Attractive asymmetric inclusions in elastic membranes under tension: cluster phases and membrane invaginations

Abstract

International audienc

Nanodomains in Biomembranes with Recycling

“…Below we first choose α = 2, the low tension case where (Fig S4), and we arrive to similar qualitative conclusions in this case. The order of magnitudes of the parameters have already been discussed in connection with biophysical data [18,22,28]: The value of f0 = −(fatt+frep) > 0, in the 10 to 30 kBT range, is in fact of little interest because it is f0 + µ which eventually determines the value of φ; γ has the same order of magnitude as f0. If we choose α = 2, χ appears to be of order 0.1 to get equilibrium clusters containing few dozens of particles as observed experimentally.…”

“…The coupling between inclusion concentration and membrane curvature has recently received a striking experimental demonstration [27]. When grouped in a cluster, asymmetric proteins collectively shape the membrane and lead to spherical buds, the elastic energy of which grows faster than the number of proteins [28]. This is equivalent to the existence of a long-range repulsion of elastic origin which destabilizes too large clusters, because the energetic cost would overcome the gain in terms of line tension if macroscopic clusters grew [21,18,19].…”

“…This is equivalent to the existence of a long-range repulsion of elastic origin which destabilizes too large clusters, because the energetic cost would overcome the gain in terms of line tension if macroscopic clusters grew [21,18,19]. A typical finite cluster size emerges [22,28], controlled by the attraction/repulsion competition.…”

“…[ 31 ]), it combines a classical liquid droplet approximation in two dimensions (the first two terms) and a repulsive contribution leading to the finite size of clusters at equilibrium (the last term) [10]. The value of α has been thoroughly explored [28] and typically lies between 1.5 and 2, the exact value depending on the membrane tension. Below we first choose α = 2, the low tension case where (Fig S4), and we arrive to similar qualitative conclusions in this case.…”

“…The dashed line is then a power-law fit of the six last dots c 1 ∝ j ν with ν 0.32 (Eq. [ 28 ]). Log-log coordinates.…”