Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise

The study of fluctuations in gene regulatory networks is extended to the case of Gaussian colored noise. Firstly, the solution of the corresponding Langevin equation with colored noise is expressed in terms of an Ito integral. Then, two important lemmas concerning the variance of an Ito integral and the covariance of two Ito integrals are shown. Based on the lemmas, we give the general formulae for the variances and covariance of molecular concentrations for a regulatory network near a stable equilibrium explicitly. Two examples, the gene auto-regulatory network and the toggle switch, are presented in details. In general, it is found that the finite correlation time of noise reduces the fluctuations and enhances the correlation between the fluctuations of the molecular components.Comment: 10 pages, 4 figure

Stochastic neural network models for gene regulatory networks

Recent advances in gene-expression profiling technologies provide large amounts of gene expression data. This raises the possibility for a functional understanding of genome dynamics by means of mathematical modelling. As gene expression involves intrinsic noise, stochastic models are essential for better descriptions of gene regulatory networks. However, stochastic modelling for large scale gene expression data sets is still in the very early developmental stage. In this paper we present some stochastic models by introducing stochastic processes into neural network models that can describe intermediate regulation for large scale gene networks. Poisson random variables are used to represent chance events in the processes of synthesis and degradation. For expression data with normalized concentrations, exponential or normal random variables are used to realize fluctuations. Using a network with three genes, we show how to use stochastic simulations for studying robustness and stability properties of gene expression patterns under the influence of noise, and how to use stochastic models to predict statistical distributions of expression levels in population of cells. The discussion suggest that stochastic neural network models can give better description of gene regulatory networks and provide criteria for measuring the reasonableness o mathematical models

Cross-talk and interference enhance information capacity of a signaling pathway

A recurring motif in gene regulatory networks is transcription factors (TFs) that regulate each other, and then bind to overlapping sites on DNA, where they interact and synergistically control transcription of a target gene. Here, we suggest that this motif maximizes information flow in a noisy network. Gene expression is an inherently noisy process due to thermal fluctuations and the small number of molecules involved. A consequence of multiple TFs interacting at overlapping binding-sites is that their binding noise becomes correlated. Using concepts from information theory, we show that in general a signaling pathway transmits more information if 1) noise of one input is correlated with that of the other, 2) input signals are not chosen independently. In the case of TFs, the latter criterion hints at up-stream cross-regulation. We demonstrate these ideas for competing TFs and feed-forward gene regulatory modules, and discuss generalizations to other signaling pathways. Our results challenge the conventional approach of treating biological noise as uncorrelated fluctuations, and present a systematic method for understanding TF cross-regulation networks either from direct measurements of binding noise, or bioinformatic analysis of overlapping binding-sites.Comment: 28 pages, 5 figure

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

BACKGROUND: Noise 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. RESULTS: Based 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. CONCLUSION: In 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

Noise processing by microRNA-mediated circuits: The Incoherent Feed-Forward Loop, revisited

The intrinsic stochasticity of gene expression is usually mitigated in higher eukaryotes by post-transcriptional regulation channels that stabilise the output layer, most notably protein levels. The discovery of small non-coding RNAs (miRNAs) in specific motifs of the genetic regulatory network has led to identifying noise buffering as the possible key function they exert in regulation. Recent in vitro and in silico studies have corroborated this hypothesis. It is however also known that miRNA-mediated noise reduction is hampered by transcriptional bursting in simple topologies. Here, using stochastic simulations validated by analytical calculations based on van Kampen's expansion, we revisit the noise-buffering capacity of the miRNA-mediated Incoherent Feed Forward Loop (IFFL), a small module that is widespread in the gene regulatory networks of higher eukaryotes, in order to account for the effects of intermittency in the transcriptional activity of the modulator gene. We show that bursting considerably alters the circuit's ability to control static protein noise. By comparing with other regulatory architectures, we find that direct transcriptional regulation significantly outperforms the IFFL in a broad range of kinetic parameters. This suggests that, under pulsatile inputs, static noise reduction may be less important than dynamical aspects of noise and information processing in characterising the performance of regulatory elements

Living with noise: The evolution of gene expression noise in gene regulatory networks

One of the keystones of evolutionary biology is the study of how organismal traits change in time. Technological advancements in the past twenty years have enabled us to study the variation of an important trait, gene expression level, at single cell resolution. One of the sources of gene expression level variation is gene expression noise, a result of the innate stochasticity of the gene expression process. Gene expression noise is gene-specific and can be tuned by selection, but what drives the evolution of gene-specific expression noise remains an open question. In this thesis, I explore the selective pressure and evolvability of gene-specific expression noise in gene regulatory networks. I use evolutionary simulations by applying rounds of mutation, recombination and reproduction to populations of model gene regulatory networks in different selection scenarios. In the first chapter, I investigate the response of gene-specific expression noise in gene regulatory networks in constant environments, which imposes stabilizing selection on gene expression level. The probability of responding to selection and the strength of the selective response was affected by local network centrality metrics. Furthermore, global network features, such as network diameter, centralization and average degree affected the average expression variance and average selective pressure acting on constituent genes. In the second chapter, I investigate the response of mean gene expression level and gene-specific expression noise in isolated genes and genes in gene regulatory networks in changing environments. Gene-specific expression noise of genes increased under fluctuating selection, indicating the evolution of a bet-hedging strategy. Under directional selection gene-specific expression noise transiently increased, showing that expression noise plays a role in the adaptation process towards a new mean expression optimum