Theoretical Model of Chemomechanical Self-Oscillation in a Two-Enzyme Core–Shell Hydrogel With pH-Gated Microcapsules

Abstract

A chemo–mechanical coupled oscillator integrating catalytic reactions with stimuli-responsive hydrogels is a promising platform for autonomous soft actuators. We propose a theoretical model of a pH-responsive hydrogel system where pH and gel volume are autonomously regulated by internal chemical reactions without external flow control. In a core–shell multilayered hydrogel, an acid-producing enzyme and a base-producing enzyme are spatially separated in the core and shell layers, respectively, while slowed proton transport between the two regions introduces a characteristic time delay into the system. By coupling these enzymatic reactions with the hysteretic volume phase transition of the pH-responsive hydrogel, dynamic swelling–deswelling behavior is controlled. Using nondimensionalization and bifurcation analysis, we classify regimes of monostability, bistability, and sustained oscillations as a function of key parameters: substrate concentration, permeability, and the ratio between gel relaxation time and chemical reaction timescale. Unlike single-enzyme models, where oscillations require the reaction timescale to exceed the gel relaxation time, our dual-enzyme model enables sustained oscillations even when these timescales are comparable. These results provide design guidelines for biocompatible autonomous oscillating hydrogels, offering greater flexibility in selecting gel size and relaxation properties for soft robotic applications.