A universal route to pattern formation in multicellular systems
A general framework for the generation of long wavelength patterns in multi-cellular (discrete) systems is proposed, which extends beyond conventional reaction-diffusion (continuum) paradigms. The standard partial differential equations of reaction-diffusion framework can be considered as a mean-fie...
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| Veröffentlicht in: | The European physical journal. B, Condensed matter physics Condensed matter physics, 2020-07, Vol.93 (7), Article 135 |
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| container_title | The European physical journal. B, Condensed matter physics |
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| creator | Asllani, Malbor Carletti, Timoteo Fanelli, Duccio Maini, Philip K. |
| description | A general framework for the generation of long wavelength patterns in multi-cellular (discrete) systems is proposed, which extends beyond conventional reaction-diffusion (continuum) paradigms. The standard partial differential equations of reaction-diffusion framework can be considered as a mean-field like ansatz which corresponds, in the biological setting, to sending to zero the size (or volume) of each individual cell. By relaxing this approximation and, provided a directionality in the flux is allowed for, we demonstrate here that instability leading to spatial pattern formation can always develop if the (discrete) system is large enough, namely, composed of sufficiently many cells, the units of spatial patchiness. The macroscopic patterns that follow the onset of the instability are robust and show oscillatory or steady state behavior.
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| doi_str_mv | 10.1140/epjb/e2020-10206-3 |
| format | Article |
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| subjects | Complex Systems Condensed Matter Physics Fluid- and Aerodynamics Partial differential equations Physics Physics and Astronomy Regular Article Solid State Physics |
| title | A universal route to pattern formation in multicellular systems |
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