Numerical Methods for Genetic Regulatory Network Identification Based on a Variational Approach

Abstract

This paper studies differential equation-based mathematical models and their numerical solutions for genetic regulatory network identification. The primary objectives are to design, analyze, and test a general variational framework and numerical methods for seeking its approximate solutions for reverse engineering genetic regulatory networks from microarray datasets. In the proposed variational framework, no structure assumption on the genetic network is presumed, instead, the network is solely determined by the microarray profile of the network components and is identified through a well chosen variational principle which minimizes an energy functional. The variational principle serves not only as a selection criterion to pick up the right solution of the underlying differential equation model but also provides an effective mathematical characterization of the small-world property of genetic regulatory networks which has been observed in lab experiments. Five specific models within the variational framework and efficient numerical methods and algorithms for computing their solutions are proposed and analyzed. Model validations using both synthetic network datasets and subnetwork datasets of Saccharomyces cerevisiae (yeast) and E. coli are performed on all five proposed variational models and a performance comparison versus some existing genetic regulatory network identification methods is also provided.