Determining equilibrium affinity and stoichiometry in solution via light scattering

Sophia Kenrick and Daniel Some look at efficient automation of composition-gradient multi-angle light scattering measurements for quantifying protein-protein interactions.

Understanding macromolecular interactions is essential for a wide range of applications - from uncovering the mechanisms of intracellular pathways to the development of biopharmaceuticals.

Proteins, nucleic acids and other biomolecules assemble, change conformation and form intricate networks with a variety of ligands to provide functions necessary for life.

Although numerous techniques exist for probing a single aspect of a complex interaction landscape, such as surface plasmon resonance (SPR), ELISA and functional assays, a label-free technique for observing a full range of associations is most desirable for quantifying physiologically relevant reactions.

Composition-gradient multi-angle static light scattering (CG-MALS) is a powerful, label-free technique for quantifying macromolecular interactions, without the influence of fluorescent or radioactive tags or surface immobilization.

CG-MALS not only provides absolute characterisation of affinity and stoichiometry but also enables elucidating the effects of solvent composition, pH and small molecule cofactors on the interaction of interest.

At the crux of this technique is the power of multi-angle static light scattering to measure directly the apparent weight-average molar mass (Mw,app) of macromolecules in solution.

Through appropriate modeling of the relationship between Mw,app and composition, CG-MALS quantifies multiple interactions existing in an equilibrium solution, not simply at a single binding site or functional domain.

This tutorial describes the measurement of an equilibrium antibody-antigen association by CG-MALS, automated using the Wyatt Calypso system. To perform this experiment, stock solutions of each protein - human thrombin and a monoclonal anti-thrombin antibody - are loaded onto the Calypso hardware along with a reservoir of buffer.

The system automatically prepares and injects into a MALS detector a series of compositions of a protein solution. After each injection, the flow stops to permit the reaction to reach equilibrium. The Calypso software analyzes MALS and concentration data to compute the Mw,app for each step in the gradient and then quantifies the equilibrium association constant and stoichiometry of all complexes formed in solution.

The Calypso is compatible with Wyatt DAWN HELEOS and miniDAWN TREOS multi-angle light scattering detectors. The concentration of each binding partner can be measured using in-line UV/Vis absorption or a differential refractometer such as the Wyatt Optilab T-rEX.

Alternatively, the nominal concentrations based on calculated stock solution dilutions are automatically computed and saved with the data and can be used for analysis for experiments where no concentration detector is appropriate.

Experimental set-up

Human thrombin a (Thr) and mouse monoclonal anti-human thrombin antibody (Ab) were purchased from Haematologic Technologies Inc. All experiments were performed in phosphate buffered saline (PBS; 137 mM NaCl, 2.7 mM KCl, 8.1 mM Na2HPO4, 1.76 mM KH2PO4, 200ppm NaN3, pH 7.4). Prior to analysis, all protein solutions were filtered to 0.02µm by means of Anotop syringe filters (Whatman).

CG-MALS experiments were performed with a Calypso II composition gradient system (Wyatt Technology Corp) to prepare different compositions of protein and buffer and deliver to an online UV/Vis absorption detector (Waters Corp) and HELEOS MALS detector (Wyatt).

Anodisc filter membranes of 0.1-µm pore size were installed in the Calypso for sample and buffer filtration (Whatman). Thr and Ab were each diluted to stock concentrations of 20µg/mL in PBS, filtered to 0.02µm, and loaded on the Calypso II.

An automated Calypso method was run consisting of three distinct segments: two single component concentration gradients to quantify any self association and a dual-component 'crossover' composition gradient to assess the hetero-association behaviour (Fig.1). For each composition, 0.8mL of protein solution at the appropriate concentration was injected into the UV and MALS detectors. The flow was then stopped for 180s (single protein gradients) or 300s (crossover gradient) to allow the solution to come to equilibrium within the MALS flow cells. Data collection and analysis of equilibrium association constants were performed using Calypso software.

Results and discussion

The automated Calypso method measured twenty-two different protein compositions to probe the potential interactions present in a solution of thrombin (Thr) and a monoclonal anti-thrombin antibody (Ab). A single-species concentration gradient for each protein was used to determine whether Thr or Ab homo-oligomerised. This data, combined with light scattering and concentration measurements at 12 different ratios of Thr and Ab, is all that is needed to determine the affinity and stoichiometry of the Thr-Ab binding.

Under these conditions, no self-interactions are observed for Thr or Ab. The weight-average molar mass at each step in the self-association gradient for Ab corresponds to the expected monomer molecular weight. Likewise, Mw,app for Thr is calculated as 37kDa at all steps in the Thr self-association gradient.

Heterocomplex formation is evident in the crossover gradient light scattering profile. In the absence of a Thr-Ab interaction, this would consist of a simple linear 'staircase' of values (dashed purple plot, Fig. 2A). In fact, we observed an increase in scattering intensity indicating complex formation, reaching a maximum at the step where the Ab concentration becomes limiting (solid blue plot, Fig. 2A). The position of the light scattering peak corresponds to the Ab:Thr stoichiometry, and the height of the peak gives a measure of the affinity. Binding kinetics, though clearly visible in the data, are not utilised to evaluate equilibrium constants. Analysis of binding kinetics via CG-MALS will be addressed in a separate tutorial.

As expected, the light scattering data in Fig. 2 is best fit in the Calypso software by an association model which describes two equivalent thrombin binding sites per antibody molecule. As the ratio of Ab:Thr concentration changes, so also does the fraction of bound species present. At high Ab:Thr ratios, the (1 Ab): (1 Thr) complex is most abundant; as the thrombin concentration increases and antibody concentration decreases, the (1 Ab):(2 Thr) complex dominates (Fig.3). The equilibrium dissociation constant determined by CG-MALS, KD = 8nM, agrees well with the manufacturer's data of KD = 15nM, as measured by ELISA. Furthermore, both thrombin and the antibody exhibit no propensity for self-association, a finding that could not be evaluated by conventional ELISA or SPR.

Thus, CG-MALS as automated by the Calypso system provides direct observation of multiple interactions in solution. By measuring the weight-average molar mass of the ensemble of molecules in solution, the presence of both the (1 Ab): (1 Thr) and (1 Ab):(2 Thr) species can be tracked as a function of Ab and Thr concentration.

In addition, the monomeric state of both the antibody and antigen is confirmed. This simultaneous tracking of all affinities and stoichiometries present in solution makes CG-MALS unique among biophysical characterisation techniques and enables unambiguous quantification of macromolecular interactions.

Sophia Kenrick, Application Development Engineer, and Daniel Some, Principal Scientist, are with Wyatt Technology Corporation, Santa Barbara, CA, USA.

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