State Space Models and Differential Equations for Dynamic Gene Regulatory Network Identification

Thesis (Ph.D.)--University of Rochester. School of Medicine & Dentistry. Dept. of Biostatistics and Computational Biology, 2013.Gene regulation has been extensively studied for biological systems. Expression profiles from time-course experiments along with appropriate mathematical models allow us to identify dynamic gene regulatory networks. However, it is no surprised that challenges fall on the high-dimensional nature of such noisy data. In my thesis work, a high-dimensional linear State Space Model (SSM) with a new Expectation-Regularization-Maximization (ERM) algorithm is proposed to construct the dynamic Gene Regulatory Network (GRN). The approach has been shown to meet the purpose of overcoming the challenges of high dimensionality and separation of both the system noise and the measurement noise. Simulation studies are performed to evaluate the proposed ERM algorithm for variable selection. The method is applied to identify the dynamic GRN from time-course gene expression data of yeast cell cycle experiments. A stochastic differential equations (SDE) model is further proposed for the same purpose. The method and connection between SSM, SDE models, and ordinary differential equations (ODE) models is illustrated and discussed