Stochastic perturbation theory and its application to complex biological networks -- a quantification of systematic features of biological networks

Stochastic dynamical system;Fokker-Planck equation;Systematic measure

Li, Yao ; Yi, Yengfei Mathematics Zhou, Hao-min Kemp, Melissa Lambeth Chow, Shui-Nee Bakhtin, Yuri ; Yi, Yengfei

University:Georgia Institute of Technology

Department:Mathematics

关键词: Stochastic dynamical system;    Fokker-Planck equation;    Systematic measure;   

Others  :  https://smartech.gatech.edu/bitstream/1853/49013/1/li_yao_201208_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

The primary objective of this thesis is to make a quantitative study of complex biological networks. Our fundamental motivation is to obtain the statistical dependency between modules by injecting external noise. To accomplish this, a deep study of stochastic dynamical systems would be essential. The first chapter is about the stochastic dynamical system theory. The classical estimation of invariant measures of Fokker-Planck equations is improved by the level set method. Further, we develop a discrete Fokker-Planck-type equation to study the discrete stochastic dynamical systems. In the second part, we quantify systematic measures including degeneracy, complexity and robustness. We also provide a series of results on their properties and the connection between them. Then we apply our theory to the JAK-STAT signaling pathway network.