Fluctuation Analysis of Mechanochemical Coupling Depending on the Type of Biomolecular Motors

Mechanochemical coupling was studied for myosin II and V consistently. The fluctuation in myosin V motility was determined by correlating the stochasticity of the ATPase reaction with regular displacements per one ATP, consistent with a tight mechanochemical coupling. In contrast, myosin II, working in an ensemble, was explained by a loose coupling, generating variable step sizes which depend on [ATP] and realizing a much larger step (200 nm) per one ATP than myosin V through its cooperativity at zero load. These different mechanics are ideal for their physiological functions.

Figure 1

Schematic of the experiments and typical traces of myosin motility. (a) Single molecule motility assay of myosin V. The single molecule movement of myosin V along the actin filament was directly measured. Myosin molecules were genetically fused with GFP (Green Fluorescent Protein) for observation (green star). Fluorescence from myosin in solution was not imaged because of its fast diffusion whereas molecules moving along actin filaments were seen as moving bright spots. The experiments were performed at $25°\mathrm{C}$. (b) In vitro actin gliding assay. The movement of an individual actin filament driven by a myosin II ensemble was measured. Actin filaments were attached to the fluorescent dye tetramethyl—rhodamine phalloidin for observation (colored in orange). Myosin molecules were neither labeled nor observed. The experiments were performed at $28°\mathrm{C}$. (c) Typical displacement time series obtained from the motility assays. ATP concentration, [ATP], was $100\mu M$ in both assays.

Figure 2

The dependence of the mean velocity on [ATP] in motility assays. Solid lines show the fit of Eq. (1) to the experimental data. See text for details. Error bar shows the fluctuation of displacement per unit time, $\sqrt{{\sigma }_v^2}$ obtained from the fit of MSD.

Figure 3

Relationship between ${\mu }_v$ and ${\sigma }_v^2$. To simplify comparisons between myosin V and II, we normalized the variables as follows: ${\overline{\mu }}_v={\mu }_v/V_{\max }^{\mathrm{mot}}$ and ${\overline{\sigma }}_v^2={\sigma }_v^2/V_{\max }^{\mathrm{mo}{\mathrm{t}}^2}$. Lines show the results of stochastic simulations. Parameters used in the simulations are as follows: $k_2=18.5{\mathrm{s}}^{-1}$ and $k_1=0.750{\mathrm{s}}^{-1}\mu M^{-1}$ for myosin V; $k_2=596{\mathrm{s}}^{-1}$ and $k_1=6.40{\mathrm{s}}^{-1}\mu M^{-1}$ for myosin II with 10 nm step, and $k_2=30.0{\mathrm{s}}^{-1}$ and $k_1=0.320{\mathrm{s}}^{-1}\mu M^{-1}$ for myosin II with 200 nm step.

Figure 4

Comparison with our proposed model to the experimental data of myosin II. Symbols are the same as for the myosin II data in Fig. 3. Solid lines show the simulated relationship of our model. See text for details. Inset, the dependence of ${\mu }_v$ on [ATP]. Symbols are the same as myosin II data in Fig. 2. Red solid line is the stochastic simulation. The parameters are $d_{\max }=200\mathrm{nm}$, $K_m^{\mathrm{ATP}}=2\mu M$, $K_m^{\mathrm{mot}}=93\mu M$, respectively.