Parameter estimation and identifiability analysis for a bivalent analyte model of monoclonal antibody-antigen binding
Authors: Nguyen Kyle , Li Kan , Flores Kevin , Tomaras Georgia D. , Dennison S. Moses , McCarthy Janice M. 
Published: December 2022

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Discovery research for therapeutic antibodies and vaccine development requires an in-depth understanding of antibody-antigen interactions. Label-free techniques such as Surface Plasmon Resonance (SPR) enable the characterization of biomolecular interactions through kinetics measurements, typically by binding antigens in solution to monoclonal antibodies immobilized on a SPR chip. 1:1 Langmuir binding model is commonly used to fit the kinetics data and derive rate constants. However, in certain contexts it is necessary to immobilize the antigen to the chip and flow the antibodies in solution. One such scenario is the screening of monoclonal antibodies (mAbs) for breadth against a range of antigens, where a bivalent analyte binding model is required to adequately describe the kinetics data unless antigen immobilizaion density is optimized to eliminate avidity effects. A bivalent analyte model is offered in several existing software packages intended for standard throughput SPR instruments, but lacking for high throughput SPR instruments. Existing methods also do not explore multiple local minima and parameter identifiability, issues common in non-linear optimization. Here, we have developed a method for analyzing bivalent analyte binding kinetics directly applicable to high throughput SPR data collected in a non-regenerative fashion, and have included a grid search on initial parameter values and a profile likelihood method to determine parameter identifiability. We fit the data of a broadly neutralizing HIV-1 mAb binding to HIV-1 envelope glycoprotein gp120 to a system of ordinary differential equations modeling bivalent binding. Our identifiability analysis discovered a non-identifiable parameter when data is collected under the standard experimental design for monitoring the association and dissociation phases. We used simulations to determine an improved experimental design, which when executed, resulted in the reliable estimation of all rate constants. These methods will be valuable tools in analyzing the binding of mAbs to an array of antigens to expedite therapeutic antibody discovery research.

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Author summary

While commercial software programs for the analysis of bivalent analyte binding kinetics are available for low-throughput instruments, they cannot be easily applied to data generated by high-throughput instruments, particularly when the chip surface is not regenerated between titration cycles. Further, existing software does not address common issues in fitting non-linear systems of ordinary differential equations (ODEs) such as optimizations getting trapped in local minima or parameters that are not identifiable. In this work, we introduce a pipeline for analysis of bivalent analyte binding kinetics that 1) allows for the use of high-throughput, non-regenerative experimental designs, 2) optimizes using several sets of initial parameter values to ensure that the algorithm is able to reach the lowest minimum error and 3) applies a profile likelihood method to explore parameter identifiability. In our experimental application of the method, we found that one of the kinetics parameters (kd2) cannot be reliably estimated with the standard length of the dissociation phase. Using simulation and identifiability analysis we determined the optimal length of dissociation so that the parameter can be reliably estimated, saving time and reagents. These methodologies offer robust determination of the kinetics parameters for high-throughput bivalent analyte SPR experiments.