Coexistence and efficiency of normal and anomalous transport by molecular motors in living cells

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included

Fluctuating-friction molecular motors

We show that the correlated stochastic fluctuation of the friction coefficient can give rise to long-range directional motion of a particle undergoing Brownian random walk in a constant periodic energy potential landscape. The occurrence of this motion requires the presence of two additional independent bodies interacting with the particle via friction and via the energy potential, respectively, which can move relative to each other. Such three-body system generalizes the classical Brownian ratchet mechanism, which requires only two interacting bodies. In particular, we describe a simple two-level model of fluctuating-friction molecular motor that can be solved analytically. In our previous work [M.K., L.M and D.P. 2000 J. Nonlinear Opt. Phys. Mater. vol. 9, 157] this model has been first applied to understanding the fundamental mechanism of the photoinduced reorientation of dye-doped liquid crystals. Applications of the same idea to other fields such as molecular biology and nanotechnology can however be envisioned. As an example, in this paper we work out a model of the actomyosin system based on the fluctuating-friction mechanism.Comment: to be published in J. Physics Condensed Matter (http://www.iop.org/Journals/JPhysCM

Elastically coupled molecular motors

We study the influence of filament elasticity on the motion of collective molecular motors. It is found that for a backbone flexibility exceeding a characteristic value (motor stiffness divided through the mean displacement between attached motors), the ability of motors to produce force reduces as compared to rigidly coupled motors, while the maximum velocity remains unchanged. The force-velocity-relation in two different analytic approximations is calculated and compared with Monte-Carlo simulations. Finally, we extend our model by introducing motors with a strain-dependent detachment rate. A remarkable crossover from the nearly hyperbolic shape of the Hill curve for stiff backbones to a linear force-velocity relation for very elastic backbones is found. With realistic model parameters we show that the backbone flexibility plays no role under physiological conditions in muscles, but it should be observable in certain in vitro assays.Comment: REVTeX, 13 pages, 11 figures; presentation improved; to appear in European Physical Journal B; a Java applet showing the simulation is accessible at http://www.physik.tu-muenchen.de/~avilfan/ecmm

Traffic of Molecular Motors

Molecular motors perform active movements along cytoskeletal filaments and drive the traffic of organelles and other cargo particles in cells. In contrast to the macroscopic traffic of cars, however, the traffic of molecular motors is characterized by a finite walking distance (or run length) after which a motor unbinds from the filament along which it moves. Unbound motors perform Brownian motion in the surrounding aqueous solution until they rebind to a filament. We use variants of driven lattice gas models to describe the interplay of their active movements, the unbound diffusion, and the binding/unbinding dynamics. If the motor concentration is large, motor-motor interactions become important and lead to a variety of cooperative traffic phenomena such as traffic jams on the filaments, boundary-induced phase transitions, and spontaneous symmetry breaking in systems with two species of motors. If the filament is surrounded by a large reservoir of motors, the jam length, i.e., the extension of the traffic jams is of the order of the walking distance. Much longer jams can be found in confined geometries such as tube-like compartments.Comment: 10 pages, latex, uses Springer styles (included), to appear in the Proceedings of "Traffic and Granular Flow 2005

Interaction of molecular motors can enhance their efficiency

Particles moving in oscillating potential with broken mirror symmetry are considered. We calculate their energetic efficiency, when acting as molecular motors carrying a load against external force. It is shown that interaction between particles enhances the efficiency in wide range of parameters. Possible consequences for artificial molecular motors are discussed.Comment: 6 pages, 8 figure

Theoretical Analysis of Dynamic Processes for Interacting Molecular Motors

Biological transport is supported by collective dynamics of enzymatic molecules that are called motor proteins or molecular motors. Experiments suggest that motor proteins interact locally via short-range potentials. We investigate the fundamental role of these interactions by analyzing a new class of totally asymmetric exclusion processes where interactions are accounted for in a thermodynamically consistent fashion. Theoretical analysis that combines various mean-field cal- culations and computer simulations suggests that dynamic properties of molecular motors strongly depend on interactions, and correlations are stronger for interacting motor proteins. Surprisingly, it is found that there is an optimal strength of interactions (weak repulsion) that leads to a maxi- mal particle flux. It is also argued that molecular motors transport is more sensitive to attractive interactions. Applications of these results for kinesin motor proteins are discussed

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

Toy model for molecular motors

A hopping model for molecular motors is presented consisting of a state with asymmetric hopping rates with period 2 and a state with uniform hopping rates. State changes lead to a stationary unidirectional current of a particle. The current is explicitly calculated as a function of the rate of state changes, including also an external bias field. The Einstein relation between the linear mobility of the particle and its diffusion coefficient is investigated. The power input into the system is derived, as well as the power output resulting from the work performed against the bias field. The efficiency of this model is found to be rather small.Comment: 11 pages Latex, 7 postscript figures, to be published in Physica