Miscalculating Equilibrium Constants for Multivalent Protein Complexes: Site-Binding Concentration or Protein Molecular Concentration?

Because the authors continue to note instances in the scientific literature of failure to use the correct receptor binding site concentration for determining binding constants, herein we discuss the fundamental concepts that need to be considered to determine correct binding constants or conversely calculate accurate reactant concentrations with known equilibrium constants. We also show the derivation and analytical solutions of the cubic and quartic equations that give the exact free ligand concentration in bivalent and trivalent receptor systems at equilibrium as a function of the macroscopic equilibrium dissociation constants and the total concentrations of ligand and multivalent protein. These equations and solutions strongly reemphasize the critical dependency of deriving the correct concentrations of bound or free ligand and multivalent protein on the choice of the correct concentration basis for the multivalent protein, which is in turn dependent upon the type of equilibrium constant used.

Biacore surface matrix effects on the binding kinetics and affinity of an antigen/antibody complex.

To characterize a proprietary therapeutic monoclonal antibody (mAb) candidate, a rigorous biophysical study consisting of 53 Biacore and kinetic exclusion assay (KinExA) experiments was undertaken on the therapeutic mAb complexing with its target antigen. Unexpectedly, the observed binding kinetics depended on the chip used, suggesting that the negatively charged carboxyl groups on CM5, CM4, and C1 chips were adversely affecting the Biacore kinetic results. To study this hypothesis, Biacore solution-phase and KinExA equilibrium titrations, as well as KinExA kinetic measurements, were performed to establish accurate values for the affinity and kinetic rate constants of the binding reaction between antigen and mAb.

A strategic and systematic approach for the determination of biosensor regeneration conditions.

Determining the optimal conditions for surface regeneration is fundamental for performance of efficient and robust protein-protein interaction kinetic studies. We devised a systematic methodology comprised of an automated seven-cycle analyte and buffer injection Biacore scheme and data interpretation algorithm. The efficiency and utility is illustrated using an antigen/monoclonal antibody interaction that required ultimately six pulses of acid for regeneration.

Surrogate approaches in development of monoclonal antibodies.

When cross-reactivity of a lead antibody across species is limited, antibody development programs require the generation of surrogate molecules or surrogate animal models necessary for the conduct of preclinical pharmacology and safety studies. When surrogate approaches are employed, the complexities and challenges for translation of preclinical safety and efficacy results to the clinic are undoubtedly enhanced. Because there are no currently established criteria or regulatory guidance regarding the application of surrogate approaches, a science-based strategy for translation of preclinical information to the clinic is vital for effective development of the lead antibody.

Translational strategies for development of monoclonal antibodies from discovery to the clinic.

Successful strategies for the development of monoclonal antibodies require integration of knowledge with respect to target antigen properties, antibody design criteria such as affinity, isotype selection, Fc domain engineering, PK/PD properties and antibody cross-reactivity across species from the early stages of antibody development. Biophysical measurements are one of the critical components necessary for the design of effective translational strategies for lead selection and evaluation of relevant animal species for preclinical safety and efficacy studies. Incorporation of effective translational strategies from the early stages of the antibody development process is a necessity; when considered it not only reduces development time and cost, but also fosters implementation of rational decision-making throughout all phases of antibody development.

A global benchmark study using affinity-based biosensors.

To explore the variability in biosensor studies, 150 participants from 20 countries were given the same protein samples and asked to determine kinetic rate constants for the interaction. We chose a protein system that was amenable to analysis using different biosensor platforms as well as by users of different expertise levels. The two proteins (a 50-kDa Fab and a 60-kDa glutathione S-transferase [GST] antigen) form a relatively high-affinity complex, so participants needed to optimize several experimental parameters, including ligand immobilization and regeneration conditions as well as analyte concentrations and injection/dissociation times.

Detection of high- and low-affinity antibodies against a human monoclonal antibody using various technology platforms.

The effect of monoclonal antibody (mAb) affinity on the detection limit of enzyme-linked immunosorbent assay (ELISA), surface plasmon resonance (SPR), and electrochemiluminescence (ECL) methods was evaluated using a panel of murine mAbs with affinities ranging from 0.057 to 340 nM. M1 and M7 are anti-idiotypic mAbs against a human mAb, ABX10, with dissociation equilibrium constant (KD) values of 0.

Application of analytical detection concepts to immunogenicity testing.

The cut point and detection limit of any immunogenicity assay are two of the most important quantities that define the adequacy of an assay for detecting anti-drug antibodies against therapeutic proteins. To date in the immunogenicity testing literature, only the type I (alpha) error (i.e.

