Complex movements of motor protein relay helices during the power stroke

We use the Toda soliton formalism to propose a possible complex movement of $\alpha$ helices with a very important role in energy transduction during the power stroke of motor proteins. We find that this approach has advantages in comparison with the Davydov soliton model and its variants. We estimated the model’s parameters and calculated corresponding properties of the predicted solitary waves including propagation velocities and energies. The energies are found to be within the expected range.

Figure 1

$\alpha$-helix backbone geometry. (a) Hydrogen bond network shown as thin cylinders. (b) A close-up of three amino acids; in one an amide linkage has been marked, as has the carbonyl bond of another. Also marked are the bonds about which the $\varphi$ and $\psi$ torsions occur. The atoms of the side chain have been trucated to a single $R$ atom for clarity.

Figure 2

Secondary structure in myosin showing locations of the switch-II loop, the relay helix, and the adenosine phosphate. Figure prepared using MOLMOL [4] and Protein Data Bank entry 1BR2 [5].

Figure 3

$\alpha$-helix geometry showing the hydrogen-bond network. The cylindrical structure has been flattened, splitting the backbone (thick line), with the cylindrical axis running horizontally across the page. The $3.8\mathrm{\AA }$ distance is the ${\mathrm{C}}_{\alpha }$ to ${\mathrm{C}}_{\alpha }$ distance in sequential amino acids.

Figure 4

Dimensions of the hydrogen bond. (a) Distances between atomic centers with the hydrogen bonds. (b) The single-site Toda potential well $U_{Tn}$ (upper curve) and an approximation to it, $U_{Tn}^{\prime }$; see Eq. (23) (lower curve).

Figure 5

Toda soliton chain dynamics: (a) relaxed chain (no soliton); (b) local contraction caused by a TS and displacement of sites ${\rho }_n\left(x\right)$.