Time-varying gene interaction network modeling by sequential Monte Carlo

Most current methods used for gene regulatory network identification are dedicated to inference of steady state networks which are prevalent over all time instants. However, gene interactions evolve over time. Information about the gene interactions in different stages of a life cycle is of high importance for biology. Usually to model relations between genes in a network gene expression data are used. A large amount of gene expression data measured at a single time instant can be found in the literature. Only a limited amount of sources present experimental data on temporal sequences for gene expression, for example during the yeast cell cycle and the life cycle of Drosophila Melanogaster. However, for most of them only one temporal sequence dataset is available for each gene. Moreover, all experimental data are measured for a quite short time length. This lack of experimental information significantly limits the success of inference on network topology. In the statistical graphical models literature one can find a number of methods for studying the network structure while the study of time varying networks is rather recent. A sequential Monte Carlo method namely particle filtering (PF) provides a powerful tool for dynamic network inference. In this work, the PF technique is proposed for time varying gene expression network tracking rk. The data used are time evolution of synthetic data proposed by the DREAM4 challenge generated from known network topologies obtained from transcriptional regulatory networks of E. coli and S. cerevisiae. In order to infer time-evolving networks we propose a multivariate linear regression model relating the expression value of each gene at a given time to the gene expression values of the previous time instant. Application of particle filtering method to synthetic gene expression time series dataset for a network of genes helped us to follow with high accuracy the changes in gene expression data undergone due to different external perturbations. Moreover, gene expression temporal sequence data were utilized for online learning of time varying gene network structure. The proposed model is capable of discovering causal relationships, interactions between genes that vary in time. Our future goals are to extend a multivariate linear regression model in order to accommodate the delayed interactions, i.e. relate the expression value of each gene at a given time to the gene expression values of the previous time instants, t-1, t-2, ..., t-n.