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The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized [1] in 1988 by using the entropy S q =The theory which emerges is usually referred to as nonextensive statistical mechanics and recovers the standard theory for q = 1. During the last two decades, this q-generalized statistical mechanics has been successfully applied to a considerable amount of physically interesting complex phenomena. A conjecture[2] and numerical indications available in the literature have been, for a few years, suggesting the possibility of q-versions of the standard central limit theorem by allowing the random variables that are being summed to be strongly correlated in some special manner, the case q = 1 corresponding to standard probabilistic independence. This is what we prove in the present paper for 1 ≤ q < 3. The attractor, in the usual sense of a central limit theorem, is given by a distribution of the form p(x) = C q [1 − (1 − q)βx 2 ] 1/(1−q) with β > 0, and normalizing constant C q . These distributions, sometimes referred to as q-Gaussians, are known to make, under appropriate constraints, extremal the functional S q (in its continuous version). Their q = 1 and q = 2 particular cases recover respectively Gaussian and Cauchy distributions. Mathematics Subject Classification (2000). Primary 60F05; Secondary 60E07, 60E10, 82Cxx.

Lipid rafts isolated by detergent extraction and sucrose gradient fractionation from mast cells are enriched for the glycosylphosphatidylinositol-linked protein Thy-1, the ganglioside GM1, palmitoylated LAT, and cross-linked IgE receptors, Fc⑀RI. This study addresses the relationship of fractionation data to the organization of raft markers in native membranes. Immunogold labeling and electron microscopy shows there is little or no colocalization of the raft markers Thy-1, GM1, and LAT with each other or with Fc⑀RI on native membrane sheets prepared from unstimulated cells. External cross-linking of Thy-1 promotes coclustering of Thy-1 with LAT, but not with GM1. Thy-1 and LAT clusters occur on membrane regions without distinctive features. In contrast, external cross-linking of Fc⑀RI and GM1 causes their redistribution to electron-dense membrane patches independently of each other and of Thy-1. The distinctive patches that accumulate cross-linked Fc⑀RI and GM1 also accumulate osmium, a stain for unsaturated lipids, and are sites for coated vesicle budding. Electron microscopy reveals a more complex and dynamic topographical organization of membrane microdomains than is predicted by biochemical analysis of detergent-resistant membranes. INTRODUCTIONOrdered regions of membrane, known as microdomains, lipid rafts, detergent-resistant membranes (DRMs), and other abbreviations are thought to be critical sites of signal propagation and membrane trafficking (Edidin, 1997(Edidin, , 2001Simons and Ikonen, 1997;Anderson, 1998; London, 1998, 2000;Jacobson and Dietrich, 1999;Langlet et al., 2000;Anderson and Jacobson, 2002). Analysis of these regions typically begins with detergent solubilization of whole cells followed by sucrose density gradient centrifugation and the recovery of detergent-resistant membranes from the light fractions of the gradient. The DRMs are enriched for caveolin, glycosylphosphatidylinositol-linked (GPI-linked) proteins, glycosphingolipids, GM1 ganglioside, and cholesterol, suggesting that these components are associated in the liquid-ordered (l o ) phase of the lipid bilayer (Schroeder et al., 1994;Ahmed et al., 1997). The interpretation of gradient centrifugation experiments remains controversial. There is evidence that detergents may force associations between components that are not colocalized in intact cells (Mayor and Maxfield, 1995), and fractionation results are known to be dramatically altered by varying the concentration of Triton X-100 (Field et al., 1999;Parolini et al., 1999), by use of alternative detergents (Montixi et al., 1998;Surviladze et al., 1998) or by omission of detergent altogether (Ilangumaran et al., 1999;Harder and Kuhn, 2000;Surviladze et al., 2001). Methods to observe membrane segregation in situ have also generated controversy. Results based on light and fluorescence microscopy of proteins and lipids, including refinements of the established fluorescence recovery after photobleaching methods and new single particle tracking methods, have led some investigators to co...

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