Gene Regulatory Network Modeling with Multiple Linear Regressions

Abstract

Gene regulatory network modeling is a difficult inverse problem. Given limited amount of experimental data about gene expressions, a dynamic model is sought to fit the data to infer interesting biological processes. In this study, a well-known ecological system, the Lotka-Volterra system of differential equations, is used to model the dynamics of genes regulations. After replacing derivatives by estimated slopes, this system is decoupled into several independent systems of linear equations. Coefficients of the original Lotka-Volterra system are inferred from these linear systems by using multiple linear regressions. Two function approximation techniques, namely the cubic spline and the artificial neural network, are used to help estimate the stated slopes. It is found that the cubic spline interpolation and multiple linear regressions have provided useful solutions to the gene regulatory network problem.