[Membrane organization in the plane of the layer and cell shape. Statistical approach]

Relationship between the structure and mechanical properties of membranes and the shape of cells was analysed. Fluid-mosaic model of the membrane with several components was studied. The components could move freely in the membrane plane, interacted with each other and had different mechanical properties, such as bending rigidity and spontaneous curvature. For such a multicomponent system free energy was found, and integral-differential equations relating the distribution of membrane components and the membrane local curvature were obtained from the condition of free energy minimum. A number of consequences were obtained from the equation. With a change of intramembrane interactions phase separation or calsterization of particles is initiated. This in its turn may cause a strong change in the local curvature. The numerical solution of the system for two -- dimensional case made it possible to find the distribution of structural components along the membrane and calculate the cell shape. Some transformation of erythrocytes were described.