Interleaflet coupling and domain registry in phase-separated lipid bilayers.

There is clear evidence of an interleaflet coupling in model lipid/cholesterol membranes exhibiting liquid-liquid phase separation. The strength of this coupling is quantified by the mismatch free energy, γ. We calculate it using a molecular mean-field model of a phase-separated lipid/cholesterol bilayer and obtain values that increase as the concentration of saturated lipids in the coexisting phases is increased. These values lie in the range 0.01-0.03 k(B)T/nm(2). We clarify the relationship between the interleaflet coupling and the extent of interleaflet alignment of liquid domains by analyzing a statistical mechanical model of coupled fluctuating domain interfaces. The model is solved exactly using the correspondence between statistical mechanics and quantum mechanics, yielding an expression for the characteristic size of fluctuations out of domain registry. This length scale depends only weakly on the strength of the interleaflet coupling and inevitably is only of the order of nanometers, which explains the experimental result that fluctuations out of domain registry have not been observed by optical microscopy.

Ionic effects on the electric field needed to orient dielectric lamellae.

We consider the effect of mobile ions on the applied potential needed to reorient a lamellar system of two different materials placed between two planar electrodes. The reorientation occurs from a configuration parallel to the electrodes favored by surface interactions to an orientation perpendicular to the electrodes favored by the electric field. The system consists of alternating A and B layers with different dielectric constants. The mobile ions are assumed to be insoluble in the B layers and hence confined to the A layers. We find that the ions reduce the needed voltage most strongly when they are constrained such that each A lamella is electrically neutral. In this case, a macroscopic separation of charge and its concomitant lowering of free energy, is attained only in the perpendicular orientation. When the ions are free to move between different A layers, such that charge neutrality is only required globally, their effect is smaller and depends upon the preferred surface interaction of the two materials. Under some conditions, the addition of ions can actually stabilize the parallel configuration. Our predictions are relevant to recent experiments conducted on lamellar phases of diblock copolymer films with ionic selective impurities.

Theory of raft formation by the cross-linking of saturated or unsaturated lipids in model lipid bilayers.

We consider the effect of cross-linking a small fraction of lipids, either saturated or unsaturated, in a mixture of saturated and unsaturated lipids and cholesterol. The change in phase behavior is examined utilizing a recent phenomenological model of the ternary system, which is extended to include a fourth component representing the cross-linked lipids. These lipids are taken to be identical to monomeric ones except for their reduced entropy of mixing. We find that even a relatively small amount of cross-linked lipids, less than 5 mol %, is sufficient to significantly expand the range of compositions within which there is coexistence between liquid-ordered and liquid-disordered phases. Equivalently, the cross-linking of lipids increases the liquid-liquid miscibility transition temperature, and therefore could bring about phase separation at a temperature at which, before cross-linking, there was only a single liquid phase.

Phase behavior of a model bilayer membrane with coupled leaves.

We discuss the thermodynamic behavior of a bilayer composed of two coupled leaves and derive the Gibbs Phase Rule for such a system. A simple phenomenological model of such a system is considered in which the state of the bilayer is specified by the relative number of ordering lipids in the outer leaf, and in the inner leaf. Two cases are treated. In the first, both inner and outer leaves could undergo phase separation when uncoupled from one another. The bilayer can exist in four different phases, and can exhibit three-phase coexistence. In the second case, an outer layer which can undergo phase separation by itself is coupled to an inner leaf which cannot. We find that when the coupling is weak, the bilayer can exist in only two phases, one in which the outer layer is rich in ordering lipids and the inner leaf is somewhat richer in them than when uncoupled, and another in which the outer layer is poor in ordering lipids and the inner leaf is poorer in them than when uncoupled. Increasing the coupling increases the effect on the inner leaf composition due to small changes in those of the outer leaf. For sufficiently large coupling, a phase transition occurs and the bilayer exhibits four phases as in the first case considered. Our results are in accord with several observations made recently.

Phenomenological model and phase behavior of saturated and unsaturated lipids and cholesterol.

We present a phenomenological theory for the phase behavior of ternary mixtures of cholesterol and saturated and unsaturated lipids, one that describes both liquid and gel phases. It leads to the following description of the mechanism of the phase behavior: In a binary system of the lipids, phase separation occurs when the saturated chains are well ordered, as in the gel phase, simply due to packing effects. In the liquid phase, the saturated ones are not sufficiently well ordered for separation to occur. The addition of cholesterol, however, increases the saturated lipid order to the point that phase separation is once again favorable. Our theory addresses this last mechanism-the means by which cholesterol-mediated ordering of membrane lipids leads to liquid-liquid immiscibility. It produces, for the system above the main chain transition of the saturated lipid, phase diagrams in which there can be liquid-liquid phase separation in the ternary system but not in any of the binary ones, while below that temperature it yields the more common phase diagram in which a gel phase, rich in saturated lipid, appears in addition to the two liquid phases.

Insights on raft behavior from minimal phenomenological models.

We construct a simple phenomenological theory of phase separation in ternary mixtures of cholesterol and saturated and unsaturated lipids. Such separation is relevant to the formation of 'rafts' in the plasma membrane. We also show how simple cross-linking of proteins which prefer one form of lipid to the other can trigger raft-formation, the first step in a signaling pathway.