A Synchronized Ensemble Of Genetic Clocks Coupled By Quorum Sensing

Organisms are of biochemical dynamics. They are continuously subjected to time-varying conditions in the form of both extrinsic driving from the environment and intrinsic rhythms generated by specialized cellular clocks within the organism itself. These rhythm generators are composed of thousands of clock cells that are intrinsically diverse but nevertheless manage to function in a coherent oscillatory state. Synchronized clocks are of fundamental importance in the coordination of rhythmic behaviour among individual elements in a community or a large complex sytem. Thus, there is considerable interest in investigating the mechanisms by which this collective behavior arises.By virtue of the including of quorum sensing, which makes synchronization possible, it is unresistable to add a noise source to the system. Hence the analysis of noise effect to system is necessary.This thesis consists of the following section:1. Some element concepts, such as system biology, synchronization and so on, are presented of the article associated with the significance of their application. A review is also introduced.2. Summarizing the theoretical principle concerning complex network, this article is focusing on explaining the applications of important ideas in nolinear dynamics and statistical physics. In the area of nonlinear dynamics, based on the variational principle, variation equation of the synchronous solution is presented for continuous-time system and then decouples by diagonalization. This leads to a networkof simplification driving by an autonomous oscillator; in the level of statistical physics, in the light of continuous phase transition researchers, to characterize quantitatively the transition to synchronization, define a quantity called order parameter with value that changes abruptly at the transition point as a certain control parameter varies.3. Improved J-O model. Based the ideas that synchronous clocks in nautre can responde to environment fastly, we modify the J-O model. The numerical results of them reveal that the improved one can synchronize more rapidly; meanwhile, we characterize qunantitatively the relations between coupling parameter and order parameter. The result indicates the process of the transition to synchronization is abruptly, not gradually.4. Noise analysis. We contrast two stochastic simulation algorithm:ssSSA and Euler-Maruyama and we employ the EM algorithm because it is a conceptional easy approach. We firstly address the noise effect averaged over a population of 3 repressilators. Simulation results manifest that coupling reduces the noise effect to system;furthermore, using 3-dimension picture in Matlab we associate the noise effect with the number of repressilators.