Model analysis of the bases of multistationarity in the humoral immune response.

A formal analysis of the regulation of antibody production has been developed. It comprises two complementary approaches: a logical analysis in terms of discrete (boolean) variables and functions and a more classical analysis in terms of differential equations. A first paper dealt mostly with the logical description which provided global information on how complex the network needs to be in order to account for some main aspects of the immune response, without having to specify the details of the cellular interactions or to introduce a great number of parameters. Here we present the continuous approach and, in particular, a detailed study of the steady states and a discussion of their role in the dynamics of the immune response. The model subject to this analysis is a minimal one, which takes into account a small number of well-established facts concerning lymphocyte interactions and some reasonable assumptions. The core of the model is a negative feedback loop between the helper (TH) and suppressor (TS) T lymphocytes on which autocatalytic loops of the TH and TS populations on themselves are grafted. The salient feature of this minimal scheme is the prediction, for given environmental and parametrical conditions, of a multiplicity of steady states. This multistationarity occurs both in the absence of antigen or for constant antigen levels. Variations in the external constraints provoke switches among the steady states which might be related to the various modes of the humoral immune response, and depend on the doses of antigen injected and on the previous antigenic history of the system. In particular, high and low dose paralysis appear to be associated with two distinct steady state branches.