Methods for assessing molecular self-association

Abstract

Methods of assessing molecular or particulate association (e.g., self-association) in a liquid are disclosed. Also disclosed are methods of determining and prediction colloidal stability of polymers and biological molecules such as proteins.

Description

[0001] METHODS FOR ASSESSING MOLECULAR SELF-ASSOCIATION

[0002] This application claims priority to U.S. provisional patent application no. 63 / 568,279 filed March 21, 2024, the entirety of which is incorporated herein by reference.

[0003] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0004] This invention was made with government support under R21AI 178218 awarded by the National Institutes of Health. The government has certain rights in the invention.

[0005] BACKGROUND

[0006] Self-association and non-specific molecular interactions are among the attributes that can distinguish between approved protein therapeutics and those that are not. Starr, C. G. et al., “Ultradilute Measurements of Self-Association for the Identification of Antibodies with Favorable High-Concentration Solution Properties” Mol Pharm 18, 2744-2753 (2021). High self-association and poor solution behavior can lead to complications in the development of monoclonal antibodies (mAbs) for subcutaneous administration, where a high concentration of protein is typically required due to limited injection volume. High viscosity, opalescence, phase separation, and aggregation have been reported to be among the immediate problems faced by drug developers, while overall long-term stability is hard to achieve when proteins self-associate. See, e.g., id. ,- Sukumar, M. et al., “Opalescent Appearance of an IgGl Antibody at High Concentrations and its Relationship to Noncovalent Association” Pharm Res 21, 1087-1093 (2004); Anselmo, A. C. et al., “Non-invasive Delivery Strategies for Biologies” Nat Rev Drug Discov 18, 19-40 (2019); Lewus, R.A. et al., “A Comparative Study of Monoclonal Antibodies” 1. Phase Behavior and Protein-protein Interactions, Biotechnol Prog 31, 268-276 (2015). Therefore, methods are needed that identify variants of a molecule with favorable solution behavior during the discovery and early development process, before proceeding to clinical development. Jiskoot, W. et al., “Ongoing Challenges to Develop High Concentration Monoclonal Antibody -based Formulations for Subcutaneous Administration: Quo Vadis?” J Pharm Sci 111, 861-867 (2022).

[0007] Existing methods used to measure self-association are limited. Those currently used are mostly based on complex, indirect measurements that cannot be performed under pharmaceutically relevant conditions. Notably, Kingsbury and coworkers studied the diffusion interaction parameter (kD) for a set of 59 mAbs and showed that kD can predict the solution behavior of antibodies as represented by viscosity and opalescence at high concentration (150 mg / ml which is relevant for mAbs that are administered subcutaneously). Kingsbury, J.S., et al. “A single molecular descriptor to predict solution behavior of therapeutic antibodies” Sci Adv 2020:6. However, kD was only measured for molecules dissolved in a single buffer and a fixed pH in the absence of all the relevant excipients due to limitations of the method. In addition, kD measurements are extremely sensitive to presence of impurities, protein aggregates, variations protein size, and temperature, all of which limit the reliability of the method.

[0008] One analytical tool that appears to have not been explored in attempts to measure self-association is Quartz Crystal Microbalance (QCM) or its variant Quartz Crystal Microbalance with Dissipation monitoring (QCM-D). Both are established tools that can provide real-time information on the adsorption of molecule s / particles to solid surfaces, with sensitivities as low as few nanograms per square centimeter, by monitoring the change in the resonance frequency of an oscillating piezoelectric sensor. Adamczyk, Z. et al., “Applicability of QCM-D for Quantitative Measurements of Nano- and Microparticle Deposition Kinetics: Theoretical Modeling and Experiments” Anal Chem 92, 15087-15095 (2020). The amplitude of the oscillations is influenced by dissipative energy losses caused by the viscoelastic properties of the adsorbed molecules, which can be quantified by measuring the changes in frequency bandwidth or the magnitude of decay of the induced oscillations.

[0009] QCM and QCM-D are so-named because of the fact that quartz is a commonly used piezoelectric material. However, the methods may also be employed using other piezoelectric materials. See, e.g., Liu, Huicong, et al. “A Comprehensive Review on Piezoelectric Energy Harvesting Technology: Materials, Mechanisms, and Applications” Applied Physics Reviews, 5 (4):041306 (December 2018).

