Abstract:
Microtubules are hollow cylindrical protein structures found in all eukaryotic cells, and
essential in several cellular processes, including cell motility, cell division, vesicle trafficking and maintenance of cell shape. The building block of microtubtles, tubulin, is one
of the proven targets for anticancer drugs. A microtubule exhibits a remarkable property, termed dynam,i.c i,nstabi,Ii.ty, 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 pìausible mathematical modeìs for microtubule dynamics 'in ui,tro are
developed. Two of the models are developed with the exclusion of dynamic insiability
while the others are with its inclusion. Aiso considered are two different modes of nucleation 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 i,n ui,tro. Results indicate that
dynamic instability induces the formation of microtubules from the tubuÌin subunits, and
that dynamic instability depends on the GTP-tubulin concentration
