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

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× and distance-dependent edge weights improve accuracy 2.4× over binary coupling.