Modelling the effect of antibody depletion on dose-response behavior for common immunostaining protocols

Abstract

Dose-response curves of immunostaining experiments are commonly described as Langmuir isotherm. However, for common immunostaining protocols the equilibrium assumption is violated and the dose-response behavior is governed by antibody accumulation. If bound antibodies are replenished, i.e. the concentration of unbound antibodies is constant, the accumulation model can easily be solved analytically. Yet, in many experimental setups the overall amount of antibodies is fixed such that antibody binding reduces the concentration of free antibodies. Solving the accumulation model for this case is more difficult and seems to be impossible if the epitopes are heterogeneous. In this paper, we solve the accumulation model with antibody depletion analytically for the simple case of identical epitopes. We derive inequalities between the depletion-free accumulation model, the accumulation model and the Langmuir isotherm. This allows us to characterize the antibody depletion effect. We generalize the problem to heterogeneous epitopes, where we prove the existence and uniqueness of a solution that behaves as expected by the experimental setting. With these properties we derive bounds for the resulting multi-epitope-class accumulation model and investigate the depletion effect in the case of heterogeneous epitopes.