Turing Instabilities are Not Enough to Ensure Pattern Formation

Bulletin of Mathematical Biology, Journal Year: 2024, Volume and Issue: 86(2)

Published: Jan. 22, 2024

Abstract Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying diversity of patterns observed nature, such as Turing’s reaction–diffusion theory, which connects cellular signalling and transport with development growth form. Extensive literature focuses on linear stability analysis homogeneous equilibria these systems, culminating a set conditions for transport-driven that are commonly presumed to initiate self-organisation. We demonstrate selection simple, canonical models only mild multistable non-linearities can satisfy Turing instability while also robustly exhibiting transient patterns. Hence, Turing-like is insufficient existence patterned state. While it known theory fail predict formation patterns, we failures appear systems multiple stable equilibria. Given biological gene regulatory networks spatially distributed ecosystems often exhibit high degree multistability nonlinearity, this raises questions how analyse prospective

Language: Английский

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Modern perspectives on near-equilibrium analysis of Turing systems

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences, Journal Year: 2021, Volume and Issue: 379(2213)

Published: Nov. 8, 2021

In the nearly seven decades since publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both mathematical and biological aspects his proposed reaction-diffusion theory. Some these developments were nascent paper, others have due to new insights from modern techniques, advances numerical simulations, extensive experiments. Despite such progress, there are still important gaps between theory experiment, with many examples patterning where underlying mechanisms unclear. Here we review pioneered by Turing, showing how approach generalized a range settings beyond classical two-species framework, including evolving complex manifolds, systems heterogeneous space time, more general reaction-transport equations. While substantial complicated models, remaining challenges that highlight throughout. We focus theory, particular linear stability analysis `trivial' base states. emphasise open questions developing this further, discuss obstacles using techniques understand reality.

Language: Английский

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Turing patterns in systems with high-order interactions

Chaos Solitons & Fractals, Journal Year: 2022, Volume and Issue: 166, P. 112912 - 112912

Published: Nov. 30, 2022

Language: Английский

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Dynamical Pattern Formation without Self-Attraction in Quorum-Sensing Active Matter: The Interplay between Nonreciprocity and Motility

Physical Review Letters, Journal Year: 2023, Volume and Issue: 131(14)

Published: Oct. 3, 2023

We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations the microscopic and linear stability analysis associated coarse-grained field theory, we identify mechanism for dynamical pattern formation that does not rely on standard route intraspecies effective attractive interactions. Instead, our results reveal highly phase chasing bands induced only by combined effects self-propulsion nonreciprocity in interspecies couplings. Turning self-attraction, find system may separate into macroscopic domain such chaotic coexisting with dilute gas. show dynamics at interfaces this phase-separated anomalously slow coarsening.Received 13 June 2023Accepted 31 August 2023DOI:https://doi.org/10.1103/PhysRevLett.131.148301Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution to author(s) published article's title, journal citation, DOI. Open access publication funded Max Planck Society.Published SocietyPhysics Subject Headings (PhySH)Research AreasEmergence patternsNonequilibrium statistical mechanicsSelf-organized systemsPhysical SystemsMulticomponent systemsTechniquesBrownian dynamicsTheories collective & active matterStatistical Physics ThermodynamicsPolymers Soft Matter

Language: Английский

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General conditions for Turing and wave instabilities in reaction -diffusion systems

Journal of Mathematical Biology, Journal Year: 2023, Volume and Issue: 86(3)

Published: Jan. 28, 2023

Abstract Necessary and sufficient conditions are provided for a diffusion-driven instability of stable equilibrium reaction–diffusion system with n components diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary reproduced there to exist rates that cause bifurcation homogeneous state in the absence diffusion. The method proof here though, which is based on study dispersion relations contrasting limits wavenumber tends zero $$\infty $$ ∞ , gives constructive choosing constants. results illustrated 3-component FitzHugh–Nagumo-like model proposed excitable wavetrains, two different coupled Brusselator systems 4-components.

