Dynamics of Microtubule Instabilities

We investigate the dynamics of an idealized model of microtubule growth that evolves by: (i) attachment of guanosine triphosphate (GTP) at rate lambda, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of GDP at rate mu. As a function of these rates, a microtubule can grow steadily or its length can fluctuate wildly. For mu=0, we find the exact tubule and GTP cap length distributions, and power-law length distributions of GTP and GDP islands. For mu=infinity, we argue that the time between catastrophes, where the microtubule shrinks to zero length, scales as exp(lambda). We also find the phase boundary between a growing and shrinking microtubule.