in the plasma. Limited characterization of this residual viremia has been done because of the low number of virions per sample. Using intensive sampling, we analyzed residual viremia and compared these viruses to latent proviruses in resting CD4+ T cells in peripheral blood. For each patient, we found some viruses in the plasma that were identical to viruses in resting CD4+ T cells by pol gene sequencing. However, in a majority of patients, the most common viruses in the plasma were rarely found in resting CD4+ T cells even when the resting cell compartment was analyzed with assays that detect replication-competent viruses. Despite the large diversity of pol sequences in resting CD4+ T cells, the residual viremia was dominated by a homogeneous population of viruses with identical pol sequences. In the most extensively studied case, a predominant plasma sequence was also found in analysis of the env gene, and linkage by long-distance reverse transcriptase PCR established that these predominant plasma sequences represented a single predominant plasma virus clone. The predominant plasma clones were released for months to years without evident sequence change. Thus, in some patients on antiretroviral therapy, the major mechanism for residual viremia involves prolonged production of a small number of viral clones without evident evolution, possibly by cells other than circulating CD4+ T cells. The sequences have been deposited in GenBank. The accession numbers are DQ 391282 to DQ 391351 (for env) and DQ 391352 to DQ 392955 (for RT).

Antiretroviral Therapy, Highly Active↗
PubMed2005

Tradeoff between short-term and long-term adaptation in a changing environment.

We investigate the competition dynamics of two microbial or viral strains that live in an environment that switches periodically between two states. One of the strains is adapted to the long-term environment, but pays a short-term cost, while the other is adapted to the short-term environment and pays a cost in the long term. We explore the tradeoff between these alternative strategies in extensive numerical simulations and present a simple analytic model that can predict the outcome of these competitions as a function of the mutation rate and the time scale of the environmental changes. Our model is relevant for arboviruses, which alternate between different host species on a regular basis.

Adaptation, Physiological↗
PubMed2005

A single determinant dominates the rate of yeast protein evolution.

A gene's rate of sequence evolution is among the most fundamental evolutionary quantities in common use, but what determines evolutionary rates has remained unclear. Here, we carry out the first combined analysis of seven predictors (gene expression level, dispensability, protein abundance, codon adaptation index, gene length, number of protein-protein interactions, and the gene's centrality in the interaction network) previously reported to have independent influences on protein evolutionary rates. Strikingly, our analysis reveals a single dominant variable linked to the number of translation events which explains 40-fold more variation in evolutionary rate than any other, suggesting that protein evolutionary rate has a single major determinant among the seven predictors. The dominant variable explains nearly half the variation in the rate of synonymous and protein evolution. We show that the two most commonly used methods to disentangle the determinants of evolutionary rate, partial correlation analysis and ordinary multivariate regression, produce misleading or spurious results when applied to noisy biological data. We overcome these difficulties by employing principal component regression, a multivariate regression of evolutionary rate against the principal components of the predictor variables. Our results support the hypothesis that translational selection governs the rate of synonymous and protein sequence evolution in yeast.

Amino Acid Substitution↗
PubMed2005

Why highly expressed proteins evolve slowly.

Much recent work has explored molecular and population-genetic constraints on the rate of protein sequence evolution. The best predictor of evolutionary rate is expression level, for reasons that have remained unexplained. Here, we hypothesize that selection to reduce the burden of protein misfolding will favor protein sequences with increased robustness to translational missense errors. Pressure for translational robustness increases with expression level and constrains sequence evolution. Using several sequenced yeast genomes, global expression and protein abundance data, and sets of paralogs traceable to an ancient whole-genome duplication in yeast, we rule out several confounding effects and show that expression level explains roughly half the variation in Saccharomyces cerevisiae protein evolutionary rates. We examine causes for expression's dominant role and find that genome-wide tests favor the translational robustness explanation over existing hypotheses that invoke constraints on function or translational efficiency. Our results suggest that proteins evolve at rates largely unrelated to their functions and can explain why highly expressed proteins evolve slowly across the tree of life.

Computational Biology↗
PubMed2005

Predicting the tolerance of proteins to random amino acid substitution.

We have recently proposed a thermodynamic model that predicts the tolerance of proteins to random amino acid substitutions. Here we test this model against extensive simulations with compact lattice proteins, and find that the overall performance of the model is very good. We also derive an approximate analytic expression for the fraction of mutant proteins that fold stably to the native structure, Pf(m), as a function of the number of amino acid substitutions m, and present several methods to estimate the asymptotic behavior of Pf(m) for large m. We test the accuracy of all approximations against our simulation results, and find good overall agreement between the approximations and the simulation measurements.

Amino Acid Sequence↗
PubMed2005

Quasispecies theory in the context of population genetics.

BACKGROUND: A number of recent papers have cast doubt on the applicability of the quasispecies concept to virus evolution, and have argued that population genetics is a more appropriate framework to describe virus evolution than quasispecies theory. RESULTS: I review the pertinent literature, and demonstrate for a number of cases that the quasispecies concept is equivalent to the concept of mutation-selection balance developed in population genetics, and that there is no disagreement between the population genetics of haploid, asexually-replicating organisms and quasispecies theory. CONCLUSION: Since quasispecies theory and mutation-selection balance are two sides of the same medal, the discussion about which is more appropriate to describe virus evolution is moot. In future work on virus evolution, we would do good to focus on the important questions, such as whether we can develop accurate, quantitative models of virus evolution, and to leave aside discussions about the relative merits of perfectly equivalent concepts.

Biological Evolution↗
PubMed2005

On the conservative nature of intragenic recombination.

