Inference of Noisy Nonlinear Differential Equation Models for Gene Regulatory Networks Using Genetic Programming and Kalman Filtering

A key issue in genomic signal processing is the inference of gene regulatory networks. These are used both to understand the role of biological regulation in phenotypic determination and to derive therapeutic strategies for genetic-based diseases. In this paper, gene regulatory networks are inferred via evolutionary modeling based on time-series microarray measurements. A nonlinear differential equation model is adopted. It includes random noise parameters for intrinsic noise arising from stochasticity in transcription and translation and for external noise arising from factors such as the amount of RNA polymerase, levels of regulatory proteins, and the effects of mRNA and protein degradation. An iterative algorithm is proposed for model identification. Genetic programming is applied to identify the structure of the model and Kalman filtering is used to estimate the parameters in each iteration. Both standard and robust Kalman filtering are considered. The effectiveness of the proposed scheme is demonstrated by using synthetic data and by using microarray measurements pertaining to yeast protein synthesis.