Diffusionsprozesse in zweidimensionalen Umgebungen von Membranen

Following the presentation of historical concepts associated with diffusion, the recent experiments on different types of obstructed and anomalous diffusion are reviewed, with a special account of transport measurements in biological cells and membranes, outlining the effect of crowding and trapping processes on the effective diffusion coefficient. The diffusion coefficient of a number of tracers meandering on a lattice through a field of immobilized traps is derived as a function of concentration of diffusing species and fixed traps, as well as complexation rates. An increase of the diffusion coefficient with the increase of the lattice gas concentration is identified, and recognized as crowding-enhanced diffusion. The diffusion coefficient involves the Gauss hypergeometric function with two large parameters. In the absence of satisfactory analytic approaches, the asymptotic expansions for these functions are presented. As a prototypic example of a crowded interface, supported membranes decorated by the variant surface glycoprotein of Trypanosoma brucei is discussed. Two types of diffusion corresponding to the two conformations of the protein are found to coexist using a new likelihood-based analysis method presented in this thesis. Finally, complex diffusion of protein markers and lipids in a membrane of the growing Nicotiana tabaccum pollen tubes is modelled by a single Fokker-Planck diffusion equation with sinks and sources, corresponding to the endocytosis and exocytosis. It is shown that the classical model for pollen tube tip growth appropriately describes the material traffic in the tube. Unexpected behaviour in complex diffusion on two-dimensional surfaces, emerging from the competition of crowding and trapping is summarised. While these insights may help in understanding a number of experiments concerning crowding and trapping, this work can also be a starting point for studying diffusion in analogous more complex 2D systems in physics and biology