In the mammalian plasma membrane, cholesterol can translocate rapidly between the exoplasmic and cytoplasmic leaves, so that its distribution between them should be given by the equality of its chemical potential in the leaves. Due to its favorable interaction with sphingomyelin, which is almost entirely in the outer leaf, one expects the great majority of cholesterol to be there also. Experimental results do not support this, implying that there is some mechanism attracting cholesterol to the inner leaf. We hypothesize that it is drawn there to reduce the bending free energy of the membrane caused by the presence of PE (phosphatidylethanolamine). It does this in two ways: first by simply diluting the amount of PE in the inner leaf, and second by ordering the tails of the PE to reduce its spontaneous curvature. Incorporating this mechanism into a model free energy for the bilayer, we find that between 50 and 60% of the total cholesterol should be in the inner leaf of human erythrocytes.

Abstract. Equilibrium equations and stability conditions are derived for a general class of multicomponent biological membranes. The analysis is based on a generalized Helfrich energy that accounts for geometry through the stretch and curvature, the composition, and the interaction between geometry and composition. The use of nonclassical differential operators and related integral theorems in conjunction with appropriate composition and mass conserving variations simplify the derivations. We show that instabilities of multicomponent membranes are significantly different from those in single component membranes, as well as those in systems undergoing spinodal decomposition in flat spaces. This is due to the intricate coupling between composition and shape as well as the nonuniform tension in the membrane. Specifically, critical modes have high frequencies unlike single component vesicles and stability depends on system size unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We show that the predictions of the analysis are in qualitative agreement with experimental observations. Key words. stability, membrane, biological, spherical, heterogeneous AMS subject classifications. 74K25, 92C05, 49Q10 DOI. 10.1137/110831301 1. Introduction. Biological membranes (BMs) are fundamental building blocks of cell walls, mitochondria, and other organelles. They protect the cell by providing a barrier, and control almost all interaction with the surroundings, including transport, signaling, transduction, and adhesion. A key to this diverse functionality is the coupling between mechanical signals carried by the BM and biochemical events in the cell [13,24,31,37,47] and the rich phenomena that this coupling creates; see, e.g., [3,16,34,28,36]. For example, gated mechano-sensitive ion channels open to form a large conductance pore in response to membrane stretching [14,17,18,33,38,25].BMs are primarily made of a lipid bilayer, but also contain proteins, rigid cholesterol molecules, and other functional molecules [9]. Moreover, for the same lipid, various phases may be found, such as gels, liquid disordered phases, and liquid ordered phases. These phases differ in their mechanical properties, which makes the BM a heterogeneous mechanical structure. Moreover, BMs are dynamic structures whose molecular arrangements can change with conditions. Depending on the type of lipids and the functional molecules involved, as well as the external conditions like osmotic pressure and temperature, the BM can remain homogeneous or segregate into different phases/domains. The latter changes the stress distribution in the BM and either absorbs or releases energy. Therefore, just like other heterogeneous materials, deformation of the BM is dictated by composition. However, unlike standard mechanical structures, composition is modulated by the shape of the BM [26].

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The distribution of cholesterol between the two leaves of the plasma membrane in mammalian cells presents a conundrum; given cholesterol's known affinity for sphingomyelin, which resides predominantly in the exoplasmic leaf, why is it that experiment finds a majority of the cholesterol in the cytoplasmic leaf? This article reviews a recently proposed solution to this puzzle.

We consider a model plasma membrane, one that describes the outer leaf as consisting of sphingomyelin, phosphatidylcholine, and cholesterol, and the inner leaf of phosphatidylethanolamine, phosphatidylserine, phosphatidylcholine, and cholesterol. Their relative compositions are taken from experiment, and the cholesterol freely interchanges between leaves. Fluctuations in composition are coupled to fluctuations in the membrane height as in the Leibler-Andelman mechanism. Provided that the membrane is of relatively constant thickness, this coupling of fluctuations also provides a coupling between the composition fluctuations of the two leaves. Structure functions display, for components in both leaves, a peak at non-zero wavevector. This indicates that the disordered fluid membrane is characterized by structure on a scale given by membrane properties. From measurements on the plasma membrane, this scale is on the order of 100 nm. The theory provides a tenable basis for the origin of "rafts". Statement of SignificanceThe hypothesis that the plasma membrane is not homogeneous, but rather is heterogeneous, with rafts" of one composition floating in a sea of another, has overturned conventional views of this membrane and how it functions. Proteins prefer either the raft or the sea, and so are not uniformly distributed. Hence they perform more efficiently. From experiment, rafts are thought to be about 100 nm. However there is no realistic model that provides: a length scale for the rafts; a raft in both leaves of the membrane; the composition of the raft. We provide such a model. In contrast to other theories, the raft and sea are distinguished not only by composition, but also by a difference in curvature.