Abstract

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.

Highlights

  • The formation of multicellular organisms from the assembly of single-celled ones constitutes one of the most striking and complex problems tackled by biology

  • When a cyanobacteria filament is deprived of combined nitrogen, some vegetative cells differentiate into heterocysts, which are terminally differentiated nitrogen-fixing cells

  • Modeling and Simulation of Heterocyst Pattern Formation 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

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Summary

Introduction

The formation of multicellular organisms from the assembly of single-celled ones constitutes one of the most striking and complex problems tackled by biology. The most salient feature that characterizes multicellular organisms is the presence of different cell types, in such a way that the organism associates a different function to each cell type In each of these cellular types, only a subset of the genes that constitute the genome of the organism (genotype) are expressed, which identify the function and morphology of the cell (phenotype). The development of specialized cells involves differentiation processes, which lead to alterations in gene expression producing different phenotypes from a given genotype. These processes are highly dynamical, directed by complex regulatory networks involving cell-to-cell interactions, and often triggered by external stimuli. Due to the large number of scales involved, ranging from protein binding to diffusion of specific elements throughout the organism, a correct mathematical modeling of differentiation processes and their associated pattern formation demands an integrative approach combining tools from statistical mechanics and the theory of dynamical systems (see [1, 2] for instance)

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