Coarse-grained Piezo 2 nanodome in a tensionless membrane.

(a) Exemplary conformations and average nanodome shape, average nanodome contours, and average lipid density within quadratic membrane patches with side length a ≃ 2 nm for the constrained Piezo 2 cryo-EM structure and the relaxed Piezo 2 structure in a coarse-grained tensionless membrane. The relaxed nanodome shape is an average over conformations from the last microseconds of 10 independent simulation runs with a length of 8 μs. The nanodome shape for the constrained Piezo 2 cryo-EM structure is an average over the last microseconds of three independent simulation runs with a length of 4 μs for a harmonic force constant of 1000 kJ mol−1 nm−2 per bead. (b) Radial membrane profiles of the average nanodome shapes. The shaded areas represent the error of the mean obtained from the shape profiles of the independent runs. (c) Mean curvature M along the shape profiles calculated from first and second derivatives at radial distance r, which are obtained from local quadratic fits of profile segments r ± 2 nm. (d) Average displacement of the center of mass (COM) of 4 TM-helix units versus average radial distance. The 4 TM-helix units are numbered as in Figure 7. Only protein residues in the TM sections of the 4-TM units are included in the calculation of COMs (see Methods).

Tension-induced flattening of the coarse-grained Piezo 2 protein-membrane nanodome.

(a) Average nanodome shapes, (b) average nanodome contours, and (c) average lipid density within quadratic membrane patches with sidelength a ≃ 2 nm at membrane tensions γ from 0 to 20.8 mN/m. The nanodome shapes and lipid densities are averages over conformations from the last microseconds of 10 independent simulation runs with lengths of 8 μs for γ = 0 and with lengths of 4 μs for γ > 0. (d) Radial membrane profiles of the average nanodome shapes in (a). The shaded areas represent the error of the mean obtained from the shape profiles of the independent runs. (e) Average displacement of the center of mass (COM) of 4 TM-helix units versus average radial distance. The 4 TM-helix units are numbered as in Figure 7. Only protein residues in the TM sections of the 4-TM units are included in the calculation of COMs.

Flattening of the Piezo 2 protein-membrane nanodome in atomistic simulations.

(a) Average nanodome shape, (b) average nanodome contours, and (c) average lipid density in a tensionless membrane. The nanodome shapes and lipid densities are averages over conformations from the last 50 ns of 5 independent atomistic simulation runs with lengths of 300 ns. (d) Radial membrane profiles of the nanodome shapes at membrane tensions γ from 0 to 18 mN/m obtained from averaging over conformations from the last 50 ns of 5 independent atomistic simulation runs. (e) Excess area ΔA of the protein-membrane nanodome versus membrane tension γ from coarse-grained simulations of membrane-embedded Piezo 1 and Piezo 2 and atomistic simulations with Piezo 2. The values and errors of excess area ΔA are obtained from the extrapolations to long timescales shown in Fig. 4.

Extrapolation of the excess area ΔA of the protein-membrane nanodome in coarse-grained simulations with (a) Piezo 2 and (b) Piezo 1 and (c) in atomistic simulations with Piezo 2 to long timescales. In these extrapolations, the trajectories lengths are divided into 5 equal time intervals, and the excess area ΔA in each time interval is calculated for the nanodome shape obtained from averaging over conformations of all independent simulation runs in this time interval. The ΔA values are plotted against the inverse of the centers of the time intervals, and the values of the last three intervals are linearly fitted with the function LinearModelFit of Mathematica 13. The errors of the data points represent the error of the mean of ΔA values obtained for the individual simulation runs, and the shaded error region of the linear fits represent prediction bands with confidence level 0.5. The ΔA values with error shown in Figure 4 are determined as the extrapolated values with prediction band error at t−1 = 0.

Extrapolation of the membrane bending energy Eb of the nanodome in coarse-grained simulations with (a) Piezo 2 and (b) Piezo 1 to long timescales, akin to the extrapolations of ΔA in Figure 4.

Elasticity modelling of the Piezo 2 protein based on coarse-grained simulation data.

