Steady state relations between control proteins regulating the formation of the alternative pathway C3 convertase

A steady state algebraic Mass Action analysis of the factors controlling the concentration of the alternative pathway C3 convertase is presented. The positive feedback loop does not make this portion of the complement system insensitive to variation in control protein concentrations; on the contrary, a hyperbolic relationship is revealed between C3 convertase and a complex product of the control protein concentrations which contains some mathematical non-linearities. The consequences of this relationship are explored. It is found that variations in the concentration of any one control protein will have an effect which can only be predicted if its initial concentration and those of the other control proteins are known. The system is capable of responding with a considerable range of amplitudes to a given signal which raises the question as to whether the feedback loop confers biological advantage, not only by augmenting the activation of C3 to C3b, but through its potential for flexibility in responding to an activating stimulus. The analysis may also prove useful in the design and evaluation of experiments to determine the reaction rate constants governing the interactions between the control proteins in the fluid phase in vitro.