A mathematical approach to identifying antibody affinity with modern biosensors, for pharmaceutical and clinical settings

Patient antibody reacting against foreign antigen is a key part of both primary and secondary immune responses. However previous methods of studying the affinity of these reactions have been semi-quantitative and do not allow for the unique identification of the affinity of interactions. The goal of this PhD project was to produce mathematical models and experimental protocols that could be used with existing biosensor technology to accurately and repeatably determine the kinetic rate constants for monoclonal antibody as well as clinical samples of patient antibody. Surface Plasmon Resonance (SPR) experiments with human antibody were conducted and repeated. A variety of models was developed and fit alongside models from the literature, until one model was able to consistently and accurately estimate the kinetic constants of the interaction as well as minimize residuals, the Bivalent effective rate constant spacial model (BERCS). This model was applied to further biosensor experiments in which each antibody was reacted against multiple samples of antigen, each presenting the same epitope alongside different structural features. The BERCS model dramatically reduced the residual sum of squares of the fit, compared to the fits done with commercially available software and models, and produced little variation in rate constant estimates between replicate experiments. This allowed for measurements of how the rate constants varied between the different structures of antigen that present the same epitope. However, structural identifiability analysis consistently showed that SPR technology would not be able to identify the affinity of antibody in unknown concentrations - limiting the applicability of the technology for dealing with samples taken from patients. The growing complexity of these models lead to the necessity of novel methods for approaching xvii ABBREVIATIONS structural identifiability. New algorithms for analysing structural identifiability were created alongside new concepts relating to structural identifiability allowing users to distinguish between identifiability problems arising from the underlying state-space system and problems caused by its output. SPR experiments with antibody samples taken from sensitised kidney transplant patients were initially processed with the XPR Proteon Manager software, which measured affinities as high as 3:7 _ 1