Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

Wang, Hui; Cheng, Xian; Duan, Jinqiao; Kurths, Jürgen; Li, Xiaofan

doi:10.1063/1.5010026

Cited by 20 publications

(10 citation statements)

References 53 publications

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“…In this framework, we begin with the most detailed description of the individual-molecularbased and stochastic dynamics, the chemical master equation, and systematically construct the piecewise deterministic Markov processes (PDMP), which retains the discrete and stochastic switching nature of the genetic states. This framework is a natural generalisation of our previous work [11,21,22], and the derived PDMP has been shown to be a powerful mathe-matical tool to model coloured noise in stochastic gene expression [12,33,34,35,36,37,38,39,40,41]. Our analyses showed that for the models we investigated, the PDMP faithfully captures dynamical features of the individual-molecular-based models.…”

Section: Discussion and Future Outlooksupporting

confidence: 57%

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

Lin

Buchler

2018

J. R. Soc. Interface.

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Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the properties of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Last, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.

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Section: Discussion and Future Outlooksupporting

confidence: 57%

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

Lin

Buchler

2018

J. R. Soc. Interface.

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“…However, random fluctuations in complex biological and physical systems are often non-Gaussian rather than Gaussian [34,32,31]. Lévy motions are appropriate models for a class of important non-Gaussian processes with jumps or bursts [5].…”

Section: Introductionmentioning

confidence: 99%

The Onsager–Machlup function as Lagrangian for the most probable path of a jump-diffusion process

Chao

Duan

2019

Nonlinearity

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This work is devoted to deriving the Onsager-Machlup function for a class of stochastic dynamical systems under (non-Gaussian) Lévy noise as well as (Gaussian) Brownian noise, and examining the corresponding most probable paths. This Onsager-Machlup function is the Lagrangian giving the most probable path connecting metastable states for jump-diffusion processes. This is done by applying the Girsanov transformation for measures induced by jump-diffusion processes. Moreover, we have found this Lagrangian function is consistent with the result in the special case of diffusion processes. Finally, we apply this new Onsager-Machlup function to investigate dynamical behaviors analytically and numerically in several examples. These include the transitions from one metastable state to another metastable state in a double-well system, with numerical experiments illustrating most probable transition paths for various noise parameters.

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“…There are various studies about Gaussian noise in gene regulation [27][28][29][30][31]. However, the transcription of a gene can be a discontinuous or burstlike event, and mRNA is synthesized in intermittent but intense pulses or bursts [21,22,[32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Most probable dynamics of a genetic regulatory network under stable Lévy noise

Chen

Duan

et al. 2019

Applied Mathematics and Computation

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Numerous studies have demonstrated the important role of noise in the dynamical behaviour of a complex system. The most probable trajectories of nonlinear systems under the influence of Gaussian noise have recently been studied already. However, there has been only a few works that examine how most probable trajectories in the two-dimensional system (MeKS network) are influenced under non-Gaussian stable Lévy noise. Therefore, we discuss the most probable trajectories of a two-dimensional model depicting the competence behaviour in B. subtilis under the influence of stable Lévy noise. On the basis of the Fokker-Planck equation, we describe the noise-induced most probable trajectories of the MeKS network from the low ComK protein concentration (vegetative state) to the high ComK protein concentration (competence state) under stable Lévy noise.We demonstrate choices of the non-Gaussianity index α and the noise intensity ǫ which generate the ComK protein escape from the low concentration to the high concentration. We also reveal the optimal combination of both parameters α and ǫ making the tipping time shortest. Moreover, we find that different initial concentrations around the low ComK protein concentration evolve to a metastable state, and provide the optimal α and ǫ such that the distance between the deterministic competence state and the metastable state is smallest.

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Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

Cited by 20 publications

References 53 publications

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

The Onsager–Machlup function as Lagrangian for the most probable path of a jump-diffusion process

Most probable dynamics of a genetic regulatory network under stable Lévy noise

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