Network Effects Lead to Self-Organization in Metabolic Cycles of Self-Repelling Catalysts

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Network Effects Lead to Self-Organization in Metabolic Cycles of Self-Repelling Catalysts

Vincent Ouazan-Reboul, Ramin Golestanian, and Jaime Agudo-Canalejo

Phys. Rev. Lett. 131, 128301 – Published 19 September 2023

See synopsis: Self-Repelling Species Still Self-Organize

Abstract

Mixtures of particles that interact through phoretic effects are known to aggregate if they belong to species that exhibit attractive self-interactions. We study self-organization in a model metabolic cycle composed of three species of catalytically active particles that are chemotactic toward the chemicals that define their connectivity network. We find that the self-organization can be controlled by the network properties, as exemplified by a case where a collapse instability is achieved by design for self-repelling species. Our findings highlight a possibility for controlling the intricate functions of metabolic networks by taking advantage of the physics of phoretic active matter.

Received 18 April 2023
Accepted 27 July 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.128301

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Biological self-organization Clustering Diffusiophoresis Emergence of patterns Phase separation

Colloids Enzymes Living matter & active matter Multicomponent systems Nonequilibrium systems

Brownian dynamics Pattern formation

Physics of Living SystemsPolymers & Soft MatterStatistical Physics & Thermodynamics

synopsis

Self-Repelling Species Still Self-Organize

Published 19 September 2023

Catalytically active particles form clusters when they respond not only to their own chemical targets but to those of other catalysts, too.

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Authors & Affiliations

Vincent Ouazan-Reboul ¹, Ramin Golestanian ^1,2,*, and Jaime Agudo-Canalejo ^1,†

¹Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany
²Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom

^*ramin.golestanian@ds.mpg.de
^†jaime.agudo@ds.mpg.de

Article Text

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Supplemental Material

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References

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Issue

Vol. 131, Iss. 12 — 22 September 2023

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Images

Figure 1
(a) Emergence of field-mediated, nonreciprocal interactions between particle $n$ , which perturbs the chemical field $c^{(k)}$ around itself, and particle $m$ , which develops a velocity in response to the resulting chemical gradient. (b) Metabolic cycle of three species. Each converts their substrate into a product that acts as the substrate of the next species and moves in response to gradients of both chemicals. (c) Example of a set of species-species interactions emerging from the combination of effective field-mediated interactions and metabolic cycle topology. With this particular choice of parameters, each species is self-repelling, and the species pair 1–3 exhibits chasing interactions.
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Figure 2
Stability phase diagram for cycles involving at least one self-repelling species. Species 1 taken to be self-repelling ( $α_{1} Δ μ_{1} > 0$ ). Solid line: stability line in normalized self-interaction plane for a specific choice of parameters. Dashed line: parameter-free instability line below which cycles with null product mobilities $μ_{1, 2, 3}^{(p)} = 0$ are unstable. Note that this line lies always below the top-right, all-self-repelling quadrant. Dash-dotted line: parameter-free boundary between overall self-attracting and self-repelling catalytic mixtures. Gray markers: coordinates of Brownian dynamics simulations, found to be unstable if the marker is a circle or stable if it is a triangle. The blue marker corresponds to the coordinates of the simulation shown in Fig. 3. For the expressions of the stability lines and the values of the parameters, see the Supplemental Material [43].
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Figure 3
Instability of a generic three-enzyme cycle triggered by the presence of a single instability-favoring pair. (a1)–(a3) Single-species interactions: all particle species are self-repelling, and thus single-species suspensions stay homogeneous. (b1)–(b3) Pair interactions: of the two-species mixtures, 1-2 and 3-1 mixtures form small molecules but remain homogeneous, while 2-3 is unstable and results in the formation of a 2-3 cluster coexisting with a gas of species 2. (c) Despite all species being self-repelling, the instability of the 2-3 pair causes the instability of the full three-species mixture, resulting in the formation of a cluster, which coexists with a gas of species 2. Note that species 1 (red) also participates in the cluster, despite not aggregating with either of the other species (b1),(b3). In all panels, the inset at the top represents the effective interactions among species, whereas the corresponding chemical reaction network is depicted at the bottom. The reaction networks in (a),(b) are open, as they involve substrates and products that must be externally supplied or removed (boxed $s_{m}$ and $p_{m}$ ). The full reaction network in (c) is closed. See also the Supplemental Material and Videos 1–7 in [43] for a description of the simulation parameters and videos.
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