Flexible-to-semiflexible chain crossover on the pressure-area isotherm of lipid bilayer

TL;DR

This paper presents a theoretical model predicting a crossover in the pressure-area isotherm of lipid bilayers due to competition between chain conformational energies, allowing inference of elastic properties from experimental data.

Contribution

The study introduces a microscopic model linking lipid chain elasticity to pressure-area isotherm crossover, enabling extraction of elastic moduli from experimental measurements.

Findings

Prediction of a pressure-area isotherm crossover from n=5/3 to n=3.

Derivation of a relation for the crossover area involving elastic moduli.

Calculation of crossover effects on compressibility and order parameters.

Abstract

We found theoretically that competition between ~Kq^4 and ~Qq^2 terms in the Fourier transformed conformational energy of a single lipid chain, in combination with inter-chain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)~(A-A_0)^{-n}. The crossover manifests itself in the transition from n=5/3 to n=3. Our microscopic model represents a single lipid molecule as a worm-like chain with finite irreducible cross-section area A_0, flexural rigidity K and stretching modulus Q in a parabolic potential with self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area per lipid A* obeys relation Q^2/(KB(A*))~1 . We predict a peculiar possibility to deduce effective elastic moduli K and Q of the individual hydrocarbon chain from the analysis of the isotherm possessing such crossover. Also calculated is crossover-related behavior of the area compressibility modulus K_a, equilibrium area per lipid A_t, and chain order parameter S.