A continuous model for microtubule dynamics with catastrophe, rescue and   nucleation processes
  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. 
Peter Hinow, Vahid Rezania, Jack A. Tuszynski