Dynamic instabilities in the kinetics of growth and disassembly of   microtubules
  Dynamic instability of microtubules is considered using frameworks of non-linear thermodynamics and non-equilibrium reaction-diffusion systems. Stochastic assembly/disassembly phases in the polymerization dynamics of microtubules are treated as a result of collective clusterization of microdefects (holes in structure). The model explains experimentally observed power law dependence of catastrophe frequency from the microtubule growth rate. Additional reaction-diffusion-precipitation model is developed to account for kinetic limitations in microtubule dynamics. It is shown that large scale periodic microtubules length fluctuations are accompanied by concentration autowaves. We built corresponding parametric diagram mapping areas of stationary, non-stationary and metastable solutions. The loss of stability for the stationary solutions happens through bifurcation of Andronov-Hopf. Using parametric diagram we classify cytostatic effect of microtubule stabilizing drugs in four major classes and analyze their compatibility and possible synergistic effect for cancer treatment therapy. 
Eugene Katrukha
q-bio.SC