Channel-facilitated membrane transport. (i) We developed a general time-dependent theory of transport through membrane channels. We used the theory to demonstrate that the fluctuation theorem is equally applicable for transport of both interacting and non-interacting particles. (ii) We also worked out the problem of fluctuations of the ion current through a membrane channel due to partial blocking of the channel by translocating molecules. [unreadable] [unreadable] Two-state protein folding. We generalized Kramers-Langer theory of activated rate processes to the case of discrete underlying stochastic dynamics. Application of our theory to folding of two-state proteins allows one to find folding and unfolding rates as well as most probable folding/unfolding pathways. [unreadable] [unreadable] Non-Markovian asymmetric random walks. We suggested a new approach which allowed us to find the Laplace transform of the propagator and related descriptors for non-Markovian asymmetric random walks with and without boundaries. These results were used when developing the general time-dependent theory of transport through membrane channels mentioned above. [unreadable] [unreadable] Cell-to cell communication in cultures of suspended cells. We developed a theory of ligand internalization in cultures of suspended cells, which communicate by diffusing ligands. Our theory shows how the time and length scales characterizing the ligand internalization depend on the properties of the cells and ligands as well as on the parameters of the assay like the cell concentration, etc.. The theory was used to analyze experimental data on Interferon signaling in experiments on early response of cultured human dendritic cells to virial infection.[unreadable] [unreadable] Dynamics of morphogen gradients in the Drosophila Embrio. We analyzed various aspects of the dynamics of different maternal morphogen gradients in the Drosophila Embryo. The goal of our analysis was to rationalize experimental observations made in Professor Shvartsman's Lab. at Princeton University. [unreadable] [unreadable] Transport in porous structures with entropy traps and barriers. We developed theories of diffusion in tubes with periodic entropy traps formed by dead ends and in tubes with periodic entropy barriers formed by contacting spheres. In the future we are going to use these results to analyze compartmentalization of second messengers in dedritic spines.