Shudo Emi, Iwasa Yoh
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan.
J Theor Biol. 2004 May 7;228(1):17-29. doi: 10.1016/j.jtbi.2003.12.001.
When attacked by pathogens, higher vertebrates produce specific immune cells that fight against them. We here studied the host's optimal schedule of specific immune cell production. The damage caused by the pathogen increases with the pathogen amount in the host integrated over time. On the other hand, there is also a cost incurred by the production of specific immune cells, not only in terms of the energy needed to produce and maintain the cells, but also with respect to damages sustained by the host's body as a result of immune activity. The optimal strategy of the host is the one that minimizes the total cost, defined as a weighted sum of the damage caused by pathogens and the costs caused by the specific immune cells. The problem is solved by using Pontryagin's maximum principle and dynamic programming. The optimal defense schedule is typically as follows: In the initial phase after infection, immune cells are produced at the fastest possible rate. The amount of pathogen increases temporarily but is eventually suppressed. When the pathogen amount is suppressed to a sufficiently low level, the immune cell number decreases and converges to a low steady level, which is maintained by alternately switching between fastest production and no production. We examine the effect of time delay required to have fully active immune cells by comparing cases with different number of rate limiting steps before producing immune cells. We examine the effect of the duration of time (time delay) required before full-scale production of active immune cells by comparing cases with different numbers of rate-limiting steps before immune-cell production. We also discuss the role of immune memory based on the results of the optimal immune reaction.
当受到病原体攻击时，高等脊椎动物会产生特定的免疫细胞来对抗它们。我们在此研究了宿主产生特定免疫细胞的最优时间表。病原体造成的损害会随着宿主体内病原体数量随时间的累积而增加。另一方面，产生特定免疫细胞也会产生成本，这不仅体现在产生和维持这些细胞所需的能量方面，还体现在免疫活动给宿主身体带来的损害上。宿主的最优策略是使总成本最小化，总成本被定义为病原体造成的损害与特定免疫细胞造成的成本的加权和。这个问题通过使用庞特里亚金极大值原理和动态规划来解决。最优防御时间表通常如下：在感染后的初始阶段，以尽可能快的速度产生免疫细胞。病原体数量会暂时增加，但最终会被抑制。当病原体数量被抑制到足够低的水平时，免疫细胞数量会减少并收敛到一个低稳态水平，这个水平通过在最快产生和不产生之间交替切换来维持。我们通过比较产生免疫细胞之前具有不同限速步骤数量的情况，来研究拥有完全活跃的免疫细胞所需的时间延迟的影响。我们还基于最优免疫反应的结果讨论了免疫记忆的作用。
