Scientific African (Sep 2021)
Dynamic structure factors of fluid membranes exhibiting lateral and flip-flop transitions: Effects of inclusions and the presence of an interacting wall
Abstract
In this paper, we consider a fluid membrane formed by a mixture of two chemically incompatible lipid molecules A and B. The variation of an adequate parameter (temperature, PH, lateral pressure, etc.) may lead the amphiphile molecules of the bilayer to undergo lateral or flip-flop separations. The physical system is modeled by a two-order parameter field theory. The composition fluctuations relative to the sheets are denoted φ and ψ, standing in fact for the two fields. We first investigate the effect of inclusions like flippase proteins on the dynamics of the lipid mixture, assumed to be suddenly cooled by passing from a starting temperature Ti, towards a temperature Tf nearby to the consolute point Tc. To compute exactly the structure factors use is made of the extended Van Hove approach written as two coupled Langevin equations (with noise). We show that the dynamics is entirely ruled by two kinds of relaxation rates τL and τS. The first is the pertinent time, which is related to long-wavelength fluctuations leading to the formation of macrophase domains. Whereas the local dynamics is characterized by the second one τS, which is a short scale time. We show, notably, that the presence of attractive inclusions tends to lower the relaxation time τL, and consequently the flip-flop transition is accelerated. The existence of two relaxation times is in good agreement with a certain experimental study on the kinetics of binary lipid mixtures phase transitions, namely DMPC-DSPC and DMPC-DPPC. We investigate, in the second part of this work, the effect of the presence of an interacting wall, assumed to adsorb strongly one or both species, on the parallel structure factors S(z,z′). These latter are exactly calculated in all cases: below Tc, above Tc and at T=Tc, as well as their associated local compressibilities S(z). Scaling laws, for these latter, are also derived.
