  Microtubules are a major component of the cytoskeleton distinguished by
highly dynamic behavior both in vitro and in vivo. We propose a general
mathematical model that accounts for the growth, catastrophe, rescue and
nucleation processes in the polymerization of microtubules from tubulin dimers.
Our model is an extension of various mathematical models developed earlier
formulated in order to capture and unify the various aspects of tubulin
polymerization including the dynamic instability, growth of microtubules to
saturation, time-localized periods of nucleation and depolymerization as well
as synchronized oscillations exhibited by microtubules under various
experimental conditions. Our model, while attempting to use a minimal number of
adjustable parameters, covers a broad range of behaviors and has predictive
features discussed in the paper. We have analyzed the resultant behaviors of
the microtubules changing each of the parameter values at a time and observing
the emergence of various dynamical regimes.
