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Johannes Berg

Publications and source records attributed to Johannes Berg.

At least 37 records · Page 2Linked to original sources
arXiv2009

Adaptive gene regulatory networks

Regulatory interactions between genes show a large amount of cross-species variability, even when the underlying functions are conserved: There are many ways to achieve the same function. Here we investigate the ability of regulatory networks to reproduce given expression levels within a simple model of gene regulation. We find an exponentially large space of regulatory networks compatible with a given set of expression levels, giving rise to an extensive entropy of networks. Typical realisations of regulatory networks are found to share a bias towards symmetric interactions, in line with empirical evidence.

q-bio.MN↗
arXiv2008

Dynamics of gene expression under feedback

Gene expression is a stochastic process governed by the presence of specific transcription factors. Here we study the dynamics of gene expression in the presence of feedback, where a gene regulates its own expression. The nonlinear coupling between input and output of gene expression can generate a dynamics different from simple scenarios such as the Poisson process. This is exemplified by our findings for the time intervals over which genes are transcriptionally active and inactive. We apply our results to the lac system in E. coli, where parametric inference on experimental data results in a broad distribution of gene activity intervals.

q-bio.CB↗
arXiv2008

Dynamics of gene expression and the regulatory inference problem

From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription factor molecules to regulatory DNA. Here, we construct stochastic models of gene expression dynamics and test them on experimental time-series data of messenger-RNA concentrations. The models are used to infer biophysical parameters of gene transcription, including the statistics of transcription factor-DNA binding and the target genes controlled by a given transcription factor.

q-bio.MN↗
arXiv2007

Non-equilibrium dynamics of gene expression and the Jarzynski equality

In order to express specific genes at the right time, the transcription of genes is regulated by the presence and absence of transcription factor molecules. With transcription factor concentrations undergoing constant changes, gene transcription takes place out of equilibrium. In this paper we discuss a simple mapping between dynamic models of gene expression and stochastic systems driven out of equilibrium. Using this mapping, results of nonequilibrium statistical mechanics such as the Jarzynski equality and the fluctuation theorem are demonstrated for gene expression dynamics. Applications of this approach include the determination of regulatory interactions between genes from experimental gene expression data.

q-bio.MN↗
arXiv2007

From Protein Interactions to Functional Annotation: Graph Alignment in Herpes

Sequence alignment forms the basis of many methods for functional annotation by phylogenetic comparison, but becomes unreliable in the `twilight' regions of high sequence divergence and short gene length. Here we perform a cross-species comparison of two herpesviruses, VZV and KSHV, with a hybrid method called graph alignment. The method is based jointly on the similarity of protein interaction networks and on sequence similarity. In our alignment, we find open reading frames for which interaction similarity concurs with a low level of sequence similarity, thus confirming the evolutionary relationship. In addition, we find high levels of interaction similarity between open reading frames without any detectable sequence similarity. The functional predictions derived from this alignment are consistent with genomic position and gene expression data.

q-bio.MN↗
arXiv2006

Bayesian analysis of biological networks: clusters, motifs, cross-species correlations

An important part of the analysis of bio-molecular networks is to detect different functional units. Different functions are reflected in a different evolutionary dynamics, and hence in different statistical characteristics of network parts. In this sense, the {\em global statistics} of a biological network, e.g., its connectivity distribution, provides a background, and {\em local deviations} from this background signal functional units. In the computational analysis of biological networks, we thus typically have to discriminate between different statistical models governing different parts of the dataset. The nature of these models depends on the biological question asked. We illustrate this rationale here with three examples: identification of functional parts as highly connected \textit{network clusters}, finding \textit{network motifs}, which occur in a similar form at different places in the network, and the analysis of \textit{cross-species network correlations}, which reflect evolutionary dynamics between species.

q-bio.MN↗
arXiv2006

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 {\em 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 co-expression networks between human and mouse. 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.

q-bio.MN↗
arXiv2004

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

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. 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. 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.

cond-mat.stat-mech↗
arXiv2004

Adaptive evolution of transcription factor binding sites

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. 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. 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.

cond-mat.stat-mech↗
arXiv2004

Local graph alignment and motif search in biological networks

Interaction networks are of central importance in post-genomic 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 paper, 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 E. coli.

cond-mat.stat-mech↗
arXiv2002

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 $Z=\sum_{\c} \exp {[}-β\H(\c) {]}$. The simplest cases are uncorrelated random networks such as the well-known Erdös-Rény graphs. Here we study more general interactions $\H(\c)$ which lead to {\em correlations}, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in {\em optimized} networks described by partition functions in the limit $β\to \infty$. They are argued to be a crucial signature of evolutionary design in biological networks.

cond-mat.stat-mech↗
arXiv2002

Testing the Edwards hypothesis in spin systems under tapping dynamics

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way the blocked configurations are dynamically accessed): for thermal tapping ergodicity is a good approximation, while it fails to describe the asymptotic stationary state reached by the random tapping dynamics.

cond-mat.stat-mech↗
arXiv2001

Metastable configurations of spin models on random graphs

One-flip stable configurations of an Ising-model on a random graph with fluctuating connectivity are examined. In order to perform the quenched average of the number of stable configurations we introduce a global order-parameter function with two arguments. The analytical results are compared with numerical simulations.

cond-mat.dis-nn↗
arXiv2001

Glassy dynamics in granular compaction: sand on random graphs

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric frustration. We define an athermal dynamics designed to model repeated taps of a given strength. Amplitude cycling and the effect of permanently constraining a subset of the spins at a given amplitude is discussed. Finally we check the validity of Edwards' hypothesis for the athermal tapping dynamics.

cond-mat.dis-nn↗
arXiv2001

On random graphs and the statistical mechanics of granular matter

The dynamics of spins on a random graph with ferromagnetic three-spin interactions is used to model the compaction of granular matter under a series of taps. Taps are modelled as the random flipping of a small fraction of the spins followed by a quench at zero temperature. We find that the density approached during a logarithmically slow compaction - the random-close-packing density - corresponds to a dynamical phase transition. We discuss the the role of cascades of successive spin-flips in this model and link them with density-noise power fluctuations observed in recent experiments.

cond-mat.stat-mech↗
arXiv2001

Statistical mechanics of asset markets with private information

Traders in a market typically have widely different, private information on the return of an asset. The equilibrium price of the asset may reflect this information more accurately if the number of traders is large enough compared to the number of the states of the world that determine the return of the asset. We study the transition from markets where prices do not reflect the information accurately into markets where it does. In competitive markets, this transition takes place suddenly, at a critical value of the ratio between number of states and number of traders. The Nash equilibrium market behaves quite differently from a competitive market even in the limit of large economies.

cond-mat.stat-mech↗
arXiv1999

Statistical mechanics of random two-player games

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate quantities such as the number of equilibrium points, the expected payoff, and the fraction of strategies played with non-zero probability as a function of the correlation between the payoff matrices of both players and compare the results with numerical simulations.

cond-mat.dis-nn↗