The Stochastic Resonance In A Class Of Synthetic Gene Networks With Lévy Noise

The synthetic gene network with the genetic toggle is obtained from the natural gene network.It is a typical gene network module,which reduces the research complexity of natural gene networks and makes the theoretical analysis and the experimental research to be simpler and more effective.It is significant to solve some practical problems such as the information storage and code,biotechnology and so on.Besides,based on the biological fluctuation framework,there exists large amount of non-gaussian Lévy random disturbances in the external environment.Thus,the effect of the external Lévy random noises on a synthetic gene network with genetic toggle and the induced stochastic resonance are studied in this dissertation.The main innovational part is that,based on the previous study of stability,the stochastic resonances induced by non-Gaussian Lévy noise are investigated,such as classical stochastic resonance,coherence resonance,logical stochastic resonance,switch of logic gates etc.Also,the information-based measure methodologies for coherence resonance and logical stochastic resonance in this system are builded.Then the specific contents are shown as follows.(1)The distribution of the stable states of the synthetic gene network with genetic toggle induced by Lévy noise is analyzed.Through the biochemical reaction,the model of the synthetic gene network with genetic toggle and are analyzed and builded,the stable states are also analyzed.The distribution of the states excited with Lévy noise caused by the external environment of Lévy flight superdiffusion are analyzed.The effects of stability index,skewness parameter and noise intensity of Lévy noise are discussed on the stationary probability distribution function of the switch of the stable state.It is found that the decreasing of stability index and the increasing of skewness parameter and noise intensity can improve more switch of the protein concentration between the high and low stable states.(2)The classical stochastic resonance of the synthetic gene network with genetic toggle induced by Lévy noise and harmonic excitation is investigated.Through the analysis of signalto-noise-ratio(SNR),it is observed that Lévy noise induces the optimal nonlinear trends of SNR which represent the classical stochastic resonance.When Lévy noise and harmonic excitation are within the protein at high or low concentration,the increasing of Lévy noise intensity can promote the switch of the protein concentration between the high and low stable states.Moreover,the increasing of stability index,skewness parameter of Lévy noise and amplitude of harmonic excitation can suppress or strengthen the optimum collaboration of classical stochastic resonance.(3)The coherence resonance of the synthetic gene network with genetic toggle induced by Lévy noise is investigated.The information-based methodology is proposed to measure the coherence resonance phenomenon.The optimal nonlinear trends of the symbol switch ratio,the noise entropy and the channel capacity as the noise intensity under different parameters of Lévy noise are analyzed.That is Lévy noise can induce the coherence resonance phenomenon.The increasing of stability index and skewness parameter of Lévy noise can improve the symbol switch ratio and the channel capacity and decrease the noise entropy during the switch of the stable states.(4)The logical stochastic resonance of the synthetic gene network with genetic toggle induced by Lévy noise and square wave signal is investigated.The information-based methodology is proposed to measure logical stochastic resonance.The symbol error rate,the noise entropy,the mutual information and the synchronization degree of the mutual information of the logical information transmission are analyzed.It is found that the logic gates of NOR/OR are implemented in some certain parameters.The symbol error rate,the noise entropy and the mutual information show the optimal nonlinear trends,which demonstrate that Lévy noise can induce the logical stochastic resonance phenomenon under the obtained logic gates.Moreover,the increasing of stability index of Lévy noise can decrease the symbol switch ratio and the noise entropy and improve the mutual information of the logical information transmission.The decreasing of stability index of Lévy noise can accelerate the change of the mutual information synchronously.(5)The switch of logic gates and logical stochastic resonance of the synthetic gene network with genetic toggle induced by Lévy noise and square wave signal are investigated.The logical information transmissions under three sets of system parameters and Lévy noise parameters are analyzed.It is found that the transformations of the logic gates of NOR/OR,NAND/AND and NSGN/SGN are implemented by the adjustment of parameters.Then through the twodimensional logical success probability concerning the pairwise parameters of stability index,skewness parameter and noise intensity of Lévy noise,the reliabilities of the obtained logic gates are analyzed.The logical success probabilities as the noise intensity show the optimal nonlinear trends.It is also demonstrated that Lévy noise can induce logical stochastic resonance phenomenon under three sets of the obtained logic gates.