BackgroundA popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it.ResultsWe applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered.ConclusionsThe algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.

Abstract. A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. We applied the proposed algorithm in a case study of the budding yeast cell cycle network using an artificial dataset. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered. We have shown that this analysis can be used as the first step for gene relationships detection with a high flexibility to include biological knowledge. What we envisage with our method is a model that points out which connections should be checked in the wet lab and consequently facilitate some biological experiments.

The yeast (Saccharomyces cerevisiae) cell cycle has been studied for years, providing us a good knowledge about this cellular process. However, behind this process, there are still complex interactions between genes and proteins that are not fully understood. In this paper, we present a yeast cell cycle modeled by a context-sensitive probabilistic Boolean network (cPBN). The importance of understanding the cell cycle process under this model is that this knowledge may be useful for inferring other gene regulatory networks (cPBNs) from biological data. Furthermore, this work shows an application of the cPBN model for a real biological system.

Models of gene regulatory networks (GRN) have been proposed along with algorithms for inferring their structure. By structure, we mean the relationships among the genes of the biological system under study. Despite the large number of genes found in the genome of an organism, it is believed that a small set of genes is responsible for maintaining a specific core regulatory mechanism (small subnetworks). We propose an algorithm for inference of subnetworks of genes from a small initial set of genes called seed and time series gene expression data. The algorithm has two main steps: First, it grows the seed of genes by adding genes to it, and second, it searches for subnetworks that can be biologically meaningful. The seed growing step is treated as a feature selection problem and we used a thresholded Boolean network with a perturbation model to design the criterion function that is used to select the features (genes). Given that the reverse engineering of GRN is a problem that does not necessarily have one unique solution, the proposed algorithm has as output a set of networks instead of one single network. The algorithm also analyzes the dynamics of the networks which can be time-consuming. Nevertheless, the algorithm is suitable when the number of genes is small. The results showed that the algorithm is capable of recovering an acceptable rate of gene interactions and to generate regulatory hypotheses that can be explored in the wet lab.