Department of Electrical and Computer Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran.
Computer Science Department, Brandenburg University of Technology, 03013, Cottbus, Germany.
Sci Rep. 2019 Sep 4;9(1):12764. doi: 10.1038/s41598-019-48865-z.
Macrophages play a key role in tissue regeneration by polarizing to different destinies and generating various phenotypes. Recognizing the underlying mechanisms is critical in designing therapeutic procedures targeting macrophage fate determination. Here, to investigate the macrophage polarization, a nonlinear mathematical model is proposed in which the effect of IL4, IFNγ and LPS, as external stimuli, on STAT1, STAT6, and NFκB is studied using bifurcation analysis. The existence of saddle-node bifurcations in these internal key regulators allows different combinations of steady state levels which are attributable to different fates. Therefore, we propose dynamic bifurcation as a crucial built-in mechanism of macrophage polarization. Next, in order to investigate the polarization of a population of macrophages, bifurcation analysis is employed aligned with agent-based approach and a two-layer model is proposed in which the information from single cells is exploited to model the behavior in tissue level. Also, in this model, a partial differential equation describes the diffusion of secreted cytokines in the medium. Finally, the model was validated against a set of experimental data. Taken together, we have here developed a cell and tissue level model of macrophage polarization behavior which can be used for designing therapeutic interventions.
巨噬细胞通过极化到不同的命运并产生各种表型在组织再生中发挥关键作用。认识潜在的机制对于设计针对巨噬细胞命运决定的治疗程序至关重要。在这里，为了研究巨噬细胞极化，提出了一个非线性数学模型，该模型使用分岔分析研究了 IL4、IFNγ 和 LPS 等外部刺激对 STAT1、STAT6 和 NFκB 的影响。这些内部关键调节剂中的鞍结分岔的存在允许不同的稳态水平组合归因于不同的命运。因此，我们提出动态分岔作为巨噬细胞极化的关键内置机制。接下来，为了研究巨噬细胞的极化，采用基于代理的分岔分析方法并提出了一个两层模型，该模型利用单细胞的信息来模拟组织水平的行为。此外，在该模型中，偏微分方程描述了介质中分泌细胞因子的扩散。最后，该模型通过一组实验数据进行了验证。总之，我们在这里开发了一种用于设计治疗干预的巨噬细胞极化行为的细胞和组织水平模型。
