An Integrative Approach for Modeling and Simulation of Heterocyst Pattern Formation in Cyanobacteria Filaments

Heterocyst differentiation in cyanobacteria filaments is one of the simplest examples of cellular differentiation and pattern formation in multicellular organisms. Despite of the many experimental studies addressing the evolution and sustainment of heterocyst patterns and the knowledge of the genetic circuit underlying the behavior of single cyanobacterium under nitrogen deprivation, there is still a theoretical gap connecting these two macroscopic and microscopic processes. As an attempt to shed light on this issue, here we explore heterocyst differentiation under the paradigm of systems biology. This framework allows us to formulate the essential dynamical ingredients of the genetic circuit of a single cyanobacterium into a set of differential equations describing the time evolution of the concentrations of the relevant molecular products. As a result, we are able to study the behavior of a single cyanobacterium under different external conditions, emulating nitrogen deprivation, and simulate the dynamics of cyanobacteria filaments by coupling their respective genetic circuits via molecular diffusion. These two ingredients allow us to understand the principles by which heterocyst patterns can be generated and sustained. In particular, our results point out that, by including both diffusion and noisy external conditions in the computational model, it is possible to reproduce the main features of the formation and sustainment of heterocyst patterns in cyanobacteria filaments as observed experimentally. Finally, we discuss the validity and possible improvements of the model.Author Summary: Cyanobacteria filaments are paradigmatic examples of prokaryotic cellular differentiation and cooperative pattern formation. When a cyanobacteria filament is deprived of combined nitrogen, some vegetative cells differentiate into heterocysts, which are terminally differentiated nitrogen-fixing cells. Interestingly, most cells do not differentiate, but remain in their initial vegetative state. The coexistence of heterocysts and vegetative cells is essential for the survival of the filament since (i) heterocysts lose their photosynthetic capacity so they need vegetative cells around to be provided with a source of fixed carbon and (ii) cell division, i.e. reproduction, is only accomplished by vegetative cells. From such a paradigmatic example it is clear that differentiation processes are the result of the interplay of complex regulatory networks acting inside the cell and external stimuli, coming from both the adjacent cells and the environment. In this article we present an integrative approach that combines the study of internal regulatory processes, diffusion, and noisy environments in order to capture the key mechanisms leading to the differentiation of vegetative cyanobacteria into heterocysts and the subsequent pattern formation.