  Under conditions of limited fixed-nitrogen, some filamentous cyanobacteria
develop a regular pattern of heterocyst cells that fix nitrogen for the
remaining vegetative cells. We examine three different heterocyst placement
strategies by quantitatively modelling filament growth while varying both
external fixed-nitrogen and leakage from the filament. We find that there is an
optimum heterocyst frequency which maximizes the growth rate of the filament;
the optimum frequency decreases as the external fixed-nitrogen concentration
increases but increases as the leakage increases. In the presence of leakage,
filaments implementing a local heterocyst placement strategy grow significantly
faster than filaments implementing random heterocyst placement strategies. With
no extracellular fixed-nitrogen, consistent with recent experimental studies of
Anabaena sp. PCC 7120, the modelled heterocyst spacing distribution using our
local heterocyst placement strategy is qualitatively similar to experimentally
observed patterns. As external fixed-nitrogen is increased, the spacing
distribution for our local placement strategy retains the same shape while the
average spacing between heterocysts continuously increases.
