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. 2022 Sep 27;119(40):e2208034119. doi: 10.1073/pnas.2208034119

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Copyright © 2022 the Author(s). Published by PNAS.

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

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Fig. 4. — Mechanics of Piezo activation. (A) Three-dimensional plots of the Piezo dome and its (partial) membrane footprint in the limit of an asymptotically planar membrane. We assume here that the closed state of Piezo approximately corresponds to the intrinsic Piezo dome radius of curvature $R_{P} = R_{c} \approx 42 nm$ (Left) and that the open state of Piezo approximately corresponds to a flat Piezo dome shape with radius of curvature $R_{P} = R_{o} \to \infty$ (Right). We calculated the shape of the membrane footprint by minimizing the shape energy of the Piezo–membrane system, $G_{sys} (R_{P})$ in Eq. 5, at fixed $R_{P}$ with $A_{P} = 450 {nm}^{2}$ . In A, Left, we used a nominal lateral membrane tension $γ = 0.01 \frac{k_{B} T}{{nm}^{2}}$ . The membrane areas occupied by the Piezo dome as well as by the membrane footprint are identical in A, Left and Right. (B–D) Piezo gating curves, $P_{o} (γ)$ in Eq. 6, for the elastic properties of the Piezo dome estimated in Fig. 3, $R_{0} \approx 42 nm$ and $K_{P} \approx 18 k_{B} T$ , with the Piezo dome area $A_{P} = 450 {nm}^{2}$ (black curves) and with (B) a modified intrinsic Piezo dome radius of curvature $\frac{1}{2} R_{0}$ (blue solid curve) or $2 R_{0}$ (blue dashed curve), (C) a modified Piezo dome bending rigidity $\frac{3}{2} K_{P}$ (thick red curve) or $2 K_{P}$ (thin red curve), and (D) a modified Piezo dome area $\frac{2}{3} A_{P}$ (thick green curve) or $\frac{1}{2} A_{P}$ (thin green curve). For the predicted Piezo gating curve with $R_{0} \approx 42 nm$ , $K_{P} \approx 18 k_{B} T$ , and $A_{P} = 450 {nm}^{2}$ , Eq. 6 yields $P_{o} = \frac{1}{2}$ at the gating tension $γ_{1 / 2} \approx 0.33 \frac{k_{B} T}{{nm}^{2}}$ (black curves). In B, $γ_{1 / 2} \approx 0.34 \frac{k_{B} T}{{nm}^{2}}$ for $\frac{1}{2} R_{0}$ and $γ_{1 / 2} \approx 0.32 \frac{k_{B} T}{{nm}^{2}}$ for $2 R_{0}$ . In C, $γ_{1 / 2} \approx 0.56 \frac{k_{B} T}{{nm}^{2}}$ for $\frac{3}{2} K_{P}$ and $γ_{1 / 2} \approx 0.83 \frac{k_{B} T}{{nm}^{2}}$ for $2 K_{P}$ . In D, $γ_{1 / 2} \approx 0.49 \frac{k_{B} T}{{nm}^{2}}$ for $\frac{2}{3} A_{P}$ and $γ_{1 / 2} \approx 0.65 \frac{k_{B} T}{{nm}^{2}}$ for $\frac{1}{2} A_{P}$ .