Kinetic and thermodynamic aspects of lipid translocation in biological membranes

A theoretical analysis of the lipid translocation in cellular bilayer membranes is presented. We focus on an integrative model of active and passive transport processes determining the asymmetrical distribution of the major lipid components between the monolayers. The active translocation of the aminophospholipids phosphatidylserine and phosphatidylethanolamine is mathematically described by kinetic equations resulting from a realistic ATP-dependent transport mechanism. Concerning the passive transport of the aminophospholipids as well as of phosphatidylcholine, sphingomyelin, and cholesterol, two different approaches are used. The first treatment makes use of thermodynamic flux-force relationships. Relevant forces are transversal concentration differences of the lipids as well as differences in the mechanical states of the monolayers due to lateral compressions. Both forces, originating primarily from the operation of an aminophospholipid translocase, are expressed as functions of the lipid compositions of the two monolayers. In the case of mechanical forces, lipid-specific parameters such as different molecular surface areas and compression force constants are taken into account. Using invariance principles, it is shown how the phenomenological coefficients depend on the total lipid amounts. In a second approach, passive transport is analyzed in terms of kinetic mechanisms of carrier-mediated translocation, where mechanical effects are incorporated into the translocation rate constants. The thermodynamic as well as the kinetic approach are applied to simulate the time-dependent redistribution of the lipid components in human red blood cells. In the thermodynamic model the steady-state asymmetrical lipid distribution of erythrocyte membranes is simulated well under certain parameter restrictions: 1) the time scales of uncoupled passive transbilayer movement must be different among the lipid species; 2) positive cross-couplings of the passive lipid fluxes are needed, which, however, may be chosen lipid-unspecifically. A comparison of the thermodynamic and the kinetic approaches reveals that antiport mechanisms for passive lipid movements may be excluded. Simulations with kinetic symport mechanisms are in qualitative agreement with experimental data but show discrepancies in the asymmetrical distribution for sphingomyelin.