AIMS:

Cyanobacteria forming one-dimensional filaments are paradigmatic model organisms of the transition between unicellular and multicellular living forms. Under nitrogen-limiting conditions, in filaments of the genus Anabaena, some cells differentiate into heterocysts, which lose the possibility to divide but are able to fix environmental nitrogen for the colony. We recently developed a mathematical theory for the regulation of heterocyst differentiation in Anabaena PCC 7120  [1]. We have now analyzed this theory, finding that the wild type lies very close to a critical point in parameter space, a so-called codimension 2 bifurcation. This means that small variations in parameter values are enough to produce big qualitative changes in phenotypes, since the wild type lies close to all the different kinds of phenotypes available to the system. This is an indication that the regulatory machinery of heterocyst differentiation has optimized evolvability, in the sense that small changes in parameter space, that can be produced in different way by small mutations, are enough to adapt the system to permanent changes in environmental conditions. [1] J. Muñoz-García and S. Ares, Formation and maintenance of nitrogen fixing cell patterns in filamentous cyanobacteria, Proc. Natl. Acad. Sci. USA 113, 6218-6223 (2016)