Effect Of Non-Gaussian Noise On Random Delay Of Feed-forward Loop System

As a typical gene network module,the feed-forward gene regulatory network has been attracting widespread attention in recent years regarding its structure,function and dynamic characteristics.The gene regulation network is composed of the expression rela-tionship of mutual influence and restriction between genes during gene expression.Due to the complexity and randomness of gene expression regulation,it is often affected by some factors such as fluctuation and time delay.In recent years,researches on dynamic systems of noise and time delay have also made many achievements,for example,noise and time delay are inevitable in the study of systems biology.And the synergy of the two often affects the dynamic characteristics of the system,making the system more com-plex.However,regarding the influence of the synergy of noise and time delay on the feed-forward gene regulatory network,research work in this area at home and abroad is still rare.Therefore,this paper studies the effect of adding non-Gaussian noise and time delay effects on the feed-forward loop system in the gene regulatory network.In this paper,the effect of non-Gaussian noise on the random delay of the feed-forward loop system is studied using stochastic differential equations and random simulation meth-ods.The main results of this paper are as follows:The path integration method,unified color noise approximation and small time delay approximation are used to transform the nonlinear Langevin equation with non-Gaussian noise and time delay into a delayed Fokker-Planck equation.Based on the delayed Fokker-Planck equation,expressions of statistical characteristics such as the steady-state prob-ability distribution and mean value of the concentration variables y and z of the two transcription factors X,Y and the target gene Z.Discuss the effect of noise intensity D,deviation from the Gaussian noise parameter q,non-Gaussian noise correlation time?₀and time delay?on steady-state probability distribution,mean,normalized variance,normalized skewness and normalized kurtosis.Specifically:?1?Time delay will weaken the stability of intermediate factor Y and downstream factor Z,increase the concentration of y,at this time the concentration of z decreases,that is suppress the output of target gene Z.?2?Non-Gaussian noise will weaken the stability of the intermediate factor Y and the downstream factor Z,and increase the concentration of y and z,which will ultimately benefit the output of the target gene Z.That is to say,for the feed-forward loop system,the noise within a certain range is beneficial,and it is not as harmful as people usually think,and it plays a negative role.?3?The synergy between non-Gaussian noise and time delay is conducive to the activation of the transcription factors X and Y on the transcription rate of the target gene Z in the feed-forward loop system.According to the theoretical results,random simulation is used to verify,and the results are in good agreement,which proves that this approximation method is credible.Based on the research results of this paper,it can be seen that the introduction of non-Gaussian noise and time delay has great practical significance for the exploration of feed-forward gene regulatory networks,it also provides more research space for further in-depth exploration of feed-forward gene regulation networks in the future.