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

Kyle Nguyen; Kan Li; Kevin Flores; Georgia D Tomaras; S Moses Dennison; Janice M McCarthy

doi:10.1016/j.ab.2023.115263

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

Anal Biochem. 2023 Oct 15:679:115263. doi: 10.1016/j.ab.2023.115263. Epub 2023 Aug 6.

Authors

Kyle Nguyen¹, Kan Li², Kevin Flores³, Georgia D Tomaras⁴, S Moses Dennison², Janice M McCarthy⁵

Affiliations

¹ Biomathematics Graduate Program, North Carolina State University, Raleigh, 27607, NC, USA; Center for Research in Scientific Computation, North Carolina State University, Raleigh, 27607, NC, USA. Electronic address: kcnguye2@ncsu.edu.
² Center for Human Systems Immunology, Duke University, Durham, 27701, NC, USA; Department of Surgery, Duke University, Durham, 27710, NC, USA.
³ Center for Research in Scientific Computation, North Carolina State University, Raleigh, 27607, NC, USA; Department of Mathematics, North Carolina State University, Raleigh, 27607, NC, USA.
⁴ Center for Human Systems Immunology, Duke University, Durham, 27701, NC, USA; Department of Surgery, Duke University, Durham, 27710, NC, USA; Department of Integrative Immunobiology, Duke University, Durham, 27710, NC, USA; Department of Molecular Genetics and Microbiology, Duke University, Durham, 27710, NC, USA; Duke Human Vaccine Institute, Duke University, Durham, 27710, NC, USA.
⁵ Center for Human Systems Immunology, Duke University, Durham, 27701, NC, USA; Department of Biostatistics and Bioinformatics, Duke University, Durham, 27710, NC, USA.

Abstract

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.

Keywords: Binding kinetics; Bivalent analyte; Parameter identifiability; Surface plasmon resonance.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Antibodies, Monoclonal / chemistry
Antigen-Antibody Reactions*
Antigens*
Kinetics
Likelihood Functions
Surface Plasmon Resonance / methods

Substances

Antigens
Antibodies, Monoclonal