Interpretable Reaction–Diffusion Learning for Molecular Communication via Graph Kolmogorov–Arnold Networks

Abstract

Molecular communication (MC) lets biological cells coordinate collective behaviors through diffusion-mediated signaling molecules that couple intracellular reaction kinetics across a spatial graph. Existing graph neural networks are accurate but opaque, while classical reaction–diffusion models require an explicit kinetics function unavailable in most biological settings. This paper proposes Reaction–Diffusion Graph Kolmogorov–Arnold Networks (RD-GKAN), an interpretable architecture whose forward pass implements reaction–diffusion dynamics: a learnable B-spline per species captures the reaction, and diffusion uses an explicit graph Laplacian with prescribed distance-dependent weights, MC-derived where the channel parameters are available. Each learned spline is projected onto a symbolic library via sparse regression, selecting the dominant kinetics basis (e.g., Hill or Michaelis–Menten) without assuming the form a priori. Evaluation spans five independent domains: MC testbeds, bacterial quorum sensing, ERK signaling waves, and wound-healing and two-tissue spatial transcriptomics. Under leakage-controlled evaluation, graph-structured coupling improves none of the real-data tasks. A trivial persistence baseline matches or outperforms the full model on both temporal datasets. The S. aureus device suppresses diffusive coupling, so that result is a specificity check; the ERK monolayers carry documented collective waves, and there the null reflects a task dominated by temporal autocorrelation. Static spatial reconstruction reduces to local self-feature denoising rather than inter-cellular communication, a caution for spatial graph learning. On synthetic data, B-spline parameterization outperforms an MLP by $6.2\times $ and distance-dependent edge weights improve accuracy $2.4\times $ over binary coupling.