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Microtubule Organization in the Presence of Motor Proteins Open Access


Other title
Motor Proteins
Type of item
Degree grantor
University of Alberta
Author or creator
White, Diana T
Supervisor and department
de Vries, Gerda (Mathematics)
Dawes, Adriana (Mathematics, Ohio State)
Examining committee member and department
Mogilner (UC Davis)
Hillen, Thomas (Mathematics)
Pilgrim, David (Biological Sciences)
Dawes, Adriana (Mathematics, Ohio State)
de Vries, Gerda (Mathematics)
Li, Michael (Mathematics)
Department of Mathematical and Statistical Sciences
Applied Mathematics
Date accepted
Graduation date
Doctor of Philosophy
Degree level
In this thesis, we construct a non-local transport model that describes the evolution of microtubules (MTs) as they interact with motor proteins. MTs, whose organization is crucial for normal cellular development, have been found to organize into various patterns in vitro and in vivo through their interactions with motor proteins. In the first part of the thesis, we state results of a simplified version of the model, a model that describes the interaction of MTs with stationary distributions of motors. In the second part of the thesis, we state results for the full model, a model that describes the interaction of MTs with moving distributions of motors. For both models, an advection-type term accounts for directed MT transport, and an integral term accounts for reorientation of MTs due to their interactions with cross-linking motor proteins. For our simplified model, directed movement corresponds to a combination of MT treadmilling and MT sliding (where motor proteins are present). In the full model, when motors are moving, directed movement corresponds to treadmilling alone. Simulations of each model show how MT patterns depend on boundary constraints, as well as different model parameters that represent motor speed, motor processivity, cross-linking capability (activity), and directionality. For stationary motors in large domains, and using model parameter values for motors that are consistent with experimental values, we find that patterns such as asters, bundles, and vortices are able to persist. Vortex patterns have not been observed in vivo, however are found in in vitro experiments. In constrained domains, we find that similar patterns form. However, we also find that when two opposing motors are present, anti-parallel bundles are able to form. Our model quantitatively describes how motors are involved in MT patterning. To date, there are no other models that describe such patterning by explicitly incorporating motor properties (for stationary motors) into a model for MT evolution. For moving motors, we simulate our model using periodic boundary conditions, representing MT organizations in large domains. We do this to compare our simulation results with results that have been found in vitro. Also, we simulate our model using parameters consistent with fast and slow processive motors, fast non-processive motors, and slow weakly processive motors, similar to the types of motors used in experiments. Similar to experiments, we find that depending on motor type and density, various types of patterns, such as arrays of asters, arrays of vortices, and clusters of disorganized MTs exist. Also, consistent with previous theoretical models, we find that MT patters depend on motor density.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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