Perelson A S, Mirmirani M, Oster G F
J Math Biol. 1978 Mar 28;5(3):213-56. doi: 10.1007/BF00276120.
After a first encounter with most antigens, the immune system responds to susequent encounters with a faster, more efficient and more strenuous antibody response. The memory of previous antigen contacts is carried by lymphocytes. Expanding on the model developed in Part 1 of this paper, we examine the optimal strategy available to the immune system for B memory cell production. We again find that the strategy should be of the bang-bang variety. The model we consider assumes that antigen triggers a subpopulation of B-lymphocytes. These triggered lymphocytes can proliferate and secrete modest amounts of antibody, or differentiate into non-dividing plasma cells which secrete large amounts of antibody, or differentiate into non-antibody secreting memory cells. Given injections of antigen at two widely spaced times we compute the strategy which minimizes a linear combination of the primary and secondary response times. We find that for all biologically reasonable parameter values the best strategies are ones in which memory cells are produced at the end of the primary response. Exerimental results which bear on the actual strategies employed are discussed.
在首次接触大多数抗原后，免疫系统在随后再次接触时会以更快、更高效且更强烈的抗体反应做出应答。先前抗原接触的记忆由淋巴细胞携带。基于本文第一部分所建立的模型，我们研究了免疫系统产生B记忆细胞的最优策略。我们再次发现该策略应属于开关式类型。我们所考虑的模型假定抗原触发B淋巴细胞的一个亚群。这些被触发的淋巴细胞可以增殖并分泌适量抗体，或者分化为不分裂但分泌大量抗体的浆细胞，或者分化为不分泌抗体的记忆细胞。给定在两个间隔较远时间点注射抗原的情况，我们计算出使初次和二次反应时间的线性组合最小化的策略。我们发现，对于所有生物学上合理的参数值，最佳策略是在初次反应结束时产生记忆细胞。文中还讨论了与实际采用策略相关的实验结果。
