Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Radulescu, Ovidiu; Innocentini, Guilherme C. P.; Hornos, José Eduardo Martinho

doi:10.1103/physreve.85.041919

Cited by 8 publications

(9 citation statements)

References 18 publications

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“…For our problem, the front discontinuities occur at the domain boundaries and they are handled by the boundary conditions (4.4). Hyperbolicity properties are mainly visible at slow switching and should disappear at fast switching when the Liouville-master equation can be well approximated by a Fokker-Planck equation [28].…”

Section: The Finite Difference (Fd) Liouville-master Methodsmentioning

confidence: 99%

“…These simplifications were possible because the stochastic gene networks have heterogeneous variables and multiple time scales [28]. This heterogeneity comes from the fact that some variables X D such as DNA/regulatory proteins and complexes/polymerase states are discrete and other variables X C such as protein and mRNA copy numbers are continuous.…”

Section: Introductionmentioning

confidence: 99%

“…As shown in the Figure 1, the discrete variables switch between a number of discrete states. The characteristic time of this process was called switching time, τ S [28]. The trajectories of continuous variables are smooth only in the average, but for these variables, the average is a good approximation.…”

Section: Introductionmentioning

confidence: 99%

“…The trajectories of continuous variables are smooth only in the average, but for these variables, the average is a good approximation. The characteristic time of fluctuations of continuous species around their average was named discreteness time, τ D [28]. The discreteness time scales like 1/N where N is the copy number of the continuous species.…”

Section: Introductionmentioning

confidence: 99%

“…These approximations were first obtained heuristically by using partial expansions of the master equation [29,34,35] and then justified rigorously by using generators and measure theory in Crudu et al [30]. Finally, diffusion approximation was applied to PDP in the limit when the switching time is small, to obtain again deterministic and Fokker-Planck approximations [28].…”

Section: Introductionmentioning

confidence: 99%

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Time Dependent Stochastic mRNA and Protein Synthesis in Piecewise-Deterministic Models of Gene Networks

2018

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We discuss piecewise-deterministic approximations of gene networks dynamics. These approximations capture in a simple way the stochasticity of gene expression and the propagation of expression noise in networks and circuits. By using partial omega expansions, piecewise deterministic approximations can be formally derived from the more commonly used Markov pure jump processes (chemical master equation). We are interested in time dependent multivariate distributions that describe the stochastic dynamics of the gene networks. This problem is difficult even in the simplified framework of piecewise-deterministic processes. We consider three methods to compute these distributions: the direct Monte-Carlo; the numerical integration of the Liouville-master equation; and the push-forward method. This approach is applied to multivariate fluctuations of gene expression, generated by gene circuits. We find that stochastic fluctuations of the proteome and, much less, those of the transcriptome can discriminate between various circuit topologies.

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Section: The Finite Difference (Fd) Liouville-master Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time Dependent Stochastic mRNA and Protein Synthesis in Piecewise-Deterministic Models of Gene Networks

2018

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A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks

Antoneli

Ferreira

Briones

2016

Mathematical Biosciences

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Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs.

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Deciphering noise amplification and reduction in open chemical reaction networks

Pucci

Rooman

2018

J. R. Soc. Interface.

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The impact of fluctuations on the dynamical behaviour of complex biological systems is a longstanding issue, whose understanding would elucidate how evolutionary pressure tends to modulate intrinsic noise. Using the Itō stochastic differential equation formalism, we performed analytic and numerical analyses of model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. For networks of zero deficiency, which admit a detailed-or complex-balanced steady state, all molecular species are uncorrelated and their Fano factors are Poissonian. Systems of higher deficiency have nonequilibrium steady states and non-zero reaction fluxes flowing between the complexes. When they model homo-oligomerization, the noise on each species is reduced when the flux flows from the oligomers of lowest to highest degree, and amplified otherwise. In the case of hetero-oligomerization systems, only the noise on the highest-degree species shows this behaviour.& 2018 The Author(s) Published by the Royal Society. All rights reserved.transcription [11][12][13][14]. This mechanism has indeed been shown to lower noise while reducing the metabolic cost of protein production, and speeds up the rise-times of transcription units [15]. However, not all systems with negative feedback loops decrease in the intrinsic noise levels [16][17][18]. Similarly, although it is generally accepted that positive feedback loops tend to increase noise levels [19], some appear to decrease them [20]. Hence, the problem is far from being totally elucidated.Despite the many valuable advances in the field, the mechanisms used to amplify or to suppress the fluctuation levels need to be further understood and clarified. Indeed, the huge complexity of biological systems, their dependence on a large number of variables and the system-to-system variability make the unravelling of these issues, whether using experimental or computational approaches, a highly non-trivial task.More specifically, while noise control is relatively well understood for small and simple networks, it is still far from clear how the fluctuations propagate through more general and complicated networks and what is the link between network topology and complexity with noise buffering or amplification. Different investigations addressed these issues from various perspectives, for example by characterizing the stochastic properties of the chemical reaction networks (CRNs) and studying the propagation of the fluctuations [21][22][23][24]. From a physics-oriented perspective, other studies have analysed the connection between the nonequilibrium thermodynamic properties of the network and the noise level [25 -27]. It has furthermore been shown that the increase in network complexity tends to decrease intrinsic noise as well as to reduce the effect of extrinsic noise for some multistable model systems [28], whereas the dependence of noise reduction or amplification on the system parameters has been found in [29].This paper focu...

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Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Cited by 8 publications

References 18 publications

Time Dependent Stochastic mRNA and Protein Synthesis in Piecewise-Deterministic Models of Gene Networks

Time Dependent Stochastic mRNA and Protein Synthesis in Piecewise-Deterministic Models of Gene Networks

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks

Deciphering noise amplification and reduction in open chemical reaction networks

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