Finite pool of subunits as a length-control mechanism. (a)
Schematic of the model. We model a cell as a compartment with one filament
(orange) and a fixed total number of subunits
(N
t, red and orange) within the
compartment. The subunits that are not in the filament (red)
are freely diffusing in the cell compartment. (b) The assembly
rate of the filament [r =
r′ (Nt −
l), blue] decreases linearly with
its length, due to the depletion of the free subunit pool. Coupled with a
constant disassembly rate (γ, green),
this process can lead to a well-defined steady-state length
l*. (c) The
steady-state length distribution is a peaked function around the mean filament
length. For purposes of illustration, we chose the rates
r′ = 0.51/(subunit
− s), γ = 5/s, and
Nt = 200 subunits.