A storage-based model of heterocyst commitment and patterning in cyanobacteria

Mathematical models of nitrogen-fixing cell patterns in filamentous cyanobacteria

The Anabaena genus is a model organism of filamentous cyanobacteria whose vegetative cells can differentiate under nitrogen-limited conditions into a type of cell called a heterocyst. These heterocysts lose the possibility to divide and are necessary for the filament because they can fix and share environmental nitrogen. In order to distribute the nitrogen efficiently, heterocysts are arranged to form a quasi-regular pattern whose features are maintained as the filament grows. Recent efforts have allowed advances in the understanding of the interactions and genetic mechanisms underlying this dynamic pattern. Here, we present a systematic review of the existing theoretical models of nitrogen-fixing cell differentiation in filamentous cyanobacteria. These filaments constitute one of the simplest forms of multicellular organization, and this allows for several modeling scales of this emergent pattern. The system has been approached at three different levels. From bigger to smaller scale, the system has been considered as follows: at the population level, by defining a mean-field simplified system to study the ratio of heterocysts and vegetative cells; at the filament level, with a continuous simplification as a reaction-diffusion system; and at the cellular level, by studying the genetic regulation that produces the patterning for each cell. In this review, we compare these different approaches noting both the virtues and shortcomings of each one of them.

Terminal heterocyst differentiation in the Anabaena patA mutant as a result of post-transcriptional modifications and molecular leakage

The Anabaena genus is a model organism of filamentous cyanobacteria whose vegetative cells can differentiate under nitrogen-limited conditions into a type of cell called heterocyst. These heterocysts lose the possibility to divide and are necessary for the colony because they can fix and share environmental nitrogen. In order to distribute the nitrogen efficiently, heterocysts are arranged to form a quasi-regular pattern whose features are maintained as the filament grows. Recent efforts have allowed advances in the understanding of the interactions and genetic mechanisms underlying this dynamic pattern. However, the main role of the patA and hetF genes are yet to be clarified; in particular, the patA mutant forms heterocysts almost exclusively in the terminal cells of the filament. In this work, we investigate the function of these genes and provide a theoretical model that explains how they interact within the broader genetic network, reproducing their knock-out phenotypes in several genetic backgrounds, including a nearly uniform concentration of HetR along the filament for the patA mutant. Our results suggest a role of hetF and patA in a post-transcriptional modification of HetR which is essential for its regulatory function. In addition, the existence of molecular leakage out of the filament in its boundary cells is enough to explain the preferential appearance of terminal heterocysts, without any need for a distinct regulatory pathway.

Understanding multicellular pattern formation is key for the study of both natural and synthetic developmental processes. Arguably one of the simplest model systems for this is the filamentous cyanobacterium Anabaena, that in conditions of nitrogen deprivation undergoes a dynamical differentiation process that differentiates roughly one in every ten cells into nitrogen-fixing heterocysts, in a quasi-regular pattern that is maintained as the filament keeps growing. One of the most characteristic mutations affecting this process forms heterocysts mostly constrained to the terminal cells of the filament. We have used experimental observations to propose a mathematical model of heterocyst differentiation able to reproduce this striking phenotype. The model extends our understanding of the regulations in this pattern-forming system and makes several predictions on molecular interactions. Importantly, a key aspect is the boundary condition at the filament’s ends: inhibitors of differentiation should be able to leak out of the filament, or otherwise the terminal cells would not differentiate. This highlights, in a very clear example, the importance of considering physical constraints in developmental processes.

