Mathematical model of tumor-macrophage interactions: Elucidating the tumor-driven macrophage phenotype reprogramming

TL;DR

This paper presents a mathematical model of tumor-macrophage interactions that elucidates how macrophage phenotypes influence tumor progression and identifies potential prognostic markers for cancer outcomes.

Contribution

The study introduces a novel mathematical framework incorporating multiple macrophage phenotypes and analyzes their roles in tumor dynamics, providing insights into immune-tumor interactions and prognosis.

Findings

Lower tumor burden correlates with higher M1 macrophage infiltration.

Delayed M3 macrophage activation associates with longer survival.

Model successfully reproduces tumor sample trajectories.

Abstract

The interplay between tumor cells and macrophages plays a central regulatory role in cancer progression. In this study, we developed a mathematical model that incorporates tumor cells, M1 type macrophages, M2 type macrophages and an M3 type macrophage population characterized by dual phenotypic features. First, we analyzed the fundamental mathematical properties of the model and derived the conditions under which the system attains a tumor free stable state or a coexistence state of tumor and immune cells. Second, global sensitivity analysis revealed that key parameters governing macrophage polarization and intercellular communication vary dynamically during tumor development. Bifurcation analysis further identified the polarization rate of M1 type macrophages $\kappa$ and the baseline level of resting macrophages $M_0$ as critical determinants of the system's dynamical behavior. Notably, using approximate Bayesian computation for parameter inference and dynamic simulations, the model successfully recapitulated the evolutionary trajectories of eight tumor samples. The results demonstrate that lower tumor burden is significantly associated with higher M1 type macrophage infiltration and delayed peak time of M3 type macrophage activation. Moreover, survival analysis indicated that both enhanced M1 type macrophage infiltration and delayed peak time of M3 type macrophage activation are correlated with longer survival time. In summary, this study not only provides a theoretical framework for understanding the dynamic mechanisms underlying tumor macrophage interactions but also proposes two potential clinical prognostic markers: the level of M1 type macrophage infiltration and the peak time of M3 type macrophage activation.