Liquid-ordered lipid domains represent a lateral inhomogeneity in cellular membranes. these domains have elastic and physicochemical properties different from those of the surrounding membrane. in particular, their thickness exceeds that of the disordered membrane. thus, elastic deformations arise at the domain boundary in order to compensate for the thickness mismatch. in equilibrium, the deformations lead to an incomplete register of monolayer ordered domains: the elastic energy is minimal if domains in opposing monolayers lie on the top of each other, and their boundaries are laterally shifted by about 3 nm. This configuration introduces a region, composed of one ordered and one disordered monolayers, with an intermediate bilayer thickness. Besides, a jump in a local monolayer curvature takes place in this intermediate region, concentrating here most of the elastic stress. This region can participate in a lateral sorting of membrane inclusions by offering them an optimal bilayer thickness and local curvature conditions. In the present study, we consider the sorting of deformable lipid inclusions, undeformable peripheral and deeply incorporated peptide inclusions, and undeformable transmembrane inclusions of different molecular geometry. With rare exceptions, all types of inclusions have an affinity to the ordered domain boundary as compared to the bulk phases. the optimal lateral distribution of inclusions allows relaxing the elastic stress at the boundary of domains.Cellular membranes are laterally heterogeneous 1-3 . Many membrane proteins are believed to function properly only inside lipid-protein domains, also referred to as rafts 4-7 . Proteins in these domains are surrounded by a more or less thick lipid shell [8][9][10][11] . In model purely lipidic systems it is demonstrated that lipids can form similar domains, in which they are in a liquid-ordered (L o ) phase state, while the surrounding membrane is liquid-disordered (L d ) [12][13][14][15] . Ordered domains are usually bilayer, i.e. exist in both membrane leaflets at the same lateral position [14][15][16][17] . Such transbilayer coupling could be driven by elastic deformations arising at the domain boundary and by membrane thermal fluctuations 18-21 . The mechanism of this coupling is not specific to the exact lipid composition of the domain: only the higher ordering of lipids with respect to the surrounding membrane is important [22][23][24] . A bilayer structure of rafts is believed to be a key property in providing raft-dependent signal transduction across the plasma membrane 4,5 . There are increasing evidences that a raft interior itself may be laterally inhomogeneous: some molecules may prefer its boundary region rather than its bulk part. In particular, the fusion peptide of the human immunodeficiency virus (HIV) gp41 protein functions with the highest efficiency only in the presence of the L o /L d phase boundary in the target membrane 25,26 . In addition, the HIV receptor CCR5 preferentially localizes at the domain boundary 26 . It means t...