Collective dynamics of kinesin

Abstract

Motor proteins are biological enzymes that convert chemical energy to mechanical work in cells. Kinesin-1 is a motor protein that transports vesicles along microtubules and is widely believed to be responsible for anterograde transport of synaptic vesicles in neurons. Advances in single-molecule techniques have shown that single kinesin motors are capable of processive movement along the microtubule at a maximum velocity of approximately 1 microm/s . The velocity decreases roughly linearly in response to load until reaching stall at a load of approximately 6 pN. Several theoretical models have been proposed that describe the steady-state motion of single kinesin motors. Growing evidence suggests that kinesin functions collectively in cells, whereby several motors work in a coordinated manner to transport a vesicle. A transient description is required to describe collective dynamics, as the interactions among coupled motors induce time-varying forces on each motor. Herein a mechanistic model of kinesin is proposed that is capable of accurately describing transient and steady-state dynamics. Each domain of the protein is modeled via a mechanical potential. The mechanical potentials are related explicitly to the chemical kinetics of each motor domain. The mechanistic model was used to simulate the collective behavior of coupled kinesin motors under varying loads, cargo linker stiffnesses, and numbers of motors. To analyze the simulations of coordinated transport, several metrics were developed that are specifically tailored to characterizing the synchronization of nonlinear nonsmooth oscillators such as kinesin. The model results suggest that, in the cell, the dynamics of coupled motors under low loads are loosely correlated. When the load is increased, such as when the cargo encounters an obstacle such as another vesicle or the cytoskeleton, motors become more correlated in response to increased loads, allowing them to produce greater forces. Increasing the number of motors involved in the transport does not appreciably increase the dimension of the trajectory, implying large numbers of motors are able to function in a highly correlated manner without becoming fully synchronized.