Caveolae as Invaginated Lipid Rafts

Caveolae are one example of lipid domains in the cell membrane [2]. These domains and other lipid "rafts" are characterized by a high concentration of cholesterol and saturated lipids. Although many controversies exist regarding the size and lifetime of lipid rafts, the morphology of caveolae seems much better defined. One likely reason for this is the stabilization of these membrane domains by the protein caveolin, and in particular the fact that they are invaginated. In this section, we present some general physical arguments concerning the behavior of membrane domains in a flexible, fluid lipid bilayer [16], without discussing the origin of their formation. Here, we assume that the phase separation is driven by chemical incompatibility between the raft and the non-raft phase, regardless of the mechanical state of the membrane. In Physical terms, chemical incompatibility can be accounted for by an energy cost of creating an interface between the two phases. Since the membrane is in two dimensions, the interface between the two phases is a line, and the immiscibility parameter is a "line tension", termed s For a given domain size, the line energy is the smallest when the interface is smallest, meaning that we can expect domains to be circular with a radius R = öS/p (S is the domain area). Unless the line tension is very small, in which case the rafts are very small and their shape can fluctuate significantly. This signifies that they are only weakly phase separating from the non-raft membrane and are close to dissolving back into it.

Figure 2.2 illustrates how chemical incompatibility alone can have a strong influence on the domain shape. Indeed, a flat domain (Fig. 2.2a) has a large interface with its surrounding, costing a line energy of order sR. If the domain is large, this can be quite a large energy, and may cause the domain to bud off the membrane in an attempt to reduce the size of the interface to the membrane neck connecting the bud to the rest of the membrane. On the other hand, an invaginated domain costs the energy of bending the membrane into a spherical shape. The bending energy of a sphere is proportional to the bending rigidity of the membrane k, and it has the remarkable feature that it does not depend on the size of the sphere for a symmetrical domain (it is equal to 8pk). Since the line energy increases with domain size, and the bending energy does not, there is a critical domain size for which we can expect the domain to invaginate spontaneously [16] (Fig. 2.2c). The

Fig.2.2 Invagination of a membrane domain (in gray) due to chemical incompatilibity. (a) A flat domain has a large line energy, due to a large interface with the surrounding membrane. (b) An invaginated domain has a small interface, but is accompanied with a bending energy. (c) Comparison of the energy of a flat domain (sloping line) and of an invaginated domain (horizontal line). The invagination is favored for domains larger than a critical size, estimated to be of order 100 nm.

Fig.2.2 Invagination of a membrane domain (in gray) due to chemical incompatilibity. (a) A flat domain has a large line energy, due to a large interface with the surrounding membrane. (b) An invaginated domain has a small interface, but is accompanied with a bending energy. (c) Comparison of the energy of a flat domain (sloping line) and of an invaginated domain (horizontal line). The invagination is favored for domains larger than a critical size, estimated to be of order 100 nm.

domain size at which this occurs is of the order R ~ 4k/s. The actual value of the physical parameters k and s vary from membrane to membrane, but we have a good idea of the order of magnitude of such parameters. The bending rigidity of biological membrane is typically of the order k ~ 20kBT The line tension arises from unfavorable contacts at the molecular scale (the size of a lipid molecule, or the thickness of the bilayer). It is estimated to be of the order s~ kBT/nm, although its actual value is very sensitive to the nature of the two phases in contact (in a raft, it is the contact between liquid-ordered and-liquid disordered lipid phases). Using those numbers, the critical size for domain invagination is R = 80 nm (corresponding to a spherical bud of radius 40 nm). Caveolae are precisely in this range of size, which is a good indication that the physical phenomena of membrane bending energy and raft line energy play a crucial role in caveolae formation and stability.

One possible picture of the formation of caveolae is the following [16] (see Fig. 2.2). Imagine a given amount of caveolin, cholesterol, and raft-forming lipids (in particular sphingo lipids), dispersed in the cell membrane. With time, these various components diffuse into the membrane and find each other, forming growing membrane domains. Although the rate of this phase separation might be quite slow [17], domains should eventually grow to a large size if they are not perturbed by other dynamical phenomena at the cell membrane, and even more so if the presence of caveolin promotes the phase separation. Membrane recycling, endocytosis, and exocytosis might perturb domain growth, and may be invoked to explain the small size of the non-caveolae rafts observed in vivo (see [17].) When domains grow beyond the critical size discussed above (Fig. 2.2), they are at their lowest energy N and therefore most stable N when invaginated rather than flat.

Such a scenario is still qualitatively valid if the membrane supports a tension and the domain has a spontaneous curvature. In this case, however, the critical budding size depends upon the membrane tension. Indeed, work against membrane tension must be performed to invaginate a domain, and this stabilizes the flat shape. As a result, this simple theory applied to caveolae would predict that the size of the invagination increases with membrane tension. However, caveolae have very similar sizes across several cell types that can, presumably, bear different membrane tensions. As will be seen in Section 2.5, this indicates that the structure of the protein caveolin might play a crucial role in controlling the size of the invaginated domains.

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