Experimental observation of boundary-driven oscillations in a reaction–diffusion–advection system

Eckstein, Torsten; Vidal-Henriquez, Estefania; Gholami, Azam

doi:10.1039/c9sm02291k

Cited by 3 publications

(4 citation statements)

References 34 publications

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“…The influence of advective flow on biological pattern formation has rarely been studied, both experimentally and theoretically, and remains an active topic of research 23 , 42 , 44 , 52 – 54 . Our findings on the Min protein system’s response to flow suggest that additional molecular features of the protein reaction network, not yet accounted for by the current Min models, are necessary to quantitatively explain the observed phenomena.…”

Section: Discussionmentioning

confidence: 99%

Directing Min protein patterns with advective bulk flow

et al. 2023

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The Min proteins constitute the best-studied model system for pattern formation in cell biology. We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns for low MinE:MinD concentration ratios, upstream propagation for large ratios, but multistability of both propagation directions in between. Whereas downstream propagation can be described by a minimal model that disregards MinE conformational switching, upstream propagation can be reproduced by a reduced switch model, where increased MinD bulk concentrations on the upstream side promote protein attachment. Our study demonstrates that a differential flow, where bulk flow advects protein concentrations in the bulk, but not on the surface, can control surface-pattern propagation. This suggests that flow can be used to probe molecular features and to constrain mathematical models for pattern-forming systems.

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Section: Discussionmentioning

confidence: 99%

Directing Min protein patterns with advective bulk flow

et al. 2023

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“…The same holds true for the influence of advective flow on biological pattern formation, which has rarely been studied, both experimentally and theoretically. 23,23,42,44,[52][53][54] Insight into the detailed biochemical mechanisms of the MinD-MinE interactions (such as cooperative MinD self-recruitment, dimerization of MinD and MinE, MinE membrane binding, etc.) is likely needed to make progress.…”

Section: Discussionmentioning

confidence: 99%

Directing Min protein patterns with advective bulk flow

Meindlhumer

Brauns

Finžgar

et al. 2021

Preprint

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We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns relative to the bulk flow direction for low MinE:MinD concentration ratios, but upstream propagation for large MinE:MinD ratios, with multistability of both propagation directions in between. A theoretical model for the Min system reveals the mechanism underlying the upstream propagation and links it to the fast conformational switching of MinE in the bulk. For high MinE:MinD ratios, upstream propagation can be reproduced by a reduced model in which increased MinD bulk concentrations on the upstream side promote protein attachment and hence, propagation in that direction. For low MinE:D ratios, downstream propagation is described by the minimal model, as additionally confirmed by experiments with a non-switching MinE mutant. No advection takes place on the membrane surface where the protein patterns form, but advective bulk flow shifts the protein-concentration profiles in the bulk relative to the membrane-bound pattern. From a broader perspective, differential flows in a bulk volume relative to a surface are a relevant general feature in bulk-surface coupled systems. Our study shows how such a differential flow can control surface-pattern propagation and demonstrates how the global pattern's response may depend on specific molecular features of the reaction kinetics.

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“…In a spatially extended medium, the ability to spike gives rise to distinctive spatiotemporal patterns ( 13 – 23 ) appearing in processes ranging from morphogenesis ( 24 – 34 ) to spiral waves observed in electrograms of the heart ( 35 – 37 ). While analytical studies have revealed important features of excitable media whose properties are spatially homogeneous ( 38 – 42 ), less is understood about abrupt heterogeneities such as sample edges or interfaces ( 43 – 54 ). As is often the case with wave mechanics, edges and interfaces can have properties that differ qualitatively from those of the bulk medium ( 55 – 61 ).…”

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confidence: 99%

“… * Notice that Eqs. 3 and 4 do not contain advective transport, which has also been shown to give rise oscillations near Dirichlet boundaries, for example, in models of and experiments on Dictyostelium discoideum ( 44 , 45 ). …”

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confidence: 99%

Spiking at the edge: Excitability at interfaces in reaction–diffusion systems

Scheibner,

Ori,

Cohen

et al. 2024

Proc. Natl. Acad. Sci. U.S.A.

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Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator–prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction–diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

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Experimental observation of boundary-driven oscillations in a reaction–diffusion–advection system

Abstract: Boundary-driven oscillations are observed experimentally in a reaction-diffusion-advection system, namely in the signaling population of Dictyostelium discoideum cells.

Cited by 3 publications

References 34 publications

Directing Min protein patterns with advective bulk flow

Directing Min protein patterns with advective bulk flow

Directing Min protein patterns with advective bulk flow

Spiking at the edge: Excitability at interfaces in reaction–diffusion systems

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