Abstract
In the beginning of the last century immunologists discovered that increasing the concentration of antibody does not always increase the binding of antigen. On the contrary, at a high enough concentration range the amount of antibody-antigen complexes decreased. This phenomenon was later referred to as the “prozone effect” or the “high-dose hook effect” and seemed to exist in many multivalent proteins. In a later study it was discovered that allosterically regulated proteins are less susceptible to this effect. Our aim is to investigate the mathematical basis of how allostery mitigates the prozone effect.
A combinatorial account of the prozone effect and its behaviour under allosteric conditions was developed and illustrated in MATLAB. Kinetic simulations were done by formulating reactions with the mass action law and running parameter scans in COPASI.
We developed a combinatorial theory that provides an explanation of the impact of cooperativity on the prozone effect. The mitigation of the prozone effect under these conditions reappeared in simulations of ligand binding to dimeric and tetrameric proteins thereby confirming the validity of the theory.