An Integrated Pipeline for Combining in vitro Data and Mathematical Models Using a Bayesian Parameter Inference Approach to Characterize Spatio-temporal Chemokine Gradient Formation

Abstract

All protective and pathogenic immune and inflammatory responses rely heavily on leukocyte migration and localization. Chemokines are secreted chemoattractants that orchestrate the positioning and migration of leukocytes through concentration gradients. The mechanisms underlying chemokine gradient establishment and control include physical as well as biological phenomena. Mathematical models offer the potential to both understand this complexity and suggest interventions to modulate immune function. Constructing models that have powerful predictive capability relies on experimental data to estimate model parameters accurately, but even with a reductionist approach most experiments include multiple cell types, competing interdependent processes and considerable uncertainty. Therefore, we propose the use of reduced modeling and experimental frameworks in complement, to minimize the number of parameters to be estimated. We present a Bayesian optimization framework that accounts for advection and diffusion of a chemokine surrogate and the chemokine CCL19, transport processes that are known to contribute to the establishment of spatio-temporal chemokine gradients. Three examples are provided that demonstrate the estimation of the governing parameters as well as the underlying uncertainty. This study demonstrates how a synergistic approach between experimental and computational modeling benefits from the Bayesian approach to provide a robust analysis of chemokine transport. It provides a building block for a larger research effort to gain holistic insight and generate novel and testable hypotheses in chemokine biology and leukocyte trafficking.

Keywords: Bayesian parameter inference; MCMC methods; chemokine transport dynamics; microfluidic device; model validation; partial differential equations; sequential Bayesian updating.