A Master equation approach to modeling an artificial protein motor

Linear bio-molecular motors move unidirectionally along a track by coordinating several different processes, such as fuel (ATP) capture, hydrolysis, conformational changes, binding and unbinding from a track, and center-of-mass diffusion. A better understanding of the interdependencies between these processes, which take place over a wide range of different time scales, would help elucidate the general operational principles of molecular motors. Artificial molecular motors present a unique opportunity for such a study because motor structure and function are a priori known. Here we describe use of a Master equation approach, integrated with input from Langevin and molecular dynamics modeling, to stochastically model a molecular motor across many time scales. We apply this approach to a specific concept for an artificial protein motor, the Tumbleweed.Comment: Submitted to Chemical Physics; 9 pages, 7 figure

Collective dynamics of actomyosin cortex endow cells with intrinsic mechanosensing properties

Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent, purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodelling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger an intrinsic mechanical response of the actomyosin cortex. Cortical retrograde flow resulting from actin polymerisation at the edges is shown to be modulated by the stress resulting from myosin contractility, which in turn regulates the cell size in a force-dependent manner. The model describes the maximum force that cells can exert and the maximum speed at which they can contract, which are measured experimentally. These limiting cases are found to be associated with energy dissipation phenomena which are of the same nature as those taking place during the contraction of a whole muscle. This explains the fact that single nonmuscle cell and whole muscle contraction both follow a Hill-like force-velocity relationship

Extreme-value statistics of stochastic transport processes

We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in molecular motor motion along linear filaments. For one-dimensional biased random walks, we derive exact results which tighten bounds for entropy production extrema obtained with martingale theory and reveal a symmetry between the distribution of the maxima and minima of entropy production. Furthermore, we show that the relaxation spectrum of the full generating function, and hence of any moment, of the finite-time extrema distributions can be written in terms of the Marcenko-Pastur distribution of random-matrix theory. Using this result, we obtain efficient estimates for the extreme-value statistics of stochastic transport processes from the eigenvalue distributions of suitable Wishart and Laguerre random matrices. We confirm our results with numerical simulations of stochastic models of molecular motors