  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.
