Self-organization of primitive metabolic cycles due to non-reciprocal interactions

TL;DR

This paper investigates how non-reciprocal interactions in a model metabolic cycle lead to self-organization and clustering, with the cycle's size and parity influencing the resulting dynamics and steady states.

Contribution

It introduces a model demonstrating self-organization in metabolic cycles driven by non-reciprocal interactions, highlighting the impact of cycle size and parity on collective behavior.

Findings

Even-numbered cycles form two distinct clusters of alternating species.

Odd-numbered cycles can exhibit oscillatory steady states.

Self-organization depends strongly on the number and parity of species.

Abstract

We study analytically and numerically a model metabolic cycle composed of an arbitrary number of species of catalytically active particles. Each species converts a substrate into a product, the latter being used as the substrate by the next species in the cycle. Through a combination of catalytic activity and chemotactic mobility, the active particles develop effective non-reciprocal interactions with particles belonging to neighbouring species in the cycle. We find that such model metabolic cycles are able to self-organize through a macroscopic instability, with a strong dependence on the number of species they incorporate. The parity of that number has a key influence: cycles containing an even number of species are able to minimize repulsion between their component particles by aggregating all even-numbered species in one cluster, and all odd-numbered species in another. Such a grouping is not possible if the cycle contains an odd number of species, which can lead to oscillatory steady states in the case of chasing interactions.