Membrane-mediated interactions between circular particles in the strongly curved regime

Abstract

Particles binding to a fluid lipid membrane can induce bilayer deformations, for instance when these particles are curved. Since the energy of two overlapping warp fields depends on the mutual distance between the two particles creating them, they will experience forces mediated by the curvature of the membrane. If the deformations are sufficiently weak, the associated differential equations for the membrane shape are linear, and the resulting interactions are understood very well; but very little is known for stronger curvature imprint, owing to the highly nonlinear nature of the problem. Here we numerically calculate the magnitude of such membrane-mediated interactions in the case of two axisymmetric particles over a wide range of curvature imprints, deep into the nonlinear regime. We show that over an intermediate distance range the sign of the force reverses beyond a sufficiently strong deformation. These findings are quantitatively confirmed by a simple analytical close-distance expansion. The sign flip can be traced to a change in magnitude between the two principal curvatures midway between the two particles, which can only occur at sufficient particle tilt, a condition which is by construction ruled out in the linearized description. We also show these large perturbation results to agree with coarse-grained molecular dynamics simulations and suggest that a favorable comparison is indeed more likely to hold in the strongly deformed regime.

Pointlike Inclusion Interactions in Tubular Membranes

“…Compared to the scale of the plasma membrane which can be approximately considered as a flat surface, the curved nature of such a tubular membrane can significantly affect these interactions. Recently, it has been revealed that hard particles and semiflexible polymers absorbed to soft elastic shells, collectively induce aggregates and produce a rich variety of aggregation patterns [18,[20][21][22][23][24][25][26]. Particularly, Pàmies and Cacciuto showed that spherical nanoparticles adhering to the outer surface of an elastic nanotube can selfassemble into diverse aggregates [22].…”

Ultradonut topology of the nuclear envelope

“…This principle has been successfully used to predict the interactions of membraneembedded proteins and nanoparticles (11)(12)(13). However, in the case of nuclear envelope, Fig.…”

Bilayer-thickness-mediated interactions between integral membrane proteins

“…(3) and modifications thereof have been found to capture the basic experimental phenomenology of bilayer-protein interactions in a wide range of experimental systems [4-11, 24-28, 31, 38-47, 81-83, 88-97], only involve parameters which can be measured directly in experiments, and are simple enough to allow analytic solutions. Analogous models have been formulated [7,48] to describe protein-induced curvature deformations [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] and fluctuation-mediated interactions [49,[61][62][63][64][65][66][67][68]. In general, thickness-, curvature-, and fluctuation-mediated interactions all contribute to bilayer-mediated interactions between integral membrane proteins, but the relative strengths of these interactions depend on the specific experimental system under consideration.…”

“…(3) and the corresponding "zeroth-order" models [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] capturing curvature-and fluctuation-mediated protein interactions absorb the molecular details of lipids and membrane proteins into effective material parameters. To provide a more detailed description of bilayer-protein interactions, a number of extensions and refinements of these models have been developed [44,45,[69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86].…”

“…According to this classic theory, membrane proteins may, in addition to thickness-mediated interactions [31,[39][40][41][42][43][44][45][46][47], also interact [7,48] via bilayer curvature deformations [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] and bilayer fluctuations [49,[61][62][63][64][65][66][67][68]. While the competition between thickness-, curvature-, and fluctuation-mediated protein interactions depends on the properties of the specific lipids and membrane proteins under consideration, one generally expects [7,31] that thickness-mediated protein interactions are strong and short-ranged, and that curvature-and fluctuation-mediated protein interactions are weak and long-ranged.…”