Membrane-protein interactions in a generic coarse-grained model for lipid bilayers

Abstract

We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: direct interactions; lipid-induced depletion interactions; lipid bridging; lipid packing; and a smooth long-range contribution. The mechanisms leading to hydrophobic mismatch interactions are critically analyzed.

Figure 1

Cross-section snapshot of a model membrane with two inclusions of hydrophobic thickness L = 6θ_t and different hydrophobicity parameter ɛ_pt = 3 (top) and ɛ_pt = 6 (bottom). Light shaded lines show tail bonds, dark circles the heads (not to scale), dark cylinders the inclusions.

Figure 2

Fourier spectra of height (solid circles) and thickness fluctuations (open squares). The dashed line shows a fit of the data to the elastic theory (31) (Eqs. 13 and 14). The inset shows the thickness data alone with a fit to the Landau-de Gennes theory (Eq. 12).

Figure 3

Surface tension profile γ(z) for four different system sizes with N = 200, 288, 800, and 3200 lipids (top panel). The bottom panel shows the corresponding density profiles of solvent, head and tail beads in the smallest system (200 lipids) for comparison.

Figure 4

Radial membrane thickness profiles in the vicinity of inclusions with different hydrophobic thickness L and hydrophobicity parameter ɛ_pt as indicated. Solid symbols show data for inclusions with fixed orientation along the z axis, open symbols correspond to unconstrained inclusions. The solid and dashed lines are fits to the elastic theory (Eqs. 20 with 17 and 18) with fit parameters t_R and ${\tilde{c}}_0$.

Figure 5

Membrane thickness profiles in the vicinity of an inclusion with hydrophobic thickness L = 4σ_t, 6σ_t, and 8σ_t, and hydrophobicity parameter ɛ_pt = 6, compared with fits to the Landau-de Gennes theory (dashed lines), to the elastic theory with fixed c₀ = −0.05/σ_t and k_G = −0.26ɛ (solid lines), and to the elastic theory with the additional fit parameter ${\tilde{c}}_0$ replacing c₀ (dotted line). The shaded lines indicate the range of the fit at fixed c₀ if c₀ and k_G are varied within the error given in Table 1.

Figure 6

Radial profiles of various quantities as a function of the distance from the center of an inclusion with hydrophobic thickness L = 4σ_t (solid circles), L = 6σ_t (crosses), and L = 8σ_t (open squares) at ɛ_pt = 6. (Upper left) Bead density in the bilayer. (Upper right) Nematic order parameter for bonds. (Middle left) Heads per area in the monolayers. (Middle right) Hydrophilic shielding parameter (see text and (51)). (Lower left and lower right) Monolayer overlap, evaluated according to two different prescriptions (see text for definitions).

Figure 7

Potential of mean force between two inclusions with hydrophobic thickness L = 4σ_t (negative mismatch, top panel), L = 6σ_t (no mismatch, middle panel), and L = 8σ_t (positive mismatch, bottom panel) for different values of the hydrophobicity parameter ɛ_pt as indicated. The inset in the bottom panel shows the interactions generated outside of the membrane (solvent-mediated depletion interaction and direct interaction) for hydrophobically matched inclusions (solid line), and the additional contribution of solvent-induced interactions at L = 4σ_t (dashed line) and L = 8σ_t (dotted line).

Figure 8

Effective interaction potential between two inclusions according to the Landau-de Gennes theory (thin lines) and the elastic theory (thick lines) for inclusions with different hydrophobic thickness L as indicated. The thick shaded line shows the simulation data for L = 4σ_t, ɛ_pt = 6 for comparison.