Discrete Kinetic Models for Molecular Motors: Asymptotic Velocity and Gaussian Fluctuations

Faggionato, Alessandra; Silvestri, Vittoria

doi:10.1007/s10955-014-1106-8

Cited by 3 publications

(18 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [15] we study also the gaussian fluctuations of the skeleton process, proving an invariance principle if E 0 * (S 2 ) < +∞. We concentrate here on large deviations.…”

Section: Main Results For Random Walks On Quasi 1d Latticesmentioning

confidence: 89%

Random walks on quasi one dimensional lattices: Large deviations and fluctuation theorems

Faggionato¹,

Silvestri²

2017

Ann. Inst. H. Poincaré Probab. Statist.

Self Cite

View full text Add to dashboard Cite

Several stochastic processes modeling molecular motors on a linear track are given by random walks (not necessarily Markovian) on quasi 1d lattices and share a common regenerative structure. Analyzing this abstract common structure, we derive information on the large fluctuations of the stochastic process by proving large deviation principles for the first-passage times and for the position. We focus our attention on the Gallavotti-Cohen-type symmetry of the position rate function (fluctuation theorem), showing its equivalence with the independence of suitable random variables. In the special case of Markov random walks, we show that this symmetry is universal only inside a suitable class of quasi 1d lattices.

show abstract

“…In [15] we study also the gaussian fluctuations of the skeleton process, proving an invariance principle if E 0 * (S 2 ) < +∞. We concentrate here on large deviations.…”

Section: Main Results For Random Walks On Quasi 1d Latticesmentioning

confidence: 89%

Random walks on quasi one dimensional lattices: Large deviations and fluctuation theorems

Faggionato¹,

Silvestri²

2017

Ann. Inst. H. Poincaré Probab. Statist.

Self Cite

View full text Add to dashboard Cite

show abstract

“…ψ x has finite mean for all vertices x in G. It is then simple to show that E(S 1 ) < ∞. As derived in [16], since E(S 1 ) < ∞, almost surely the skeleton process and therefore also the cell process admit an asymptotic velocity:…”

Section: Previous Results On the Asymptotic Velocity And Large Deviatmentioning

confidence: 85%

“…We refer the interested reader to [16] for what concerns the Gaussian fluctuations of X * . In the rest of this section we concentrate on large deviations.…”

Section: Previous Results On the Asymptotic Velocity And Large Deviatmentioning

confidence: 99%

“…1 "Good" means that the level sets of I are compact Moreover, via Legendre transform, the above identities (10), (11) and (12) correspond respectively to the following (15), (16) and (17):…”

Section: 2mentioning

confidence: 99%

“…We point out that in [16] the GC symmetry for the LD rate function of the cell process is analyzed for a larger class of random processes, having a suitable regenerative structure. Moreover, it has been proved (cf.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fluctuation theorems for discrete kinetic models of molecular motors

Faggionato

Silvestri

2017

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a linear fashion. We show that, for a suitable class of quasi-1d lattices, the large deviation rate function associated to the position of the walker satisfies a Gallavotti-Cohen symmetry for any choice of the dynamical parameters defining the stochastic walk. This class includes the linear model considered in [31]. We also derive fluctuation theorems for the timeintegrated cycle currents and discuss how the matrix approach of [31] can be extended to derive the above Gallavotti-Cohen symmetry for any Markov random walk on Z with periodic jump rates. Finally, we review in the present context some large deviation results of [17] and give some specific examples with explicit computations.

show abstract

A parity breaking Ising chain Hamiltonian as a Brownian motor

Cornu¹,

Hilhorst²

2014

EPL

View full text Add to dashboard Cite

We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonianand let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio U 3 /U 2 and of the conserved magnetization M = k s k . The symmetry of the U 3 term in the Hamiltonian is discussed.

show abstract

Discrete Kinetic Models for Molecular Motors: Asymptotic Velocity and Gaussian Fluctuations

Cited by 3 publications

References 22 publications

Random walks on quasi one dimensional lattices: Large deviations and fluctuation theorems

Random walks on quasi one dimensional lattices: Large deviations and fluctuation theorems

Fluctuation theorems for discrete kinetic models of molecular motors

A parity breaking Ising chain Hamiltonian as a Brownian motor

Contact Info

Product

Resources

About