Determining the Gaussian Curvature Modulus of Lipid Membranes in Simulations

Abstract

The Gaussian curvature modulus κ¯ of lipid bilayers likely contributes more than 100 kcal/mol to every cellular fission or fusion event. This huge impact on membrane remodeling energetics might be a factor that codetermines the complex lipid composition of biomembranes through tuning of κ¯. Yet, its value has been measured only for a handful of simple lipids, and no simulation has so far determined it better than a factor of two, rendering a systematic investigation of such enticing speculations impossible. Here we propose a highly accurate method to determine κ¯ in computer simulations. It relies on the interplay between curvature stress and edge tension of partially curved axisymmetric membrane disks and requires determining their closing probability. For a simplified lipid model we obtain κ¯ and its relation to the normal bending modulus κ for membranes differing both in stiffness and spontaneous lipid curvature. The elastic ratio κ¯/κ can be determined with a few percent statistical accuracy. Its value agrees with the scarce experimental data, and its change with spontaneous lipid curvature is compatible with theoretical expectations, thereby granting additional information on monolayer properties. We also show that an alternative determination of these elastic parameters based on moments of the lateral stress profile gives markedly different and unphysical values.

Coupling between pore formation and phase separation in charged lipid membranes

“…Under the assumption that 0 0  c and '    [47], the free energy F of the membrane with a surface area of 2 D  can be written as,…”

Elastic properties and line tension of self-assembled bilayer membranes

“…[19], the difference between Gaussian moduli of two types of lipid bilayers was obtained. The Gaussian modulus has also been determined in simulations by quantifying the probability that a membrane patch closes up to form a vesicle [20]. Finally, a third important elastic parameter of membranes is the spontaneous curvature c 0 .…”

Peptide-induced membrane curvature in edge-stabilized open bilayers: A theoretical and molecular dynamics study

“…[40][41][42][43][44][45][46][47][48][49] The Gaussian curvature modulus κ G does not differ too much from κ b : κ G ≈ 0.7-0.9 · κ b . 50 The line tension γ l can be inferred from experimental data (γ l ≈ 10-50 pN, see, e.g., Ref. 34) or calculated by analytical techniques 51 and from MD simulations.…”