[Geometry and mechanics of the morphogenesis of active membranes on the example of plant trichome cells of the genus Draba L].

The stages of the early morphogenesis of simple (unbranched) and complex (branched) unicellular trichomes are studied in two species of the genus Draba--D. sibirica (Pall.) Thell. and D. daurica DC. The geometry of morphogenesis is estimated by analyzing intraindividual variation of quantitative morphological characteristics of the developing leaf blade and peduncle trichomes. The surface of all types oftrichome cells first acquires a spherical shape, followed by a U-shaped configuration with cylindrical proximal and spherical distal regions. In the development of complex trichomes, the area of the distal zone grows at a higher rate, which leads to separation of its volume into individual spherical regions, the morphogenesis of which repeats the early morphogenetic stages of the overall trichome cell, forming simple (unbranched) or complex (branched) trichome rays. As a rule, the lateral polarity of a trichome cell coincides with the proximodistal polarity of the leaf. Quantitative morphological data make it possible to infer an algorithm of the changes in shape common for all trichome cells, namely, the growth cycle comprising alternation of the phases of increase and decrease in the curvature of the outer cell surface. This surface is an active membrane expanded by the internal pressure and concurrently capable of actively increasing its area by incorporation of new structural elements. A distinctive feature of the proposed model is the geometrical inhomogeneity of the surface movement, changing the radius of curvature and creating internal (active) mechanical stresses in this membrane. A decrease in the ratio of the membrane surface area to the volume deprives the spatially homogeneous shape of its stability; correspondingly, the transition from elastic resistance to internal pressure to active resistance with the help of curvature differentiation becomes more energetically favorable. The source for growth and morphogenesis of the active membrane is alternation of the phases of local curvature leveling, which "charges" the membrane with active mechanical stresses and "discharge" of these stresses, leading to differentiation of the membrane's local curvatures.