On the attenuation and amplification of molecular noise in genetic regulatory networks

Bor-Sen Chen,Yu-Chao Wang

doi:10.1186/1471-2105-7-52

Abstract

BackgroundNoise has many important roles in cellular genetic regulatory functions at the nanomolar scale. At present, no good theory exists for identifying all possible mechanisms of genetic regulatory networks to attenuate the molecular noise to achieve regulatory ability or to amplify the molecular noise to randomize outcomes to the advantage of diversity. Therefore, the noise filtering of genetic regulatory network is an important topic for gene networks under intrinsic fluctuation and extrinsic noise.ResultsBased on stochastic dynamic regulation equation, the intrinsic fluctuation in reaction rates is modeled as a state-dependent stochastic process, which will influence the stability of gene regulatory network, especially, with low concentrations of reacting species. Then the mechanisms of genetic regulatory network to attenuate or amplify extrinsic fluctuation are revealed from the nonlinear stochastic filtering point of view. Furthermore, a simple measure of attenuation level or amplification level of extrinsic noise for genetic regulatory networks is also introduced by nonlinear robust filtering method. Based on the global linearization scheme, a convenient method is introduced to measure noise attenuation or amplification for each gene of the nonlinear stochastic regulatory network by solving a set of filtering problems, which correspond to a set of linearized stochastic regulatory networks. Finally, by the proposed methods, several simulation examples of genetic regulatory networks are given to measure their robust stability under intrinsic fluctuations, and to estimate the genes' attenuation and amplification levels under extrinsic noises.ConclusionIn this study, a stochastic nonlinear dynamic model is developed for genetic regulatory networks under intrinsic fluctuation and extrinsic noise. By the method we proposed, we could determine the robust stability under intrinsic fluctuations and identify the genes that are significantly affected by extrinsic noises, which we call the weak structure of the network. This method will be potential for robust gene circuit design in future, on which a drug design could be based.

Highlights

Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale
We found that the dynamic stability of a nonlinear perturbative genetic regulatory network under intrinsic noise is guaranteed if we can find a Lyapunov function which satisfies the Hamilton Jacobi inequality (HJI) in (8)
By the global linearization method, the robust stability condition of nonlinear gene regulatory network is reduced by solving linear matrix inequalities (LMIs) in (10) for the convenience of computation

Summary

Introduction

Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale. Phase variation in pathogenic bacteria, where cells alternate randomly between expressing certain genes and silencing others, is thought to be a form of cultivated noise [8]. These molecular-level noisy phenomena are deeply rooted in the statistical mechanical behavior of so-called nanoscale chemical systems, where concentrations of reacting species are extremely low and, fluctuations (noises) in the reaction rates are large [9]. Even though the molecular fluctuations leading to phase variation seem random in the individual, regulatory factors tune the variation to ensure mean levels of heterogeneity for the population, i.e., the random noises can be shown to be filtered or attenuated by the genetic regulatory networks [1]. Many observations suggest that molecular events underlying cellular physiology are subject to fluctuations and have lead to the proposal of a stochastic model for gene expressions and biofunctions [9,10,11,12,13]

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Discussion

Conclusion