Significance analysis and statistical mechanics: an application to clustering

This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements? The computation of this cluster p-value for randomly distributed vectors is mapped onto a well-defined problem of statistical mechanics. We solve this problem analytically, establishing a connection between the physics of quenched disorder and multiple testing statistics in clustering and related problems. In an application to gene expression data, we find a remarkable link between the statistical significance of a cluster and the functional relationships between its genes.Comment: to appear in Phys. Rev. Let

Gene-network inference by message passing

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics 2007, Kyot

Gene-network inference by message passing

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics 2007, Kyot

Gene-network inference by message passing

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics 2007, Kyot

Dynamics of Coupled Adaptive Elements : Bursting and Intermittent Oscillations Generated by Frustration in Networks

Adaptation to environmental change is a common property of biological systems. Cells initially respond to external changes in the environment, but after some time, they regain their original state. By considering an element consisting of two variables that show such adaptation dynamics, we studied a coupled dynamical system containing such elements to examine the diverse dynamics in the system and classified the behaviors on the basis of the network structure that determined the interaction among elements. For a system with two elements, two types of behaviors, perfect adaptation and simple oscillation, were observed. For a system with three elements, in addition to these two types, novel types of dynamics, namely, rapid burst-type oscillation and a slow cycle, were discovered; depending on the initial conditions, these novel types of dynamics coexisted. These behaviors are a result of the characteristic dynamics of each element, i.e., fast response and slow adaptation processes. The behaviors depend on the network structure (in specific, a combination of positive or negative feedback among elements). Cooperativity among elements due to a positive feedback loop leads to simple oscillation, whereas frustration involving alternating positive and negative interactions among elements leads to the coexistence of rapid bursting oscillation and a slow cycle. These behaviors are classified on the basis of the frustration indices defined by the network structure. The period of the slow cycle is much longer than the original adaptation time scale, while the burst-type oscillation is a continued response that does not involve any adaptation. We briefly discuss the universal applicability of our results to a network of a larger number of elements and their possible relevance to biological systems.Comment: 12 pages, 13 figure

Information capacity of genetic regulatory elements

Changes in a cell's external or internal conditions are usually reflected in the concentrations of the relevant transcription factors. These proteins in turn modulate the expression levels of the genes under their control and sometimes need to perform non-trivial computations that integrate several inputs and affect multiple genes. At the same time, the activities of the regulated genes would fluctuate even if the inputs were held fixed, as a consequence of the intrinsic noise in the system, and such noise must fundamentally limit the reliability of any genetic computation. Here we use information theory to formalize the notion of information transmission in simple genetic regulatory elements in the presence of physically realistic noise sources. The dependence of this "channel capacity" on noise parameters, cooperativity and cost of making signaling molecules is explored systematically. We find that, at least in principle, capacities higher than one bit should be achievable and that consequently genetic regulation is not limited the use of binary, or "on-off", components.Comment: 17 pages, 9 figure

Flexible Promoter Architecture Requirements for Coactivator Recruitment

Background: The spatial organization of transcription factor binding sites in regulatory DNA, and the composition of intersite sequences, influences the assembly of the multiprotein complexes that regulate RNA polymerase recruitment and thereby affects transcription. We have developed a genetic approach to investigate how reporter gene transcription is affected by varying the spacing between transcription factor binding sites. We characterized the components of promoter architecture that govern the yeast transcription factors Cbf1 and Met31/32, which bind independently, but collaboratively recruit the coactivator Met4. Results: A Cbf1 binding site was required upstream of a Met31/32 binding site for full reporter gene expression. Distance constraints on coactivator recruitment were more flexible than those for cooperatively binding transcription factors. Distances from 18 to 50 bp between binding sites support efficient recruitment of Met4, with only slight modulation by helical phasing. Intriguingly, we found that certain sequences located between the binding sites abolished gene expression. Conclusion: These results yield insight to the influence of both binding site architecture and local DNA flexibility on gene expression, and can be used to refine computational predictions of gene expression from promoter sequences. In addition, our approach can be applied to survey promoter architecture requirements for arbitrary combinations of transcription factor binding sites

Conservation and Evolution of Cis-Regulatory Systems in Ascomycete Fungi

Relatively little is known about the mechanisms through which gene expression regulation evolves. To investigate this, we systematically explored the conservation of regulatory networks in fungi by examining the cis-regulatory elements that govern the expression of coregulated genes. We first identified groups of coregulated Saccharomyces cerevisiae genes enriched for genes with known upstream or downstream cis-regulatory sequences. Reasoning that many of these gene groups are coregulated in related species as well, we performed similar analyses on orthologs of coregulated S. cerevisiae genes in 13 other ascomycete species. We find that many species-specific gene groups are enriched for the same flanking regulatory sequences as those found in the orthologous gene groups from S. cerevisiae, indicating that those regulatory systems have been conserved in multiple ascomycete species. In addition to these clear cases of regulatory conservation, we find examples of cis-element evolution that suggest multiple modes of regulatory diversification, including alterations in transcription factor-binding specificity, incorporation of new gene targets into an existing regulatory system, and cooption of regulatory systems to control a different set of genes. We investigated one example in greater detail by measuring the in vitro activity of the S. cerevisiae transcription factor Rpn4p and its orthologs from Candida albicans and Neurospora crassa. Our results suggest that the DNA binding specificity of these proteins has coevolved with the sequences found upstream of the Rpn4p target genes and suggest that Rpn4p has a different function in N. crassa

Spectral analysis of Gene co-expression network of Zebrafish

We analyze the gene expression data of Zebrafish under the combined framework of complex networks and random matrix theory. The nearest neighbor spacing distribution of the corresponding matrix spectra follows random matrix predictions of Gaussian orthogonal statistics. Based on the eigenvector analysis we can divide the spectra into two parts, first part for which the eigenvector localization properties match with the random matrix theory predictions, and the second part for which they show deviation from the theory and hence are useful to understand the system dependent properties. Spectra with the localized eigenvectors can be characterized into three groups based on the eigenvalues. We explore the position of localized nodes from these different categories. Using an overlap measure, we find that the top contributing nodes in the different groups carry distinguished structural features. Furthermore, the top contributing nodes of the different localized eigenvectors corresponding to the lower eigenvalue regime form different densely connected structure well separated from each other. Preliminary biological interpretation of the genes, associated with the top contributing nodes in the localized eigenvectors, suggests that the genes corresponding to same vector share common features.Comment: 6 pages, four figures (accepted in EPL