Emergence of spatiotemporal patterns in a fuel-driven coupled cooperative supramolecular system

TL;DR

This paper presents a reaction-diffusion model demonstrating how chemically fueled supramolecular systems can spontaneously generate complex, life-like spatiotemporal patterns such as oscillations and traveling waves, driven by non-equilibrium dynamics.

Contribution

It introduces a minimal theoretical model linking reaction kinetics and diffusion to emergent patterns in fuel-driven supramolecular systems, providing new design principles.

Findings

Autonomous oscillations arise via Hopf bifurcation.

Spatiotemporal patterns include traveling waves and polygonal structures.

The model bridges molecular self-assembly with active matter dynamics.

Abstract

Chemically fueled supramolecular systems can exhibit complex, time-dependent behaviors reminiscent of living matter when maintained far from equilibrium by continuous energy or fuel consumption. Here, we introduce a minimal reaction-diffusion model that captures the essential dynamics of a cooperative supramolecular polymerization network driven by monomer activation and deactivation. We show that a balance between autocatalytic growth and inhibitory decay sustains a nonequilibrium steady state in the model that undergoes a Hopf bifurcation, giving rise to autonomous oscillations. When spatial transport is introduced through diffusion, the system displays rich spatiotemporal phenomena, such as traveling wavefronts and transient polygonal patterns. Our results demonstrate that the interplay between reaction kinetics and diffusion can spontaneously generate self-organized, life-like dynamics in synthetic supramolecular polymer systems. This theoretical framework not only bridges molecular self-assembly and active matter dynamics but also provides design principles for creating adaptive, oscillatory, and self-patterning materials powered by chemical fuels.