Intragenic recombination rapidly creates protein sequence diversity compared with random mutation, but little is known about the relative effects of recombination and mutation on protein function. Here, we compare recombination of the distantly related beta-lactamases PSE-4 and TEM-1 to mutation of PSE-4. We show that, among beta-lactamase variants containing the same number of amino acid substitutions, variants created by recombination retain function with a significantly higher probability than those generated by random mutagenesis. We present a simple model that accurately captures the differing effects of mutation and recombination in real and simulated proteins with only four parameters: (i) the amino acid sequence distance between parents, (ii) the number of substitutions, (iii) the average probability that random substitutions will preserve function, and (iv) the average probability that substitutions generated by recombination will preserve function. Our results expose a fundamental functional enrichment in regions of protein sequence space accessible by recombination and provide a framework for evaluating whether the relative rates of mutation and recombination observed in nature reflect the underlying imbalance in their effects on protein function.

Evolution, Molecular↗
PubMed2005

Thermodynamic prediction of protein neutrality.

We present a simple theory that uses thermodynamic parameters to predict the probability that a protein retains the wild-type structure after one or more random amino acid substitutions. Our theory predicts that for large numbers of substitutions the probability that a protein retains its structure will decline exponentially with the number of substitutions, with the severity of this decline determined by properties of the structure. Our theory also predicts that a protein can gain extra robustness to the first few substitutions by increasing its thermodynamic stability. We validate our theory with simulations on lattice protein models and by showing that it quantitatively predicts previously published experimental measurements on subtilisin and our own measurements on variants of TEM1 beta-lactamase. Our work unifies observations about the clustering of functional proteins in sequence space, and provides a basis for interpreting the response of proteins to substitutions in protein engineering applications.

Amino Acid Substitution↗
PubMed2004

Molecular clock in neutral protein evolution.

BACKGROUND: A frequent observation in molecular evolution is that amino-acid substitution rates show an index of dispersion (that is, ratio of variance to mean) substantially larger than one. This observation has been termed the overdispersed molecular clock. On the basis of in silico protein-evolution experiments, Bastolla and coworkers recently proposed an explanation for this observation: Proteins drift in neutral space, and can temporarily get trapped in regions of substantially reduced neutrality. In these regions, substitution rates are suppressed, which results in an overall substitution process that is not Poissonian. However, the simulation method of Bastolla et al. is representative only for cases in which the product of mutation rate micro and population size Ne is small. How the substitution process behaves when micro Ne is large is not known. RESULTS: Here, I study the behavior of the molecular clock in in silico protein evolution as a function of mutation rate and population size. I find that the index of dispersion decays with increasing micro Ne, and approaches 1 for large micro Ne. This observation can be explained with the selective pressure for mutational robustness, which is effective when micro Ne is large. This pressure keeps the population out of low-neutrality traps, and thus steadies the ticking of the molecular clock. CONCLUSIONS: The molecular clock in neutral protein evolution can fall into two distinct regimes, a strongly overdispersed one for small micro Ne, and a mostly Poissonian one for large micro Ne. The former is relevant for the majority of organisms in the plant and animal kingdom, and the latter may be relevant for RNA viruses.

Amino Acid Substitution↗
PubMed2004

Adaptive radiation from resource competition in digital organisms.

Species richness often peaks at intermediate productivity and decreases as resources become more or less abundant. The mechanisms that produce this pattern are not completely known, but several previous studies have suggested environmental heterogeneity as a cause. In experiments with evolving digital organisms and populations of fixed size, maximum species richness emerges at intermediate productivity, even in a spatially homogeneous environment, owing to frequency-dependent selection to exploit an influx of mixed resources. A diverse pool of limiting resources is sufficient to cause adaptive radiation, which is manifest by the origin and maintenance of phenotypically and phylogenetically distinct groups of organisms.

Adaptation, Biological↗
PubMed2004

Stability and the evolvability of function in a model protein.

Functional proteins must fold with some minimal stability to a structure that can perform a biochemical task. Here we use a simple model to investigate the relationship between the stability requirement and the capacity of a protein to evolve the function of binding to a ligand. Although our model contains no built-in tradeoff between stability and function, proteins evolved function more efficiently when the stability requirement was relaxed. Proteins with both high stability and high function evolved more efficiently when the stability requirement was gradually increased than when there was constant selection for high stability. These results show that in our model, the evolution of function is enhanced by allowing proteins to explore sequences corresponding to marginally stable structures, and that it is easier to improve stability while maintaining high function than to improve function while maintaining high stability. Our model also demonstrates that even in the absence of a fundamental biophysical tradeoff between stability and function, the speed with which function can evolve is limited by the stability requirement imposed on the protein.

Biophysics↗
PubMed2004

Replication at periodically changing multiplicity of infection promotes stable coexistence of competing viral populations.

RNA viruses are widely used to study evolution experimentally. Many standard protocols of virus propagation and competition are done at nominally low multiplicity of infection (m.o.i.), but lead during one passage to two or more rounds of infection, of which the later ones are at high m.o.i. Here, we develop a model of the competition between wild type (wt) and a mutant under a regime of alternating m.o.i. We assume that the mutant is deleterious when it infects cells on its own, but derives a selective advantage when rare and coinfecting with wt, because it can profit from superior protein products created by the wt. We find that, under these assumptions, replication at alternating low and high m.o.i. may lead to the stable coexistence of wt and mutant for a wide range of parameter settings. The predictions of our model are consistent with earlier observations of frequency-dependent selection in vesicular stomatitis virus and human immunodeficiency virus type 1. Our results suggest that frequency-dependent selection may be common in typical evolution experiments with viruses.

Cell Line↗