Model Reduction of Multicellular Communication Systems via Singular Perturbation: Sender Receiver Systems

TL;DR

This paper develops a model reduction technique for multicellular communication systems involving PDE-ODE couplings, enabling scalable simulation by approximating diffusion dynamics with a quasi steady state and deriving a finite-dimensional multiagent network.

Contribution

The authors introduce a singular perturbation-based reduction method that simplifies complex PDE-ODE models of multicellular systems into manageable multiagent networks.

Findings

Reduced model closely matches full system dynamics

Diffusion dynamics converge exponentially to steady state

Scalable simulation of large cell populations achieved

Abstract

We investigate multicellular sender receiver systems embedded in hydrogel beads, where diffusible signals mediate interactions among heterogeneous cells. Such systems are modeled by PDE ODE couplings that combine three dimensional diffusion with nonlinear intracellular dynamics, making analysis and simulation challenging. We show that the diffusion dynamics converges exponentially to a quasi steady spatial profile and use singular perturbation theory to reduce the model to a finite dimensional multiagent network. A closed form communication matrix derived from the spherical Green's function captures the effective sender receiver coupling. Numerical results show the reduced model closely matches the full dynamics while enabling scalable simulation of large cell populations.