Centro de Ciências Naturais e Humanas, UFABC, Santo André, 09210-170, SP, Brazil.
Departamento de Imunologia, Universidade de São Paulo, São Paulo, 05508-000, SP, Brazil.
J Theor Biol. 2019 Jun 21;471:42-50. doi: 10.1016/j.jtbi.2019.03.025. Epub 2019 Mar 29.
Human cancers display intra-tumor heterogeneity in many phenotypic features, such as expression of cell surface receptors, growth, and angiogenic, proliferative, and immunogenic factors, which represent obstacles to a successful immune response. In this paper, we propose a nonlinear mathematical model of cancer immunosurveillance that takes into account some of these features based on cell-mediated immune responses. The model describes phenomena that are seen in vivo, such as tumor dormancy, robustness, immunoselection over tumor heterogeneity (also called "cancer immunoediting") and strong sensitivity to initial conditions in the composition of tumor microenvironment. The results framework has as common element the tumor as an attractor for abnormal cells. Bifurcation analysis give us as tumor attractors fixed-points, limit cycles and chaotic attractors, the latter emerging from period-doubling cascade displaying Feigenbaum's universality. Finally, we simulated both elimination and escape tumor scenarios by means of a stochastic version of the model according to the Doob-Gillespie algorithm.
人类癌症在许多表型特征上表现出肿瘤内异质性，如细胞表面受体的表达、生长以及血管生成、增殖和免疫因子，这些特征构成了成功免疫反应的障碍。在本文中，我们提出了一个基于细胞介导的免疫反应的癌症免疫监视的非线性数学模型，该模型考虑了其中的一些特征。该模型描述了体内观察到的现象，如肿瘤休眠、稳健性、肿瘤异质性的免疫选择（也称为“癌症免疫编辑”）以及对肿瘤微环境组成中初始条件的强烈敏感性。结果框架的共同要素是肿瘤作为异常细胞的吸引子。分岔分析为我们提供了肿瘤吸引子的平衡点、极限环和混沌吸引子，后者从周期加倍级联中出现，表现出费根鲍姆的普遍性。最后，我们根据 Doob-Gillespie 算法通过模型的随机版本模拟了消除和逃避肿瘤的场景。
