Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction–Diffusion and Chemotaxis
Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven instability and chemotactic patterning. Inspired by these findings we develop and analyse a mathematical model that couples chemotaxis to a reaction–d...
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Published in | Bulletin of mathematical biology Vol. 86; no. 1; p. 4 |
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Main Authors | , , , , , |
Format | Journal Article |
Language | English |
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Springer US
01.01.2024
Springer Nature B.V |
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Abstract | Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven instability and chemotactic patterning. Inspired by these findings we develop and analyse a mathematical model that couples chemotaxis to a reaction–diffusion system exhibiting diffusion–driven (Turing) instability. While both systems, reaction–diffusion systems and chemotaxis, can independently generate spatial patterns, we were interested in how the coupling impacts the stability of the system, parameter region for patterning, pattern geometry, as well as the dynamics of pattern formation. We conduct a classical linear stability analysis for different model structures, and confirm our results by numerical analysis of the system. Our results show that the coupling generally increases the robustness of the patterning process by enlarging the pattern region in the parameter space. Concerning time scale and pattern regularity, we find that an increase in the chemosensitivity can speed up the patterning process for parameters inside and outside of the Turing space, but generally reduces spatial regularity of the pattern. Interestingly, our analysis indicates that pattern formation can also occur when neither the Turing nor the chemotaxis system can independently generate pattern. On the other hand, for some parameter settings, the coupling of the two processes can extinguish the pattern formation, rather than reinforce it. These theoretical findings can be used to corroborate the biological findings on morphogenesis and guide future experimental studies. From a mathematical point of view, this work sheds a light on coupling classical pattern formation systems from the parameter space perspective. |
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AbstractList | Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven instability and chemotactic patterning. Inspired by these findings we develop and analyse a mathematical model that couples chemotaxis to a reaction–diffusion system exhibiting diffusion–driven (Turing) instability. While both systems, reaction–diffusion systems and chemotaxis, can independently generate spatial patterns, we were interested in how the coupling impacts the stability of the system, parameter region for patterning, pattern geometry, as well as the dynamics of pattern formation. We conduct a classical linear stability analysis for different model structures, and confirm our results by numerical analysis of the system. Our results show that the coupling generally increases the robustness of the patterning process by enlarging the pattern region in the parameter space. Concerning time scale and pattern regularity, we find that an increase in the chemosensitivity can speed up the patterning process for parameters inside and outside of the Turing space, but generally reduces spatial regularity of the pattern. Interestingly, our analysis indicates that pattern formation can also occur when neither the Turing nor the chemotaxis system can independently generate pattern. On the other hand, for some parameter settings, the coupling of the two processes can extinguish the pattern formation, rather than reinforce it. These theoretical findings can be used to corroborate the biological findings on morphogenesis and guide future experimental studies. From a mathematical point of view, this work sheds a light on coupling classical pattern formation systems from the parameter space perspective. |
ArticleNumber | 4 |
Author | Glover, James Painter, Kevin John Matthäus, Franziska Headon, Denis Gerisch, Alf Fraga Delfino Kunz, Camile |
Author_xml | – sequence: 1 givenname: Camile surname: Fraga Delfino Kunz fullname: Fraga Delfino Kunz, Camile organization: Frankfurt Institute for Advanced Studies and Department of Computer Science and Mathematics, Goethe-University Frankfurt – sequence: 2 givenname: Alf surname: Gerisch fullname: Gerisch, Alf organization: Department of Mathematics, Technical University Darmstadt – sequence: 3 givenname: James surname: Glover fullname: Glover, James organization: The Roslin Institute and R(D)SVS, University of Edinburgh – sequence: 4 givenname: Denis surname: Headon fullname: Headon, Denis organization: The Roslin Institute and R(D)SVS, University of Edinburgh – sequence: 5 givenname: Kevin John surname: Painter fullname: Painter, Kevin John organization: Dipartimento Interateneo di Scienze, Progetto e Politiche del Territorio (DIST), Politecnico di Torino – sequence: 6 givenname: Franziska orcidid: 0000-0001-6042-1366 surname: Matthäus fullname: Matthäus, Franziska email: matthaeus@fias.uni-frankfurt.de organization: Frankfurt Institute for Advanced Studies and Department of Computer Science and Mathematics, Goethe-University Frankfurt |
BackLink | https://www.ncbi.nlm.nih.gov/pubmed/38038776$$D View this record in MEDLINE/PubMed |
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Keywords | Morphogenesis Biological development Chemotaxis Reaction–diffusion |
Language | English |
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Snippet | Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven... |
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SubjectTerms | Cell Biology Chemotaxis Coupling Diffusion Dynamic stability Life Sciences Mathematical and Computational Biology Mathematical Concepts Mathematical models Mathematics Mathematics and Statistics Models, Biological Models, Theoretical Morphogenesis Numerical analysis Original Original Article Parameters Pattern analysis Pattern formation Patterning Regularity Robustness (mathematics) Stability analysis |
Title | Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction–Diffusion and Chemotaxis |
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