Parameter estimation and identifiability analysis for a bivalent analyte model of monoclonal antibody-antigen binding

Surface plasmon resonance (SPR) is an extensively used technique to characterize antigen-antibody interactions. Affinity measurements by SPR typically involve testing the binding of antigen in solution to monoclonal antibodies (mAbs) immobilized on a chip and fitting the kinetics data using 1:1 Langmuir binding model to derive rate constants. However, when it is necessary to immobilize antigens instead of the mAbs, a bivalent analyte (1:2) binding model is required for kinetics analysis. This model is lacking in data analysis packages associated with high throughput SPR instruments and the packages containing this model do not explore multiple local minima and parameter identifiability issues that are common in non-linear optimization. Therefore, we developed a method to use a system of ordinary differential equations for analyzing 1:2 binding kinetics data. Salient features of this method include a grid search on parameter initialization and a profile likelihood approach to determine parameter identifiability. Using this method we found a non-identifiable parameter in data set collected under the standard experimental design. A simulation-guided improved experimental design led to reliable estimation of all rate constants. The method and approach developed here for analyzing 1:2 binding kinetics data will be valuable for expeditious therapeutic antibody discovery research.