Quantifying Protein–Protein Interactions by Molecular Counting with Mass Photometry

Abstract Interactions between biomolecules control the processes of life in health and their malfunction in disease, making their characterization and quantification essential. Immobilization‐ and label‐free analytical techniques are desirable because of their simplicity and minimal invasiveness, but they struggle with quantifying tight interactions. Here, we show that mass photometry can accurately count, distinguish by molecular mass, and thereby reveal the relative abundances of different unlabelled biomolecules and their complexes in mixtures at the single‐molecule level. These measurements determine binding affinities over four orders of magnitude at equilibrium for both simple and complex stoichiometries within minutes, as well as the associated kinetics. These results introduce mass photometry as a rapid, simple and label‐free method for studying sub‐micromolar binding affinities, with potential for extension towards a universal approach for characterizing complex biomolecular interactions.

Understanding how biomolecules interact with each other is central to the life sciences. The complexity thereof ranges from specific binary interactions, such as between antibodies and antigens [1][2][3] , to the formation of complex macromolecular machines [4,5] . Conversely, undesired interactions are often associated with disease, such as the formation of protein aggregates in neurodegenerative disease [6] , or the engagement of a virus with its target cell [7,8] . The highspecificity and critical role of these interactions make them an ideal target for intervention, either in promoting a certain response by presenting an alternative binding partner, or preventing (dis)assembly [9][10][11] . This diversity comes with a broad range of binding strengths and dynamics, measured in terms of thermodynamic and kinetic quantities such as equilibrium constants (e.g. for dissociation, K d ), free energies and rate constants (k off and k on ).
In broad terms, existing biophysical methods can be categorised into size-based approaches performing quantification and separation by size or diffusion coefficient, physical interaction with functionalised surfaces, direct mass measurement, enthalpy changes or light scattering [12][13][14][15][16][17] . These ensemble-based methods are complemented by fluorescence-based approaches [18] capable of operating at the single molecule level, providing additional information on sample heterogeneity and dynamics [19,20] . All of the above methods operate in the context of various practical shortcomings such as non-native environments, artefacts caused by protein immobilization and labelling, lack of sensitivity at low concentrations or lack of resolution [21][22][23] . Biological systems can pose additional challenges from particularly fast or slow kinetics to complexities arising from multiple co-existing species. Label-free methods struggle particularly for strong binding affinities (K d <µM), which are often encountered for interactions of particular relevance for biopharmaceuticals in the context of antibody-based drugs [24] .
We have recently developed mass photometry (MP), originally introduced as interferometric scattering mass spectrometry (iSCAMS), as a means for detecting and measuring the mass of single proteins and the complexes they form in solution. MP detects single biomolecules by their light scattering as they bind non-specifically to a microscope cover glass surface. Each binding event leads to a change in refractive index at the glass/water interface, which effectively alters the local reflectivity and can be detected with high accuracy by taking advantage of optimized interference between scattered and reflected light (Figure 1a) [25] . The magnitude of the reflectivity change can be converted into a molecular mass, for polypeptides with ~2% mass accuracy and up to 20 kDa mass resolution by calibration with biomolecules of known mass [26] . Both the original [26] , and subsequent studies have proposed methods to extract binding affinities from MP distributions of biomolecular mixtures [27] , and shown that the obtained affinities agree broadly with alternative approaches [26][27][28] . The degree to which these MP distributions are indeed quantitative, and how they can be used to efficiently extract not only binding affinities but also kinetics, however, remain unexplored.
Label-free single molecule detection in principle provides the purest and most direct measurement of sample concentration by counting individual molecules. To explore this capability in the context of biomolecules, we chose monomers and dimers of the HIV-1 neutralizing antibody 2G12 (Supplementary Figures 1-3), which produced mass distributions with the expected major bands at 147 kDa and 291 kDa (Figure 1b). Repeating these experiments for monomer/dimer ratios ranging from 0.15 to 8.1 (Figure 1c) revealed close agreement with UV-VIS-based characterisation within the experimental error (4.6% RMS), except for noticeable deviations (~20%) for the lowest ratios (Figure 1d). We found that such deviations could almost exclusively be attributed to sample preparation, such as an additional dilution step for the data shown (Supplementary Figure 4

