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

Abstract

We found theoretically that competition between 4 f K q ∼ and 2 Qq ∼ 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 0 ( ) ( ) P A A A α − − ∼ . The crossover manifests itself in the transition from α=5/3 to α=3. Our microscopic model represents a single lipid molecule as a worm-like chain with finite irreducible cross-section area 0 A , flexural rigidity K f 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 * A obeys relation * / ( ) 2 f Q K B A ≈ . We predict a peculiar possibility to deduce effective elastic moduli K f and Q of the individual hydrocarbon chain from the analysis of the isotherm possessing such crossover. Also calculated is crossoverrelated behavior of the area compressibility modulus A K , equilibrium area per lipid t A , and chain order parameter ( ) S θ .