Research On Noise Propagation Mechanism In Feed-forward Gene Regulatory Networks

The biological world is dominated by the interaction of deterministic laws and randomness.Fluctuation and noise have penetrated into every aspect of the biological system.More and more evidences show that the expression noise has significant impacts on many cellular processes.As a typical gene module,feed-forward gene regulatory network is attracting more and more attention in the past ten years,including the randomness of the structure,function and noise of feed-forward loop and so on.A large number of experiments show that the number of cells involved in biochemical reactions in life is relatively small,fluctuations and noise is very obvious and the effect of different network module to noise is also different.Therefore,it is necessary to study the relationship between the expression of noise in the biochemical system and the structure of the feed-forward loop.It is one of the most important contents in the research of system biology to trace the source of the noise and understand their role in the feed-forward regulation path.It is pointed out that noise is the propagation mechanism and general principle of the propagation in the feed-forward loop.In this paper,we analyze the stochastic dynamical properties and the mechanism of noise propagation in feed-forward gene regulatory networks based on a dynamic model of feed-forward gene regulatory networks by using the stochastic dynamic method and computer simulation technique.The following results are obtained in this paper.(i)By using the coherent feed-forward transcriptional regulation loop as the research object,this paper applies the stochastic dynamics theory and the computer simulation method to obtain the random noise propagation characteristics and the noise decomposition principle.Based on the dynamic model of feed-forward gene transcriptional regulatory network,the feed-forward gene transcription regulatory loop is divided into two parts:the main road and the branch.Then,the chemical master equation for the joint probability distribution is obtained.By using the linear noise approximation,the fluctuation dissipation formula is obtained.Then,a formula that can describe the variance and covariance of the statistical properties of random variables is derived.By using the knowledge of linear algebra and the concept of using the logarithmic gain function,normalizing the fluctuation dissipation formula is derived for total noise,whole loop of the main road and branch noise theory expression.Then,the theoretical results are verified by Gillespie simulation.We find that comparing with the noise of the main road and the noise of the branch,the full model can effectively reduce the output noise level.There is a transition point in the system,when the system is below the switching point,the noise of the main channel dominates,when the system is above the switching point,the noise of the branch dominates.We use a very simple signal transduction module as an example to reveal the mechanism of noise generation and transmission.(ii)The output noise characteristics and propagation mechanisms of various kinds of feed-forward transcriptional control circuits are studied,including the consistency of the "and gate ","or gate" case and the incoherent feed-forward loop.The theoretical formula of noise decomposition is derived by introducing the logarithmic gain coefficient and the linear noise approximation method.The theoretical results are verified by Gillespie simulation.Based on the theoretical and simulation results of the noise decomposition algorithm,we analyze the nonlinear behavior of the feed-forward gene network,and obtain three general conclusions.Firstly,the two level noise propagation of upstream factor in the incoherent feed-forward loop of " and gate " is negative,that is,the upstream factor can suppress the noise of the downstream factor indirectly.Secondly,the one level noise propagation of upstream factor of the "or gate" coherent feed-forward loop is non monotonic,so the direct control of the upstream factor to the downstream factor noise presents the nonlinear phenomenon.Finally,when the branch in the feedforward loop is negative,the total noise of the downstream factor increases monotonically.We theoretically analyzed the noise characteristics and propagation mechanism of feed-forward regulatory network.The theory of noise propagation through complex biological networks is described,which enables researchers to understand the role of noise in function and evolution.Our work provides a preliminary result for the noise decomposition of gene regulatory networks.