A rigorous multiple independent binding site model for determining cell-based equilibrium dissociation constants.

A new 4-parameter nonlinear equation based on the standard multiple independent binding site model (MIBS) is presented for fitting cell-based ligand titration data in order to calculate the ligand/cell receptor equilibrium dissociation constant and the number of receptors/cell. The most commonly used linear (Scatchard Plot) or nonlinear 2-parameter model (a single binding site model found in commercial programs like Prism(R)) used for analysis of ligand/receptor binding data assumes only the K(D) influences the shape of the titration curve. We demonstrate using simulated data sets that, depending upon the cell surface receptor expression level, the number of cells titrated, and the magnitude of the K(D) being measured, this assumption of always being under K(D)-controlled conditions can be erroneous and can lead to unreliable estimates for the binding parameters.

Kinetic analysis of a high-affinity antibody/antigen interaction performed by multiple Biacore users.

To explore the reliability of Biacore-based assays, 22 study participants measured the binding of prostate-specific antigen (PSA) to a monoclonal antibody (mAb). Each participant was provided with the same reagents and a detailed experimental protocol. The mAb was immobilized on the sensor chip at three different densities and a two-step assay was used to determine the kinetic and affinity parameters of the PSA/mAb complex.

Screening antibody-antigen interactions in parallel using Biacore A100.

Label-free optical biosensor technology has become a standard tool for characterizing monoclonal antibodies for therapeutic and diagnostic applications. The availability of high-quality binding data at an early stage greatly improves the ability to select antibodies for further development. This article shows how Biacore A100, a protein interaction array system, is capable of providing high-quality data with increased throughput.

Characterizing high-affinity antigen/antibody complexes by kinetic- and equilibrium-based methods.

Two biophysical methods, Biacore and KinExA, were used to kinetically and thermodynamically characterize high-affinity antigen/antibody complexes. Three to five independent experiments were performed on each platform with three different antigen/antibody complexes possessing nanomolar to picomolar equilibrium dissociation constants. By monitoring the dissociation phase on Biacore for 4 h, we were able to measure dissociation rate constants (kd) on the order of 1 x 10(-5)s(-1).

Kinetic screening of antibodies from crude hybridoma samples using Biacore.

Experimental and data analysis protocols were developed to screen antibodies from hybridoma culture supernatants using Biacore surface plasmon resonance biosensor platforms. The screening methods involved capturing antibodies from crude supernatants using Fc-specific antibody surfaces and monitoring antigen binding at a single concentration. After normalizing the antigen responses for the amount of antibody present, a simple interaction model was fit to all of the binding responses simultaneously.

Protective interactive noncondensing (PINC) polymers for enhanced plasmid distribution and expression in rat skeletal muscle.

We have developed protective interactive noncondensing (PINC) polymers, such as poly(N-vinyl pyrrolidone) (PVP) and poly(vinyl alcohol) (PVA), to protect plasmids from extracellular nuclease degradation while allowing the flexible complex to diffuse throughout the muscle tissue. Molecular modeling, zeta potential modulation, and ethidium bromide intercalation studies were performed to assess the mechanism of interaction between PVP and plasmid. The effect of salt concentration, pH, and polymer-plasmid ratios were investigated.

Lanthanide ion luminescence as a probe of DNA structure. 2. Non- guanine-containing oligomers and nucleotides.

Oligo(dC)8, oligo(dA)8, and oligo(dT)8 as well as d-CMP, d-AMP, and d-TMP, when complexed to Eu(3+), possess two classes of Eu(3+) binding environment. The binding environments consist of two classes, tight sites which coordinate two H2O molecules, and weaker sites which coordinate six or seven, analogous to the previously studied guanine-containing molecules. It is inferred that the tight class of Eu(3+) ion site observed with these oligomers and nucleotides corresponds to dimeric or polymeric structures.

Lanthanide ion luminescence as a probe of DNA structure. 1. Guanine-containing oligomers and nucleotides.

Laser-induced Eu(3+) luminescence spectroscopy is used to probe the interaction of Eu(3+) ion with guanine-containing nucleotides and single-stranded oligomers. By using time-resolved and non-time-resolved Eu(3+) luminescence techniques, two classes of Eu(3+) binding site are observed in oligo(dG)10, oligo(dG)8, oligo(dG)6, oligo(dG)4, and d-GMP. One class of site binds Eu(3+) ions more strongly than the other.