From chemical oscillators to biological synchrony: a programmable reaction-diffusion model for studying signal...

The self-organization of asynchronous rhythms into synchronized beating in in vitro cardiomyocyte networks is a fundamental problem in systems biology research. Inspired by the dynamics of chemical oscillators, this paper presents a programmable model framework based on a discretized Belousov-Zhabotinsky reaction-diffusion system to study signal propagation and synchronization in cardiomyocyte networks. We propose a hybrid discrete-continuous geometry in which active excitable units (simulating cells) are embedded in a passive diffusive medium, with the dynamics of each unit governed by the Rovinsky-Zhabotinsky equations. Unlike conventional continuous media models, the present framework represents each cell as an independently programmable discrete unit, thereby explicitly capturing the discreteness and cell-to-cell variability inherent in in vitro cardiomyocyte networks. We systematically compare model simulations with in vitro experiments on neonatal rat cardiomyocyte networks using calcium imaging and mechanical stimulation. The framework reproduces multi-scale dynamical features: (i) intracellular excitation-propagation-recovery cycles, (ii) topology-dependent signal transmission in both regular and irregular networks, and (iii) the self-organized transition from cell-to-cell synchronization to global population synchronization. These qualitative agreements demonstrate that a simplified, programmable reaction-diffusion framework can capture the signalling dynamics of cardiomyocyte excitable systems, offering a new perspective for investigating signal coordination in cardiomyocyte networks.