Microtubule Organization in the Presence of Motor Proteins

  • Author / Creator
    White, Diana T
  • 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.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • de Vries, Gerda (Mathematics)
    • Dawes, Adriana (Mathematics, Ohio State)
  • Examining committee members and their departments
    • Pilgrim, David (Biological Sciences)
    • Mogilner (UC Davis)
    • Dawes, Adriana (Mathematics, Ohio State)
    • Hillen, Thomas (Mathematics)
    • de Vries, Gerda (Mathematics)
    • Li, Michael (Mathematics)