Flexible String Model Analytical Description of Main Phase Transition in Lipid Bilayers

Abstract

Flexible string model [1,2,3] expanded with van der Waals attraction [4]: VdW= -g/a∧{5/2}, between hydrophobic chains, occupying each an average area a (in dimensionless units) in bilayer plane, is shown to provide analytical description of the main phase transition in lipid bilayers. Single lipid is modeled as a flexible string with a given bending rigidity and a finite incompressible area. Entropic repulsion between fluctuating lipid tails is represented by a parabolic potential, its stiffness parameter, b, is found self-consistenly: ∂F/∂b = ν·(√a-1)², where ν≪1 is small parameter of the theory. The free energy with added van der Waals interaction between adjacent hydrocarbon chains: F = log(b) + ∑log(1 + b/c·4ₙ⁴) + VdW. Here b is dimensionless entropic repulsion parameter, and cₙ coefficients are characteristics of energies of lipid's elementary modes. The theory, being microscopic, allows to study analytically an evolution of membrane properties in the vicinity of the main transition such as temperature dependence of the lateral lipid self-diffusion coefficient. It is also possible to study thermodynamic fluctuations of the lateral pressure near phase transition temperature in the random-phase approximation. [1] S.Mukhin, S.Baoukina. 2005. Analytical derivation of thermodynamic characteristics of lipid bilayer from a flexible string model. Phys. Rev. E. 71: 061918. [2] S. Mukhin, B. Kheyfets. 2010. Analytical Approach to Thermodynamics of Bolalipid Membranes. Phys. Rev. E. 82: 051901. [3] S. Mukhin, B. Kheyfets. 2014. Pore formation phase diagrams for lipid membranes. JETP Lett. 99: 358-362. [4] L. Salem. 1962. Attractive Forces between Long Saturated Chains at Short Distances. J. Chem. Phys. 37: 2100-2113.