A mathematical model describing the mechanical kinetics of kinesin stepping

Abstract

Kinesin is a smart motor protein that steps processively forward and backward along microtubules (MTs). The mechanical kinetics of kinesin affecting its stepping behavior is not fully understood. Here, we propose a mathematical model to study the mechanical kinetics of forward and backward stepping of kinesin motor based on the four-state discrete stochastic model of the motor. Results show that the probabilities of forward and backward stepping can be modeled using the mean probabilities of forward and backward kinetic transitions, respectively. We show that the backward stepping of kinesin motor starts when the probability of adenosine diphosphate (ADP) binding to the motor is much higher than that of adenosine triphosphate (ATP) binding. Furthermore, our results indicate that the backward stepping is related to both ATP hydrolysis and synthesis with rate limiting factor being ATP synthesis. Low rate of ATP synthesis under high backward loads above 10 pN is also suggested as a reason for the detachment of kinesin motor from MT in the kinetic state MTċKinesinċADPċPi. The code for this work is written in Visual C# and is available by request from the authors.