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Cyanobacteria forming one-dimensional filaments are paradigmatic modelorganisms of the transition between unicellular and multicellular living forms.Under nitrogen limiting conditions, in filaments of the genus Anabaena, somecells differentiate into heterocysts, which lose the possibility to divide butare able to fix environmental nitrogen for the colony. These heterocysts form aquasi-regular pattern in the filament, representing a prototype of patterningand morphogenesis in prokaryotes. Recent years have seen advances in theidentification of the molecular mechanism regulating this pattern. We use thisdata to build a theory on heterocyst pattern formation, for which both geneticregulation and the effects of cell division and filament growth are keycomponents. The theory is based on the interplay of three generic mechanisms:local autoactivation, early long range inhibition, and late long rangeinhibition. These mechanisms can be identified with the dynamics of hetR, patSand hetN expression. Our theory reproduces quantitatively the experimentaldynamics of pattern formation and maintenance for wild type and mutants. Wefind that hetN alone is not enough to play the role as the late inhibitorymechanism: a second mechanism, hypothetically the products of nitrogen fixationsupplied by heterocysts, must also play a role in late long range inhibition.The preponderance of even intervals between heterocysts arises naturally as aresult of the interplay between the timescales of genetic regulation and celldivision. We also find that a purely stochastic initiation of the pattern,without a two-stage process, is enough to reproduce experimental observations.

Formation and maintenance of nitrogen fixing cell patterns in filamentous cyanobacteria