Mixed lipid bilayers with locally varying spontaneous curvature and bending

Abstract

Abstract. A model of lipid bilayers made of a mixture of two lipids with different average compositions on both leaflets, is developed. A Landau hamiltonian describing the lipid-lipid interactions on each leaflet, with two lipidic fields ψ1 and ψ2, is coupled to a Helfrich one, accounting for the membrane elasticity, via both a local spontaneous curvature, which varies as C0 + C1(ψ1 − ψ2)/2, and a bending modulus equal to κ0 + κ1(ψ1 + ψ2)/2. This model allows us to define curved patches as membrane domains where the asymmetry in composition, ψ1 − ψ2, is large, and thick and stiff patches where ψ1 + ψ2 is large. These thick patches are good candidates for being lipidic rafts, as observed in cell membranes, which are composed primarily of saturated lipids forming a liquid-ordered domain and are known to be thick and flat nanodomains. The lipid-lipid structure factors and correlation functions are computed for globally spherical membranes and planar ones and for a whole set of parameters including the surface tension and the coupling in the two leaflet compositions. Phase diagrams are established, within a Gaussian approximation, showing the occurrence of two types of Structure Disordered phases, with correlations between either curved or thick patches, and an Ordered phase, corresponding to the divergence of the structure factor at a finite wave vector. The varying bending modulus plays a central role for curved membranes, where the driving force κ1C 2 0 is balanced by the line tension, to form raft domains of size ranging from 10 to 100 nm. For planar membranes, raft domains emerge via the cross-correlation with curved domains. A global picture emerges from curvature-induced mechanisms, described in the literature for planar membranes, to coupled curvature-and bending-induced mechanisms in curved membranes forming a closed vesicle.

Nanodomains in Biomembranes with Recycling

“…However, we have argued that the chosen recycling scheme is realistic. Note also that the proximity of a phase transition can be relevant in the present context [39]. We have chosen here to focus on the simplest case of a system that is far from this transition (and below the transition temperature) in order not to obscure the interplay between equilibrium and out-of-equilibrium processes of interest.…”

“…We have kept F (n * ) in the exponential because it does not tend to zero at large n * (or large σ), contrary to the other terms, which justifies to expand the exponentials. The relation [ 39 ] holds for all n close to n * . Equating order-1 terms in (n − n * ), we get c1 = e F (n * ) , i.e.…”

“…Strictly speaking, to infer two equations from the relation in Eq. [ 39 ] valid for any n close to n * , we only need two different values of n, e.g. n * and n * + 1.…”

Equilibrium microphase separation in the two-leaflet model of lipid membranes

“…In nonequilibrium systems, an analog of the microphase separation can be observed when energetically activated reactions between two components are included [5,6]. The nonequilibrium scenario has inspired a variety of proposals in the context of the cell membrane [7][8][9][10][11][12].Equilibrium microphase separation in two-component lipid membranes was found in two-leaflet models with different lipid composition in each leaflet [13][14][15][16]. In these models, coupling between the local membrane curvature and the difference of local lipid compositions in two layers could give rise to an instability at finite wave numbers.…”

“…Equilibrium microphase separation in two-component lipid membranes was found in two-leaflet models with different lipid composition in each leaflet [13][14][15][16]. In these models, coupling between the local membrane curvature and the difference of local lipid compositions in two layers could give rise to an instability at finite wave numbers.…”