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Abstract

The cytoskeleton is a macromolecular scaffold which gives the cell its shape and controls cellular motion. Actin is the most abundant proteins in the cytoskeleton and an impor tant determinant of its structure and mechanical properties. Actin monomers polymerize into filaments that are then linked to one another by a variety of binding proteins. Fil aments can organize into unipolar and bipolar bundles as well as orthogonal networks. The formation of these structures and the transitions between them depend on the types, quantities, and properties of the binding proteins. The problem addressed in this thesis concerns interactions of actin filaments with actin binding proteins. I investigate the main mechanisms governing the formation of a variety of cytoskeletal actin structures as well as transitions between them. In particular I discuss how the type of binding protein and its binding kinetics affects the structures formed. I further investigate the influence of the geometry of the molecules and the dimensionality of the environment (for example the presence of a surface near which the structures form). Dynamic continuum models analogous to the mean field approximation in physics are used to study the time evolution of angular distributions of actin filaments. Integro partial differential equations are derived for two types of events: (a) rapid binding of filaments, and (b) gradual turning and alignment of filaments. Linear stability analysis is applied to 2D and 3D versions of such models. Numerical analysis and explicit solutions are discussed in special cases. It is found that as the actin filament density increases in the cell, a spontaneous tendency to organize into bundles or networks occurs. Both the linear stability anal ysis and the nnmerical results indicate that the structures formed are highly sensitive to changes in the parameters including the total mass of actin filaments, the rotational diffusion coefficient and rate constants representing binding and unbinding. Criteria (in volving combinations of these parameters) are obtained for instability of the homogeneous steady state and appearance of order. Similar results are obtained for both rapid and gradual alignment models, suggesting robustness of the modelling approach.