Klein P, Sterzl J, Dolezal J
J Math Biol. 1981;13(1):67-86. doi: 10.1007/BF00276866.
A mathematical model of B lymphocyte differentiation, based on experimental results, has been developed. The model focuses on the role of antigen in initiating and regulating B cell differentiation while other mechanisms, acting in concert with antigen but the functioning of which can be circumvented under appropriate conditions, are not considered. The importance of presence of antigen at individual stages of B cell differentiation was studied in experiments with an easily metabolizable antigen. Immunocompetent cells (ICC), arising by antigen-independent differentiation of stem cells, are activated by antigen (they become immunologically activated cells--IAC). Excess of antigen drives IAC into the terminal stage (antibody-forming cells--AFC) thereby restricting proliferation. Exhaustive terminal differentiation results in tolerance. A low primary dose permits IAC to escape antigen; IAC proliferate and later give rise to resting memory cells (MC) which are amenable to reactivation. MC have higher avidity for antigen (due to higher affinity, number and density of receptors) and the effect of different doses of antigen on MC is diverse. A very low secondary dose induces tolerance, a medium dose secondary response, and the administration of a high dose of antigen also brings about tolerance. The model suggests that the fate of memory cells is controlled by the ratio R:Ag, of the number of immunoglobulin receptors on B cells (R) to the number of available antigenic molecules (Ag), low values R:Ag favouring stimulation to differentiation while high values of R:Ag favouring inactivation. A nonlinear system of ordinary differential equations, describing the development of the populations involved in antigen-driven B cell differentiation, was used to simulate experiments and good qualitative agreement was achieved.
基于实验结果，已建立了B淋巴细胞分化的数学模型。该模型聚焦于抗原在启动和调节B细胞分化中的作用，而未考虑与抗原协同作用但在适当条件下其功能可被规避的其他机制。在使用易于代谢的抗原进行的实验中，研究了抗原在B细胞分化各个阶段存在的重要性。由干细胞通过抗原非依赖性分化产生的免疫活性细胞（ICC）被抗原激活（它们成为免疫激活细胞——IAC）。过量的抗原促使IAC进入终末阶段（抗体形成细胞——AFC），从而限制增殖。彻底的终末分化导致耐受。低的初次剂量使IAC逃避抗原；IAC增殖，随后产生易于再次激活的静止记忆细胞（MC）。MC对抗原具有更高的亲和力（由于受体的亲和力、数量和密度更高），不同剂量抗原对MC的作用是多样的。非常低的二次剂量诱导耐受，中等剂量引发二次反应，而高剂量抗原的给予也会导致耐受。该模型表明，记忆细胞的命运由B细胞上免疫球蛋白受体数量（R）与可用抗原分子数量（Ag）的比值R:Ag控制，低的R:Ag值有利于刺激分化，而高的R:Ag值有利于失活。使用一个描述抗原驱动的B细胞分化中所涉及群体发展的常微分方程非线性系统来模拟实验，并取得了良好的定性一致性。
