FURTHER-STUDIES ON THE PROBLEM OF IMMUNE NETWORK MODELING

In a previous work we have analysed a family of antibody and B-cell ne twork models (basic AB models) of the immune system. This analysis foc used principally on the physiological interpretation of their paramete rs. Our approach consisted in building a detailed and general mathemat ical model (referred to as the GIB model) and then simplifying it form ally 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 th at study it was clear that some of the assumptions necessary to simpli fy 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 po int of view. All this raised the issue of the reliability, or even the heuristic value, of theoretical studies based on current network mode ls 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 compartme nts were merged into a single one (labelled IGB model). Because all th ose models rely critically on certain B-cell activation functions, whi ch constitute the core of an implicit model of individual B-cell react ivity or ''local rules'', we focused the present numerical study, to a great extent, on two parameters determining those activation function s (Hill coefficient and thresholds). Our results indicate that: (1) th e RIB and IGB models display in general a much larger diversity of ste ady states than the AB models; (2) only under a very restricted parame ter 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 though not as much as in (2); and (4) even relatively small quantitative changes (within reasonable val ues) in the postulated ''local rules'' can induce very large quantitat ive 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 pos tulating a set of ''local rules'' solidly based on experimental eviden ce as a necessary condition for the reliability of current network mod els. (C) 1997 Academic Press Limited.