Figure 1.
Schematic of Bilayer Deformations due to MscL
Mismatch between the hydrophobic regions of the lipid bilayer and an integral membrane protein gives rise to bending and compression deformations in each leaflet of the bilayer. The largest deformations occur at the protein–lipid interface, and over the scale of a few nanometers the bilayer returns to its unperturbed state. MscL is shown schematically at zero tension in its closed and open states with relevant dimensions. The red region of the protein indicates the hydrophobic zone. The hydrophobic mismatch at the protein–lipid interface is denoted by uo. The deformation profile, denoted by u(r), is measured with reference to the unperturbed leaflet thickness (l) from the protein center at r = 0.
Figure 2.
Elastic Potentials between two MscL Proteins
To minimize deformation energy, two transmembrane proteins exert elastic forces on each other. MscL has three distinct interaction potentials between its two distinct conformations. External tension weakens the interaction between two open channels (Voo) and strengthens the interaction between two closed channels (Vcc), but has almost no effect on the interaction between an open and closed channel (Voc). The open–open and closed–closed interactions are both more strongly attracting than the open–closed interaction, indicating that elastic potentials favor interactions between channels in the same state. The “hard core” distance is where the proteins' edges are in contact.
Figure 3.
Conformational Statistics of Interacting MscL Proteins
Interactions between neighboring channels lead to shifts in the probability that a channel will be in the open state (dashed lines). The sensitivity and range of response to tension, dPopen/dτ, are also affected by bilayer deformations (solid lines). Popen and dPopen/dτ are shown for separations of 0.5 nm (red) and 1.5 nm (green) with reference to noninteracting channels at d = ∞ (blue). Interactions shift the critical gating tension for the closest separation by ∼12%. Additionally, the peak sensitivity is increased by ∼90% from ∼5 nm2/kBT to ∼9.5 nm2/kBT, indicating a Hill coefficient of ∼2.
Figure 4.
Elastic Interactions Lower Open Probability Transition and Couple Conformation Changes
Two MscL proteins in a square box of area A diffuse and interact via their elastic potentials.
(A) At low areal density, the response to tension is the same as an independent channel. As the areal density increases, the more beneficial open–open interaction (see Figure 2) shifts the open probability to lower tensions and decreases the range of response (dashed lines) while increasing the peak sensitivity, indicating that areal density can alter functional characteristics of a transmembrane protein.
(B) The probability for exactly one channel to be open (P1, solid lines) is shown at a low (blue) and high (red) areal density. For tensions past the critical tension, interacting channels are ∼1,000 times less likely to gate individually. The probability for both channels to be open simultaneously (P2, dashed lines) is shown for low (blue) and high (red) areal density. The tension at which two simultaneously open channels are favored is significantly lower for interacting channels. Together these facts signify a tight coupling of the conformational changes for two interacting channels.
Figure 5.
Average Separation between Proteins Drops Significantly due to Elastic Interactions
The average separation between two diffusing MscL proteins in a box of area A is plotted as a function of tension for a range of areal densities, each shown as a different line color. The grey region roughly indicates when gating is occurring. At low areal density (mostly blue), the conformational change does not draw the proteins significantly closer together. As the areal density increases, the conformational change is able to draw the proteins up to ∼100 times closer than they would otherwise be. At the highest areal density (mostly red), the steric constraint of available area intrinsically positions the proteins close to one another regardless of their conformation. The average separation begins to increase again as higher tension weakens the open–open interaction.
Figure 6.
Elastic Interactions Tightly Couple Conformational Change with Protein Dimerization
Diffusing MscL proteins are considered dimerized when they are close enough that they attract with an energy greater than kBT. At high areal density, the net attractive closed–closed interaction is sufficient to dimerize the two channels part of the time. As the areal density decreases, the closed–closed interaction is not strong enough to dimerize the two channels—now dimerization only happens at higher tensions after both channels have switched to the open conformation. As the areal density decreases further, the open–open interaction is no longer strong enough to overcome entropy. This loss of dimerization is amplified by the fact that the open–open interaction is weaker at higher tensions (see Figure 2). The white dashed lines roughly indicate the range of areal densities for which dimerization probability and open channel probability are equal to each other (see Figure 4).