A simple kinetic model describes the processivity of myosin-v

Abstract

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness-a quantitative measure of the stochastic deviations from uniform, constant-speed motion-with ATP concentration under both resisting and assisting loads, and indicates a substep of size d(0) approximately 13-14 nm (from the ATP-binding state) that appears to accord with independent observations.

FIGURE 1

Specification of the simplest N-state periodic stochastic model. A motor in state j_l can undertake a forward transition at rate u_j or it can make a backward transition at rate w_j. The bound state N_l is identified with 0_l+1.

FIGURE 2

Fits to the data of Mehta et al. (1999) for the mean dwell times of myosin-V: (A) as a function of external load, F, at different ATP concentrations; (B) as a function of [ATP] under an external load F = 0.4 pN and a prediction for F = 2.3 pN. The solid curves represent Eq. 11 with the central parameter values in Eqs. 12 and 13; the dashed curves represent the mean dwell times predicted for a 50:50 mixture of short, d₍₋₎ = 30.5 nm, and long, d₍₊₎ = 41.5 nm steps using the same values for the other parameters: see Variability of Step Sizes. (Note that in B the dashed curve for F = 0.4 pN cannot be distinguished from the solid curve.)

FIGURE 2

Fits to the data of Mehta et al. (1999) for the mean dwell times of myosin-V: (A) as a function of external load, F, at different ATP concentrations; (B) as a function of [ATP] under an external load F = 0.4 pN and a prediction for F = 2.3 pN. The solid curves represent Eq. 11 with the central parameter values in Eqs. 12 and 13; the dashed curves represent the mean dwell times predicted for a 50:50 mixture of short, d₍₋₎ = 30.5 nm, and long, d₍₊₎ = 41.5 nm steps using the same values for the other parameters: see Variability of Step Sizes. (Note that in B the dashed curve for F = 0.4 pN cannot be distinguished from the solid curve.)

FIGURE 3

The force-velocity or (F, V) dependence of myosin-V at various concentrations of ATP as predicted using the parameter values in Eqs. 12 and 13: solid curves. The corresponding dashed curves follow from a model with alternating long and short steps (d₍₊₎ = 41.5 nm and d₍₋₎ = 30.5 nm) but otherwise the same zero-load rate constants and load distribution factors, The superimposed data bars (for [ATP]=1 μM and 2 mM) derive from the observed dwell times by using the approximate relation (with d = 36 nm); they track the predictions for V(F) fairly well because of the paucity of reverse or backward steps under loads

FIGURE 4

Predictions for the variation of the randomness, r, of myosin-V as a function of [ATP] at low (F = 0.4 pN) and high external load (F = 2.3 pN).

FIGURE 5

Predicted behavior of myosin-V under assisting (i.e., negative) and resisting (positive) external loads, F, for two ATP concentrations: (A) mean dwell time; (B) randomness. See the text for appropriate caveats.

FIGURE 5

Predicted behavior of myosin-V under assisting (i.e., negative) and resisting (positive) external loads, F, for two ATP concentrations: (A) mean dwell time; (B) randomness. See the text for appropriate caveats.