| Despite the immense progress made by molecular biology in cataloging and characterizing molecular elements of life and the success in genome sequencing, there have not been comparable advances in the functional study of complex phenotypes. This is because isolated study of one molecule, or one gene, at a time is not enough by itself to characterize the complex interactions in organism and to explain the functions that arise out of these interactions. Mathematical modeling of biological systems is one way to meet the challenge.;My research formulates the modeling of gene regulation as a control problem and applies systems and control theory to the identification, analysis, and optimal control of genetic regulatory networks. The major contribution of my work includes biologically constrained estimation, dynamical analysis, and optimal control of genetic networks. In addition, parameter estimation of nonlinear models of biological networks is also studied, as a parameter estimation problem of a general nonlinear dynamical system. Results demonstrate the superior predictive power of biologically constrained state-space models, and that genetic networks can have differential dynamic properties when subjected to different environmental perturbations. Application of optimal control demonstrates feasibility of regulating gene expression levels. In the difficult problem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of the method to synthetic and real world data shows promising results. |
