Lipid lateral self-diffusion drop at liquid-gel phase transition

A drop of lipid lateral self-diffusion coefficient at the liquid-gel phase transition in lipid membranes is calculated. So far this drop was missing theoretical description. Our microscopic model captures so-called subdiffusion regime, which takes place on 1 ps–100 ns timescale and reveals a jump of self-diffusion coefficient. Calculation of the jump is based on our recent study of liquid-gel phase transition. Subdiffusive regime is described within the free volume theory. Calculated values of self-diffusion coefficient are in agreement with quasielastic neutron scattering measurements. Self-diffusion coefficient is found to be composed of two factors: one is related to an area per lipid change at the phase transition, and the other one is due to an order of magnitude change in the stiffness of entropic repulsive potential.

Figure 1

Hydrocarbon tails of lipid are modeled as a flexible string. Schematic representations.

Figure 2

Collisions with neighboring lipids are modeled by self-consistent confining potential. Potential is parabolic in the string deviation from axis $z$ (arrows size mimics local force strength).

Figure 3

Entropic repulsion stiffness $B$ at the phase transition changes by an order of magnitude: in gel phase area per lipid $A/A_n\approx 1.9$, $B\approx 9\times {10}^9$ erg/${\mathrm{cm}}^3$, whereas in liquid phase $A/A_n\approx 3.4$, $B\approx 1\times {10}^9$ erg/${\mathrm{cm}}^3$. DPPC lipid bilayer is used as a reference. The choice of the microscopic model parameters: $L_R=17\AA$, $A_n=20{\AA }^2$, $K_f=5.797\times {10}^{-21}$ erg cm, and $U=745$ kcal ${\AA }^6$/mol, are made to match respective DPPC micro- and macroscopic parameters, such as main transition temperature and area per lipid in the vicinity of the transition.

Figure 4

Calculation results of self-diffusion coefficient for the DPPC in rattling in a cage mode obtained using hybrid equation (20). Our approach is limited to homogeneous phases, hence, in the vicinity of the phase transition calculation is shown with dashes. Two points with error bars are QENS measurements [45].

Figure 5

“Compression” (solid) and “activation” (dashed) factors of the self-diffusion coefficient [see Eq. (22)].