de Boer R J, Hogeweg P
J Theor Biol. 1986 Jun 7;120(3):331-51. doi: 10.1016/s0022-5193(86)80205-3.
In a mathematical model of the cellular immune response we investigate immune reactions to tumors that are introduced in various doses. The model represents macrophage T-lymphocyte interactions that generate cytotoxic macrophages and cytotoxic T-lymphocytes. In this model antigens (tumors) can induce infinitely large T-lymphocyte effector populations because effector T-lymphocytes are capable of repeated proliferation and we have omitted immunosuppression. In this (proliferative) model small doses of weakly antigenic tumors grow infinitely large (i.e. sneak through) eliciting an immune response of limited magnitude. Intermediate doses of the same tumor induce larger immune responses and are hence rejected. Large doses of the tumor break through, but their progressive growth is accompanied by a strong immune response involving extensive lymphocyte proliferation. Similarly a more antigenic tumor is rejected in intermediate doses and breaks through in large doses. Initially small doses however lead to tumor dormancy. Thus although the model is devoid of explicit regulatory mechanisms that limit the magnitude of its response (immunosuppression is such a mechanism), the immune response to large increasing tumors may either be a stable reaction of limited magnitude (experimentally known as tolerance or unresponsiveness) or a strong and ever increasing reaction. Unresponsiveness can evolve because in this model net T-lymphocyte proliferation requires the presence of a minimum number of helper T cells (i.e. a proliferation threshold). Unresponsiveness is caused by depletion of helper T cell precursors.
在细胞免疫反应的数学模型中,我们研究了对以不同剂量引入的肿瘤的免疫反应。该模型描述了巨噬细胞与T淋巴细胞之间的相互作用,这种相互作用会产生细胞毒性巨噬细胞和细胞毒性T淋巴细胞。在这个模型中,抗原(肿瘤)能够诱导无限大的T淋巴细胞效应群体,因为效应T淋巴细胞能够反复增殖,而且我们忽略了免疫抑制作用。在这个(增殖性)模型中,小剂量的弱抗原性肿瘤会无限生长(即逃逸),引发有限强度的免疫反应。相同肿瘤的中等剂量会诱导更大的免疫反应,因此会被排斥。大剂量的肿瘤会突破防线,但它们的渐进性生长伴随着强烈的免疫反应,包括广泛的淋巴细胞增殖。同样,抗原性更强的肿瘤在中等剂量下会被排斥,在大剂量下会突破防线。然而,最初的小剂量会导致肿瘤休眠。因此,尽管该模型缺乏明确限制其反应强度的调节机制(免疫抑制就是这样一种机制),但对不断增大的大肿瘤的免疫反应可能要么是有限强度的稳定反应(实验中称为耐受或无反应性),要么是强烈且不断增强的反应。无反应性会出现,是因为在这个模型中,T淋巴细胞的净增殖需要存在最少数量的辅助性T细胞(即增殖阈值)。无反应性是由辅助性T细胞前体的耗竭引起的。