  We study the stochastic dynamics of growth and shrinkage of single actin
filaments or microtubules taking into account insertion, removal, and ATP/GTP
hydrolysis of subunits. The resulting phase diagram contains three different
phases: a rapidly growing phase, an intermediate phase and a bound phase. We
analyze all these phases, with an emphasis on the bound phase. We also discuss
how hydrolysis affects force-velocity curves. The bound phase shows features of
dynamic instability, which we characterize in terms of the time needed for the
ATP/GTP cap to disappear as well as the time needed for the filament to reach a
length of zero, i.e., (to collapse) for the first time. We obtain exact
expressions for all these quantities, which we test using Monte Carlo
simulations.
