Survival and residence times in disordered chains with bias

Pury, Pedro A.; Cáceres, Manuel O.

doi:10.1103/physreve.66.021112

Cited by 13 publications

(23 citation statements)

References 48 publications

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“…Please remark that the probability to stay put [Eq. (12)] is the only solution that gives the correct results for both v 0 and D 0 for arbitrary values of ⑀ when we want the ratio p + / p − to be consistent with Boltzmann statistics. Therefore, no valid fixed-time LMC algorithm exists with sЈ = 0.…”

Section: ͑9͒mentioning

confidence: 83%

“…In other cases, the simulation results are apparently limited to small biases, although it is not always explicitly mentioned (see, e.g., [ [7][8][9][10]]). For instance, one can look at the problem of the survival probability of a biased random walker in a disordered medium [11,12]. Biased random walks can also be studied in the context of continuous time random walks (CTRW) [13,14].…”

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confidence: 99%

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Building reliable lattice Monte Carlo models for real drift and diffusion problems

Gauthier

Slater

2004

Phys. Rev. E

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We revisit the well-known issue of representing an overdamped drift-and-diffusion system by an equivalent lattice random-walk model. We demonstrate that commonly used Monte Carlo algorithms do not conserve the diffusion coefficient when a driving field of arbitrary amplitude is present, and that such algorithms would actually require fluctuating jumping times and one clock per Cartesian direction to work properly. Although it is in principle possible to construct valid algorithms with fixed time steps, we show that no such algorithm can be used in more than two dimensions if the jumps are made along only one axis at each time step.

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Section: ͑9͒mentioning

confidence: 83%

mentioning

confidence: 99%

Building reliable lattice Monte Carlo models for real drift and diffusion problems

Gauthier

Slater

2004

Phys. Rev. E

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“…The backward equation method has been widely used to calculate mean first-passage time and other average values (16)(17)(18)(19). However, this method has limited value for obtaining distribution functions such as dwell-time distributions.…”

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confidence: 99%

Extending the absorbing boundary method to fit dwell-time distributions of molecular motors with complex kinetic pathways

Liao¹,

Spudich

Parker

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

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Dwell-time distributions, waiting-time distributions, and distributions of pause durations are widely reported for molecular motors based on single-molecule biophysical experiments. These distributions provide important information concerning the functional mechanisms of enzymes and their underlying kinetic and mechanical processes. We have extended the absorbing boundary method to simulate dwell-time distributions of complex kinetic schemes, which include cyclic, branching, and reverse transitions typically observed in molecular motors. This extended absorbing boundary method allows global fitting of dwell-time distributions for enzymes subject to different experimental conditions. We applied the extended absorbing boundary method to experimental dwell-time distributions of single-headed myosin V, and were able to use a single kinetic scheme to fit dwell-time distributions observed under different ligand concentrations and different directions of optical trap forces. The ability to use a single kinetic scheme to fit dwell-time distributions arising from a variety of experimental conditions is important for identifying a mechanochemical model of a molecular motor. This efficient method can be used to study dwell-time distributions for a broad class of molecular motors, including kinesin, RNA polymerase, helicase, F1 ATPase, and to examine conformational dynamics of other enzymes such as ion channels.myosin ͉ single molecule ͉ waiting-time distributions ͉ pause durations T he movements of molecular motors are frequently recorded in biophysical experiments using tools such as optical trap assays and single molecule fluorescence assays. Due to transitions of conformational and chemical states, the motions of molecular motors usually show alternations between an enzyme's moving and pausing behaviors. For example, doubleheaded myosin VI moving on an actin filament demonstrates a mechanical stepping behavior ( Fig. 1a) (1), whereas the events of actin binding and unbinding of a single-headed myosin V construct show alternate phases of oscillating and pausing (Fig. 1b) (2). Collecting a large number of these events and performing statistical analysis provides insight into the kinetics and mechanochemical characteristics of an individual molecule.Dwell events arise from pauses in mechanical stepping (Fig. 1a) or stochastic delays before a binding-unbinding transition (Fig. 1b). Each dwell represents an experimentally observable event, which can be a single conformational or chemical state, or a collective number of states. The dwell time, or the duration of a dwell, is determined by the probability of exiting a dwell after the time entering it. Histograms of dwell times, also called dwell-time distributions, waiting-time distributions, or distributions of pause durations, are widely used to decipher single molecule kinetics.The dynamics of an enzyme's activity can be modeled as a number of kinetic states using kinetic equations (3) or mechanical coordinates using diffusion-based (Fokker-Planck) equations (4). For quest...

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“…Therefore, the model does not present anomalous diffusion [1]. For the MFPT averaged over disorder with the AA boundary conditions, we obtain up to first order in ǫ [22,26], The asymmetry in the hopping transitions links the strength of the bias with the fluctuation of the disorder, defined by F ≡ β 2 − β 2 1 /β 2 1 . In our particular case, we get β 1 = 4/3, and F = 1/4.…”

Section: Models Of Disordered Chainsmentioning

confidence: 89%

Multifractal spectra of mean first-passage-time distributions in disordered chains

Pury

Cáceres²

2003

Phys. Rev. E

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Survival and residence times in disordered chains with bias

Cited by 13 publications

References 48 publications

Building reliable lattice Monte Carlo models for real drift and diffusion problems

Building reliable lattice Monte Carlo models for real drift and diffusion problems

Extending the absorbing boundary method to fit dwell-time distributions of molecular motors with complex kinetic pathways

Multifractal spectra of mean first-passage-time distributions in disordered chains

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