Coupling vs decoupling approaches for PDE/ODE systems modeling intercellular signaling

TL;DR

This paper compares coupling and decoupling methods for PDE/ODE systems modeling intercellular signaling, demonstrating that coupling approaches are more efficient for biologically relevant scenarios.

Contribution

It provides a systematic sensitivity analysis and numerical comparison showing the superiority of coupling methods over decoupling in this context.

Findings

Coupling approaches outperform decoupling in relevant biological models.

Sensitivity analysis guides the comparison of methods.

Numerical results support the efficiency of coupling methods.

Abstract

We consider PDE/ODE systems for the simulation of intercellular signaling in multicellular environments. The intracellular processes for each cell described here by ODEs determine the long-time dynamics, but the PDE part dominates the solving effort. Thus, it is not clear if commonly used decoupling methods can outperform a coupling approach. Based on a sensitivity analysis, we present a systematic comparison between coupling and decoupling approaches for this class of problems and show numerical results. For biologically relevant configurations of the model, our quantitative study shows that a coupling approach performs much better than a decoupling one.