Contribution Of Dynamic Instability To Microtubule Organization

Abstract

Microtubules are hollow cylindrical protein structures found in all eukaryotic cells, and

essential in several cellular processes, including cell motility, cell division, vesicle tra±ck-

ing and maintenance of cell shape. The building block of microtubules, tubulin, is one

of the proven targets for anticancer drugs. A microtubule exhibits a remarkable prop-

erty, termed dynamic instability, in which it is able to switch stochastically between two

distinct states. In one state, the microtubule grows while in the other, it shrinks. The

balance between the growing and shrinking states is crucial for the normal functioning of

the cell. One of the interesting questions that cell biologists have pondered over the years

is: what is the biological function of dynamic instability? While some great strides have

been made in answering this question, the details of the precise nature of the mechanism

of dynamic instability in relation to their roles are not well understood. In this thesis

some biologically plausible mathematical models for microtubule dynamics in vitro are

developed. Two of the models are developed with the exclusion of dynamic instability

while the others are with its inclusion. Also considered are two di®erent modes of nu-

cleation of microtubules: saturating and non-saturating mode. The models are analyzed

and numerical simulations conducted, with an aim of mathematically assessing the role of

dynamic instability in the integral microtubule dynamics in vitro. Results indicate that

dynamic instability induces the formation of microtubules from the tubulin subunits, and

that dynamic instability depends on the GTP-tubulin concentration.