Membrane mechanics as a probe of ion-channel gating mechanisms

The details of conformational changes undergone by transmembrane ion channels in response to stimuli, such as electric fields and membrane tension, remain controversial. We approach this problem by considering how the conformational changes impose deformations in the lipid bilayer. We focus on the role of bilayer deformations in the context of voltage-gated channels because we hypothesize that such deformations are relevant in this case as well as for channels that are explicitly mechanosensitive. As a result of protein conformational changes, we predict that the lipid bilayer suffers deformations with a characteristic free-energy scale of $10k_{\mathrm{B}}T$. This free energy is comparable to the voltage-dependent part of the total gating energy, and we argue that these deformations could play an important role in the overall free-energy budget of gating. As a result, channel activity will depend upon mechanical membrane parameters such as tension and leaflet thickness. We further argue that the membrane deformation around any channel can be divided into three generic classes of deformation that exhibit different mechanosensitive properties. Finally, we provide the theoretical framework that relates conformational changes during gating to tension and leaflet thickness dependence in the critical gating voltage. This line of investigation suggests experiments that could discern the dominant deformation imposed upon the membrane as a result of channel gating, thus providing clues as to the channel deformation induced by the stimulus.

Figure 1

Models of gating in terms of three types of deformation induced in the membrane. We discard all molecular details of the channel and focus solely on how it deforms the membrane. The types of deformation are (a) bending of the midplane; (b) normal compression or stretching of the bilayer; (c) enlarging or shrinking of the channel areal footprint (shown with top view). The two rows represent protein shapes associated with different conformations. The figure exaggerates the deformations and does not specifically associate deformations with either the closed or open conformation because in general, deformations could be induced by either.

Figure 2

Definition of the variables that characterize midplane bending and compression deformations. (a) $h\left(r\right)$ describes the deviation of the midplane from the flat reference plane as a function of $r$, the distance from the center of the pore. $R$ is the radius of the channel, and changes during footprint dilations. $\theta$ is a coarse-grained representation of the angle formed by the midplane at the protein-lipid interface. (b) $u\left(r\right)$ describes the compression of the bilayer and $d_{\mathrm{o}}$ is the reference thickness of a leaflet. The size of the deformations in this schematic have been exaggerated for clarity.

Figure 3

Schematic representation of sources of deformation energy. (a) A bilayer in the undeformed state. (b) Elastic compression or stretch leads to an increase in free energy that is accompanied by a change in leaflet thickness from its equilibrium value. (c) Yielding to membrane tension decreases free energy. This is modeled as a loading force applied to the edge of the membrane by weights hanging over pulleys. As the protein increases in size, the weights lower, thereby decreasing the total energy. (d) Bending deformations in the membrane are caused by torques on the membrane.

Figure 4

Schematic demonstrating tension-induced thinning. Under tension, the bilayer (light gray region) thins, whereas the thickness along the protein (dark gray rectangle) remains unchanged. The membrane thickness decreases from $d_{\mathrm{o}}$ to ${\tilde{d}}_{\mathrm{o}}$, and the boundary compression changes from $U_{\mathrm{o}}$ to ${\tilde{U}}_{\mathrm{o}}$. The effect is exaggerated in the figure for clarity.

Figure 5

Expected shifts in half activation voltage as functions of tension (a), (b) and bilayer thickness (c), (d) for the three deformation types. $\Delta V_{0.5}$ is expressed as a shift from $V_{0.5}$ at the reference tension and thickness in mV. The solid gray lines represent compression deformations, the dotted gray lines represent footprint dilations, and the solid black lines represent midplane-bending deformations. Plots (a) and (c) assume the closed channel state deforms the bilayer, whereas (b) and (d) assume the open channel deforms the bilayer. We present our results as though one type of deformation were dominant, though a physiological system may lack a dominant deformation type, existing as a mixture of different types.