Adiabatic Brownian motor with a stepwise potential perturbed by a dichotomous harmonic sygnal

We obtained an analytical expression for the average motion velocity of an adiabatic Brownian motor (ratchet), which operates due to small dichotomous spatially harmonic fluctuations of a stepwise potential. The symmetry properties of the average velocity as a functional of the stationary and fluctuating components of the nanoparticle potential energy are revealed, and the ranges of values of the system parameters that ensure the rightward and leftward motion of the motor are determined. We showed that the average motor velocity is a non-monotonic function of the stepwise potential height. For a singular (infinitely high and narrow) potential barrier, the average velocity depends non-monotonically on the «power» of this barrier (the barrier width multiplied by the exponent of the ratio of the barrier height to the thermal energy). The article continues the further development of theoretical methods of symmetry analysis by applying the general approaches proposed by the authors to specific motor systems.

A Brownian ratchet model explains the biased sidestepping movement of single-headed kinesin-3 KIF1A

The kinesin-3 motor KIF1A is involved in long-ranged axonal transport in neurons. In order to ensure vesicular delivery, motors need to navigate the microtubule lattice and overcome possible roadblocks along the way. The single-headed form of KIF1A is a highly diffusive motor that has been shown to be a prototype of Brownian motor by virtue of a weakly-bound diffusive state to the microtubule. Recently, groups of single-headed KIF1A motors were found to be able to sidestep along the microtubule lattice, creating left-handed helical membrane tubes when pulling on giant unilamellar vesicles in vitro. A possible hypothesis is that the diffusive state enables the motor to explore the microtubule lattice and switch protofilaments, leading to a left-handed helical motion. Here we study microtubule rotation driven by single-headed KIF1A motors using fluorescene-interference contrast (FLIC) microscopy. We find an average rotational pitch of ≃ 1.4 μm which is remarkably robust to changes in the gliding velocity, ATP concentration and motor density. Our experimental results are compared to stochastic simulations of Brownian motors moving on a two-dimensional continuum ratchet potential, which quantitatively agree with the FLIC experiments. We find that single-headed KIF1A sidestepping can be explained as a consequence of the intrinsic handedness and polarity of the microtubule lattice in combination with the diffusive mechanochemical cycle of the motor.