A kinetic model describing the processivity of myosin-V

Abstract

The precise details of how myosin-V coordinates the biochemical reactions and mechanical motions of its two head elements to engineer effective processive molecular motion along actin filaments remain unresolved. We compare a quantitative kinetic model of the myosin-V walk, consisting of five basic states augmented by two further states to allow for futile hydrolysis and detachments, with experimental results for run lengths, velocities, and dwell times and their dependence on bulk nucleotide concentrations and external loads in both directions. The model reveals how myosin-V can use the internal strain in the molecule to synchronize the motion of the head elements. Estimates for the rate constants in the reaction cycle and the internal strain energy are obtained by a computational comparison scheme involving an extensive exploration of the large parameter space. This scheme exploits the fact that we have obtained analytic results for our reaction network, e.g., for the velocity but also the run length, diffusion constant, and fraction of backward steps. The agreement with experiment is often reasonable but some open problems are highlighted, in particular the inability of such a general model to reproduce the reported dependence of run length on ADP concentration. The novel way that our approach explores parameter space means that any confirmed discrepancies should give new insights into the reaction network model.

FIGURE 1

Sketch of the complete reaction network of the model. The Y-shaped molecule is the myosin-V protein which walks on actin filaments. The black actin monomers indicate the attachment sites spaced at ≃36 nm. The labels T, D, and P_i stand for ATP, ADP, and inorganic phosphate, respectively, being bound to the head.

FIGURE 2

The main and futile cycles combined in one scheme showing all the reaction paths between the seven states in the complete model. See also Fig. 1. The reaction rates are given by the corresponding equations in the text. Reaction steps which release and bind ADP, P_i, or ATP are indicated.

FIGURE 3

The mechanical movement of myosin-V takes place in two separate steps. The first step, through a distance d_W ≃ 25 nm, is from the highly strained state 1 to state 2 where the internal strain balances the external force. When the molecule diffuses to state 3, through a further distance d_D ≃ 11 nm, the internal strain increases to bE_strain.

FIGURE 4

The one-dimensional energy landscape that we find for the walk of myosin-V in which the states in the model are indicated by the solid circles. Energy is measured in units of k_BT. The energy changes associated with the dashed transitions are E_strain and bE_strain, being the energy barriers involved in moving away from state 2. Also shown is the rate-limiting activation energy between state 4 and state 5. The generalized reaction coordinate X can be thought of as measuring the progress around the main reaction cycle (Fig. 1). As such, it reflects a combination of physical motion and the progress of biochemical reactions, according to the substep. The shape of the curve is somewhat arbitrary, but the peaks and the troughs are at the correct energies determined by the optimal values ( and ΔG_i) where the energies are recalculated for the reference concentrations [ATP] = 1 nM, [ADP] = [P_i] = 0.1 μM, i.e., the log of each concentration appears in the energy barriers.

FIGURE 5

Predictions of velocity of myosin-V as a function of ADP, ATP, and P_i concentration that arise from our optimized (best) model with parameter values as shown in Table 1 (and used in all subsequent figures). In each case the other two reference concentrations are taken from [ATP] = 1 mM, [ADP] = 0.1 μM, or [P_i] = 0.1 μM. The experimental data for varying [ATP] (squares) and [ADP] (circles) are from Baker et al. (23).

FIGURE 6

The velocity as a function of force. The solid line (and circles) show results when [ATP] = 1 mM and [ADP] = 200 μM, the dashed line (and squares) when [ATP] = 1 mM and [ADP] = 1 μM, while for the dotted line (and diamonds) we have [ATP] = 10 μM and [ADP] = 1 μM. The model (the lines) shows similar trends to what is found experimentally (the circles, squares, and diamonds) (25).

FIGURE 7

Dwell time for [ATP] = 2 mM (solid line/circles), [ATP] = 10 μM (dotted line/squares), and [ATP] = 1 mM and [ADP] = 200 μM (dashed line/triangles). The experimental data are from Mehta et al. (11) (circles) and Uemura et al. (25) (squares and triangles).

FIGURE 8

The duty ratio, r_d, as a function of force for [ATP] = 1 mM, [ADP] = [P_i] = 0.1 μM.

FIGURE 9

Run length L for different concentrations of ATP when the ADP concentration is equal to 1 mM (dotted-dashed line), 100 μM (dashed line), and 10 μM (solid line). At low ADP concentration, the run length becomes independent of ATP concentration. The prediction of the model is compared with experimental results at low ADP concentrations (circles) (23).

FIGURE 10

Run length L for different strengths of the external force when [ATP] = 1 mM and [ADP] = 200 μM. For negative external force, the run length has a nonmonotonic behavior, where it increases 10-fold before decreasing again.

FIGURE 11

The fraction of backward steps, π₋, is insignificant in the model until an external force of ∼2 pN is reached. The solid line is for [ATP] = 2 mM and [ADP] = 200 μM, while the dashed line is for a reduced ATP concentration of 100 μM.

FIGURE 12

The randomness ratio, ρ, as a function of force at different ATP concentrations.

FIGURE 13

The circle shows the unperturbed velocity and run length for [ATP] = 1 mM, [ADP] = [P_i] = 0.1 μM, and zero external force. The squares show the influence on run length and velocity of changes of ±5% in each of the nine free parameters of the model (while keeping the other parameters fixed). The run length is very sensitive to changes in Also perturbing in E_strain gives quite a large change in run length. Large variation in velocity was only observed when perturbing the parameter ΔG₄.

FIGURE 14

Temperature dependence of velocity and run length (when [ATP] = 1 mM and [ADP] = 200 μM). The model predicts an increase in velocity with temperature, but a decrease of the run length. The velocity is found to be more sensitive to changes in temperature than the run length.