An alternative route to the system-size expansion

Cianci, Claudia; Schnoerr, David; Piehler, Andreas; Grima, Ramon

doi:10.1088/1751-8121/aa85aa

Cited by 6 publications

(5 citation statements)

References 28 publications

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“…In this form, the validity and usefulness of the method was demonstrated in many works, e.g. [1,11,12,14,18,20,21,35].…”

Section: Discussionmentioning

confidence: 91%

Intrinsic ratchets: A Hamiltonian approach

Plyukhin

2018

Phys. Rev. E

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An asymmetric Brownian particle subjected to an external time-dependent force may acquire a net drift velocity, and thus operate as a motor or ratchet, even if the external force is represented by an unbiased time-periodic function or by a zero-centered noise. For an adequate description of such ratchets, a conventional Langevin equation linear in the particle's velocity is insufficient, and one needs to take into account the first nonlinear correction to the dissipation force which emerges beyond the weak coupling limit. We derived microscopically the relevant nonlinear Langevin equation by extending the standard projection operation technique beyond the weak coupling limit. The particle is modeled as a rigid cluster of atoms and its asymmetry may be geometrical, compositional (when a cluster is composed of atoms of different types), or due to a combination of both factors. The drift velocity is quadratic in the external force's amplitude and increases with decreasing the force's frequency (for a periodic force) and inverse correlation time (for a fluctuating force). The maximum value of the drift velocity is independent on the particle's mass and achieved in the adiabatic limit, i.e. for an infinitely slow change of the external field.

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“…In this form, the validity and usefulness of the method was demonstrated in many works, e.g. [1,11,12,14,18,20,21,35].…”

Section: Discussionmentioning

confidence: 91%

Intrinsic ratchets: A Hamiltonian approach

Plyukhin

2018

Phys. Rev. E

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“…Although LNA was historically derived as a second order system size approximation of the chemical master equation, resulting in a Fokker-Planck equation with a stochastic differential equation interpretation and a Gaussian steady state distribution [20], this is not necessary. LNA, as well as higher order approximations, could be derived as Taylor expansions on the moment equations [21]. In fact, it could be shown that LNA could be interpreted as a linear propensity CRN approximation that preserves discreteness and non-negativity of the state variables (see Section V-B).…”

Section: B Linear Noise Approximationmentioning

confidence: 99%

Coupled Reaction Networks for Noise Suppression

Xiao

Fang

Yan

et al. 2019

2019 American Control Conference (ACC)

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Noise is intrinsic to many important regulatory processes in living cells, and often forms obstacles to be overcome for reliable biological functions. However, due to stochastic birth and death events of all components in biomolecular systems, suppression of noise of one component by another is fundamentally hard and costly. Quantitatively, a widelycited severe lower bound on noise suppression in biomolecular systems was established by Lestas et. al. in 2010, assuming that the plant and the controller have separate birth and death reactions. This makes the precision observed in several biological phenomena, e.g. cell fate decision making and cell cycle time ordering, seem impossible. We demonstrate that coupling, a mechanism widely observed in biology, could suppress noise lower than the bound of Lestas et. al. with moderate energy cost. Furthermore, we systematically investigate the coupling mechanism in all two-node reaction networks, showing that negative feedback suppresses noise better than incoherent feedforward achitectures, coupled systems have less noise than their decoupled version for a large class of networks, and coupling has its own fundamental limitations in noise suppression. Results in this work have implications for noise suppression in biological control and provide insight for a new efficient mechanism of noise suppression in biology.

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“…Although LNA was historically derived as a second order system size approximation of the chemical master equation, resulting in a Fokker-Planck equation with a stochastic differential equation interpretation and a Gaussian steady state distribution [26], this is not necessary. LNA, as well as higher order approximations, could be derived as Taylor expansions on the moment equations [27]. In fact, it could be shown that LNA could be interpreted as a linear propensity CRN approximation that preserves discreteness and non-negativity of the state variables (see Section V-B).…”

Section: B Linear Noise Approximationmentioning

confidence: 99%

Coupled Reaction Networks for Noise Suppression

Xiao

Fang

Doyle

2018

Preprint

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Noise is intrinsic to many important regulatory processes in living cells, and often forms obstacles to be overcome for reliable biological functions. However, due to stochastic birth and death events of all components in biomolecular systems, suppression of noise of one component by another is fundamentally hard and costly. Quantitatively, a widelycited severe lower bound on noise suppression in biomolecular systems was established by Lestas et. al. in 2010, assuming that the plant and the controller have separate birth and death reactions. This makes the precision observed in several biological phenomena, e.g., cell fate decision making and cell cycle time ordering, seem impossible. We demonstrate that coupling, a mechanism widely observed in biology, could suppress noise lower than the bound of Lestas et. al. with moderate energy cost. Furthermore, we systematically investigate the coupling mechanism in all two-node reaction networks, showing that negative feedback suppresses noise better than incoherent feedforward achitectures, coupled systems have less noise than their decoupled version for a large class of networks, and coupling has its own fundamental limitations in noise suppression. Results in this work have implications for noise suppression in biological control and provide insight for a new efficient mechanism of noise suppression in biology.

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An alternative route to the system-size expansion

Cited by 6 publications

References 28 publications

Intrinsic ratchets: A Hamiltonian approach

Intrinsic ratchets: A Hamiltonian approach

Coupled Reaction Networks for Noise Suppression

Coupled Reaction Networks for Noise Suppression

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