& 5).
Equipped with these benchmarking results, we set out to investigate the suitability of MP to characterise interactions of varying affinities, using the immunoglobulin G (IgG) monoclonal antibody trastuzumab (Herceptin) binding to soluble domains of IgG Fc receptors or ErbB2 (HER2) antigens. Trastuzumab, herein referred to as IgG, and FcRIa by themselves revealed monodisperse distributions at 154 ± 1 kDa and 50 ± 1 kDa, respectively (  [29] resulting in a 1:1 mixture of FcRIa and deglycosyated IgG exhibiting considerably less bound antibody (~50%) (Figure 2b), corresponding to an apparent K d = 1.0 ± 0.1 nM (Supplementary Figure 9).
This simple single-shot approach presented so far, however, necessarily neglects the importance of kinetics and equilibration conditions. To address this, we probed FcRIa binding to deglycosylated IgG at a 1:1 ratio and 5, 1 and 0.3 nM final protein concentrations ( Figure   2c, Supplementary Figure 10). At concentrations above the K d we found mostly bound complexes, with free species dominating below the K d , but all measurements providing similar binding affinities (K d =1.0 ± 0.1, 0.6 ± 0.1 and 0.7 ± 0.3 nM), suggesting that they were performed at or close to equilibrium (Supplementary Figure 11). These binding affinities were confirmed after equilibration time screening (Supplementary Figures 12 & 13).
For quantification of the expected tighter interaction between FcRIa and IgG, the screening at a range of concentrations was essential to ensure the observed mass distributions were representative of the interaction to be quantified (Supplementary Figures 14-16). As an additional example, for the HER2-IgG interaction, a simple single-shot experiment at nM concentration would have led to a K d,1 = 1.4 ± 0.1 nM and K d,2 = 4.8 ± 0.3 nM (Supplementary Figure 17). By simply recording distributions at a few different concentrations, however, we could reveal a linear dependence of our K d values on concentration, indicating a very tight K d < 70 pM, and/or slow interactions with off-rates on the order of hours. Therefore, performing a few measurements at a range of concentrations is crucial to prevent misinterpreting data derived from a single-shot K d approach for very strong interactions. Irrespective, our approach provides a rapid and clear distinction between interactions with vastly different binding affinities, which only need to be refined if highly accurate measurements are required.
The importance of (dis)association rates in addition to thermodynamic quantitites raises the question to which degree we can use MP to directly visualise and quantify interaction kinetics.
As MP measurements currently take place in the <100 nM concentration range, we should be able to access disassociation kinetics by simply diluting to total protein concentrations around the estimated K d (approx. 1:1 ratio bound:unbound species for a 1:1 interaction), and monitoring the bound:unbound ratio throughout (Figure 2f, Supplementary Figure 18a). The observed exponential decay of a complex upon rapid dilution below the K d reveals the desired kinetic information, while the plateau yields the K d , ultimately enabling us to also determine k off and k on . For FcRIa binding to deglycosylated IgG, this approach yielded K d = 1.1 ± 0.2 nM in good agreement with our single shot measurements (Figure 2c), k on = 6.0 ± 1.7 × 10 6 M -1 s -1 , and k off = 6.8 ± 1.6 × 10 -3 s -1 . The corresponding experiment with glycosylated IgG-FcRIa yielded K d = 26 ± 22 pM with an off-rate one order of magnitude slower (5.2 ± 2.5 × 10 -4 s -1 ) than for deglycosylated IgG but an almost identical on-rate (1. analogous fashion, although we found them more susceptible to protein loss due to nonspecific adsorption (Supplementary Figures 22-24). Overall, our results were in good agreement with SPR measurements (Figures 2e & 2f), subject to on-rate differences expected between a matrix and surface-immobilization based approach compared to ours, where all interactions take place in free solution (Supplementary Figures 25).
A key advantage of MP over ensemble-based approaches is our ability to easily distinguish between different species contributing to a multicomponent system, as given by the IgG:FcRn interaction involving as many as five different interacting species. FcRn regulates serum IgG half-life and transcytosis to the fetus via a pH gradient in endosomes, yet the interplay between self-assembly and IgG binding is disputed [30,31]  SPR results for similar systems reporting an ensemble K d =760 ± 60 nM for all interactions [31] .
At pH = 6 and 7, our current sensitivity only allowed for an estimate of the binding affinities to be >200 nM (Figure 3b, Supplementary Figures 33 and 34). These results highlight pHdependent FcRn dynamics and IgG engagement, and reveals cooperativity where the second receptor binds IgG tighter than the first and with a weaker pH sensitivity.
Taken together, we have demonstrated that molecular counting with MP is sensitive, quantitative and accurate in determining the relative abundances of different biomolecules and their complexes in solution. When implemented in the vicinity of the binding affinity, a single measurement lasting typically 30 s, or 240 s for continuous flow injection, yields accurate binding affinities spanning four orders of magnitude from 30 pM to 200 nM, while enabling kinetic probing with a time-resolution on the order of 30 s in the range of minutes to hours. As a result, MP affords real-time assessment of (dis)assembly completely label-free and entirely independent of immobilization, minimising any possible perturbations, as well as being intrinsically sensitive to binding stoichiometries and oligomerization. The current limitation to sub-µM affinities and concentration range can be addressed in the future by a combination of surface passivation approaches [32] , as well as improvements to hardware and software, with which we expect to reach the µM range in the near future. This will enable measurements up to 100 µM affinities, making MP a powerful approach for characterising biomolecular interactions without labels and single-molecule sensitivity in a minimally perturbative fashion.
Furthermore, the applicability of MP to both nucleic acids [33] and large multimolecular machines provides scope for MP becoming a universal tool for studying biomolecular interactions and dynamics in a rapid, label-free and yet single molecule sensitive fashion.

