A simple formulation of microtubule dynamics: quantitative implications of the dynamic instability of microtubule populations in vivo and in vitro.

A simple formulation of microtubule dynamic instability is presented, which is based on the experimental observations by T. Horio and H. Hotani of coexisting, interconverting growing and shrinking microtubules. Employing only three independent, experimentally determined parameters for a given microtubule end, this treatment accounts quantitatively for the principal features of the observed dynamic behaviour of steady-state tubulin microtubules in vitro. Experimental data are readily reproduced for microtubule length redistribution, and for the kinetics of tubulin exchange processes, including pulse-chase properties. The relative importance of dynamic incorporation and that due to treadmilling are assessed. Dynamic incorporation is found to dominate the overall exchange properties; polarized incorporation due to treadmilling generally becomes significant only when the dynamics are largely suppressed. This treatment also permits simulation of certain cellular phenomena, showing how microtubule renucleation can control microtubule growth, by means of changes in microtubule number concentration in a system at constant microtubule mass. A relatively simple extension of the formulation accounts quantitatively for non-steady-state microtubule properties, e.g. dilution-induced rapid disassembly and the oscillatory mode of microtubule assembly. The principles relating dynamic instability and oscillatory behaviour are clearly indicated. Possible mechanisms of the switching of microtubules are briefly discussed.