Landscape-Based View on the Stepping Movement of Myosin VI

Figures

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  Figure 1. Schematic comparison of two models. (A) Spudich model and (B) Houdusse–Sweeney model.

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  Figure 2. Simulation setup. (A) Typical snapshot showing the setup for the Langevin molecular dynamics simulations. The structures of the leading head (red) and the rear head (blue) of myosin VI and the actin filament (black) were explicitly represented by the elastic network model, whereas the SAH domains were implicitly considered as Λ-shaped elastic rods connecting the C-terminals of the two heads of myosin VI. The cylindrical coordinate system (z, θ, r) was defined around the actin filament. The rear head was bound to the filament at (z, θ) = (0 nm, 0°), and the leading head was cast toward the z < 0 direction. (B) Implicit representation of the two SAH domains as the Λ-shaped elastic rods. In order to represent the elastic bending and twisting of the rods in the model, we defined potential functions among six amino acid residues, A, B, C, D, P, and Q; the elastic energy of rod bending was calculated by representing the bending angle θbend as a function of the distance . The center angle was fixed at its stable value as when d ≤ d0 with , and varied as when d0 < d ≤ 2L. See the Interactions subsection of the Methods section and the Supporting Information for details.

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  Figure 3. Free energy landscapes F(z, θ) and the step-size distributions P(z). (A, B) Free energy landscapes obtained with the parameter set corresponding to the Spudich model.12 (C) Free energy landscape obtained with the parameter set corresponding to the Houdusse–Sweeney model.9 Leading head is in the prestroke state in A and C and in the poststroke state in B. (D) Step-size distribution derived from A, (E) the step-size distribution derived from B, and (F) the step-size distribution derived from C. (G) Snapshot structure in the Spudich model with the leading head residing at (z, θ) = (− 33 nm, – 11°) near the minimum in the free energy landscape A, and (H) a snapshot structure in the Houdusse–Sweeney model with the leading head residing at (z, θ) = (− 6 nm, 108°) near the minimum in the free energy landscape C. In G and H, the three-helix bundles in the leading and rear heads are colored red, the other part of the leading head is blue, and the other part of the rear head is green; the actin filament is black and the implicit SAH domains connecting the leading and rear heads are not drawn.

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  Figure 4. Decomposition of free energy obtained with the Spudich model12 into contributions from energies and the conformational entropy. The free energy landscape F(z, θ) = E(z, θ) – TS(z, θ) of Figure 3A is decomposed into (A) the effective energy landscape E(z, θ) and (B) the conformational entropy landscape −S(z, θ). (C) The landscape of the myosin-actin interface energy, and (D) the landscape of the elastic energy of the SAH domains.

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  Figure 5. Decomposition of free energy obtained with the Houdusse–Sweeney model9 into contributions from energies and the conformational entropy. Free energy landscape F(z, θ) = E(z, θ) – TS(z, θ) of Figure 3C is decomposed into (A) the effective energy landscape, E(z, θ), and (B) the conformational entropy landscape, −S(z, θ). (C) Landscape of the myosin–actin interface energy, and (D) the landscape of the elastic energy of the SAH domains.

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  Figure 6. Free energy landscapes with the altered folding/unfolding states of the three-helix bundles. (A) Free energy landscape obtained for the Spudich model except that the three-helix bundles are unfolded, and (B) free energy landscape obtained for the Houdusse–Sweeney model except that the three-helix bundles are folded. The leading head is in the prestroke state.

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  Figure 7. Free energy landscape for the Spudich model with the persistence length modified from 22.4 to 5 nm. The leading head is in the prestroke state.