Frickenhaus S., Heinrich R.

Humboldt University Berlin, Biology / Theoretical Biophysics Invalidenstr. 42, D-10115 Berlin, Germany

Most lipid components of membranes of a variety of eukaryotic cells
have been found to be asymmetrically distributed between the inner and
the outer monolayers. In the case of red blood cells, it has been demonstrated
that an ATP-dependent aminophospholipid selective transport protein may
be the cause of a highly unsymmetrical distribution of phosphatidylserine
(PS) and phosphatidylethanolamine (PE). The latter phenomenon of inward
directed transport of PS and PE has recently been modelled on the basis
of kinetic equations of a corresponding carrier mechanism taking into account
competitive binding and an irreversible translocation step. The experimental
fact of uneven distribution of other lipid components such as phosphatidylcholine
(PC), sphingomyelin (SM) and cholesterol (Ch) may be attributed to the
restrictions caused by coupling of the monolayers. The active transport
of PS and PE will be accompanied by a passive redistribution of all lipid
components between the monolayers. It is shown, how the latter process
may be described in a thermodynamic modeling approach by making use of
phenomenological linear flux-force relations (see also).

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.