Calibrating tissue level PDE models of ligand dynamics using single cell and spatial transcriptomics data.

Many physiological processes rely on cellular communication through ligand mediated signalling, where ligands secreted by cells diffuse through the extracellular space and bind to receptors to trigger downstream responses. Although reaction diffusion models capture these dynamics, parameter calibration often lags behind model development due to limited data that reflect the biological microenvironment and the lack of a unified framework for integrating such data into mechanistic models. We propose that single cell RNA sequencing and spatial transcriptomics provide a rich, abundant, and underused source of information for calibrating such models at tissue scale. We develop a computational pipeline that integrates these data to infer model parameters, combining finite volume solvers with bioinformatics preprocessing, Approximate Bayesian Computation (ABC), and gradient based optimization. Using two open source human skin datasets as case studies, we calibrate parameters governing the isoforms of Transforming Growth Factor Beta, a key regulator of tissue repair and fibrosis, and compare the resulting spatial concentration fields with local cell type distributions. Benchmarking on synthetic datasets helps evaluate the inference accuracy and shows the benefits of combining ABC with gradient based methods. Overall, the pipeline provides a flexible and rigorous approach for calibrating tissue level mechanistic models using modern transcriptomics data.