Membrane Composition Variation and Underdamped Mechanics near Transmembrane Proteins and Coats

Abstract

We study the effect of transmembrane proteins on the shape, composition and thermodynamic stability of the surrounding membrane. When the coupling between membrane composition and curvature is strong enough the nearby membrane composition and shape both undergo a transition from over-damped to under-damped spatial variation, well before the membrane becomes unstable in the bulk. This transition is associated with a change in the sign of the thermodynamic energy and hence favors the early stages of coat assembly necessary for vesiculation (budding) and may suppress the activity of mechanosensitive membrane channels and transporters. Our results suggest an approach to obtain physical parameters of the membrane that are otherwise difficult to measure. [4][5][6][7]. Here, we are primarily interested in the non-specific lipid-protein interactions that arise from the coupling of their hydrophobic regions [8][9][10][11][12][13][14], although we can also allow for selective enrichment of membrane component(s) near the protein.We employ a continuum theory in which small deformations of the lipid environment near a rigid inclusion can be described by a number of local field variables, such as the profile of the mid-plane of the bilayer, its composition and membrane thickness . Furthermore, the free-energy cost associated with thickness deformation is completely decoupled at lowest order [21], and it can be independently analyzed although we do not do so here.We allow for selective enrichment/depletion of curvature sensitive inclusions in the vicinity of a membrane protein or, equivalently, lipid asymmetry between leaflets that is characterized by a local spontaneous curvature, the preferred mean curvature in the absence of any mechanical stresses on the membrane [33][34][35][36][37][38][39][40][41]. This local variation may be relatively large near a membrane protein if its geometry is such that it bends or deforms the surrounding membrane (see Fig 1). Our approach leads to a real-space description of the membrane around an inclusion of arbitrary symmetry.We consider a two-component membrane in which the local compositional asymmetry between the different layers and/or the density of curvature-sensitive inclusions is phenomenologically coupled to the local mean curvature of the membrane [33,34]. When the compositional variation is weak and the membrane displacement is small, the free-energy can be written as a Landau-Ginzburg ex- The surface variation of the rigid inclusion in theẑ direction is coarse-grained out so that the geometry is defined by its radius r0 and two functions describing the height U(θ) and contact angle U (θ) of the hydrophobic belt. These parameterize the protein-membrane interface (red line), where u(r0, θ) = U(θ) andn · ∇u(r0, θ) = U (θ), withn as the inward unit normal vector. We require both the normal force and the torque on the inclusion to vanish. The latter can lead to an equilibrium tilt angle ψ about the axis labeled by ε.pansion [33][34][35][42][43][44],where only the lowest-order terms ar...

Thermodynamic equilibrium of binary mixtures on curved surfaces

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Protein induced lipid demixing in homogeneous membranes

“…In particular, it was suggested that they may stabilize membrane composition fluctuations above T c , fostering ordering around the perturbation cen-ters [13]. Furthermore, direct coupling between membrane composition, spontaneous curvature and protein recruitment was clearly demonstrated theoretically [14][15][16][17][18] and experimentally using membrane tethers [19,20]. In these systems, proteins with hydrophobic mismatch (different length of the hydrophobic core as compared to the lipids [21][22][23][24][25]), attract lipids that fit the spontaneous curvature, thereby building a concave or convex shape to fill in the height mismatch.…”