# Molecular Synchronization Waves in Arrays of Allosterically Regulated Enzymes

## TL;DR

This paper investigates how enzyme arrays can spontaneously form complex wave patterns through molecular synchronization, driven by stochastic effects and bifurcations, revealing new insights into enzyme reaction dynamics.

## Contribution

It introduces a novel analysis of pattern formation in enzyme arrays, demonstrating the emergence of synchronization waves via stochastic simulations and mean-field bifurcation analysis.

## Key findings

- Enzymes can synchronize their catalytic cycles at high concentrations.
- Complex wave patterns emerge from stochastic enzyme interactions.
- Bifurcation analysis explains the transition to synchronized wave states.

## Abstract

Spatiotemporal pattern formation in a product-activated enzymic reaction at high enzyme concentrations is investigated. Stochastic simulations show that catalytic turnover cycles of individual enzymes can become coherent and that complex wave patterns of molecular synchronization can develop. The analysis based on the mean-field approximation indicates that the observed patterns result from the presence of Hopf and wave bifurcations in the considered system.