Enhanced Diffusion of Molecular Motors in the Presence of Adenosine Triphosphate and External Force

Shinagawa, Ryota; Sasaki, Kazuo

doi:10.7566/jpsj.85.064004

Cited by 12 publications

(28 citation statements)

References 34 publications

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“…The philosophy underlying the analysis of mapping trajectories on kinetic model, proposed here on kinesin-1 as well as others on F 1 -ATPase [29,46], is in essence similar to the one by the recent study which has quantified circulating flux on configurational phase space (or mode space) to diagnose broken DB and non-equilibrium dynamics at mesoscopic scale [37,38]. Lastly, our study confers quantitative insights into how much of the chemical free energy supplied to active systems (enzymes, molecular motors) is converted to mechanical movement in space and eventually dissipated into heat.…”

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confidence: 99%

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Hwang

Hyeon

2016

Preprint

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Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related to each other. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1 whose dynamics is confined on one-dimensional tracks is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers thermodynamic basis to understand the heat enhanced self-diffusion of exothermic enzymes.Together with recent studies [1][2][3][4], Riedel et al. [5] have demonstrated a rather surprising result, from a perspective of equilibrium statistical mechanics: Diffusion constants (D) of exothermic enzymes, measured from fluorescence correlation spectroscopy (FCS), increase linearly with their catalytic turnover rates V cat , so that the enhancement of diffusivity at maximal activity (maximum V cat ) is as large aswhere D 0 and D max are the diffusion constants measured by FCS at V cat = 0 and maximal V cat , respectively. Their enigmatic observation [5] has called much attention of biophysics community to the physical origin of the activity-dependent diffusivity of a single enzyme. Golestanian [6] considered four distinct scenarios (self-thermophoresis, boost in kinetic energy, stochastic swimming, collective heating) to account for this observation quantitatively; however, the extent of enhancement observed in the experiment was still orders of magnitude greater than the theoretical estimates from the suggested mechanisms. Bai et al.[7] also drew a similar conclusion by considering hydrodynamic coupling between the conformational change of enzyme and surrounding media. The experimental demonstration of enzymes' enhanced diffusion with multiple control experiments in Ref.[5] is straightforward; however, physical insight of the observed phenomena is currently missing [5,6,8,9].While seemingly entirely different from freely diffusing enzymes, kinesin-1 [10-15] is also a substrate-catalyzing enzyme. Conformational dynamics of kinesin-1, induced by ATP hydrolysis and thermal fluctuations, is rectified into a unidirectional movement with a high fidelity [16,17]; hydrolysis of a single ATP almost always leads to 8 nm step [18]. Every step of kinesin-1 along 1D tracks, an outcome of cyclic chemical reaction, can be mapped (2)µ, ..., (N )µ denote distinc...

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confidence: 99%

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Hwang

Hyeon

2016

Preprint

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“…Driven underdamped particle in a periodic potential An underdamped particle being driven on a periodic potential by a constant external force is a simple system with two dynamical coordinates, position and velocity, that can exhibit non-trivial nonequilibrium properties due to competing ballistic and diffusive modes of transport. 72,73 Large deviation functions for current fluctuations in this model can be obtained by numerically exact diagonalizations of the tilted generator, and the controlled ensemble can show diverse behavior in different parameter regimes. 74 We consider this model to benchmark our variational optimization algorithm.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations

Das

Limmer

2019

The Journal of Chemical Physics

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We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis is made possible by explicit forms for the gradients of a cost function in terms of the susceptibility of driven trajectories to changes in variational parameters. We consider probabilities of time-integrated dynamical observables as characterized by their large deviation functions, and find that in many cases the variational estimate is quantitatively accurate. Additionally, we provide expressions to exactly correct the variational estimate that can be evaluated directly. We benchmark this algorithm against the numerically exact solution of a model of a driven particle in a periodic potential, where the control force can be represented with a complete basis. We then demonstrate the utility of the algorithm in a model of repulsive particles on a line, which undergo a dynamical phase transition, resulting in singular changes to the form of the optimal control force. In both systems, we find fast convergence and are able to evaluate large deviation functions with significant increases in statistical efficiency over alternative Monte Carlo approaches.

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“…In our previous work [9], it is demonstrated theoretically that the diffusion enhancement can occur in molecular motors that move autonomously by consuming free energy available from the chemical reaction catalyzed by themselves if a constant external force of appropriate magnitude is applied. In particular, it is suggested that the diffusion enhancement can be observed in the F 1 -ATPase, a biological rotary motor, which catalyzes the hydrolysis of adenosine triphosphate (ATP).…”

Section: Introductionmentioning

confidence: 99%

“…The models considered here and in the previous work [9] are of ratchet type [10][11][12], in which a moving part of the motor (e.g., the rotor in a rotary motor) is represented by a Brownian particle subject to a potential, which is switched to another upon a chemical transition associated with the reaction catalyzed by the motor. In the model used in the previous paper [9], an external force, as well as rate constants, can control the transition rates because the transition rates are assumed to depend on the particle position, which is affected by the force; the dependence of the diffusion coefficient on the force for given rate constants exhibits enhancement in a certain range of the force. By contrast, an external force is not included in the model of the present paper, and a rate constant is varied to study the diffusion enhancement.…”

Section: Introductionmentioning

confidence: 99%

Diffusion enhancement of Brownian motors revealed by a solvable model

Kanada¹,

Shinagawa²,

Sasaki³

2018

Phys. Rev. E

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A solvable model is proposed and analyzed to reveal the mechanism underlying the diffusion enhancement recently reported for a model of molecular motors and predicted to be observed in the biological rotary motor F1-ATPase. It turns out that the diffusion enhancement for the present model can approximately described by a random walk in which the waiting time for a step to occur is exponentially distributed and it takes nonzero time to proceed forward by the step. It is shown that the diffusion coefficient of such a random walk can significantly be increased when the average waiting time is comparable to the average stepping time.

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Enhanced Diffusion of Molecular Motors in the Presence of Adenosine Triphosphate and External Force

Cited by 12 publications

References 34 publications

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations

Diffusion enhancement of Brownian motors revealed by a solvable model

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