Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada.
Bull Math Biol. 2022 Jul 6;84(8):82. doi: 10.1007/s11538-022-01039-x.
CD200 is a cell membrane protein that binds to its receptor, CD200 receptor (CD200R). The CD200 positive tumor cells inhibit the cellular functions of M1 and M2 macrophages and dendritic cells (DCs) through the CD200-CD200R complex, resulting in downregulation of Interleukin-10 and Interleukin-12 productions and affecting the activation of cytotoxic T lymphocytes. In this work, we provide two ordinary differential equation models, one complete model and one simplified model, to investigate how the binding affinities of CD200R and the populations of M1 and M2 macrophages affect the functions of the CD200-CD200R complex in tumor growth. Our simulations demonstrate that (i) the impact of the CD200-CD200R complex on tumor promotion or inhibition highly depends on the binding affinity of the CD200R on M2 macrophages and DCs to the CD200 on tumor cells, and (ii) a stronger binding affinity of the CD200R on M1 macrophages or DCs to the CD200 on tumor cells induces a higher tumor cell density in the CD200 positive tumor. Thus, the CD200 blockade would be an efficient treatment method in this case. Moreover, the simplified model shows that the binding affinity of CD200R on macrophages is the major factor to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are significantly different to each other. On the other hand, both the binding affinity of CD200R and the population of macrophages are the major factors to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are close to each other. We also analyze the simplified model to investigate the dynamics of the positive and trivial equilibria of the CD200 positive tumor case and the CD200 deficient tumor case. The bifurcation diagrams show that when M1 macrophages dominate the population, the tumor cell density of the CD200 positive tumor is higher than the one of CD200 deficient tumor. Moreover, the dynamics of tumor cell density change from tumor elimination to tumor persistence to oscillation, as the maximal proliferation rate of tumor cells increases.
CD200 是一种细胞膜蛋白，它与 CD200 受体 (CD200R) 结合。CD200 阳性肿瘤细胞通过 CD200-CD200R 复合物抑制 M1 和 M2 巨噬细胞和树突状细胞 (DCs) 的细胞功能，导致白细胞介素-10 和白细胞介素-12 的产生下调，并影响细胞毒性 T 淋巴细胞的激活。在这项工作中，我们提供了两个常微分方程模型，一个完整模型和一个简化模型，以研究 CD200R 的结合亲和力和 M1 和 M2 巨噬细胞的群体如何影响 CD200-CD200R 复合物在肿瘤生长中的功能。我们的模拟表明：(i) CD200-CD200R 复合物对肿瘤促进或抑制的影响高度依赖于 M2 巨噬细胞和 DCs 上的 CD200R 与肿瘤细胞上的 CD200 的结合亲和力，以及 (ii) 肿瘤细胞上的 CD200R 与肿瘤细胞上的 CD200 的结合亲和力越强，CD200 阳性肿瘤中的肿瘤细胞密度就越高。因此，在这种情况下，CD200 阻断将是一种有效的治疗方法。此外，简化模型表明，当 M1 巨噬细胞上的 CD200R 的结合亲和力与 M1 和 M2 巨噬细胞上的 CD200R 的结合亲和力明显不同时，巨噬细胞上的 CD200R 的结合亲和力是决定 CD200 阻断治疗效果的主要因素。另一方面，当 M1 和 M2 巨噬细胞上的 CD200R 的结合亲和力接近时，CD200R 的结合亲和力和巨噬细胞的群体都是决定 CD200 阻断治疗效果的主要因素。我们还分析了简化模型，以研究 CD200 阳性肿瘤病例和 CD200 缺乏肿瘤病例的正平衡点和平凡平衡点的动力学。分岔图表明，当 M1 巨噬细胞占主导地位时，CD200 阳性肿瘤的肿瘤细胞密度高于 CD200 缺乏肿瘤的肿瘤细胞密度。此外，随着肿瘤细胞最大增殖率的增加，肿瘤细胞密度的变化从肿瘤消除到肿瘤持续到振荡。
