Run-and-tumble motion: field theory and entropy production

Garcia-Millan, Rosalba; Pruessner, Gunnar

doi:10.48550/arxiv.2012.02900

Cited by 3 publications

(7 citation statements)

References 29 publications

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“…Also, as pointed out at the end of Sec. VI, the continuous limit of our model corresponds exactly to a model of active matter run-and-tumble motion [54]. This suggests our techniques may be useful for solving a broad range of stochastic physical and biological problems.…”

Section: Discussionmentioning

confidence: 64%

“…The precise correspondence is described in Table I Effective mean concentration µ = α 1 k 12 +α 2 k 21 γ(k 12 +k 21 ) Effective mean position µ = 0 TABLE I. The parameter correspondence between the continuous birth-death-switching problem considered here, and the run-and-tumble problem considered by Garcia-Millan and Pruessner [54].…”

Section: E Switching Much Slower Than Degradationmentioning

confidence: 97%

“…153 and Eq. 154 can exactly describe the solution of an active matter run-and-tumble motion problem [54]. The precise correspondence is described in Table I Effective mean concentration µ = α 1 k 12 +α 2 k 21 γ(k 12 +k 21 ) Effective mean position µ = 0 TABLE I.…”

Section: E Switching Much Slower Than Degradationmentioning

confidence: 99%

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Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution

Vastola¹,

Gorin²,

Pachter³

et al. 2021

Preprint

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The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to solve analytically.It is particularly hard to solve for models involving bursting/gene switching, a biological feature that tends to produce heavy-tailed single cell RNA counts distributions. In this paper, we present a novel method for computing exact and analytic solutions to the CME in such cases, and use these results to explore approximate solutions valid in different parameter regimes, and to compute observables of interest. Our method leverages tools inspired by quantum mechanics, including ladder operators and Feynman-like diagrams, and establishes close formal parallels between the dynamics of bursty transcription, and the dynamics of bosons interacting with a single fermion. We focus on two problems: (i) the chemical birth-death process coupled to a switching gene/the telegraph model, and (ii) a model of transcription and multistep splicing involving a switching gene and an arbitrary number of downstream splicing steps. We work out many special cases, and exhaustively explore the special functionology associated with these problems. This is Part I in a two-part series of papers; in Part II, we explore an alternative solution approach that is more useful for numerically solving these problems, and apply it to parameter inference on simulated RNA counts data.

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Section: Discussionmentioning

confidence: 64%

Section: E Switching Much Slower Than Degradationmentioning

confidence: 97%

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Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution

Vastola¹,

Gorin²,

Pachter³

et al. 2021

Preprint

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show abstract

“…The external potential V (x) in Eq. (1a) has been moved to the perturbative part of the action, as it is usually not easily integrated, except for special cases, such as a harmonic one, similar to the effective friction potential of the velocity here [22,23]. More traditionally, one can recast the process (1) in a master equation on a lattice [17,24] and obtain Eq.…”

Section: Deriving the Field Theorymentioning

confidence: 99%

“…Because of the harmonic potential term τ −1 ∂ v (vφ) and the mixed term ivk, we cannot diagonalise the action by simply Fourier transforming in v as well. Instead we follow similar considerations for the harmonic potential acting on a particle's position using Hermite polynomials [22,23] and the eigenvalue problem of the Kramer's equation [18].…”

Section: Diagonalizing the Actionmentioning

confidence: 99%

Field Theory of free Active Ornstein-Uhlenbeck Particles

Bothe,

Pruessner

2021

Preprint

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We derive a Doi-Peliti field theory for free active Ornstein-Uhlenbeck particles, or, equivalently, free inertial Brownian particles, and present a way to diagonalise the Gaussian part of the action and calculate the propagator. Unlike previous coarse-grained approaches this formulation correctly tracks particle identity and yet can easily be expanded to include potentials and arbitrary reactions.

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Run-and-tumble motion: the role of reversibility

van Ginkel,

van Gisbergen,

Redig

2021

Preprint

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We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the 'active part' of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier-Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

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Run-and-tumble motion: field theory and entropy production

Cited by 3 publications

References 29 publications

Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution

Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution

Field Theory of free Active Ornstein-Uhlenbeck Particles

Run-and-tumble motion: the role of reversibility

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