Cooperative molecular motors moving back and forth

Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations

One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

Duty ratio of cooperative molecular motors

Molecular motors are found throughout the cells of the human body and have many different and important roles. These micromachines move along filament tracks and have the ability to convert chemical energy into mechanical work that powers cellular motility. Different types of motors are characterized by different duty ratios, which is the fraction of time that a motor is attached to its filament. In the case of myosin II (a nonprocessive molecular machine with a low duty ratio), cooperativity between several motors is essential to induce motion along its actin filament track. In this work we use statistical mechanical tools to calculate the duty ratio of cooperative molecular motors. The model suggests that the effective duty ratio of nonprocessive motors that work in cooperation is lower than the duty ratio of the individual motors. The origin of this effect is the elastic tension that develops in the filament which is relieved when motors detach from the track.

Tug of war of molecular motors: the effects of uneven load sharing

We analyze theoretically the problem of cargo transport along microtubules by motors of two species with opposite polarities. We consider two different one-dimensional models previously developed in the literature: a quite widespread model which assumes equal force sharing, here referred to as the mean field model (MFM), and a stochastic model (SM) which considers individual motor-cargo links. We find that in generic situations, the MFM predicts larger cargo mean velocity, smaller mean run time and less frequent reversions than the SM. These phenomena are found to be the consequences of the load sharing assumptions and can be interpreted in terms of the probabilities of the different motility states. We also explore the influence of the viscosity in both models and the role of the stiffness of the motor-cargo links within the SM. Our results show that the mean cargo velocity is independent of the stiffness, while the mean run time decreases with such a parameter. We explore the case of symmetric forward and backward motors considering kinesin-1 parameters, and the problem of transport by kinesin-1 and cytoplasmic dyneins considering two different sets of parameters previously proposed for dyneins.

Biased transport of elastic cytoskeletal filaments with alternating polarities by molecular motors

We present a simple model for the bidirectional dynamics of actin bundles with alternating polarities in gliding assays with nonprocessive myosin motors. The bundle is represented as an elastic chain consisting of monomers with positive and negative polarities. The motion of the bundle is induced by the pulling forces of the underlying motors which stochastically attach to the monomers and, depending on their polarities, pull them in the right or left direction. We demonstrate that perfectly apolar chains consisting of equal numbers of monomers with positive and negative polarities may exhibit biased bidirectional motion with a nonzero drift. This effect is attributed to the elastic tension developed in the chain due to the action of the myosin motors. We also show that as a result of this tension, the attachment probability of the motors is greatly reduced and becomes strongly dependent on the length of the chain.