Steady state approximation in the minimal model of the alternative pathway of complement

Abstract

Complement is a response mechanism of the immune system. Two initiation pathways have been characterized for complement. The classical pathway is antibody mediated while the alternative pathway is not. Since the alternative pathway is independent of antibodies, it is always active. For the alternative pathway we have previously developed a minimal model. Using parameters within physiological bounds, the model showed complex behavior also within physiological bounds. Thus the model seems to be an appropriate representation of the alternative pathway response. By applying a steady state assumption to the Michaelis Menten step of the minimal model, we reduce the number of variables from six to five. A comparison between the dynamics of the minimal and contracted models reveals that the two descriptions may not be compatible. Although both systems show chaotic behavior it occurs in different regions of parameter space.