Delayed and hidden variables interactions in gene regulatory networks

Reverse Engineering of Gene Regulatory Networks (GRN), i.e. Finding appropriate mathematical models to understand complex cellular systems, can be used in disease diagnosis, treatment, and drug design. There are fundamental gaps in the construction of GRN with regard to modeling of hidden/delayed interactions. Addressing these deficiencies is critical to understanding complex intracellular processes and enabling full use of the vast and ever-growing amount of available genomic data. Current modeling strategies either ignore or oversimplify time delays resulted from transcription and translation processes during gene expression. In addition, many research works do not account hidden variables such as transcription factors, repressors, small metabolites, DNA, microRNA species that regulate themselves and other genes but are not readily detectable on micro array experiments. To capture the effect of these parameters, in this paper, we utilize our developed Partially Connected Artificial Neural Networks with Evolvable Topology (PANNET) to find a more comprehensive model of GRN by considering the effects of unknown hidden variables and different time delays. This method is innovative, since the structure of the network has memory and internal states, which can model the unknown hidden variables and time delays. We furthermore use a new evolutionary optimization based on variable-length Genetic Algorithm (GA) to find a sparse structure of PANNET to predict the gene expression levels accurately. Finally we demonstrate the capability of PANNET in constructing GRN, including the effect of different delays and unknown hidden variables through modeling of E. Coli SOS inducible DNA repair system.