A stochastic automaton model for simulating kinesin processivity.

MOTIVATION: Cellular interactions of kinesin-1, an adenosine triphosphate (ATP)-driven motor protein capable of undergoing multiple steps on a microtubule (MT), affect its mechanical processivity, the number of steps taken per encounter with MT. Even though the processivity of kinesin has been widely studied, a detailed study of the factors that affect the stepping of the motor along MT is still lacking. RESULTS: We model the cellular interactions of kinesin as a probabilistic timed automaton and use the model to simulate the mechanical processivity of the motor. Theoretical analysis suggests: (i) backward stepping tends to be powered by ATP hydrolysis, rather than ATP synthesis, (ii) backward stepping powered by ATP synthesis is more likely to happen with limiting ATP concentration ([ATP]) at high loads and (iii) with increasing load the frequency of backward stepping powered by ATP hydrolysis at high [ATP] is greater than that powered by ATP synthesis at limiting [ATP]. Together, the higher frequency of backward stepping powered by ATP hydrolysis than by ATP synthesis is found to be a reason for the more dramatic falling of kinesin processivity with rising load at high [ATP] compared with that at low [ATP]. Simulation results further show that the processivity of kinesin can be determined by the number of ATP hydrolysis and synthesis kinetic cycles taken by the motor before becoming inactive. It is also found that the duration of a backward stepping cycle at high loads is more likely to be less than that of a forward stepping cycle. CONTACT: h.r.khataee@griffithuni.edu.au or a.liew@griffith.edu.au.

A mathematical model describing the mechanical kinetics of kinesin stepping.

MOTIVATION: 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: 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 MTcKinesincADPcPi. AVAILABILITY AND IMPLEMENTATION: The code for this work is written in Visual C# and is available by request from the authors.

Computational modeling of kinesin stepping.

Kinesin is a walking motor protein that shuttles cellular cargoes along microtubules (MTs). This protein is considered as an information processor capable of sensing cellular inputs and transforming them into mechanical steps. Here, we propose a computational model to describe the mechanochemical kinetics underlying forward and backward stepping behavior of kinesin motor as a digital circuit designed based on an adenosine triphosphate (ATP)-driven finite state machine. Kinetic analysis suggests that the backward stepping of kinesin is mainly driven by ATP hydrolysis, whereas ATP synthesis rises the duration of this stepping. It is shown that kinesin pausing due to waiting for ATP binding at limiting ATP concentration ([ATP]) and low backward loads could be longer than that caused by low rate of ATP synthesis under high backward loads. These findings indicate that the pausing duration of kinesin in MT-bound (M·K) kinetic state is affected by [ATP], which in turn affects its velocity at fixed loads. We show that the proposed computational model accurately simulates the forward and backward stepping behavior of kinesin motor under different [ATP] and loads.

Unbinding of Kinesin from Microtubule in the Strongly Bound States Enhances under Assisting Forces.

The ability to predict the cellular dynamics of intracellular transport has enormous potential to impact human health. A key transporter is kinesin-1, an ATP-driven molecular motor that shuttles cellular cargos along microtubules (MTs). The dynamics of kinesins depends critically on their unbinding rate from MT, which varies depending on the force direction applied on the motor, i.e. the force-unbinding rate relation is asymmetric. However, it remains unclear how changing the force direction from resisting (applied against the motion direction) to assisting (applied in the motion direction) alters the kinesin's unbinding and stepping. Here, we propose a theoretical model for the influence of the force direction on the stepping dynamics of a single kinesin. The model shows that the asymmetry of the force-unbinding rate relation is independent of ATP concentration. It also reveals that the synthesis of ATP from backward stepping under assisting forces is less likely than under resisting forces. It then finds that the unbinding of kinesin in the strongly MT-bound kinetic states enhances under assisting forces.