Master equation for dynamics of filament assembly. (a)
P(l, t) is the frequency of occurrence of
filaments of length l in an ensemble of dynamical filaments at
time t. (b) List of all transitions that lead
to a change in the probability of a filament having a length l.
A filament can either grow starting as a filament of length l
− 1 by adding a subunit with a rate r or shrink by
starting as a filament of length l + 1 by losing a
subunit with a rate. These transitions will increase
P(l, t) by
rΔt or γ
Δt, respectively. Alternatively, a filament of
length l can either shorten to a filament of length
l − 1 with a rate or add a subunit and become a
filament with length l + 1 with a rate
r. These transitions will decrease
P(l, t) by γ
Δt or
rΔt, respectively.
(c) Changes in the probability distribution due to different
molecular processes, described in panel b.