(a) Piezo 2 height change Δz versus membrane tension γ in our coarse-grained simulations of membrane-embedded Piezo 2. The protein height change is defined as Δz(γ) = z4(0) − z4(γ) where z4 is the vertical displacement of the fourth 4-TM unit of the Piezo arms relative to the channel center (see Figure 2(e)). (b) Excess area ΔA of the nanodome and (c) bending energy Eb of the lipid membrane in the nanodome versus Piezo height change Δz. The values and errors of ΔA and Eb are obtained from extrapolating simulation results at the tension values γ = 0, 1.4, 2.8, 5.5, 10.8, and 20.8 mN/m to long timescales (see Figure 4(a) and Figure 4–figure supplement 1 (a)). (d) Vertical force F determined from Equation (2) and the slopes of the fitted lines in (b) and (c) at the Δz values obtained from simulations at the tension values γ = 0, 1.4, 2.8, and 5.5 mN/m. The vertical force F is the absolute value of the opposing and in equilibrium equal forces exerted by the Piezo protein and by the membrane at a given tension value (see text). The dashed lines result from linear fitting of data points for γ ≤ 6 mN/m in (a), of data points for Δz < 2 nm in (b) and (c), and of all data points in (d) with the function LinearModelFit of Mathematica 13. The shaded error region of the linear fit in (d) represents prediction bands with confidence level 0.5.

Elasticity modelling of the Piezo 1 protein based on coarse-grained simulation data.

(a) Piezo 1 height change Δz versus membrane tension γ in our coarse-grained simulations of membrane-embedded Piezo 1. The protein height change is defined as Δz(γ) = z4(0) − z4(γ) where z4 is the vertical displacement of the fourth 4-TM unit of the Piezo arms relative to the channel center. (b) Excess area ΔA of the nanodome and (c) bending energy Eb of the lipid membrane in the nanodome versus Piezo height change Δz. The values and errors of ΔA and Eb are obtained from extrapolating simulation results at the tension values γ = 0, 3.0, 6.0, and 11.8 to long timescales (see Figure 4(b) and Figure 4–figure supplement 1 (b)). (d) Vertical force F determined from Equation (2) and the slopes of the fitted lines in (b) and (c) at the Δz values obtained from simulations at the tension values γ = 0, 3.0, and 6.0. The dashed lines result from linear fitting of all data points in the plots with the function LinearModelFit of Mathematica 13. The shaded error region of the linear fit in (d) represents prediction bands with confidence level 0.5.

Response of the Piezo 1 and Piezo 2 channels to membrane tension.

(a,b) Simulation conformations of the three TM helices 38 that line the ion channel from our coarse-grained simulations of membrane-embedded Piezo 1 at vanishing membrane tension γ = 0 and at the largest simulated tension γ = 32 nM/m. (c,d) Simulation conformations of the TM helices 38 from our coarse-grained simulations of membrane-embedded Piezo 2 at γ = 0 and the largest simulated tension γ = 30 nM/m. The 50 aligned simulation conformations in (a) to (d) are taken from the last microseconds of the 10 simulation trajectories at intervals of 0.25 μs along each trajectory (5 conformations per trajectory), with TM helices 38 depicted as spline curves of backbone atoms in Mathematica 13. (e) Average distance between the backbone beads of the residues L2469 that form the outermost constriction site of the ion channel in Piezo 1 (Yang et al., 2022) versus membrane tension γ of our simulations. The L2496 backbone beads of the three TM helices 38 are shown as beads in (a) and (b). (f) Average tilt angle of the Piezo 1 helices 38 relative to the vertical z direction of the simulation conformations in (a,b) versus membrane tension γ of our simulations. (f) Average distance between the backbone atoms of the residues L2473 that form the outermost constriction site of the ion channel in Piezo 2 (Yang et al., 2022) versus membrane tension γ. (g) Average tilt angle of the Piezo 2 helices 38 versus membrane tension γ. Error bars in (e) to (h) represent errors of the mean calculated from average values obtained for the 10 trajectories.

Structure and topology of the Piezo 2 monomer (Wang et al., 2019).

The 38 TM helices of the monomer are numbered from the N-to the C-terminus of the protein chain. The TM helices 1 to 36 are arranged in 9 TM-units with 4 helices each. The ion channel of the Piezo 2 trimer is lined by the three TM helices 38 of the three monomers. Loops not resolved in the cryo-EM structure of the Piezo 2 trimer structure in detergent micelles are indicated by dashed lines.

Lipid percentages of membrane

Embedding the Piezo 2 protein into a membrane.

(a) Piezo 2 trimer with ‘lipid envelop’ placed into planar and asymmetric membrane of area 50 nm × 50 nm. The lipid envelop was created by insertion of a Piezo 2 monomer into a planar lipid membrane and subsequent superposition of resulting lipid-enveloped monomers on the Piezo 2 cryo-EM structure (see Methods). (b) Piezo 2 trimer embedded in a continuous membrane nanodome after minimization and equilibration simulations starting from (a).