A theory of biological pattern formation
Open accessIntegrity signals
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
Sick et al. (2006) use a reaction-diffusion system (Gierer-Meinhardt equations) to model the interplay between Wnt and its antagonist Dkk with just two equations.
“Sick et al. (2006) use a reaction-diffusion system (Gierer-Meinhardt equations [104]) to model the interplay between Wnt and its antagonist Dkk with just two equations.”
From Relating simulation studies by provenance—Developing a family of Wnt signaling models (2021) · cites this paper as [104]
Cites
Quantitative analysis of cell types during growth and morphogenesis in Hydra
Bode, H., Berking, S., David, C. N., Gierer, A., Schaller, H., & Trenkner, E. (1973) · Wilhelm Roux Archiv f�r Entwicklungsmechanik der Organismen · doi:10.1007/bf00577725 · Cited by 257 · see citing works
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Design principles of biochemical oscillators
Novák, B., & Tyson, J. J. (2008) · Nature Reviews Molecular Cell Biology · doi:10.1038/nrm2530 · Cited by 1,137 · see citing works
WNT signalling molecules act in axis formation in the diploblastic metazoan Hydra
Hobmayer, B., Rentzsch, F., Kuhn, K., Happel, C. M., von Laue, C. C., Snyder, P., Rothbächer, U., & Holstein, T. W. (2000) · Nature · doi:10.1038/35025063 · Cited by 599 · see citing works
Formation of the head organizer in hydra involves the canonical Wnt pathway.
Broun, M., Gee, L., Reinhardt, B., & Bode, H. R. (2005) · Development · doi:10.1242/dev.01848 · Cited by 287 · see citing works
Evolutionary crossroads in developmental biology: Cnidaria
Technau, U., & Steele, R. E. (2011) · Development · doi:10.1242/dev.048959 · Cited by 274 · see citing works
Molenaar, P. C. M. (2008) · Developmental Psychobiology · doi:10.1002/dev.20262 · Cited by 237 · see citing works
Newman, S. A., & Bhat, R. (2009) · The International Journal of Developmental Biology · doi:10.1387/ijdb.072481sn · Cited by 208 · see citing works
Protein Phase Separation Provides Long-Term Memory of Transient Spatial Stimuli
Dine, E., Gil, A. A., Uribe, G., Brangwynne, C. P., & Toettcher, J. E. (2018) · Cell Systems · doi:10.1016/j.cels.2018.05.002 · Cited by 182 · see citing works
Stückemann, T., Cleland, J. P., Werner, S., Thi-Kim Vu, H., Bayersdorf, R., Liu, S.-Y., Friedrich, B., Jülicher, F., & Rink, J. C. (2017) · Developmental Cell · doi:10.1016/j.devcel.2016.12.024 · Cited by 133 · see citing works
Grimmelikhuijzen, C. J. P., Williamson, M., & Hansen, G. N. (2002) · Canadian Journal of Zoology · doi:10.1139/z02-137 · Cited by 119 · see citing works
Agent-based modeling of morphogenetic systems: advantages and challenges.
Glen, C. M., Kemp, M. L., & Voit, E. O. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006577 · Cited by 116 · see citing works
Distributing signaling proteins in space and time: the province of cytonemes
Kornberg, T. B. (2017) · Current Opinion in Genetics & Development · doi:10.1016/j.gde.2017.02.010 · Cited by 69 · see citing works
Notch-signalling is required for head regeneration and tentacle patterning in Hydra
Münder, S., Tischer, S., Grundhuber, M., Büchels, N., Bruckmeier, N., Eckert, S., Seefeldt, C. A., Prexl, A., Käsbauer, T., & Böttger, A. (2013) · Developmental Biology · doi:10.1016/j.ydbio.2013.08.022 · Cited by 51 · see citing works
Self-organization of intracellular gradients during mitosis
Fuller, B. G. (2010) · Cell Division · doi:10.1186/1747-1028-5-5 · Cited by 42 · see citing works
Relating simulation studies by provenance—Developing a family of Wnt signaling models
Budde, K., Smith, J., Wilsdorf, P., Haack, F., & Uhrmacher, A. M. (2021) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1009227 · Cited by 23 · see citing works
“(2006) use a reaction-diffusion system (Gierer-Meinhardt 608 equations [103]) to model the interplay between Wnt and its antagonist Dkk with just 609 two equations.”
Method
- Authors
- Gierer, A., & Meinhardt, H.
- Affiliations
- Max Planck Society (DE)
- Venue
- Kybernetik
- Published
- 1972-12
- Volume
- 12
- Issue
- 1
- Pages
- 30-39
- ISSN
- 0023-5946 (ISSN-L)
- OpenAlex
- W2089840306
- Cited by
- 3,158
- References
- 1
- Citations by year
- 2026: 88 · 2025: 124 · 2024: 133 · 2023: 121 · 2022: 117 · 2021: 146 · 2020: 134 · 2019: 113 · 2018: 150 · 2017: 120 · 2016: 94 · 2015: 101 · 2014: 98 · 2013: 129 · 2012: 122
- FWCI
- 4.11
- Type
- journal article
- Language
- en
- Open access
- green
- edoc.bbaw.de
- Licence
- Locations
- Kybernetik (publishedVersion)
- PubMed (publishedVersion)
- Publication Server (Berlin-Brandenburg Academy of Sciences and Humanities) (submittedVersion, other-oa)
- PhilPapers (PhilPapers Foundation) (submittedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Developmental Biology and Gene Regulation
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Keywords
- biological pattern formation, morphogenesis, morphogens, activator-inhibitor systems, autocatalysis, cross-catalysis, long-range inhibition, size control, aperiodic patterns, polar cells, Hydra
- MeSH terms
- Computers, Mathematics, Models, Biological, Morphogenesis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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