Accumulation model of antibody binding in staining experiments

The selective binding of antibodies to antigens has been used for decades in biological research and has become a useful tool for medical diagnostics and therapy. Perhaps one of the earliest applications are staining experiments that indicate the presence of antigens in cells or tissue. Despite the development of highly specialized applications, this simple staining still belongs to the standard repertoire of immunostaining. In this dissertation, we model the macroscopically observable binding behavior of antibodies in staining experiments. The guiding principles are two aspects that apply to most staining experiments: the finite antibody incubation time, and washing steps that remove unbound antibodies prior to the evaluation of the staining result. Thus, the staining result can only comprise antibodies that have withstood washing, leading us to describe the binding of measurable antibodies as an accumulation process with finite stopping time. We construct the equations for the accumulation model from Langmuir kinetics and corresponding adaptations to multiple binding-site types so that we can consider heterogeneous cellular structures. After describing the immediate consequences of the accumulation process, we prove that the accumulation model satisfies all the properties that are expected from the experimental setting of staining experiments. Next, we shift the focus to the estimation of the model parameters and develop the accessibility analysis, which is a characterization method for experimental systems. Using experimental data, we validate the underlying principles of the accumulation model and test the accessibility analysis that is implemented and published in the form of Julia packages. Finally, we take the opportunity to propose and illustrate two applications of the accessibility analysis: the selection of initial antibody concentrations for staining experiments and a multi-staining multiplexing method that separates staining signals based on antibody binding properties.