Piezoelectric allostery of protein

Allostery is indispensable for a protein to work, where a locally applied stimulus is transmitted to a distant part of the molecule. While the allostery due to chemical stimuli such as ligand binding has long been studied, the growing interest in mechanobiology prompts the study of the mechanically stimulated allostery, the physical mechanism of which has not been established. By molecular dynamics simulation of a motor protein myosin, we found that a locally applied mechanical stimulus induces electrostatic potential change at distant regions, just like the piezoelectricity. This novel allosteric mechanism, “piezoelectric allostery”, should be of particularly high value for mechanosensor/transducer proteins.

Figure 1

The structure of scallop myosin II employed in our MD simulation. The converter domain (cyan/pink), to which the lever arm (not shown) is attached, is subjected to the umbrella potential exerted along the long axis ($z$-axis) of the actin filament (gray). The direction of the ATP-hydrolysis-derived force is to the right, which defines the positive direction of the reaction coordinate $z$. The backward (cyan) and the forward (pink) converter positions (PDB code 1QVI [16] and 1SR6 [17], respectively) were used as the initial structures of conventional MD simulations. The ATP binding region (red) and the actin binding region [19] (blue) are also indicated.

Figure 2

(a) Electrostatic potential change, $\mathrm{\Delta }\langle \mathrm{\Phi }\rangle$, at the surface of myosin observed when the converter is moved from the most backward region ($z\in [0,0.25]$) to the most forward region ($z\in [5.5,5.75]$). Potentials are in $kT/e$ ($T=310$ K). See the color scale bar. $\mathrm{\Delta }\langle \mathrm{\Phi }\rangle$ was obtained by subtracting $\langle \mathrm{\Phi }\rangle$ for the most backward region from that for the most forward region. The direct electrostatic contributions of the converter and surface loops were eliminated. (b) Correlation plot between $\mathrm{\Delta }\langle \mathrm{\Phi }\rangle$ and the net-charge density change $\mathrm{\Delta }\langle q\rangle$. Grid point data (evaluated by trilinear interpolation) covering the entire region of myosin were used for the plot. Correlation coefficient is 0.57. The gray line indicates $\mathrm{\Delta }\langle \mathrm{\Phi }\rangle ={\left(0.186\right)}^2\mathrm{\Delta }\langle q\rangle /2{\epsilon }_0$, which is expected from the analytical solution of the Poisson equation for the center of a sphere of radius 0.186 nm (volume is 0.027 ${\mathrm{nm}}^3$) with the charge density $\mathrm{\Delta }\langle q\rangle$. (c) $\mathrm{\Delta }\langle \mathrm{\Phi }\rangle$ for the ATP-binding region (square) and that for the actin-binding acidic cluster (circle) are shown as a function of $z$ (${\langle \mathrm{\Phi }\rangle }_{[z-0.125,z+0.125]}-{\langle \mathrm{\Phi }\rangle }_{z\in [0,0.25]}$). Standard errors are drawn at 95% confidence interval.

Figure 3

(a) Rearrangements of electrostatic bonds induced when the converter is moved from the most backward region to the most forward region. An electrostatic bond was judged formed (between acidic, basic, and polar groups) when the distance between H and O (or N, e.g., imino nitrogen in histidine) is less than $0.3$ nm. First, the ensemble-averaged number of the electrostatic bonds $\langle n\rangle$ between the bond-forming residues was calculated. Then, the residue pairs that showed substantial change in $\langle n\rangle$ ($\left|\mathrm{\Delta }\langle n\rangle \right|>max\{0.1,{(\delta n_{\mathrm{F}}^2+\delta n_{\mathrm{B}}^2)}^{1/2}\}$, where $\delta n_{\mathrm{F}}$ and $\delta n_{\mathrm{B}}$ are the standard errors of $n$ in the most forward and the most backward regions, respectively) were extracted. Lines are drawn between the extracted residue pairs: red broken lines (total 372 lines) for the pairs with decreased $\langle n\rangle$ and blue solid lines (total 401 lines) for those with increased $\langle n\rangle$ (the larger $|\mathrm{\Delta }\langle n\rangle |$, the thicker the line width; the lines involving the converter residues are omitted for clarity, and shown in Fig. 4 instead). Backbone of myosin of the ensemble-averaged structure in the most forward converter position is shown in yellow (the converter in green). (b) Close-up view of the electrostatic bond rearrangement network observed in the ATP binding region. Only the bond rearrangement network involving the key residues are shown. (c) Close-up view with $\mathrm{\Delta }\langle \mathrm{\Phi }\rangle$ for the ATP binding region and (d) for the acidic cluster in the actin binding region.

Figure 4

Propagation of the electrostatic bond rearrangement. Formed/broken electrostatic bonds are extracted and drawn in the same way as in Fig. 3 by calculating $\mathrm{\Delta }\langle n\rangle$ for the changes from the most backward ensemble ($z\in [0,0.25]$) to the forward ensembles ($z\in [1.25,1.5]$, $z\in [2.25,2.5]$, $z\in [3.25,3.5]$, and $z\in [4.25,4.5]$). Successive bonds that extend from the converter, forming bond rearrangement network, are shown. Inset: bonds (formed for $z\in [0,0.25]$; cyan) involving converter residues are shown. Average backbone structure is rendered for each ensemble.