Biomedical subjects

Michael Lässig

Publications and source records attributed to Michael Lässig.

13 recordsLinked to original sources

PubMed2006

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.

Algorithms↗

PubMed2006

Freezing of random RNA.

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.

Freezing↗

PubMed2005

Evolutionary population genetics of promoters: predicting binding sites and functional phylogenies.

We study the evolution of transcription factor-binding sites in prokaryotes, using an empirically grounded model with point mutations and genetic drift. Selection acts on the site sequence via its binding affinity to the corresponding transcription factor. Calibrating the model with populations of functional binding sites, we verify this form of selection and show that typical sites are under substantial selection pressure for functionality: for cAMP response protein sites in Escherichia coli, the product of fitness difference and effective population size takes values 2NDeltaF of order 10. We apply this model to cross-species comparisons of binding sites in bacteria and obtain a prediction method for binding sites that uses evolutionary information in a quantitative way. At the same time, this method predicts the functional histories of orthologous sites in a phylogeny, evaluating the likelihood for conservation or loss or gain of function during evolution. We have performed, as an example, a cross-species analysis of E. coli, Salmonella typhimurium, and Yersinia pseudotuberculosis. Detailed lists of predicted sites and their functional phylogenies are available.

Bacteria↗

PubMed2005

Solvable sequence evolution models and genomic correlations.

We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions, and insertion of random segments. These processes are found to generate long-range correlations in the composition of letters as long as the sequence length is growing; i.e., the combined rates of duplications and insertions are higher than the deletion rate. For constant sequence length, on the other hand, all initial correlations decay exponentially. These results are obtained analytically and by simulations. They are compared with the long-range correlations observed in genomic DNA, and the implications for genome evolution are discussed.

DNA↗

PubMed2005

Biodiversity in model ecosystems, I: coexistence conditions for competing species.

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper, we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (1994, Theor. Popul. Biol. 45, 227-276). Here we review and generalize this analysis, beyond the "mean-field"-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host.

Animals↗

PubMed2005

Biodiversity in model ecosystems, II: species assembly and food web structure.

This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here, we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models the coexistence condition derived for systems at the fixed point. The ecological overlap between species and shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies.

Animals↗

PubMed2005

Toward an accurate statistics of gapped alignments.

Sequence alignment has been an invaluable tool for finding homologous sequences. The significance of the homology found is often quantified statistically by p-values. Theory for computing p-values exists for gapless alignments [Karlin, S., Altschul, S.F., 1990. Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes. Proc. Natl. Acad. Sci. USA 87, 2264-2268; Karlin, S., Dembo A., 1992. Limit distributions of maximal segmental score among Markov-dependent partial sums. Adv. Appl. Probab. 24, 13-140], but a full generalization to alignments with gaps is not yet complete. We present a unified statistical analysis of two common sequence comparison algorithms: maximum-score (Smith-Waterman) alignments and their generalized probabilistic counterparts, including maximum-likelihood alignments and hidden Markov models. The most important statistical characteristic of these algorithms is the distribution function of the maximum score S(max), resp. the maximum free energy F(max), for mutually uncorrelated random sequences. This distribution is known empirically to be of the Gumbel form with an exponential tail P(S(max)>x) approximately exp(-lambdax) for maximum-score alignment and P(F(max)>x) approximately exp(-lambdax) for some classes of probabilistic alignment. We derive an exact expression for lambda for particular probabilistic alignments. This result is then used to obtain accurate lambda values for generic probabilistic and maximum-score alignments. Although the result demonstrated uses a simple match-mismatch scoring system, it is expected to be a good starting point for more general scoring functions.

Algorithms↗

PubMed2004

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

BACKGROUND: The 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. RESULTS: We 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. CONCLUSIONS: According 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.

Biological Evolution↗

PubMed2004

Adaptive evolution of transcription factor binding sites.

BACKGROUND: The 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. RESULTS: We 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. CONCLUSIONS: The 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.

Animals↗

PubMed2004

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.

Algorithms↗

PubMed2004

Of statistics and genomes.

Higher organisms have more genes and larger genomes than simple organisms. This statement sounds almost too trivial to ask the question: why? But there are at least two different answers. Either there is an inherent necessity to increase genome size when more complexity is required or genome size increases because of other reasons that then enable complexity to "latch on". Recently, an article by Lynch and Conery, which used arguments of evolutionary population dynamics, proposed that low population size leads to larger genomes. This then provides the opportunity to generate more complex organisms.

Algorithms↗

PubMed2002

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.

Brain↗

PubMed2002

Delocalization transitions of semiflexible manifolds.

Semiflexible manifolds such as fluid membranes or semiflexible polymers undergo delocalization transitions if they are subject to attractive interactions. We study manifolds with short-ranged interactions by field-theoretic methods based on the operator product expansion of local interaction fields. We apply this approach to manifolds in a random potential. Randomness is always relevant for fluid membranes, while for semiflexible polymers there is a first-order transition to the strong coupling regime at a finite temperature.

Journal Article↗