Dwell time distributions of the molecular motor myosin V

Exact Coarse Graining Preserves Entropy Production out of Equilibrium

The entropy production rate associated with broken time-reversal symmetry provides an essential characterization of nanosystems out of equilibrium, from driven colloidal particles to molecular motors. Limited access to the dynamical states is generally expected to hinder the correct estimation of this observable. Here we show how memoryless jump processes can be coarse grained, exactly preserving its average and fluctuations at stationarity. This supports univocal applicability of fluctuation theorems for entropy and allows inference of the genuine thermodynamics together with inaccessible process details.

Characteristics of Myosin V Processivity

Myosin V is a processive doubled-headed biomolecular motor involved in many intracellular organelle and vesicle transport. The unidirectional movement is coupled with the adenosine triphosphate (ATP) hydrolysis and product release cycle. With the progress of experimental techniques and the enhancement of measuring directness, detailed knowledge of the motility of myosin V has been obtained. Following the ATPase cycle, the 4-state mechanochemical model of the myosin V's processive movement is used. The transitions between various states take place in a stochastic manner. We can use the master equation to analyze and calculate quantitatively. Meanwhile, the effect of the reverse reaction is taken fully into account. We fit the mean velocity, the mean dwell time, the mean run length, and the ratio of forward/backward steps as a functionof ATP, ADP, and Pi concertration. The theoretical curves are generally in line with the experimental data. This work provides a new insight for the characteristic of myosin V.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Tight-binding approach to overdamped Brownian motion on a bichromatic periodic potential

We present a theoretical treatment of overdamped Brownian motion on a time-independent bichromatic periodic potential with spatially fast- and slow-changing components. In our approach, we generalize the Wannier basis commonly used in the analysis of periodic systems to define a basis of S states that are localized at local minima of the potential. We demonstrate that the S states are orthonormal and complete on the length scale of the periodicity of the fast-changing potential, and we use the S-state basis to transform the continuous Smoluchowski equation for the system to a discrete master equation describing hopping between local minima. We identify the parameter regime where the master equation description is valid and show that the interwell hopping rates are well approximated by Kramers' escape rate in the limit of deep potential minima. Finally, we use the master equation to explore the system dynamics and determine the drift and diffusion for the system.

Thermal fluctuation statistics in a molecular motor described by a multidimensional master equation

We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy transfer leads to statistical correlations between thermal fluctuations in different degrees of freedom. For long times, the energy transfer is a multivariate diffusion process with constant drift and diffusion. The fluctuations and drift align in the strong-coupling limit enabling a one-dimensional description along the coupled coordinate. We derive formal expressions for the probability distribution and simulate single trajectories of the system in the near- and far-from-equilibrium limits both for strong and weak coupling. Our results show that the hopping statistics provide an opportunity to distinguish different operating regimes.