Michael Lässig

Local graph alignment and motif search in biological networks

Interaction networks are of central importance in postgenomic molecular biology, with increasing amounts of data becoming available by high-throughput methods. Examples are gene regulatory networks or protein interaction maps. The main challenge in the analysis of these data is to read off biological functions from the topology of the network. Topological motifs, i.e., patterns occurring repeatedly at different positions in the network, have recently been identified as basic modules of molecular information processing. In this article, we discuss motifs derived from families of mutually similar but not necessarily identical patterns. We establish a statistical model for the occurrence of such motifs, from which we derive a scoring function for their statistical significance. Based on this scoring function, we develop a search algorithm for topological motifs called graph alignment, a procedure with some analogies to sequence alignment. The algorithm is applied to the gene regulation network of Escherichia coli.

Structure and evolution of protein interaction networks: a statistical model for link dynamics and gene duplications

BackgroundThe structure of molecular networks derives from dynamical processes on evolutionary time scales. For protein interaction networks, global statistical features of their structure can now be inferred consistently from several large-throughput datasets. Understanding the underlying evolutionary dynamics is crucial for discerning random parts of the network from biologically important properties shaped by natural selection.ResultsWe present a detailed statistical analysis of the protein interactions in Saccharomyces cerevisiae based on several large-throughput datasets. Protein pairs resulting from gene duplications are used as tracers into the evolutionary past of the network. From this analysis, we infer rate estimates for two key evolutionary processes shaping the network: (i) gene duplications and (ii) gain and loss of interactions through mutations in existing proteins, which are referred to as link dynamics. Importantly, the link dynamics is asymmetric, i.e., the evolutionary steps are mutations in just one of the binding parters. The link turnover is shown to be much faster than gene duplications. Both processes are assembled into an empirically grounded, quantitative model for the evolution of protein interaction networks.ConclusionsAccording to this model, the link dynamics is the dominant evolutionary force shaping the statistical structure of the network, while the slower gene duplication dynamics mainly affects its size. Specifically, the model predicts (i) a broad distribution of the connectivities (i.e., the number of binding partners of a protein) and (ii) correlations between the connectivities of interacting proteins, a specific consequence of the asymmetry of the link dynamics. Both features have been observed in the protein interaction network of S. cerevisiae.

Energy-dependent fitness: a quantitative model for the evolution of yeast transcription factor binding sites.

We present a genomewide cross-species analysis of regulation for broad-acting transcription factors in yeast. Our model for binding site evolution is founded on biophysics: the binding energy between transcription factor and site is a quantitative phenotype of regulatory function, and selection is given by a fitness landscape that depends on this phenotype. The model quantifies conservation, as well as loss and gain, of functional binding sites in a coherent way. Its predictions are supported by direct cross-species comparison between four yeast species. We find ubiquitous compensatory mutations within functional sites, such that the energy phenotype and the function of a site evolve in a significantly more constrained way than does its sequence. We also find evidence for substantial evolution of regulatory function involving point mutations as well as sequence insertions and deletions within binding sites. Genes lose their regulatory link to a given transcription factor at a rate similar to the neutral point mutation rate, from which we infer a moderate average fitness advantage of functional over nonfunctional sites. In a wider context, this study provides an example of inference of selection acting on a quantitative molecular trait.

Adaptive evolution of transcription factor binding sites

BackgroundThe regulation of a gene depends on the binding of transcription factors to specific sites located in the regulatory region of the gene. The generation of these binding sites and of cooperativity between them are essential building blocks in the evolution of complex regulatory networks. We study a theoretical model for the sequence evolution of binding sites by point mutations. The approach is based on biophysical models for the binding of transcription factors to DNA. Hence we derive empirically grounded fitness landscapes, which enter a population genetics model including mutations, genetic drift, and selection.ResultsWe show that the selection for factor binding generically leads to specific correlations between nucleotide frequencies at different positions of a binding site. We demonstrate the possibility of rapid adaptive evolution generating a new binding site for a given transcription factor by point mutations. The evolutionary time required is estimated in terms of the neutral (background) mutation rate, the selection coefficient, and the effective population size.ConclusionsThe efficiency of binding site formation is seen to depend on two joint conditions: the binding site motif must be short enough and the promoter region must be long enough. These constraints on promoter architecture are indeed seen in eukaryotic systems. Furthermore, we analyse the adaptive evolution of genetic switches and of signal integration through binding cooperativity between different sites. Experimental tests of this picture involving the statistics of polymorphisms and phylogenies of sites are discussed.

