Analysis of Combinatorial Regulation: Scaling of Partnerships between Regulators with the Number of Governed Targets

Through combinatorial regulation, regulators partner with each other to control common targets and this allows a small number of regulators to govern many targets. One interesting question is that given this combinatorial regulation, how does the number of regulators scale with the number of targets? Here, we address this question by building and analyzing co-regulation (co-transcription and co-phosphorylation) networks that describe partnerships between regulators controlling common genes. We carry out analyses across five diverse species: Escherichia coli to human. These reveal many properties of partnership networks, such as the absence of a classical power-law degree distribution despite the existence of nodes with many partners. We also find that the number of co-regulatory partnerships follows an exponential saturation curve in relation to the number of targets. (For E. coli and Bacillus subtilis, only the beginning linear part of this curve is evident due to arrangement of genes into operons.) To gain intuition into the saturation process, we relate the biological regulation to more commonplace social contexts where a small number of individuals can form an intricate web of connections on the internet. Indeed, we find that the size of partnership networks saturates even as the complexity of their output increases. We also present a variety of models to account for the saturation phenomenon. In particular, we develop a simple analytical model to show how new partnerships are acquired with an increasing number of target genes; with certain assumptions, it reproduces the observed saturation. Then, we build a more general simulation of network growth and find agreement with a wide range of real networks. Finally, we perform various down-sampling calculations on the observed data to illustrate the robustness of our conclusions

A Predictive Model of the Oxygen and Heme Regulatory Network in Yeast

Deciphering gene regulatory mechanisms through the analysis of high-throughput expression data is a challenging computational problem. Previous computational studies have used large expression datasets in order to resolve fine patterns of coexpression, producing clusters or modules of potentially coregulated genes. These methods typically examine promoter sequence information, such as DNA motifs or transcription factor occupancy data, in a separate step after clustering. We needed an alternative and more integrative approach to study the oxygen regulatory network in Saccharomyces cerevisiae using a small dataset of perturbation experiments. Mechanisms of oxygen sensing and regulation underlie many physiological and pathological processes, and only a handful of oxygen regulators have been identified in previous studies. We used a new machine learning algorithm called MEDUSA to uncover detailed information about the oxygen regulatory network using genome-wide expression changes in response to perturbations in the levels of oxygen, heme, Hap1, and Co2+. MEDUSA integrates mRNA expression, promoter sequence, and ChIP-chip occupancy data to learn a model that accurately predicts the differential expression of target genes in held-out data. We used a novel margin-based score to extract significant condition-specific regulators and assemble a global map of the oxygen sensing and regulatory network. This network includes both known oxygen and heme regulators, such as Hap1, Mga2, Hap4, and Upc2, as well as many new candidate regulators. MEDUSA also identified many DNA motifs that are consistent with previous experimentally identified transcription factor binding sites. Because MEDUSA's regulatory program associates regulators to target genes through their promoter sequences, we directly tested the predicted regulators for OLE1, a gene specifically induced under hypoxia, by experimental analysis of the activity of its promoter. In each case, deletion of the candidate regulator resulted in the predicted effect on promoter activity, confirming that several novel regulators identified by MEDUSA are indeed involved in oxygen regulation. MEDUSA can reveal important information from a small dataset and generate testable hypotheses for further experimental analysis. Supplemental data are included

HIDEN: Hierarchical decomposition of regulatory networks

<p>Abstract</p> <p>Background</p> <p>Transcription factors regulate numerous cellular processes by controlling the rate of production of each gene. The regulatory relations are modeled using transcriptional regulatory networks. Recent studies have shown that such networks have an underlying hierarchical organization. We consider the problem of discovering the underlying hierarchy in transcriptional regulatory networks.</p> <p>Results</p> <p>We first transform this problem to a mixed integer programming problem. We then use existing tools to solve the resulting problem. For larger networks this strategy does not work due to rapid increase in running time and space usage. We use divide and conquer strategy for such networks. We use our method to analyze the transcriptional regulatory networks of <it>E. coli</it>, <it>H. sapiens</it> and <it>S. cerevisiae</it>.</p> <p>Conclusions</p> <p>Our experiments demonstrate that: (i) Our method gives statistically better results than three existing state of the art methods; (ii) Our method is robust against errors in the data and (iii) Our method’s performance is not affected by the different topologies in the data.</p