Mathematical expressions for entropic as well as mechanical forces are derived by taking into account coupling of the monolayers as a constraint. Both forces appear as functions of the lipid concentrations in the monolayers. The equilibrium state is characterized by a planar membrane consisting of symmetrically distributed ideally mixing lipids.
Making use of a general invariance principle of the flux-force relations, the dependencies of the phenomenological coefficients on the total lipid amounts are expressed. The matrix of phenomenological coefficients is shown to be decomposable into two different contributions. The first, diagonal part is linear in the total lipid concentrations with diffusion parameters as coefficients, characterizing independent (uncoupled) diffusion. The second part, which also contains nondiagonal terms, is bilinear in the total lipid concentrations, with coupling parameters as coefficients, representing interactions of the lipid fluxes.
Numerical simulation of the experimental data for steady state and transient states for the erythrocyte plasma membrane reveals that two prerequisites must be fulfilled for the choice of phenomenological parameters. First, the values of the diffusion parameters of PC, SM and Ch must be very different, with SM being the slowest diffusing species and Ch the fastest. Second, positive coupling parameters are required to yield the characteristic asymmetries for PC, SM and Ch, that is, a nearly symmetrical distribution of Ch, a pronounced preference of SM for the external monolayer, and an intermediate value for the asymmetry of PC.
To shed light into the mechanism of passive lipid redistribution, different kinetic schemes of lipid translocation are analyzed. A procedure for the derivation of phenomenological diffusion and coupling parameters in terms of kinetic constants is presented. Besides this, a proper treatment of mechanical effects in the kinetic models is demonstrated. It is shown, that an antiport mechanism of protein mediated lipid translocation cannot give rise to positive coupling coefficients. A symport mechanism may yield positive coupling parameters. However, the derived interrelation of diffusion and coupling parameters reveals that a slow diffusion of SM yields an insufficient extent of coupling. As an alternative mechanism is analyzed the redistribution of lipids through pores formed by peptides, which has been proposed recently. The main characteristic of such a transport in single-file is the effect of ordering of lipid molecules along the translocation co-ordinate. Flux equations are derived under special assumptions about the structure of the lipid-peptide pore. Linearization yields a relation between diffusion and coupling parameters that allows for slow diffusion and high positive coupling, especially for SM. Due to parameter restrictions from SM, the phenomenological analysis yields a plausible value for the pore-capacity of . In addition, a pore-independent lipid flip-flop must be taken into account to introduce different time constants of passive transmembrane movement.