Chemomechanical coupling and motor cycles of myosin V

Abstract

The molecular motor myosin V has been studied extensively both in bulk and single molecule experiments. Based on the chemical states of the motor, we construct a systematic network theory that includes experimental observations about the stepping behavior of myosin V. We utilize constraints arising from nonequilibrium thermodynamics to determine motor parameters and demonstrate that the motor behavior is governed by three chemomechanical motor cycles. The competition between these cycles can be understood via the influence of external load forces onto the chemical transition rates for the binding of adenosine triphosphate and adenosine diphosphate. In addition, we also investigate the functional dependence of the mechanical stepping rates on these forces. For substall forces, the dominant pathway of the motor network is profoundly different from the one for superstall forces, which leads to a stepping behavior that is in agreement with the experimental observations. Our theory provides a unified description of the experimental data as obtained for myosin V in single motor experiments.

Figure 1

Chemomechanical network for myosin V at different binding sites x of the filament, represented by a thick gray line. The nine states, that are repeated periodically along the filament with a spacing of ℓ = 36 nm, are defined by the chemical composition of the nucleotide-binding pockets of the two motor heads. A head with bound ATP or ADP is denoted by T or D, an empty head by E. Both the E and D states are strongly bound to the actin filament, whereas the T state is only weakly attached (24), as indicated by the gap between the T heads and the filament. All transitions between two connected states can occur in both forward and backward direction. Chemical transitions are drawn as solid lines (blue), with arrows indicating the direction of ATP hydrolysis. The broken lines (red) correspond to the mechanical transitions as observed experimentally, with the arrows pointing toward the forward stepping direction (13,19), i.e., toward the barbed-end of the actin filament.

Figure 2

Reduced network for the motion of myosin V, consisting of three copies of six states i = 1…6 connected by transitions |ij〉 from state i to state j, that form three pathways F, , and M. The chemomechanical forward cycle F consists of the states 〈1234′〉, which contain both chemical and mechanical transitions, while the dissipative or enzymatic slip cycle with states 〈256〉 is purely chemical. The ratcheting cycle M, on the other hand, consists only of the mechanical stepping transitions |55′〉, |5′5″〉, and so on. Each state is characterized by the chemical composition of the two motor heads, the one on the right-hand side being the leading one. The solid lines (blue) are the chemical transitions for the indicated species X = ATP, ADP, or P, while the broken lines (red) show the stepping transitions. The arrows refer to the direction of forward stepping and ATP hydrolysis, respectively.

Figure 3

Stepping velocity v in units of the saturation velocity v_sat as a function of different nucleotide concentrations [X]. The experimental data are taken from the literature (12,30,31). (Blue line) Michaelis-Menten-like increase in velocity with increasing [ATP], for [ADP] = [P] = 0.1 μM, which agrees well with the experimental values measured by different groups (blue symbols). (Green line) Dependence on [ADP] at saturating concentration of ATP, [ATP] = 1 mM, and low phosphate concentration, [P] = 0.1 μM. An increasing [ADP] concentration reduces the stepping velocity, because the flux of the reverse dicycle F⁻ increases and, thus, reduces the dicycle excess flux ΔJ(F⁺) as described by Eq. 6. We have rescaled the velocity by the saturating velocity because different experimental groups have reported different saturation velocities v_sat. Indeed, the myosin V construct studied in Baker et al. (12) was found to exhibit the saturating velocity v_sat = 550 nm/s, a value considerably higher than the value v_sat = 450 nm/s measured by other groups (1,7,11,30,34).

Figure 4

Stepping velocity v as a function of external load force F as calculated from the network in Fig. 2. We use the sign convention that positive values of F correspond to resisting forces. (Solid lines) Our theoretical results. (Symbols) Experimental data as obtained by several groups (1,8,11,13,34). These data were obtained for [ATP] ≥ 100 μM (blue symbols), [ATP] = 10 μM (red triangles), and [ATP] = 1 μM (green asterisks). (Green, blue, and red lines) Theoretical results for 1, 10, and 1000 μM ATP, respectively, with [ADP] = [P] = 0.1 μM. The theoretical value of the stall force is F_s ≃ 2 pN with a weak dependence on [ATP]. This value lies within the range −1.6 pN ≲ F_s ≲ 2.5 pN as found experimentally. For forces F < F_s, the motor velocity depends on [ATP], while it becomes independent of [ATP] for F >> F, in agreement with the measurements in Gebhardt et al. (13).

Figure 5

(Color online) Inverse step ratio q⁻¹ of backward/forward steps as a function of load force F. (Dotted, dashed, and solid lines) Calculated using Eq. 16 for [ATP] = 10, 100, and 1000 μM, respectively, with constant [ADP] = [P] = 0.1 μM. For resisting forces that do not exceed F_s, the calculated step ratio is in good agreement with the experimental data (circles) as obtained in Kad et al. (8) for [ATP] = 100 μM. Note that this ratio is virtually independent of [ATP] for forces up to 1.6 pN.

Figure 6

Run-length Δx as a function of different nucleotide concentrations [X] as explained in the inset. (Solid curves) Calculated using Eq. 18. (All symbols) Experimental data from Baker et al. (12).