Bilayer Elasticity at the Nanoscale: The Need for New Terms

Abstract

Continuum elastic models that account for membrane thickness variations are especially useful in the description of nanoscale deformations due to the presence of membrane proteins with hydrophobic mismatch. We show that terms involving the gradient and the Laplacian of the area per lipid are significant and must be retained in the effective Hamiltonian of the membrane. We reanalyze recent numerical data, as well as experimental data on gramicidin channels, in light of our model. This analysis yields consistent results for the term stemming from the gradient of the area per molecule. The order of magnitude we find for the associated amplitude, namely 13–60 mN/m, is in good agreement with the 25 mN/m contribution of the interfacial tension between water and the hydrophobic part of the membrane. The presence of this term explains a systematic variation in previously published numerical data.

Bilayer-thickness-mediated interactions between integral membrane proteins

“…(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]. For instance, the effect of bilayer-protein interactions on the elastic properties of lipid bilayers can be captured [44,81,82,86] by allowing for spatial variations in the values of the elastic bilayer parameters.…”

“…The minimal model in Eq. (3) can be extended in a variety of ways to account for more detailed properties of lipid bilayers including lipid tilt [48,[75][76][77][78][79], lipid intrinsic curvature [39-42, 45, 70, 71], inhomogeneous deformation of lipid volume and effects of Gaussian curvature on protein-induced bilayer deformations [45,70,71], asymmetric bilayer thickness deformations [45,70,71,80], and protein-induced local modulation of bilayer elastic properties [44,[81][82][83][84][85][86].…”

“…The classic elasticity theory of protein-induced lipid bilayer deformations can be extended in various ways [44,45,[69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86] to account for detailed molecular properties of lipids such as lipid tilt and lipid intrinsic curvature [39][40][41][42]48], yielding additional modes of bilayermediated protein interactions. Theoretical studies of bilayer-mediated protein interactions have largely focused on idealized (often cylindrical or conical) protein shapes which do not correspond to any particular membrane protein, and proteins at large d. In contrast, bilayer-mediated protein interactions at small d are most relevant for the crowded environment provided by cell membranes [3,[21][22][23], while modern structural biology suggests a rich picture of membrane protein shape with experimental surveys of the protein content in various cell membranes [21,23,87] indicating great diversity in the oligomeric states and symmetries of membrane proteins.…”

The effect of gramicidin inclusions on the local order of membrane components

“…It states that proteins with a given hydrophobic length insert preferentially into membranes with a similar hydrophobic thickness [4] Many studies of the interaction used as inclusion the antimicrobial peptide (AMP) Gramicidin A (GramA), which is known [5,6] to deform (stretch or compress) host membranes to bring them closer to its own hydrophobic length, so the hydrophobic matching mechanism is likely relevant. This perturbation of the membrane prole induces between the GramA pores in bilayers with various compositions [7] a repulsive interaction that can be explained based on a complete elastic model [8].…”

Small scale membrane mechanics

“…More recently, Bitbol et al (2012) have shown that the thickness gradient in the membrane observed in nanoscale studies can be explained by keeping the terms in the Hamiltonian involving the gradient and Laplacian of the area per lipid. This is consistent with what was previously derived in Deseri et al (2008) from a dimension reduction procedure.…”