A Stochastic Hybrid Framework for Obtaining Statistics of Many Random Walkers in a Switching Environment

Levien, Ethan; Bressloff, Paul C.

doi:10.1137/16m1061084

Cited by 9 publications

(12 citation statements)

References 24 publications

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“…These new statistics, which do not appear in the single cell model, are what we refer to as a population level statistics, and it has been established that their computation is highly nontrivial, even for simple networks. Existing techniques for understanding such statistics involve taking the large population limit: M → ∞ [26]. In contrast, our results are applicable when it is appropriate to take the large system size limit Ω → ∞, while keeping M fixed.…”

Section: Ethan Levien and Paul C Bressloff K=1mentioning

confidence: 87%

“…In this paper we have explored how the topological deficiency relates to the stationary behavior of a multiscale CRN. The type of multiscale dynamics we have focused on is typical in systems with intrinsic and extrinsic noise [20,28,26,11]. In such systems, a scaling limit of the extrinsic noise is not physically meaningful, and therefore a deterministic approximation of the full stochastic dynamics fails to capture important features of the dynamics.…”

Section: Correlations In Gene Expressionmentioning

confidence: 99%

“…As an application of these results, we have established conditions under which higher order statistics of a population level model vanish. These population level statistics arise when many independent chemical systems are functioning in the same random environment, and are difficult to study analytically [26,6,3,4,5].…”

Section: Correlations In Gene Expressionmentioning

confidence: 99%

“…While the chemical systems might not interact over a timescale that is relevant to the function they perform, they are correlated through the common environment in which they evolve. This interpretation leads to an entirely new set of interesting statistics, namely, those corresponding to the population level description [26,5]. These statistics measure the degree to which environmental factors introduce correlations between individuals (cells or organisms) in a population.…”

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confidence: 99%

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Robustness of Stochastic Chemical Reaction Networks to Extrinsic Noise: The Role of Deficiency

Levien¹,

Bressloff²

2018

Multiscale Model. Simul.

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The biochemical systems inside a living cell are able to reliably perform complex tasks while subjected to various sources of noise. In this study we consider stochastic models of biochemical networks evolving in the presence of dynamic random environments. These environments are themselves modeled as chemical reaction networks so that the full system can be viewed as a multiscale chemical reaction network. The multiscale structure arises from the fact that the environment and the internal system may operate on different timescales. While previous results in chemical reaction network theory have established that certain dynamic behavior can be ruled out when a topological parameter, known as the network deficiency, is zero, these results fail to capture the behavior that can be observed in multiscale networks. We demonstrate that the deficiency of the network has implications for how robust it is to environmental noise. We then show how our results can be used to prove that correlations in a population of chemical reaction networks in a random environment vanish given certain topological constraints.

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Section: Ethan Levien and Paul C Bressloff K=1mentioning

confidence: 87%

Section: Correlations In Gene Expressionmentioning

confidence: 99%

Section: Correlations In Gene Expressionmentioning

confidence: 99%

mentioning

confidence: 99%

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Robustness of Stochastic Chemical Reaction Networks to Extrinsic Noise: The Role of Deficiency

Levien¹,

Bressloff²

2018

Multiscale Model. Simul.

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“…This type of scenario is common in cell biology, where a macromolecule diffuses in some bounded intracellular domain that contains one or more narrow channels within the boundary of the domain; each channel is controlled by a stochastic gate that switches between an open and closed state [13]. Applications in biological physics include diffusion-limited reactions [14], neurotransmission [15], insect physiology [16], stochastically gated gap junctions [17], and lateral membrane diffusion [18]. In our previous studies of diffusion in domains with randomly switching boundaries, we have focused on calculating mean first passage times and related quantities using a method of moments [19,20].…”

Section: Introductionmentioning

confidence: 99%

Stochastically gated local and occupation times of a Brownian particle

Bressloff

2017

Phys. Rev. E

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We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically-gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the stochastic gate.

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Propagation of Extrinsic Fluctuations in Biochemical Birth–Death Processes

Bressloff

Levien

2018

Bull Math Biol

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A Stochastic Hybrid Framework for Obtaining Statistics of Many Random Walkers in a Switching Environment

Cited by 9 publications

References 24 publications

Robustness of Stochastic Chemical Reaction Networks to Extrinsic Noise: The Role of Deficiency

Robustness of Stochastic Chemical Reaction Networks to Extrinsic Noise: The Role of Deficiency

Stochastically gated local and occupation times of a Brownian particle

Propagation of Extrinsic Fluctuations in Biochemical Birth–Death Processes

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