Language: Английский

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Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability

Physical Review Letters, Journal Year: 2023, Volume and Issue: 131(13)

Published: Sept. 27, 2023

We develop a general classification of the nature instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo reactions driven out equilibrium by external chemostats. find analytically that these can be two types: caused intermolecular energetic interactions (E type), multimolecular out-of-equilibrium (R type). Furthermore, we identify class reaction networks, containing unimolecular networks but also extending beyond them, only E-type instabilities. illustrate our analytical findings numerical simulations models, displaying one types instability generating stable patterns.

Language: Английский

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Tunable annular plasma photonic crystals in dielectric barrier discharge

Plasma Sources Science and Technology, Journal Year: 2022, Volume and Issue: 31(2), P. 025015 - 025015

Published: Jan. 21, 2022

Abstract We demonstrate an effective method for realization of robust, tailorable annular plasma photonic crystals (PPC) in dielectric barrier discharge with two water electrodes. Fast reconfiguration between triangular lattice, core-annular lattice and concentric-annular has been achieved. An active control on the structure elements is realized by solely changing applied voltage. The changes band gaps different PPCs have studied both experimentally numerically. 28.0–30.0 GHz are verified. A phenomenological reaction–diffusion model nonlinear-coupled interacting layers established to mimic formation various structures. Experimental observations numerical simulation good agreement. Our approach provides a unique strategy create reversibly deformable PPCs, which may offer new capabilities serve as promising platform applications.

Language: Английский

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Physical interactions in non-ideal fluids promote Turing patterns

Journal of The Royal Society Interface, Journal Year: 2023, Volume and Issue: 20(204)

Published: July 1, 2023

Turing’s mechanism is often invoked to explain periodic patterns in nature, although direct experimental support scarce. Turing form reaction–diffusion systems when the activating species diffuse much slower than inhibiting species, and involved reactions are highly nonlinear. Such can originate from cooperativity, whose physical interactions should also affect diffusion. We here take into account show that they strongly patterns. find weak repulsion between activator inhibitor substantially lower required differential diffusivity reaction nonlinearity. By contrast, strong induce phase separation, but resulting length scale still typically governed by fundamental scale. Taken together, our theory connects traditional with chemically active thus describing a wider range of systems. Moreover, we demonstrate even substantially, so be incorporated modelling realistic

Language: Английский

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Robustness of Turing models and gene regulatory networks with a sweet spot

Physical review. E, Journal Year: 2024, Volume and Issue: 109(6)

Published: June 11, 2024

Traditional linear stability analysis based on matrix diagonalization is a computationally intensive process for high-dimensional systems of differential equations, posing substantial limitations the exploration Turing pattern formation where an additional wave-number parameter needs to be investigated. In this paper, we introduce efficient and intuitive technique that leverages Gershgorin's theorem determine upper limits regions space wave number beyond which instabilities cannot occur. This method offers streamlined avenue exploring phase diagrams other complex multi-parametric models, such as those found in gene regulatory networks biology. Due its suitability asymptotic limit infinitely large systems, it predicts existence sweet spot network size maximal Jacobian stability.

Language: Английский

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Spatiotemporal dynamics of periodic waves in SIR model with driving factors

New Journal of Physics, Journal Year: 2023, Volume and Issue: 25(6), P. 063028 - 063028

Published: June 1, 2023

Abstract The world faces Covid-19 waves, and the overall pattern of confirmed cases shows periodic oscillations. In this paper, we investigate spatiotemporal spread in network-organized SIR model with an extrinsic incubation period driving factors. Firstly, Our analysis occurrences Hopf bifurcation outbreaks consistent actual Covid-19. And waves on spatial scales using Turing instability, infected individuals increases localized hot spots. We study effect period, more periods generate instability resulting outbreaks. There is occurrence bursting states at peaks due to small diffusion susceptible, which means stable unstable areas try convert each other high competition among nodes. Also, note disappearance these bursts when susceptible individuals’ movements are easier; thus, dominance prevails everywhere. Effective policy interventions seasonality can cause perturbations model, therefore impact Periodic factors, show co-existing patterns. Chaotic outbreak becomes through alternating or period-2 as regulate amplitude frequency individuals. short, regulations erase chaotic interventions.

Language: Английский

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