Anticipating critical transitions in a stochastic macrophage polarization model

As dynamic and adaptable immune system sentinels, macrophages can adopt various functional phenotypes in response to environmental stimuli. The transitions between these states, pro-inflammatory (M1), anti-inflammatory (M2), and mixed M1/M2, are crucial for immune regulation and the pathogenesis of many diseases. Therefore, understanding the parameter domains that enable the coexistence of these phenotypes and the critical values that indicate shifts in macrophage phenotypes is vital. By examining two-parameter phase diagrams and one-parameter bifurcation diagrams, distinct regions of monostability and multistability are identified as cytokine signaling levels (IFNγ and IL-4) change, revealing tipping points for phenotype transitions. All three phenotypes can coexist when the cytokine signals are balanced. The study explores the resilience of macrophage phenotypes through basin stability measures and stochastic potential, highlighting the preservation of a phenotype amid environmental perturbations. Furthermore, it illustrates phenotype shifts using critical transition theory and the predictive power of early warning signals (EWSs) based on critical slowing down. EWSs are derived from stochastic trajectories generated via Monte Carlo simulation with the Gillespie algorithm, incorporating intrinsic noise. It is shown that EWSs are more effective in capturing transitions from M1→M1/M2 and M1/M2→M2 than in detecting the direct transition from M2→M1.