Stochastic Reaction–Diffusion Model of the Binding of Monoclonal Antibodies to CD4 Receptors on the Surface of T Cells

A stochastic reaction–diffusion model was developed to describe the binding of labeled monoclonal antibodies (mAbs) to CD4 receptors on the surface of T cells. The mAbs diffused to, adsorbed on, and underwent monovalent and bivalent binding to CD4 receptors on the cell surface. The model predicted the time-dependent nature of all populations involved in the labeling process. At large time, the populations reached equilibrium values, giving the number of antibodies bound to the T cell (ABC) defined as the sum of monovalently and bivalently bound mAbs. The predicted coefficient of variation (CV%) of the (ABC) values translated directly to a corresponding CV% of the measured mean fluorescence intensity (MFI). The predicted CV% was about 0.2% from the intrinsic fluctuations of the stochastic reaction process, about 5% after inclusion of the known fluctuations in the number of available CD4 receptors, and about 11% when fluctuations in bivalent binding affinity were included. The fluorescence detection process is expected to contribute approximately 7%. The abovementioned contributions to CV% sum up to approximately 13%. Work is underway to reconcile the predicted values and the measured values of 17% to 22%.