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We show in the companion paper that the free membrane shape of lipid bilayer vesicles containing the mechanosensitive ion channel Piezo can be predicted, with no free parameters, from membrane elasticity theory together with measurements of the protein geometry and vesicle size [C. A. Haselwandter, Y. R. Guo, Z. Fu, R. MacKinnon, Proc. Natl. Acad. Sci. U.S.A. , 10.1073/pnas.2208027119 (2022)]. Here we use these results to determine the force that the Piezo dome exerts on the free membrane and hence, that the free membrane exerts on the Piezo dome, for a range of vesicle sizes. From vesicle shape measurements alone, we thus obtain a force–distortion relationship for the Piezo dome, from which we deduce the Piezo dome’s intrinsic radius of curvature, 42 ± 12 nm, and bending stiffness, 18 ± 2.1   k B T , in freestanding lipid bilayer membranes mimicking cell membranes. Applying these estimates to a spherical cap model of Piezo embedded in a lipid bilayer, we suggest that Piezo’s intrinsic curvature, surrounding membrane footprint, small stiffness, and large area are the key properties of Piezo that give rise to low-threshold, high-sensitivity mechanical gating. 

Piezo proteins are mechanosensitive ion channels that can locally curve the membrane into a dome shape [Y. R. Guo, R. MacKinnon, eLife 6, e33660 (2017)]. The curved shape of the Piezo dome is expected to deform the surrounding lipid bilayer membrane into a membrane footprint, which may serve to amplify Piezo’s sensitivity to applied forces [C. A. Haselwandter, R. MacKinnon, eLife 7, e41968 (2018)]. If Piezo proteins are embedded in lipid bilayer vesicles, the membrane shape deformations induced by the Piezo dome depend on the vesicle size. We employ here membrane elasticity theory to predict, with no free parameters, the shape of such Piezo vesicles outside the Piezo dome, and show that the predicted vesicle shapes agree quantitatively with the corresponding measured vesicle shapes obtained through cryoelectron tomography, for a range of vesicle sizes [W. Helfrich, Z. Naturforsch. C 28, 693–703 (1973)]. On this basis, we explore the coupling between Piezo and membrane shape and demonstrate that the features of the Piezo dome affecting Piezo’s membrane footprint approximately follow a spherical cap geometry. Our work puts into place the foundation for deducing key elastic properties of the Piezo dome from membrane shape measurements and provides a general framework for quantifying how proteins deform bilayer membranes.