A Computational Pipeline for Physiologically Informed Calibration of Ligand Reaction-Diffusion Models Using High-Throughput Sequencing

Abstract

All physiological processes fundamentally rely on continuous cellular cross-talk to maintain organization and ensure proper function. Among the various modes of cellular communication, ligand-mediated chemical signaling, in which a ligand is secreted by one cell, diffuses through the extracellular environment, and binds to a receptor on another (or the same) cell to elicit a downstream response, is arguably the most ubiquitous and foundational. Given its importance, numerous mathematical models have been developed to describe this reaction-diffusion mechanism, capturing ligand secretion, diffusion, decay, and binding under both normal and pathological conditions. However, parameter calibration for such models often lags behind model development. This is due to limited data that faithfully represent the biological microenvironment, as well as due to the absence of a robust, rigorous framework to integrate available data into the mathematical model. To address this gap, we propose that transcriptomics (gene expression) data, namely the combination of single-cell RNA sequencing and spatial transcriptomics, provide a rich, increasingly abundant, and underutilized source of information that can be used to calibrate the parameters of the cellular reaction-diffusion models at the larger mesoscopic scale. To this end, we develop a computational pipeline that leverages these data to extract parameter values for reaction-diffusion models, and illustrate its application through two human wound-healing case studies. Using open-source transcriptomics data, we calibrate the reaction-diffusion model parameters of the isoforms of Transforming Growth Factor Beta (TGF{beta}), a signaling molecule central to tissue repair and development as well as to pathological processes such as cancer and fibrosis. Our pipeline integrates traditional numerical (finite volume) solvers for the ligand concentration fields with bioinformatics, machine learning, and Bayesian inference methods, combining existing and novel computational tools into a single framework for a physiologically informed, data-driven parameter calibration process. The pipeline is modular, allowing easy extension or adjustment depending on user needs. Overall, this framework facilitates rigorous model calibration, an essential step toward ensuring that mathematical models have meaningful research and potential translational utility.