Johannes Berg

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.

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.

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.

How epigenetic mutations can affect genetic evolution: Model and mechanism

We hypothesize that heritable epigenetic changes can affect rates of fitness increase as well as patterns of genotypic and phenotypic change during adaptation. In particular, we suggest that when natural selection acts on pure epigenetic variation in addition to genetic variation, populations adapt faster, and adaptive phenotypes can arise before any genetic changes. This may make it difficult to reconcile the timing of adaptive events detected using conventional population genetics tools based on DNA sequence data with environmental drivers of adaptation, such as changes in climate. Epigenetic modifications are frequently associated with somatic cell differentiation, but recently epigenetic changes have been found that can be transmitted over many generations. Here, we show how the interplay of these heritable epigenetic changes with genetic changes can affect adaptive evolution, and how epigenetic changes affect the signature of selection in the genetic record.

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.

Heterogeneous Mechanisms of Primary and Acquired Resistance to Third-Generation EGFR Inhibitors.

Purpose: To identify novel mechanisms of resistance to third-generation EGFR inhibitors in patients with lung adenocarcinoma that progressed under therapy with either AZD9291 or rociletinib (CO-1686). Experimental Design: We analyzed tumor biopsies from seven patients obtained before, during, and/or after treatment with AZD9291 or rociletinib (CO-1686). Targeted sequencing and FISH analyses were performed, and the relevance of candidate genes was functionally assessed in in vitro models. Results: We found recurrent amplification of either MET or ERBB2 in tumors that were resistant or developed resistance to third-generation EGFR inhibitors and show that ERBB2 and MET activation can confer resistance to these compounds. Furthermore, we identified a KRASG12S mutation in a patient with acquired resistance to AZD9291 as a potential driver of acquired resistance. Finally, we show that dual inhibition of EGFR/MEK might be a viable strategy to overcome resistance in EGFR-mutant cells expressing mutant KRAS. Conclusions: Our data suggest that heterogeneous mechanisms of resistance can drive primary and acquired resistance to third-generation EGFR inhibitors and provide a rationale for potential combination strategies. Clin Cancer Res; 22(19); 4837–47. ©2016 AACR.

Asymptotic expected number of Nash equilibria of two-player normal form games

The formula given by McLennan [The mean number of real roots of a multihomogeneous system of polynomial equations, Amer. J. Math. 124 (2002) 49-73] is applied to the mean number of Nash equilibria of random two-player normal form games in which the two players have M and N pure strategies respectively. Holding M fixed while N R I, the expected number of Nash equilibria is approximately (R(π log N) / 2)(M-1)/R M. Letting M = N R I, the expected number of Nash equilibria is exp(NM + O(log N)), where M A 0.281644 is a constant, and almost all equilibria have each player assigning positive probability to approximately 31.5915 percent of her pure strategies.

Nonlinear fitness landscape of a molecular pathway.

Genes are regulated because their expression involves a fitness cost to the organism. The production of proteins by transcription and translation is a well-known cost factor, but the enzymatic activity of the proteins produced can also reduce fitness, depending on the internal state and the environment of the cell. Here, we map the fitness costs of a key metabolic network, the lactose utilization pathway in Escherichia coli. We measure the growth of several regulatory lac operon mutants in different environments inducing expression of the lac genes. We find a strikingly nonlinear fitness landscape, which depends on the production rate and on the activity rate of the lac proteins. A simple fitness model of the lac pathway, based on elementary biophysical processes, predicts the growth rate of all observed strains. The nonlinearity of fitness is explained by a feedback loop: production and activity of the lac proteins reduce growth, but growth also affects the density of these molecules. This nonlinearity has important consequences for molecular function and evolution. It generates a cliff in the fitness landscape, beyond which populations cannot maintain growth. In viable populations, there is an expression barrier of the lac genes, which cannot be exceeded in any stationary growth process. Furthermore, the nonlinearity determines how the fitness of operon mutants depends on the inducer environment. We argue that fitness nonlinearities, expression barriers, and gene–environment interactions are generic features of fitness landscapes for metabolic pathways, and we discuss their implications for the evolution of regulation.

MATRIX GAMES, MIXED STRATEGIES, AND STATISTICAL MECHANICS

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices and derive analytical expressions for the value of the game and the distribution of strategy strengths. In particular the fraction of pure strategies not contributing to the optimal mixed strategy of a player is calculated. Both independently distributed as well as correlated elements of the payoff matrix are considered and the results compared with numerical simulations.