Robust Controller Design For Gene Regulatory Networks Under Intrinsic Parameters Fluctuation And Extrinsic Noises

The good gene regulatatory networks must have enough robustness, that is they have enough ability to resist molecular mutation and changes of the external environment and have enough ability to filtrate and attenuate random noise to make genes to normal express. Therefore, how to design robust gene regulatatory networks to tolerate more intrinsic kinetic parameter variations and attenuate external envoironmental noises will be an important topic for systems biology. But gene regulatatory networks is very complicated and elementary machanisms do not typically function in isolation, so far, no good theory exists for identifying all possible mechanisms of genetic regulatory networsks to attenuate the molecular noise achieve regulatory ability or to amplify the molecular noise to randomize outcoms to the advantage of diversity.Based on stochastic stability and stochastic H∞filtering theory, the main results of the paper come from the following three parts.First, the intrinsic fluctuation in reaction rates is modeled as a stete-dependent. Robust stability of gene regulatory networks for tolerance molecular noise will be come from steady theory of stochatic Lyapunov equation. Attenuation and amplified extrinsic noises of gene regulation network will be estimated by H∞filtering theory. Gene regulatory networks is viewed as an analog filter, these pathways function an low-pass filters to transduce low-frequency signal and to attenuate high-frequency noises. Besides, theory extends from linear gene regulatory networks to nonlinear gene regulatory networks and presents the corresponding theory.Secondly, Based on random optimal control theory, we propose the optimal performance of gene regulatory networks under intrinsic parameter variations and optimal control output of the worst of optimal interference of gene regulatory networks under extrinsic noises.Third, The classical gene regulatory network is established in a dynamic stochastic differential equation model, then we use MATLAB to simulate the gene regulatory network. Simulation results and the theoretical prediction is the consistent, therefore the theory is valid and correct.