An effective structure learning method for constructing gene networks

MOTIVATION: Bayesian network methods have shown promise in gene regulatory network reconstruction because of their capability of capturing causal relationships between genes and handling data with noises found in biological experiments. The problem of learning network structures, however, is NP hard. Consequently, heuristic methods such as hill climbing are used for structure learning. For networks of a moderate size, hill climbing methods are not computationally efficient. Furthermore, relatively low accuracy of the learned structures may be observed. The purpose of this article is to present a novel structure learning method for gene network discovery. RESULTS: In this paper, we present a novel structure learning method to reconstruct the underlying gene networks from the observational gene expression data. Unlike hill climbing approaches, the proposed method first constructs an undirected network based on mutual information between two nodes and then splits the structure into substructures. The directional orientations for the edges that connect two nodes are then obtained by optimizing a scoring function for each substructure. Our method is evaluated using two benchmark network datasets with known structures. The results show that the proposed method can identify networks that are close to the optimal structures. It outperforms hill climbing methods in terms of both computation time and predicted structure accuracy. We also apply the method to gene expression data measured during the yeast cycle and show the effectiveness of the proposed method for network reconstruction.     

Reverse Engineering Boolean Networks: From Bernoulli Mixture Models to Rule Based Systems

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.     

Annotating gene function by combining expression data with a modular gene network

MOTIVATION: A promising and reliable approach to annotate gene function is clustering genes not only by using gene expression data but also literature information, especially gene networks. RESULTS: We present a systematic method for gene clustering by combining these totally different two types of data, particularly focusing on network modularity, a global feature of gene networks. Our method is based on learning a probabilistic model, which we call a hidden modular random field in which the relation between hidden variables directly represents a given gene network. Our learning algorithm which minimizes an energy function considering the network modularity is practically time-efficient, regardless of using the global network property. We evaluated our method by using a metabolic network and microarray expression data, changing with microarray datasets, parameters of our model and gold standard clusters. Experimental results showed that our method outperformed other four competing methods, including k-means and existing graph partitioning methods, being statistically significant in all cases. Further detailed analysis showed that our method could group a set of genes into a cluster which corresponds to the folate metabolic pathway while other methods could not. From these results, we can say that our method is highly effective for gene clustering and annotating gene function.