Weisbuch G, De Boer R J, Perelson A S
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, Paris, France.
J Theor Biol. 1990 Oct 21;146(4):483-99. doi: 10.1016/s0022-5193(05)80374-1.
The present paper investigates conditions under which immunological memory can be maintained by stimulatory idiotypic network interactions. The paper was motivated by the work of (De Boer & Hogeweg, 1989b, Bull. math. Biol. 51, 381-408.) which claimed that idiotypic memory is not possible because of percolation within the network. Here we reinvestigate the issue of percolation using both the previous model and a simpler one (Weisbuch, 1990, J. theor. Biol. 143, 507-522.) that allows analytic analysis. We focus on network topologies in which each Ab1 is connected to several Ab2s, which in turn are connected to several Ab3s. It is demonstrated that, for a considerable range of parameters, both models account for the existence of localized memory-states in which only the Ab1 and the Ab2 clones are activated and the clones of the Ab3 level remain virgin. The existence of localized memory-states seems to contradict the previous percolation result. This discrepancy will be shown to depend on the system dynamics. By simulation we explore the parameter regimes for which one finds percolation and those for which localized memory-states exists. We show that the conditions required for attaining the localized memory-state are considerably more stringent than those required for its existence and local stability. We conclude that both localized memory and percolation are possible in stimulatory idiotypic networks.
本文研究了通过刺激性独特型网络相互作用维持免疫记忆的条件。本文的研究动机源于（De Boer & Hogeweg, 1989b, Bull. math. Biol. 51, 381 - 408.）的工作，该工作声称由于网络内的渗流，独特型记忆是不可能的。在此，我们使用先前的模型和一个更简单的模型（Weisbuch, 1990, J. theor. Biol. 143, 507 - 522.）重新研究渗流问题，后者允许进行解析分析。我们关注的网络拓扑结构是每个Ab1与几个Ab2相连，而每个Ab2又与几个Ab3相连。结果表明，在相当大的参数范围内，两个模型都解释了局部记忆状态的存在，在这种状态下，只有Ab1和Ab2克隆被激活，而Ab3水平的克隆保持未激活状态。局部记忆状态的存在似乎与先前的渗流结果相矛盾。这种差异将被证明取决于系统动力学。通过模拟，我们探索了发现渗流的参数范围以及存在局部记忆状态的参数范围。我们表明，达到局部记忆状态所需的条件比其存在和局部稳定性所需的条件要严格得多。我们得出结论，在刺激性独特型网络中，局部记忆和渗流都是可能的。
