Myosin V: Chemomechanical-coupling ratchet with load-induced mechanical slip

Abstract

A chemomechanical-network model for myosin V is presented on the basis of both the nucleotide-dependent binding affinity of the head to an actin filament (AF) and asymmetries and similarity relations among the chemical transitions due to an intramolecular strain of the leading and trailing heads. The model allows for branched chemomechanical cycles and takes into account not only two different force-generating mechanical transitions between states wherein the leading head is strongly bound and the trailing head is weakly bound to the AF but also load-induced mechanical-slip transitions between states in which both heads are strongly bound. The latter is supported by the fact that ATP-independent high-speed backward stepping has been observed for myosin V, although such motility has never been for kinesin. The network model appears as follows: (1) the high chemomechanical-coupling ratio between forward step and ATP hydrolysis is achieved even at low ATP concentrations by the dual mechanical transitions; (2) the forward stepping at high ATP concentrations is explained by the front head-gating mechanism wherein the power stroke is triggered by the inorganic-phosphate (Pi) release from the leading head; (3) the ATP-binding or hydrolyzed ADP.Pi-binding leading head produces a stable binding to the AF, especially against backward loading.

Figure 1

(a) A nine-state chemomechanical network model of myosin V based on a network representation consisting of 3² = 9 full chemical states connected by eighteen chemical and five mechanical transitions. The figure shows that the nine chemical states are periodically repeated along an actin filament (AF) with a spacing of l = 36 nm. The myosin-V’s heads with bound ATP or ADP are denoted by T and D, respectively, while an empty head is denoted by E. Both the D and E states are strongly bound to the AF, while the T state is basically weakly bound. The vertical displacement of the heads with the T state from the base line indicates the weak binding of the T heads. The solid lines indicate the chemical transitions and those with arrows indicate the mechanical transitions. To calculate the mean run length [Fig. 3b,e] and the detachment rate of myosin V from the AF [Fig. 3c,f], we extend the nine-state model while taking account of the detachment transitions of myosin V from states 9 (TT), 5 (DT), 2 (TD), 6 (ET), 8 (DD), 1 (ED) and 7 (EE) [see Calculation details and the Supplementary Information]. (b) External-load dependences of the motor velocity at several ATP and ADP concentrations. (c) External-load dependence of the ratio of the numbers between the forward and backward steps. The experimental data shown by symbols is obtained from the literature^,,,.

Figure 2

ATP-concentration dependences of the motor velocities, v, for forward and backward movements at (a) 5-pN and (b) 10-pN forward and backward loads. For comparison, the motor velocities at 0-pN and 5-pN forward loads are also shown in (a) and (b), respectively. The experimental data indicated by symbols are obtained from the literature. (c) and (d) show the main contributions to the total velocity caused by each mechanical transition as a function of external load at ATP concentrations of 100 µM and 1 µM, respectively.

Figure 3

ATP-concentration dependences of (a) the motor velocity v, (b) the mean run length until myosin V detaches from an actin filament and (c) the detachment rate of myosin V, at Pi concentrations of 0 and 40 mM; ADP-concentration dependences of (d) the motor velocity v, (e) the mean run length and (f) the detachment rate, at ATP concentrations of 100 µM and 1 mM. The experimental data shown by symbols are obtained from the literatures^,,,.

Figure 4

Load dependences of (a) the ratio of the number of forward steps to the number of ATP molecules undergoing hydrolysis, $\Delta J\left(\mathrm{Step}\right)/\Delta J\left(\mathrm{hydrolysis}\right)$, i.e. chemomechanical-coupling efficiency and (b) chemomechanical-transduction efficiency $\eta =Fv/\left[\Delta \mu \Delta J\left(\mathrm{hydrolysis}\right)\right]$ at several ATP concentrations, where Δμ is the difference between the chemical potentials for one molecule of ATP and for one molecule of ADP plus one molecule of Pi, i.e. $\Delta \mu =k_{\mathrm{B}}T\ln \{K_{eq}\left[\mathrm{ATP}\right]/\left[\mathrm{ADP}\right]\left[\mathrm{Pi}\right]\}$ , with the equilibrium constant K _eq = 4.9 × 10¹¹ µM; $\Delta J\left(\mathrm{hydrolysis}\right)$ is the total excess flux arising from all the ATP hydrolysis, and $\Delta J\left(\mathrm{Step}\right)$ is the total excess flux provided by all of the mechanical transitions.

Figure 5

Diagrams of the main local fluxes for high (1 mM) and low (1 µM) ATP concentrations at zero load [(a) and (b)], a forward-assisting load of 5 pN [(c) and (d)] and backward loads of 1 pN [(e) and (f)] and 5 pN [(g) and (h)], respectively. The red arrows indicate normalized local fluxes larger than 0.10, while the blue arrows indicate other normalized local fluxes larger than 0.07 and the green arrow in Fig. 5g indicates a normalized local flux of 0.03, where the normalized local flux is defined as the value of local flux divided by the sum of all the local fluxes. The red and blue letters and indicate the forward- and backward-stepping transitions, respectively. The red numbers indicate the probability of the state. The perpendicular axis for each diagram indicates the ATP-concentration level; higher states on this axis have higher probabilities at high ATP concentrations.