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

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.

💡 Research Summary

The paper presents a microscopic theory of the pressure‑area isotherm of a lipid bilayer, focusing on the crossover between flexible and semiflexible behavior of individual hydrocarbon chains. Each lipid molecule is modeled as a worm‑like chain characterized by a bending rigidity K (flexural modulus) and a stretching modulus Q. In Fourier space the conformational energy of a single chain contains two competing contributions: a ~K q⁴ term associated with bending and a ~Q q² term associated with longitudinal stretching. The authors embed this single‑chain description in a self‑consistent mean‑field potential B(A) that represents the entropic repulsion between neighboring chains in the hydrophobic core. B(A) depends on the area per lipid A, the irreducible cross‑sectional area A₀, temperature, and the number density of chains; it is obtained by a variational calculation that minimizes the free energy of the ensemble.

The central result is that the competition between the ~K q⁴ and ~Q q² terms leads to two distinct scaling regimes for the pressure‑area relation

                     P(A) ∝ (A − A₀)⁻ⁿ,

with n = 5/3 in the “bending‑dominated” regime (small A, large B) and n = 3 in the “stretching‑dominated” regime (large A, small B). The crossover occurs at an area per lipid A* defined by the condition

                     Q² /