Thermodynamics and Kinetics of a Brownian Motor

Astumian, R. Dean

doi:10.1126/science.276.5314.917

Cited by 1,340 publications

(1,032 citation statements)

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“…e.g. [2], and Doering, Ermentrout, and Oster [5], Peskin, Ermentrout, and Oster [21]. They consist either in discussions of distribution functions directly or of stochastic differential equations, which give rise to the distribution functions via the Chapman-Kolmogorov Equation.…”

Section: Introductionmentioning

confidence: 99%

Transport in a molecular motor system

2004

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Abstract. Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.Mathematics Subject Classification. 34D23, 35K50, 35K57, 92C37, 92C45.

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Section: Introductionmentioning

confidence: 99%

Transport in a molecular motor system

2004

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“…The finiteness of the state space ensures that the complexity of the model is isolated within the time dimension, avoiding in particular the issues raised in [30]. Such a process can be used to model phenomena as diverse as the fluctuation-driven transport of molecular motors [1], stochastic resonance in lasers and neuron firing [13], quasienergy banding in periodically-driven mesoscopic electric circuits [3], and seasonality in population dynamics [31], as well as periodically-driven deterministic processes amenable to coarse-graining. Continuous time models of all of these phenomena were previously outside the scope of AFTs, all of which had been proved under the assumption of homogeneous dynamics, because they rely fundamentally on a timedependent protocol driving the process.…”

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confidence: 99%

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Shargel¹,

Chou

2009

J Stat Phys

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Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.

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“…The forward motion of a tightly coupled processive molecular motor such as kinesin is inherently stochastic and constitutes a biased random walk (Berg 1993;Astumian 1997;Thomas et al 2001). Visscher et al (1999) determined the experimental randomness parameter r for kinesin, which may be defined as (Svoboda et al 1994) …”

Section: Randomnessmentioning

confidence: 99%

Kinesin: a molecular motor with a spring in its step

Thomas

Imafuku

Kamiya

et al. 2002

Proc. R. Soc. Lond. B

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A key step in the processive motion of two-headed kinesin along a microtubule is the 'docking' of the neck linker that joins each kinesin head to the motor's dimerized coiled-coil neck. This process is similar to the folding of a protein β-hairpin, which starts in a highly mobile unfolded state that has significant entropic elasticity and finishes in a more rigid folded state. We therefore suggest that neck-linker docking is mechanically equivalent to the thermally activated shortening of a spring that has been stretched by an applied load. This critical tension-dependent step utilizes Brownian motion and it immediately follows the binding of ATP, the hydrolysis of which provides the free energy that drives the kinesin cycle. A simple three-state model incorporating neck-linker docking can account quantitatively for both the kinesin force-velocity relation and the unusual tension-dependence of its Michaelis constant. However, we find that the observed randomness of the kinesin motor requires a more detailed four-state model. Monte Carlo simulations of single-molecule stepping with this model illustrate the possibility of sub-8 nm steps, the size of which is predicted to vary linearly with the applied load.

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Thermodynamics and Kinetics of a Brownian Motor

Cited by 1,340 publications

References 47 publications

Transport in a molecular motor system

Transport in a molecular motor system

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Kinesin: a molecular motor with a spring in its step

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