Pattern Formation Beyond Turing: Physical Principles of Mass-Conserving Reaction--Diffusion Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911316864663552 |
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| author | Frey, Erwin Weyer, Henrik |
| author_facet | Frey, Erwin Weyer, Henrik |
| contents | Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for understanding such patterns based on mass-conserving reaction--diffusion systems. The emergence, selection, and evolution of patterns are analyzed in terms of mass redistribution and interface motion, resulting in mesoscale laws of coarsening and wavelength selection. A geometric phase-space perspective provides a conceptual tool to link local reactive equilibria with global pattern dynamics through conserved mass fluxes. The Min protein system of \emph{Escherichia coli} provides a paradigmatic example, enabling direct comparison between theory and experiment. Successive model refinements capture both the robustness of pattern formation and the diversity of dynamic regimes observed \emph{in vivo} and \emph{in vitro}. The Min system thus illustrates how to extract predictive, multiscale theory from biochemical detail, providing a foundation for understanding pattern formation in more complex and synthetic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pattern Formation Beyond Turing: Physical Principles of Mass-Conserving Reaction--Diffusion Systems Frey, Erwin Weyer, Henrik Biological Physics Soft Condensed Matter Pattern Formation and Solitons Subcellular Processes Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for understanding such patterns based on mass-conserving reaction--diffusion systems. The emergence, selection, and evolution of patterns are analyzed in terms of mass redistribution and interface motion, resulting in mesoscale laws of coarsening and wavelength selection. A geometric phase-space perspective provides a conceptual tool to link local reactive equilibria with global pattern dynamics through conserved mass fluxes. The Min protein system of \emph{Escherichia coli} provides a paradigmatic example, enabling direct comparison between theory and experiment. Successive model refinements capture both the robustness of pattern formation and the diversity of dynamic regimes observed \emph{in vivo} and \emph{in vitro}. The Min system thus illustrates how to extract predictive, multiscale theory from biochemical detail, providing a foundation for understanding pattern formation in more complex and synthetic systems. |
| title | Pattern Formation Beyond Turing: Physical Principles of Mass-Conserving Reaction--Diffusion Systems |
| topic | Biological Physics Soft Condensed Matter Pattern Formation and Solitons Subcellular Processes |
| url | https://arxiv.org/abs/2512.12558 |