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Investigating models for cross-linker mediated actin filament dynamics

University of British Columbia

Actin, a major component of the cytoskeleton, is responsible for the shape and structural properties of many eucaryotic cells. Actin filaments are made of monomers which bind in a single strand. Cross-linkers bind two filaments together and influence the relative orientation of the filaments. Cross-linkers such as a-actinin favor parallel alignment of filaments, while others such as actin-binding protein favor orthogonal alignment. The filament length, concentration of cross-linkers and cross-linker association-dissociation rates all affect the types of network that form. The resulting network dictates the structural properties of the cell. In this thesis I study how filament length, concentration of cross-linkers and crosslinker association-dissociation rates influence actin network development. I use existing models and create new models to explore these interactions. Integro-partial differential equations and other techniques are used to model the system. Using experimentally determined biological parameters, I predict the geometry and distribution of the resulting network. Computer simulations verify the model predictions. I compare these predictions with experimental results. Increasing the cross-linker concentration first strengthens the isotropic network, but then, beyond a transition, forces the network to be inhomogeneous and more fluid-like. As the cross-linker concentration increases even further, more filaments bind to the network, resulting in a stronger, more solid actin solution. Decreasing the cross-linker dissociation rate constant has the same effects as increasing the cross-linker concentration. Finally, I find that changing the filament length greatly affects rates of diffusion, influencing instabilities. Increasing the filament length, favors alignment and clustering, as well as formation of bundles. Filament length influences the spacing between clusters. Increasing the length, forces clusters to be spaced further apart until they eventually disappear. I also find that there is an optimal length for bundle formation. When considering a distribution of filament lengths, I expect to see a wider dispersal of filaments near the bundle transition point.

Thesis/Dissertation

application/pdf

2009-06-25

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http://hdl.handle.net/2429/9594

Mathematics

University of British Columbia

UBCV

DSpace