Inactivation of Three RG(S/T)GR Pentapeptide-Containing Negative Regulators of HetR Results in Lethal Differentiation of Anabaena PCC 7120

The filamentous cyanobacterium Anabaena sp. PCC 7120 produces, during the differentiation of heterocysts, a short peptide PatS and a protein HetN, both containing an RGSGR pentapeptide essential for activity. Both act on the master regulator HetR to guide heterocyst pattern formation by controlling the binding of HetR to DNA and its turnover. A third small protein, PatX, with an RG(S/T)GR motif is present in all HetR-containing cyanobacteria. In a nitrogen-depleted medium, inactivation of patX does not produce a discernible change in phenotype, but its overexpression blocks heterocyst formation. Mutational analysis revealed that PatX is not required for normal intercellular signaling, but it nonetheless is required when PatS is absent to prevent rapid ectopic differentiation. Deprivation of all three negative regulators—PatS, PatX, and HetN—resulted in synchronous differentiation. However, in a nitrogen-containing medium, such deprivation leads to extensive fragmentation, cell lysis, and aberrant differentiation, while either PatX or PatS as the sole HetR regulator can establish and maintain a semiregular heterocyst pattern. These results suggest that tight control over HetR by PatS and PatX is needed to sustain vegetative growth and regulated development. The mutational analysis has been interpreted in light of the opposing roles of negative regulators of HetR and the positive regulator HetL.

Quantitative models of nitrogen-fixing organisms

Nitrogen-fixing organisms are of importance to the environment, providing bioavailable nitrogen to the biosphere. Quantitative models have been used to complement the laboratory experiments and in situ measurements, where such evaluations are difficult or costly. Here, we review the current state of the quantitative modeling of nitrogen-fixing organisms and ways to enhance the bridge between theoretical and empirical studies.

HetL, HetR and PatS form a reaction-diffusion system to control pattern formation in the cyanobacterium nostoc PCC 7120

Local activation and long-range inhibition are mechanisms conserved in self-organizing systems leading to biological patterns. A number of them involve the production by the developing cell of an inhibitory morphogen, but how this cell becomes immune to self-inhibition is rather unknown. Under combined nitrogen starvation, the multicellular cyanobacterium Nostoc PCC 7120 develops nitrogen-fixing heterocysts with a pattern of one heterocyst every 10-12 vegetative cells. Cell differentiation is regulated by HetR which activates the synthesis of its own inhibitory morphogens, diffusion of which establishes the differentiation pattern. Here, we show that HetR interacts with HetL at the same interface as PatS, and that this interaction is necessary to suppress inhibition and to differentiate heterocysts. hetL expression is induced under nitrogen-starvation and is activated by HetR, suggesting that HetL provides immunity to the heterocyst. This protective mechanism might be conserved in other differentiating cyanobacteria as HetL homologues are spread across the phylum.

Self-Organization in Pattern Formation

Self-organization is pervasive in development, from symmetry breaking in the early embryo to tissue patterning and morphogenesis. For a few model systems, the underlying molecular and cellular processes are now sufficiently characterized that mathematical models can be confronted with experiments, to explore the dynamics of pattern formation. Here, we review selected systems, ranging from cyanobacteria to mammals, where different forms of cell-cell communication, acting alone or together with positional cues, drive the patterning of cell fates, highlighting the insights that even very simple models can provide as well as the challenges on the path to a predictive understanding of development.

The evolution of gene regulatory networks controlling Arabidopsis thaliana L. trichome development

BACKGROUND

The variation in structure and function of gene regulatory networks (GRNs) participating in organisms development is a key for understanding species-specific evolutionary strategies. Even the tiniest modification of developmental GRN might result in a substantial change of a complex morphogenetic pattern. Great variety of trichomes and their accessibility makes them a useful model for studying the molecular processes of cell fate determination, cell cycle control and cellular morphogenesis. Nowadays, a large number of genes regulating the morphogenesis of A. thaliana trichomes are described. Here we aimed at a study the evolution of the GRN defining the trichome formation, and evaluation its importance in other developmental processes.

RESULTS

In study of the evolution of trichomes formation GRN we combined classical phylogenetic analysis with information on the GRN topology and composition in major plants taxa. This approach allowed us to estimate both times of evolutionary emergence of the GRN components which are mainly proteins, and the relative rate of their molecular evolution. Various simplifications of protein structure (based on the position of amino acid residues in protein globula, secondary structure type, and structural disorder) allowed us to demonstrate the evolutionary associations between changes in protein globules and speciations/duplications events. We discussed their potential involvement in protein-protein interactions and GRN function.

