Motifs and degree distribution in transcriptional regulatory networks play an important role towards their fault-tolerance and efficient information transport. In this paper, we designed an innovative in silico canoni...
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Motifs and degree distribution in transcriptional regulatory networks play an important role towards their fault-tolerance and efficient information transport. In this paper, we designed an innovative in silico canonical feed-forward loop motif knockout experiment in the transcriptional regulatory network of E. coli to assess their impact on the following five topological features: average shortest path, diameter, closeness centrality, global and local clustering coefficients. Additional experiments were conducted to assess the effects of such motif abundance on E. coli's resilience to nodal failures and the end-to-end transmission delay. The purpose of this study is two-fold: (i) motivate the design of more accurate transcriptional network growing algorithms that can produce similar degree and motif distributions as observed in real biological networks and (ii) design more efficient bio-inspired wireless sensor network topologies that can inherit the robust information transport properties of biological networks. Specifically, we observed that canonical feed forward loops demonstrate a strong negative correlation with the average shortest path, diameter and closeness centralities while they show a strong positive correlation with the average local clustering coefficient. Moreover, we observed that such motifs seem to be evenly distributed in the transcriptional regulatory network;however, the direct edges of multiple such motifs seem to be stitched together to facilitate shortest path based routing in such networks. Published by Elsevier B.V.
Background: Causal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs-directed graphs whose edges additionally have a sign denoting upregulation or dow...
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Background: Causal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs-directed graphs whose edges additionally have a sign denoting upregulation or downregulation-can be used to model regulatory networks within a cell. Such models allow prediction of downstream effects of regulation of biological entities;conversely, they also enable inference of causative agents behind observed expression changes. However, due to their complex nature, signed causal graph models present special challenges with respect to assessing statistical significance. In this paper we frame and solve two fundamental computational problems that arise in practice when computing appropriate null distributions for hypothesis testing. Results: First, we show how to compute a p-value for agreement between observed and model-predicted classifications of gene transcripts as upregulated, downregulated, or neither. Specifically, how likely are the classifications to agree to the same extent under the null distribution of the observed classification being randomized? This problem, which we call "Ternary Dot Product Distribution" owing to its mathematical form, can be viewed as a generalization of Fisher's exact test to ternary variables. We present two computationally efficient algorithms for computing the Ternary Dot Product Distribution and investigate its combinatorial structure analytically and numerically to establish computational complexity bounds. Second, we develop an algorithm for efficiently performing random sampling of causal graphs. This enables p-value computation under a different, equally important null distribution obtained by randomizing the graph topology but keeping fixed its basic structure: connectedness and the positive and negative in-and out-degrees of each vertex. We provide an algorithm for sampling a graph from this distribution uniformly at random. We also highlight theoretical challenges unique to signed causa
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