Figure 1

Idealized sketch of a cylindrically symmetrical membrane channel showing two schemes for tension mediated gating. In both cases the conformational changes are exaggerated for clarity. The upper two images show the closed and open states of the channel under the dilational gating model and the lower two images the same for gating-by-tilt. Under both schemes the membrane tension does work by increasing the combined projected area of the membrane and channel.Reuse & Permissions

Figure 2

The work available from the coupling of the membrane tension to a conformational change of a membrane channel $\Delta G_{\mathrm{m}\mathrm{e}\mathrm{m}\mathrm{b}}$ is plotted against the logarithm of the membrane tension $\gamma$. The dashed lines correspond to the energy change $\Delta G_{\mathrm{d}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}}$ available from dilational opening (1) and the solid lines the energy $\Delta G_{\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{t}}$ available from gating-by-tilt (6). Three curves are shown in each case corresponding to different values of the channel size. For dilational gating (dashed curves) the radius of the central pore in the open configuration is, from upper curve to lower curve, $b=1.5,1,0.5\mathrm{n}\mathrm{m}$, while for gating-by-tilt the radial distance of the exterior of the closed channel is, from upper curve to lower curve, $a=4,3,2\mathrm{n}\mathrm{m}$. These represent biologically reasonable sizes [20, 31]. In this illustrative example we have taken the change in tilt to be $\theta =\pi /6=30°$ and the membrane rigidity $\kappa =20k_{B}T$. The viability of the gating process relies on the value of the parameter $\Delta G_{\mathrm{m}\mathrm{e}\mathrm{m}\mathrm{b}}/k_{B}T$ being larger than unity, as discussed in the text. Steady state biological membrane tensions are in the ${10}^{-5}$ to ${10}^{-4}\mathrm{N}/\mathrm{m}$ range [32] while Msc channels can gate at tensions up to $\gtrsim {10}^{-2}\mathrm{N}/\mathrm{m}$ [20].Reuse & Permissions