Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090, USA.
Bull Math Biol. 2010 Apr;72(3):611-44. doi: 10.1007/s11538-009-9463-1. Epub 2009 Dec 16.
The currently accepted paradigm for the primary T cell response is that effector T cells commit to autonomous developmental programs. This concept is based on several experiments that have demonstrated that the dynamics of a T cell response is largely determined shortly after antigen exposure and that T cell dynamics do not depend on the level and duration of antigen stimulation. Another experimental study has also shown that T cell responses are robust to variations in antigen-specific precursor frequency. Various mathematical models have corroborated the first result that programmed T cell responses are insensitive to the level of antigen stimulation. However, this paper proposes that programmed responses do not entirely explain the robustness of T cell dynamics to variations in precursor frequency. This work studies the hypothesis that the dynamics of a T cell response may also be governed by a feedback loop involving adaptive regulatory cells rather than by intrinsic developmental programs. We formulate two mathematical models based on T cell developmental programs. In one model, effector cells undergo a fixed number of divisions before dying. In the second model, effector cells live for a fixed time during which they may divide. The study of these models suggests that developmental programs are not sufficiently robust as they produce an immune response that directly scales with precursor frequencies. Consequently, we derive a third model based on the principle that adaptive regulatory T cells develop in the course of an immune response and suppress effector cells. Our simulations show that this feedback mechanism responds robustly over a range of at least four orders of magnitude of precursor frequencies. We conclude that the proliferation program paradigm does not entirely capture the observed robustness of T cell responses to variations in precursor frequency. We propose an alternative mechanism by which the primary T cell response is governed by an emergent group dynamic and not by individual T cell programs.
目前,人们普遍接受的初始 T 细胞反应模式是,效应 T 细胞会自主选择发育途径。这一概念基于以下几个实验:首先,T 细胞反应的动态变化在抗原暴露后不久就基本确定,其次,T 细胞的动态变化并不依赖于抗原刺激的程度和持续时间。另一项实验研究还表明,T 细胞反应对抗原特异性前体频率的变化具有很强的鲁棒性。各种数学模型也证实了第一个结果,即程序化的 T 细胞反应对抗原刺激的程度不敏感。然而,本文提出,程序化反应并不能完全解释 T 细胞动力学对前体频率变化的鲁棒性。本研究假设 T 细胞反应的动力学也可能受到涉及适应性调节细胞的反馈回路的控制,而不是由内在的发育程序决定。我们基于 T 细胞发育程序构建了两个数学模型。在一个模型中,效应细胞在死亡前会经历固定数量的分裂。在第二个模型中,效应细胞在固定的时间内生存,在此期间它们可以分裂。对这些模型的研究表明,发育程序不够稳健,因为它们产生的免疫反应与前体频率直接相关。因此,我们基于适应性调节 T 细胞在免疫反应过程中发育并抑制效应细胞的原理,推导出第三个模型。我们的模拟结果表明,这种反馈机制在至少四个数量级的前体频率范围内具有很强的鲁棒性。我们得出的结论是,增殖程序范式并不能完全捕捉到观察到的 T 细胞反应对前体频率变化的鲁棒性。我们提出了一种替代机制,即初始 T 细胞反应是由一个新兴的群体动态而不是单个 T 细胞程序控制的。