CONCLUSIONS

We hypothesize that the divergence and/or the specialization of the trichome-forming GRN is linked to the emergence of plant taxa. Information about the structural targets of the protein evolution in the GRN may predict switching points in gene networks functioning in course of evolution. We also propose a list of candidate genes responsible for the development of trichomes in a wide range of plant species.

Morphological and isotopic changes of heterocystous cyanobacteria in response to N2 partial pressure

Earth's atmospheric composition has changed significantly over geologic time. Many redox active atmospheric constituents have left evidence of their presence, while inert constituents such as dinitrogen gas (N₂ ) are more elusive. In this study, we examine two potential biological indicators of atmospheric N₂ : the morphological and isotopic signatures of heterocystous cyanobacteria. Biological nitrogen fixation constitutes the primary source of fixed nitrogen to the global biosphere and is catalyzed by the oxygen-sensitive enzyme nitrogenase. To protect this enzyme, some filamentous cyanobacteria restrict nitrogen fixation to microoxic cells (heterocysts) while carrying out oxygenic photosynthesis in vegetative cells. Heterocysts terminally differentiate in a pattern that is maintained as the filaments grow, and nitrogen fixation imparts a measurable isotope effect, creating two biosignatures that have previously been interrogated under modern N₂ partial pressure (pN₂ ) conditions. Here, we examine the effect of variable pN₂ on these biosignatures for two species of the filamentous cyanobacterium Anabaena. We provide the first in vivo estimate of the intrinsic isotope fractionation factor of Mo-nitrogenase (ε_fix  = -2.71 ± 0.09‰) and show that, with decreasing pN₂ , the net nitrogen isotope fractionation decreases for both species, while the heterocyst spacing decreases for Anabaena cylindrica and remains unchanged for Anabaena variabilis. These results are consistent with the nitrogen fixation mechanisms available in the two species. Application of these quantifiable effects to the geologic record may lead to new paleobarometric measurements for pN₂ , ultimately contributing to a better understanding of Earth's atmospheric evolution.

Robust stochastic Turing patterns in the development of a one-dimensional cyanobacterial organism

Under nitrogen deprivation, the one-dimensional cyanobacterial organism Anabaena sp. PCC 7120 develops patterns of single, nitrogen-fixing cells separated by nearly regular intervals of photosynthetic vegetative cells. We study a minimal, stochastic model of developmental patterns in Anabaena that includes a nondiffusing activator, two diffusing inhibitor morphogens, demographic fluctuations in the number of morphogen molecules, and filament growth. By tracking developing filaments, we provide experimental evidence for different spatiotemporal roles of the two inhibitors during pattern maintenance and for small molecular copy numbers, justifying a stochastic approach. In the deterministic limit, the model yields Turing patterns within a region of parameter space that shrinks markedly as the inhibitor diffusivities become equal. Transient, noise-driven, stochastic Turing patterns are produced outside this region, which can then be fixed by downstream genetic commitment pathways, dramatically enhancing the robustness of pattern formation, also in the biologically relevant situation in which the inhibitors' diffusivities may be comparable.

Formation and maintenance of nitrogen-fixing cell patterns in filamentous cyanobacteria

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. These heterocysts form a quasiregular pattern in the filament, representing a prototype of patterning and morphogenesis in prokaryotes. Recent years have seen advances in the identification of the molecular mechanism regulating this pattern. We use these data to build a theory on heterocyst pattern formation, for which both genetic regulation and the effects of cell division and filament growth are key components. The theory is based on the interplay of three generic mechanisms: local autoactivation, early long-range inhibition, and late long-range inhibition. These mechanisms can be identified with the dynamics of hetR, patS, and hetN expression. Our theory reproduces quantitatively the experimental dynamics of pattern formation and maintenance for wild type and mutants. We find that hetN alone is not enough to play the role as the late inhibitory mechanism: a second mechanism, hypothetically the products of nitrogen fixation supplied by heterocysts, must also play a role in late long-range inhibition. The preponderance of even intervals between heterocysts arises naturally as a result of the interplay between the timescales of genetic regulation and cell division. We also find that a purely stochastic initiation of the pattern, without a two-stage process, is enough to reproduce experimental observations.