Faro J, Carneiro J, Velasco S
Departamento de Física Aplicada, Universidad de Salamanca, Spain.
J Theor Biol. 1997 Feb 21;184(4):405-21. doi: 10.1006/jtbi.1996.0252.
In a previous work we have analysed a family of antibody and B-cell network models (basic AB models) of the immune system. This analysis focused principally on the physiological interpretation of their parameters. Our approach consisted in building a detailed and general mathematical model (referred to as the GIB model) and then simplifying it formally to a version (named the RIB model) that belongs to the family of AB models, but which is more general than the basic AB models. From that study it was clear that some of the assumptions necessary to simplify the GIB model into the RIB one, as well as to recover the basic AB models from the RIB one, are quite unrealistic from a physiological point of view. All this raised the issue of the reliability, or even the heuristic value, of theoretical studies based on current network models for experimental immunologists. One approach to clarify this issue is to ask whether the unrealism of the assumptions implicit in the RIB and AB models entails qualitatively different behaviours between them compared to the GIB one. We initiate here such a work by performing a comparative study of a two-clone system of the AB and RIB models, and a variant of the GIB model in which the different molecular compartments were merged into a single one (labelled IGB model). Because all those models rely critically on certain B-cell activation functions, which constitute the core of an implicit model of individual B-cell reactivity or "local rules", we focused the present numerical study, to a great extent, on two parameters determining those activation functions (Hill coefficient and thresholds). Our results indicate that: (1) the RIB and IGB models display in general a much larger diversity of steady states than the AB models; (2) only under a very restricted parameter regime did all studied models behave similarly; (3) the parameter regime under which the AB and IGB models, but not the RIB one, behave similarly is still rather restricted through not as much as in (2); and (4) even relatively small quantitative changes (within reasonable values) in the postulated "local rules" can induce very large quantitative changes in the behaviour of the AB and RIB models but not the IGB model. In the light of the present results, we discuss the need of postulating a set of "local rules" solidly based on experimental evidence as a necessary condition for the reliability of current network models.
在之前的一项工作中，我们分析了免疫系统的一系列抗体和B细胞网络模型（基本AB模型）。该分析主要集中在对其参数的生理学解释上。我们的方法包括构建一个详细的通用数学模型（称为GIB模型），然后将其形式上简化为一个属于AB模型家族但比基本AB模型更通用的版本（称为RIB模型）。从该研究中可以清楚地看出，将GIB模型简化为RIB模型以及从RIB模型恢复基本AB模型所需的一些假设，从生理学角度来看是相当不现实的。所有这些都引发了基于当前网络模型的理论研究对实验免疫学家的可靠性甚至启发价值的问题。澄清这个问题的一种方法是询问RIB和AB模型中隐含假设的不现实性是否会导致它们与GIB模型在行为上存在质的差异。我们在此通过对AB和RIB模型的双克隆系统以及GIB模型的一个变体（其中不同的分子隔室合并为一个，标记为IGB模型）进行比较研究来开展这样一项工作。由于所有这些模型都严重依赖于某些B细胞激活函数，这些函数构成了个体B细胞反应性或“局部规则”隐含模型的核心，我们在很大程度上将当前的数值研究集中在决定这些激活函数的两个参数（希尔系数和阈值）上。我们的结果表明：（1）RIB和IGB模型通常比AB模型表现出大得多的稳态多样性；（2）只有在非常有限的参数范围内，所有研究的模型行为才相似；（3）AB和IGB模型行为相似但RIB模型不同的参数范围仍然相当有限，尽管不像（2）中那么受限；（4）即使假定的“局部规则”中相对较小的定量变化（在合理值范围内）也会导致AB和RIB模型行为上的非常大的定量变化，但不会导致IGB模型行为上的这种变化。鉴于目前的结果，我们讨论了基于实验证据提出一组“局部规则”作为当前网络模型可靠性必要条件的必要性。
