Abstract
This paper analyzes the equilibria between immunoglobulins (R 2), homo-bifunctional ligands (L 2), monovalent ligands (I), and their complexes. We present a mathematical model that can be used to estimate the concentration of each species present in a mixture of R 2, L 2, and I, given the initial conditions defining the total concentration of R 2, L 2, I, and four dissociation constants (\( K_{\rm{d}}^{\rm{inter}} \),\( K_{\rm{d}}^{\rm{intra}} \),\( K_{\rm{d}}^{\rm{mono}} \), and α). This model is based on fewer assumptions than previous models and can be used to describe exactly a broad range of experimental conditions. A series of curves illustrates the dependence of the equilibria upon the total concentrations of receptors and ligands, and the dissociation constants. We provide a set of guidelines for the design and analysis of experiments with a focus on estimating the binding constants from experimental binding isotherms. Two analytical equations relate the conditions for maximum aggregation in this system to the binding constants. This model is a tool to quantify the binding of immunoglobulins to antigens and a guide to understanding and predicting the experimental data of assays and techniques that employ immunoglobulins.
The fraction of immunoglobulin-bivalent ligand complexes that contain two or more immunoglobulins (\( {F_{{\tilde{1}}}} \)) depends on the total concentration of immunoglobulins. A series of curves illustrates the dependence of the equilibria upon the total concentrations of immunoglobulins, bivalent ligands, monovalent ligands, and the dissociation constants that describe the system
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Acknowledgments
R. Perez-Castillejos acknowledges the support from New Jersey Institute of Technology through starting faculty funds.
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Mack, E.T., Cummings, L. & Perez-Castillejos, R. Mathematical model for determining the binding constants between immunoglobulins, bivalent ligands, and monovalent ligands. Anal Bioanal Chem 399, 1641–1652 (2011). https://doi.org/10.1007/s00216-010-4477-y
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DOI: https://doi.org/10.1007/s00216-010-4477-y