Exact reconstruction of gene regulatory networks using compressive sensing.

Young Hwan Chang,Joe W Gray,Claire J Tomlin

doi:10.1186/s12859-014-0400-4

Abstract

BackgroundWe consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network’s sparseness.ResultsFor the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented.ConclusionsThe method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-014-0400-4) contains supplementary material, which is available to authorized users.

Highlights

Mathematical modeling of biological signaling pathways can provide an intuitive understanding of their behavior [1,2,3]
Since typically only incomplete knowledge of the network structure exists and the system dynamics is known to be sufficiently complex, the challenge has become to show that the identified networks and corresponding mathematical models are enough to adequately represent the underlying system
In the Human Epidermal Growth Factor Receptor2 (HER2) positive breast cancer signaling pathway that we studied in [29,30], time series data sets consist of only 8 time point measurements of 20 protein signals, and we would like to use this limited data to identify a graph structure which could have 20 × 20 or 400 edges

Summary

Introduction

Mathematical modeling of biological signaling pathways can provide an intuitive understanding of their behavior [1,2,3]. Many data-driven mathematical tools have been developed and applied to reconstruct graph representations of gene regulatory networks (GRNs) from data. These include Bayesian networks, regression, correlation, mutual information and system-based approaches [4,5,6,7,8,9,10]. We consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. If m = n and is a full rank matrix, the problem is determined and may be solved uniquely for q. To be able to recover q, CS relies on two properties: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing matrix

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