Materials & Methods
We first characterised all compounds separately by MP to assess their oligomeric composition (Supplementary Figure 10) Figure 17). Provided the K d screening was successful we proceeded with the kinetic studies for which we diluted the sample to a concentration around the estimated K d . After dilution/mixing we followed dissociation/association of the biomolecular complex by acquiring individual MP measurements at different time points. From these experiments, we obtained K d values and on-and off-rates. With the current dynamic range we can inject concentrations from 100 pM to 50 nM, and thus determine quantitate binding affinities ranging from 10 pM to 300 nM and measure kinetics ranging from a few minutes to several hours.
The 2G12 antibody was expressed and purified as described previously [34] . Briefly, Plasmids encoding 2G12 antibody heavy and light chains were transiently expressed in HEK 293F at a cell density of 1 × 10 6 cells/mL with a 1:2 construct ratio (heavy to light chain). to obtain concentrations between 0.2 to 1 absorbance at 280 nm (low μM range). Pipetting precision was checked with a microbalance (Mettler Toledo, AT261).

Relative abundance measurements:
For the experiments determining the accuracy of determining relative abundances (Figure 1a-d), we used the two SEC-fractions of the 2G12 antibody purification (Supplementary Figure 1), containing either the pure monomer or the intermolecular domain exchanged dimer version of the monomer [35] . Characterizion of the monomer fraction with MP confirmed the absence of dimerization and analogously the dimer fraction revealed absence of dissociation into monomer. Different ratios of the two noninteracting species (monomer and dimer) were mixed at μM concentration and diluted in PBS to pM-nM concentrations prior to measurement ( Table 1) Table 2 for exact concentrations). The μM mixtures were diluted in PBS to pM-nM concentrations and measured at specific incubation times ( Table 2)  Microscope coverslip cleaning and assembly was performed as described previously [26] . The experimental mass photometry setup has been described elsewhere [25,26] . Briefly, a 525 nm laser diode was used for illumination with the following instrument parameters: acquisition camera frame rate = 955 Hz, pixel binning = 4x4, 5-fold time-averaging. Data was acquired for 30 or 240 s, depending on the experiment. Particle detection and quantification was processed as described by Young et al. using custom software written in Python [26] . For each particle a time stamp, position and contrast value was obtained.
Quality Control for Quantitative Measurements: During acquisition each video was examined visually and excluded when one of the criteria listed in Table 3 was met. During data analysis we applied an xy-distance constraint filter to all confirmed counts, excluding particles which were recorded at the same xy-position in the field-of-view. This helped to exclude "blinkers" (i.e. fast binding and unbinding events at the same position) and significantly lowered the baseline/noise. For gasket experiments, we plotted the counts as a detection rate (−∆counts/∆t) of the measured species X vs. time. The resulting decay curve was exected to follow a single exponential decay, which indicates an error-free experiment. We experienced deviations from a smooth decay when one or several of the criteria in Table 3 were given.

Data Analysis
Quantification of species-specific counts: Contrast values of observed counts were converted into molecular weight via a mass calibration (Supplementary Figure 3), here with the 2G12 WT antibody monomer and dimer peaks. In the resulting molecular weight (MW) vs. counts histogram each species was identified as a resolved peak and counts were obtained from Gaussian fitting to these peaks. Molecular weights near the MP detection limit (ca. 40 kDa) were not quantified to ensure differentiation from background noise and were generally not treated as quantitative with respect to counts for larger species (Supplementary Figure 12).
The measured counts were then converted into molar concentrations following the protocol  (Figure 2e & 2f). In the future, we could combine the information from association and dissociation data and perform the fitting iteratively/simultaneously, from which k off , k on and K d can be obtained without waiting for equilibriation. This approach will extend our applicability to slow reactions by circumventing equilibration times of hours or even days (Supplementary Figure 19) and with this also reduce sample loss due to non-specific adsorption to sample tubes over time (Supplementary  for 900 s. After each run, the biosensor chip was regenerated using 10 mM glycine, pH 2.5, which breaks the antibody-FcγR interaction. The specific binding response to antibody was obtained by subtracting the response given by analytes to an uncoupled surface and a blank run of buffer only. The kinetic sensorgrams were fitted to a global 1:1 interaction model to allow calculation of k on , k off , and K d using BIAevaluation software 2.0.3 (GE Healthcare).

Native Mass Spectrometry
Proteins were buffer exchanged into 1 M aqueous ammonium acetate (Sigma-Aldrich) using P6 Biospin columns (Bio-Rad) for the first two exchanges, followed by two exchanges using Amicon Ultra centrifugal filters (0.5 ml, 30 kDa MWCO) and in a last buffer exchange to 200 mM aqueous ammonium acetate using Amicon Ultra centrifugal filters. All protein solutions were analyzed at concentrations between 5 and 10 µM. Experiments were carried out on a prototype Thermo Scientific Q Exactive Hybrid Quadrupole Orbitrap Mass Spectrometer. Data