Reverse engineering Boolean networks: from Bernoulli mixture models to rule based systems.

Mehreen Saeed,Maliha Ijaz,Kashif Javed,Haroon Atique Babri,Simon Rogers

doi:10.1371/journal.pone.0051006

Abstract

A Boolean network is a graphical model for representing and analyzing the behavior of gene regulatory networks (GRN). In this context, the accurate and efficient reconstruction of a Boolean network is essential for understanding the gene regulation mechanism and the complex relations that exist therein. In this paper we introduce an elegant and efficient algorithm for the reverse engineering of Boolean networks from a time series of multivariate binary data corresponding to gene expression data. We call our method ReBMM, i.e., reverse engineering based on Bernoulli mixture models. The time complexity of most of the existing reverse engineering techniques is quite high and depends upon the indegree of a node in the network. Due to the high complexity of these methods, they can only be applied to sparsely connected networks of small sizes. ReBMM has a time complexity factor, which is independent of the indegree of a node and is quadratic in the number of nodes in the network, a big improvement over other techniques and yet there is little or no compromise in accuracy. We have tested ReBMM on a number of artificial datasets along with simulated data derived from a plant signaling network. We also used this method to reconstruct a network from real experimental observations of microarray data of the yeast cell cycle. Our method provides a natural framework for generating rules from a probabilistic model. It is simple, intuitive and illustrates excellent empirical results.

Highlights

Boolean networks were introduced by Kauffman in the sixties and were one of the first methods to describe gene expression data [1] and model a gene regulatory network (GRN)
In this article we present a fast, efficient and accurate method called ReBMM for reverse engineering Boolean Networks by making use of a probabilistic model called a Bernoulli mixture model
We show how Bernoulli mixture models can be used to determine the parents of a node and how these mixtures lend themselves to a natural representation of logical Boolean rules, an approach which has not been explored before

Summary

Introduction

Boolean networks were introduced by Kauffman in the sixties and were one of the first methods to describe gene expression data [1] and model a gene regulatory network (GRN). There are many existing techniques for modeling GRNs, e.g., Bayesian networks [3], neural networks [4], support vector machines [5], metabolic control analysis [6] etc. A review of inference techniques of GRNs has been presented by Hecker et al [2]. The problems and methods related to GRNs have been outlined by Han et al [7], where they discuss the various network topologies and the reconstruction methods. One technique used to model GRNs is based on Boolean network models

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