Understanding microtubule organization and dynamics

Current project members: Diana White (Clarkson Math), Jonathan Martin (Clarkson Math), and Freddie -Laud Amoah Darko (PhD Candidate, Clarkson Math).

Currently, I am working on projects related to microtubule (MTs) dynamics. As MTs are crucial for normal cell development (aiding in processes such as cell movement, cell polarization, and cell division), understanding their group dynamics (spacial organization), and individual dynamics is an important problem. Further, MTs are the primary target for many commonly used chemotherapy drugs, where such drugs work to alter MT organziation and individual dynamics.

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At the individual level, MTs go through cycles of slow polymerization (growth), through the addition of
high-energy guanosine triphosphate (GTP)-tubulin, followed by very fast cycles of shortening. Some of my work involves using non-local descriptions of shortening (instead of the commonly used advective description), where I incorporate integral-type terms such that shortening is described by a probabilistic shortening kernel (i.e., the kernel describes the probability of a MT of a given length to shorten by some fixed length).

I also use PDE models to better understand the organization of microtubules within cells, and in simple in vitro environments. These models lead to interesting questions related to self-organization and pattern formation, areas of interest to both the biological and mathematical communities. In addition to individual-based MT dynamics, MTs undergo organizational shifts as they transition between different functional states. A classic example is the transition between interphase (a non-dividing state) and cell division.