Dj. Bicout, GREENS-FUNCTIONS AND FIRST PASSAGE TIME DISTRIBUTIONS FOR DYNAMIC INSTABILITY OF MICROTUBULES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(6), 1997, pp. 6656-6667
It is shown that the dynamic instability process describing the self-a
ssembly and/or disassembly of microtubules is a continuous version of
a variant of persistent random walks described by the generalized tele
grapher's equation. That is to say, a microtubule is likely to undergo
stochastic traveling waves in which catastrophe and rescue events can
not propagate faster than upsilon(-) and upsilon(+), respectively. For
this stochastic process, analytic expressions for Green's functions o
f position and velocity of a microtubule and exact solutions for the f
irst passage time distributions of a microtubule to the nucleating sit
e are obtained. It is shown that, in the omega-->infinity limit, where
omega(-1) is the persistence time, the dynamic instability process ca
n be described by a diffusion process in the presence of a drift term
that, in fact, is the steady-stare velocity of the microtubule. As a r
esult, the catastrophe time distribution (i.e., the distribution of mi
crotubule lifetimes to the nucleating site) exhibits a power law with
an exponential cutoff as F(t\x(0))similar to t(-3/2)e(-t/tau c), where
tau(c) is the time scale at which the drift term and the diffusive te
rm are comparable.