Models for cell differentiation and generation of polarity in diffusion-governed morphogenetic fields

Babloyantz, Agnessa; Hiernaux, Jean

doi:10.1016/s0092-8240(75)80051-6

Cited by 38 publications

(15 citation statements)

References 17 publications

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“…It can be shown that the mathematical content of the lateral inhibition concept, and that of Fourier-type analysis are closely related; but the demonstration is by no means straightforward. It takes time and patience to prove (Babloyantz and Hiernaux, 1975;Granero et al, 1977;Gierer, 1981). Indeed, the combination of autocatalytic activation and long range inhibition can be demonstrated mathematically to be essential, to be the only mode of pattern generation for the simplest two factor case.…”

Section: B a The Hydra Model -A Model For What? 441mentioning

confidence: 99%

The Hydra model - a model for what?

Gierer¹

2012

Int. J. Dev. Biol.

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The introductory personal remarks refer to my motivations for choosing research projects, and for moving from physics to molecular biology and then to development, with Hydra as a model system. Historically, Trembley's discovery of Hydra regeneration in 1744 was the beginning of developmental biology as we understand it, with passionate debates about preformation versus de novo generation, mechanisms versus organisms. In fact, seemingly conflicting bottom-up and top-down concepts are both required in combination to understand development. In modern terms, this means analysing the molecules involved, as well as searching for physical principles underlying development within systems of molecules, cells and tissues. During the last decade, molecular biology has provided surprising and impressive evidence that the same types of molecules and molecular systems are involved in pattern formation in a wide range of organisms, including coelenterates like Hydra, and thus appear to have been "invented" early in evolution. Likewise, the features of certain systems, especially those of developmental regulation, are found in many different organisms. This includes the generation of spatial structures by the interplay of self-enhancing activation and "lateral" inhibitory effects of wider range, which is a main topic of my essay. Hydra regeneration is a particularly clear model for the formation of defined patterns within initially near-uniform tissues. In conclusion, this essay emphasizes the analysis of development in terms of physical laws, including the application of mathematics, and insists that Hydra was, and will continue to be, a rewarding model for understanding general features of embryogenesis and regeneration. KEY WORDS: pattern formation, lateral inhibition, tissue evagination, Trembley, Caspar Friedrich Wolff How a physicist gets involved with Hydra -some personal reminiscensesIn the last decades, there were very stimulating bi-annual meetings of Hydra researchers, initiated by Charles David, in the castles of Reisensburg and of the Evangelische Akademie in Tutzing at beautiful Lake Starnberg. At each conference there was an evening lecture, usually unpublished, dedicated to more general topics, and speakers were encouraged to include personal reflections. The editor of this special issue, Brigitte Galliot, has kindly invited me to adapt my contribution for this special edition on Hydra.Let me begin with a few remarks of a personal nature on motives for the orientation of scientific interests that led me into research on Hydra. I studied physics from 1946 onwards, without the slightest trace of biology. There were two somewhat diffuse motivations when I was a teenager at High School that eventually spread that he would settle in Göttingen in 1946, I tried everything I could to enrol at Göttingen University and to find a way into his newly founded Max Planck Institute of Physics. Heisenberg was very stimulating for young scientists, in several ways. He was willing to take young people seriously right at ...

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Section: B a The Hydra Model -A Model For What? 441mentioning

confidence: 99%

The Hydra model - a model for what?

Gierer¹

2012

Int. J. Dev. Biol.

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“…The Gierer-Meinhardt equations therefore provide a good starting point for modelling axolotl heart localization; but they were developed without a specific connection to a chemical mechanism. A mechanism leading to the Gierer-Meinhardt equations was reported in Babloyantz and Hiernaux (1975). However, we found this mechanism to be unstable away from the steady state approximations used in the derivation.…”

Section: Introductionmentioning

confidence: 63%

Computations of post‐inductive dynamics in axolotl heart formation

Holloway

Harrison

Armstrong

1994

Developmental Dynamics

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This paper reports modelling of heart localization in the axolotl (Ambystoma mexicanum). The region of heart specification in the mesoderm defined by classical induction from the endoderm is larger than the area of final myocardial differentiation. For localizing the area of differentiation within the area of specification, we postulate a reaction-diffusion system that arises within the mesoderm in response to induction from the endoderm. This mechanism generates a spatial pattern for two chemicals, an activator and an inhibitor, corresponding to the area of myocardial differentiation. We postulate a diffusible chemical rescuer, which is absent in the cardiac lethal mutant, and which is a precursor to the reaction-diffusion mechanism. The activator, inhibitor, rescuer, and product of endodermal induction are presented in an enzyme mechanism with rate equations similar to the Gierer-Meinhardt equations. These equations were solved numerically in both one and two spatial dimensions. We have attained quantitative agreement with the experimental data for sizes of tissue regions and for times to heartbeat. Experiments modelled include wild-type heart localization as well as both in vitro and in vivo rescue of cardiac lethal mesoderm with wild-type mesoderm. Based upon the parameters necessary to model heart localization, we make a series of predictions. We predict: a specific profile for the endodermal inducer gradient; the possibility of producing multiple hearts in vivo; and a greater contribution to the heart from the wild-type mesoderm for in vivo transplants with cardiac lethal mesoderm. We make some suggestions as to the possible chemical nature of the substances in the model. We indicate that the inhibitory field and mechanochemical theories are probably not as promising as reaction-diffusion for the mechanism of heart localization.

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“…De nombreux autres auteurs tentèrent d'expliquer la morphogénèse à l'aide de modèles de diffusion-réaction. Parmi eux, citons [2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Morphogénèse Et éQuations De Diffusion-réaction Enzymatiqueunclassified

Apparition de motifs géométriques dans une membrane enzymatique

Joly¹,

Kernevez²

1984

RAIRO. Anal. numér.

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Models for cell differentiation and generation of polarity in diffusion-governed morphogenetic fields

Cited by 38 publications

References 17 publications

The Hydra model - a model for what?

The Hydra model - a model for what?

Computations of post‐inductive dynamics in axolotl heart formation

Apparition de motifs géométriques dans une membrane enzymatique

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