Abstract
Motivation: There are a number of algorithms to infer causal regulatory networks from time series (gene expression) data. Here we analyse the phenomena of regulator interference, where regulators with similar dynamics mutually suppress both the probability of regulating a target and the associated link strength; for instance, interference between two identical strong regulators reduces link probabilities by ∼50%.Results: We construct a robust method to define an interference-corrected causal network based on an analysis of the conditional link probabilities that recovers links lost through interference. On a large real network (Streptomyces coelicolor, phosphate depletion), we demonstrate that significant interference can occur between regulators with a correlation as low as 0.865, losing an estimated 34% of links by interference. However, levels of interference cannot be predicted from the correlation between regulators alone and are data specific. Validating against known networks, we show that high numbers of functional links are lost by regulator interference. Performance against other methods on DREAM4 data is excellent.Availability and implementation: The method is implemented in R and is publicly available as the NIACS package at http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software.Contact: N.J.Burroughs@warwick.ac.ukSupplementary information: Supplementary materials are available at Bioinformatics online.
Highlights
The falling costs of global gene expression measurement by microarrays, and more recently generation sequencing has spurred the development of network inference techniques (Werhli et al, 2006; Bansal et al, 2007; Margolin and Califano et al, 2007; Markowetz and Spang, 2007; Hache et al, 2009; Olsen et al, 2009; De Smet and Marchal, 2010; Penfold and Wild, 2011; Emmert-Streib et al, 2012; Maetschke et al, 2013)
In this paper we have proposed a method for dealing with the problem of regulators with similar dynamics suppressing causal link signals in the auto-regression model Equation (1)
By analysis of the level of interference between highly correlated regulators we are able to correct for link suppression by near identical regulators, and recover regulator links that would otherwise be lost because their posterior link probabilities are reduced below threshold
Summary
The falling costs of global gene expression (transcriptome) measurement by microarrays, and more recently generation sequencing has spurred the development of network inference techniques (Werhli et al, 2006; Bansal et al, 2007; Margolin and Califano et al, 2007; Markowetz and Spang, 2007; Hache et al, 2009; Olsen et al, 2009; De Smet and Marchal, 2010; Penfold and Wild, 2011; Emmert-Streib et al, 2012; Maetschke et al, 2013). Sparse network models (Morrissey et al, 2010, 2011) use Gibbs variable selection methods to determine which elements of the matrix B are present in the regression; the prior on Bij allows it to be zero with finite probability. In network models interference has a direct bearing on the posterior probability of links being present In these sparse network models π(γij = 1 | D) is reduced if there is another regulator k with similar dynamics to j. We developed a framework for solving this problem based on the analysis of conditional posterior link probabilities that identifies the interfering sets of regulators This allowed us to define an interference-corrected causal network and, further, the relative weights of the interfering regulators reflecting their likely contribution to the control of a given gene. We discuss the impact of these issues and the generality to other inference/fitting methods
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