Inference of gene regulatory networks using S-system: a unified approach.

With the increased availability of DNA microarray time-series data, it is possible to discover dynamic gene regulatory networks (GRNs). S-system is a promising model to capture the rich dynamics of GRNs. However, owing to the complexity of the inference problem and limited number of available data comparing to the number of unknown kinetic parameters, S-system can only be applied to a very small GRN with few parameters. This significantly limits its applications. A unified approach to infer GRNs using the S-system model is proposed. In order to discover the structure of large-scale GRNs, a simplified S-system model is proposed that enables fast parameter estimation to determine the major gene interactions. If a detailed S-system model is desirable for a subset of genes, a two-step method is proposed where the range of the parameters will be determined first using genetic programming and recursive least square estimation. Then the mean values of the parameters will be estimated using a multi-dimensional optimisation algorithm. Both the downhill simplex algorithm and modified Powell algorithm are tested for multi-dimensional optimisation. A 50-dimensional synthetic model with 51 parameters for each gene is tested for the applicability of the simplified S-system model. In addition, real measurement data pertaining to yeast protein synthesis are used to demonstrate the effectiveness of the proposed two-step method to identify the detailed interactions among genes in small GRNs.