A predictive fitness model for influenza

The seasonal human influenza A/H3N2 virus undergoes rapid evolution, which produces significant year-to-year sequence turnover in the population of circulating strains. Adaptive mutations respond to human immune challenge and occur primarily in antigenic epitopes, the antibody-binding domains of the viral surface protein haemagglutinin. Here we develop a fitness model for haemagglutinin that predicts the evolution of the viral population from one year to the next. Two factors are shown to determine the fitness of a strain: adaptive epitope changes and deleterious mutations outside the epitopes. We infer both fitness components for the strains circulating in a given year, using population-genetic data of all previous strains. From fitness and frequency of each strain, we predict the frequency of its descendent strains in the following year. This fitness model maps the adaptive history of influenza A and suggests a principled method for vaccine selection. Our results call for a more comprehensive epidemiology of influenza and other fast-evolving pathogens that integrates antigenic phenotypes with other viral functions coupled by genetic linkage.

Cross-species analysis of biological networks by Bayesian alignment

Complex interactions between genes or proteins contribute a substantial part to phenotypic evolution. Here we develop an evolutionarily grounded method for the cross-species analysis of interaction networks by alignment, which maps bona fide functional relationships between genes in different organisms. Network alignment is based on a scoring function measuring mutual similarities between networks, taking into account their interaction patterns as well as sequence similarities between their nodes. High-scoring alignments and optimal alignment parameters are inferred by a systematic Bayesian analysis. We apply this method to analyze the evolution of coexpression networks between humans and mice. We find evidence for significant conservation of gene expression clusters and give network-based predictions of gene function. We discuss examples where cross-species functional relationships between genes do not concur with sequence similarity.

From fitness landscapes to seascapes: non-equilibrium dynamics of selection and adaptation

Evolution is a quest for innovation. Organisms adapt to changing natural selection by evolving new phenotypes. Can we read this dynamics in their genomes? Not every mutation under positive selection responds to a change in selection: beneficial changes also occur at evolutionary equilibrium, repairing previous deleterious changes and restoring existing functions. Adaptation, by contrast, is viewed here as a non-equilibrium phenomenon: the genomic response to time-dependent selection. Our approach extends the static concept of fitness landscapes to dynamic fitness seascapes. It shows that adaptation requires a surplus of beneficial substitutions over deleterious ones. Here, we focus on the evolution of yeast and Drosophila genomes, providing examples where adaptive evolution can and cannot be inferred, despite the presence of positive selection.

Correlated random networks

We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix c, and the relevant statistical ensembles are defined in terms of a partition function Z= summation operator exp([-betaH(c)]. The simplest cases are uncorrelated random networks such as the well-known Erdös-Rényi graphs. Here we study more general interactions H(c) which lead to correlations, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in optimized networks described by partition functions in the limit beta--> infinity. They are argued to be a crucial signature of evolutionary design in biological networks.

Fitness flux and ubiquity of adaptive evolution

Natural selection favors fitter variants in a population, but actual evolutionary processes may decrease fitness by mutations and genetic drift. How is the stochastic evolution of molecular biological systems shaped by natural selection? Here, we derive a theorem on the fitness flux in a population, defined as the selective effect of its genotype frequency changes. The fitness-flux theorem generalizes Fisher’s fundamental theorem of natural selection to evolutionary processes including mutations, genetic drift, and time-dependent selection. It shows that a generic state of populations is adaptive evolution: there is a positive fitness flux resulting from a surplus of beneficial over deleterious changes. In particular, stationary nonequilibrium evolution processes are predicted to be adaptive. Under specific nonstationary conditions, notably during a decrease in population size, the average fitness flux can become negative. We show that these predictions are in accordance with experiments in bacteria and bacteriophages and with genomic data in Drosophila. Our analysis establishes fitness flux as a universal measure of adaptation in molecular evolution.

Clonal Interference in the Evolution of Influenza

The seasonal influenza A virus undergoes rapid evolution to escape human immune response. Adaptive changes occur primarily in antigenic epitopes, the antibody-binding domains of the viral hemagglutinin. This process involves recurrent selective sweeps, in which clusters of simultaneous nucleotide fixations in the hemagglutinin coding sequence are observed about every 4 years. Here, we show that influenza A (H3N2) evolves by strong clonal interference. This mode of evolution is a red queen race between viral strains with different beneficial mutations. Clonal interference explains and quantifies the observed sweep pattern: we find an average of at least one strongly beneficial amino acid substitution per year, and a given selective sweep has three to four driving mutations on average. The inference of selection and clonal interference is based on frequency time series of single-nucleotide polymorphisms, which are obtained from a sample of influenza genome sequences over 39 years. Our results imply that mode and speed of influenza evolution are governed not only by positive selection within, but also by background selection outside antigenic epitopes: immune adaptation and conservation of other viral functions interfere with each other. Hence, adapting viral proteins are predicted to be particularly brittle. We conclude that a quantitative understanding of influenza’s evolutionary and epidemiological dynamics must be based on all genomic domains and functions coupled by clonal interference.