The heterogeneity and plasticity of macrophages have become a topic of great interest, due to their role in various diseases ranging from cancer to bacterial infections. While initial experimental studies assumed an extreme polarisation situation, with the (anti-tumour) M1 and (pro-tumour) M2 macrophages representing the two extreme cell phenotypes, more recent studies showed a continuum of macrophages polarisation phenotypes. Here, we focus on tumour-macrophage interactions and develop a mathematical model based on kinetic equations for active particles to describe (i) the dynamics of macrophages with a continuum of diverse functional states, ranging from pro-tumour to anti-tumour states; and (ii) the dynamics of tumour cells with a variety of progression (i.e. mutation) states. With the help of this model we show that the growth of solid tumours is associated with an increased clonal heterogeneity, as well as with an increased macrophages phenotypic heterogeneity (caused by a shift from an initial anti-tumour M1-like phenotype to a mixed M1–M2 phenotype). Moreover, we show that the assumption of exponential tumour/immune cell growth leads to an unbounded macrophages growth, which is biologically unrealistic. In contrast, the assumption of logistic tumour/immune cell growth can lead to tumour dormancy (under the control of immune cells), or to tumour growth towards smaller/larger sizes which depend on various model parameters. Finally, we show that tumour dormancy is associated with an increase in the clonal heterogeneity of tumour cells and in the phenotypic heterogeneity of macrophages.

中文翻译：

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一种用于模拟癌症进展过程中肿瘤和巨噬细胞异质性和可塑性的动力学理论方法

由于巨噬细胞在从癌症到细菌感染等各种疾病中的作用，巨噬细胞的异质性和可塑性已成为一个备受关注的话题。虽然最初的实验研究假设极端极化情况，（抗肿瘤）M1 和（促肿瘤）M2 巨噬细胞代表两种极端细胞表型，但最近的研究表明巨噬细胞极化表型是连续的。在这里，我们专注于肿瘤-巨噬细胞的相互作用，并开发了一个基于活性粒子动力学方程的数学模型，以描述（i）具有多种功能状态的巨噬细胞的动力学，从促肿瘤状态到抗肿瘤状态；(ii) 具有多种进展（即突变）状态的肿瘤细胞的动力学。在该模型的帮助下，我们表明实体瘤的生长与增加的克隆异质性以及增加的巨噬细胞表型异质性相关（由最初的抗肿瘤 M1 样表型转变为混合 M1 –M2 表型）。此外，我们表明指数肿瘤/免疫细胞生长的假设会导致巨噬细胞无限生长，这在生物学上是不现实的。相反，逻辑肿瘤/免疫细胞生长的假设可能导致肿瘤休眠（在免疫细胞的控制下），或肿瘤向更小/更大的尺寸生长，这取决于各种模型参数。最后，我们表明肿瘤休眠与肿瘤细胞克隆异质性和巨噬细胞表型异质性的增加有关。