[0010] Over the past decade, the use of QCM-D has expanded to include the study of biomolecules and nanomaterials. For example, it has been used to detect molecular binding for predictive mutations for cancer therapy and for characterizing changes in the structure of immobilized bacterial outer membranes for the design of novel antibiotics. See, e.g., Srimasom, S. et al., “A Quartz Crystal Microbalance Method to Quantify the Size of Hyaluronan and Other Glycosaminoglycans on Surfaces” Sci Rep 12, 10980 (2022); Minsky, B. B. et al., “Controlled Immobilization Strategies to Probe Short Hyaluronan-Protein Interactions” Sci Rep 6, 21608 (2016); Van Lehn, R. C. et al., “Lipid Tail Protrusions Mediate the Insertion of Nanoparticles into Model Cell Membranes” Nat Commun 5, 4482 (2014); Gaj da- Walczak, A. et al., “New, Fast, and Cheap Prediction Tests for BRCA1 Gene Mutations Identification in Clinical Samples” Sci Rep 13, 7316 (2023); Hsia, C. Y, et al., “A Molecularly Complete Planar Bacterial Outer Membrane Platform” Sci Rep 6, 32715 (2016).

[0011] SUMMARY

[0012] This invention is directed, in part, to methods of using QCM or QCM-D to assess the association (e.g., self-association) of molecules or particulates in solution or in liquid mixtures.

[0013] One embodiment of the invention is a method of assessing molecular or particulate association, which method comprises: obtaining a first Afc for a first plurality of molecules or particles in a first mixture; and comparing the first Afc, or a value derived therefrom, with a second Afc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0014] Another embodiment is a method of predicting behavior (e.g., phase separation, opacity, viscosity) of a mixture (e.g., solution, emulsion), which method comprises: obtaining a first Afc for a first plurality of molecules or particles in a first mixture; and comparing the first Afc, or a value derived therefrom, with a second Afc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0015] Another embodiment is a method of assessing molecular or particulate association, which method comprises: obtaining a first ADc for a first plurality of molecules or particles in a first mixture; and comparing the first ADc, or a value derived therefrom, with a second ADc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0016] Another embodiment is method of predicting behavior of a mixture (e.g., solution, emulsion), which method comprises: obtaining a first ADc for a first plurality of molecules or particles in a first mixture; and comparing the first ADc, or a value derived therefrom, with a second ADc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0017] Another embodiment is a method of comparing a plurality of liquid mixtures, which comprises: obtaining a Afc and / or ADc value for each mixture, and; ranking or plotting the Afc and / or ADc values or values obtained therefrom.

[0018] Another embodiment is a method of predicting colloidal stability of molecules in a solution or liquid mixture having a first Afc, which method comprises comparing the first Afc, or a value derived therefrom, with a second Afc, or a value derived therefrom, which second Afc has been correlated with a diffusion interaction parameter, an osmotic second virial coefficient, or data obtained using nanoparticle spectroscopy.

[0019] BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Certain aspects of the invention are illustrated in the attached figures:

[0021] FIG. 1 provides a schematic representation of a hypothesis underlying the present invention, which depicts the adsorption of molecules / particles on a hydrophilic gold surface as detected by QCM-D. Several intermolecular forces may affect the loosely interacting layer formed on the top of the adsorbed layer: (i) hydrogen bonding, (ii) van der Waals’ interactions, (iii) steric repulsive forces, (iv) hydrophobic interactions, (v) repulsive charge-charge interactions, and (vi) attractive charge-charge interactions.

[0022] FIG. 2A shows frequency shifts due to the adsorption of bovine serum albumin (BSA) from three different formulations in 10 mM histidine, acetate, and phosphate buffers, with pHs of 6, 4.5, and 7.4, respectively.

[0023] FIG. 2B shows the number of sub-visible particles detected in formulations after storage using flow imaging microscopy. The bars show the average and range from two separate samples for different aggregate size ranges (larger than 1, 2, 5, and 10 pm).

[0024] FIG. 2C shows frequency shifts of the third resonance harmonic for loosely interacting layer of BSA prepared in different formulations with Aft = -59 Hz in 10 mM, pH 4.5 acetate buffer, Aft = -48.6 Hz in 10 mM, pH 6 histidine buffer, and Aft = -51.07 in 10 mM, pH 7.4 phosphate buffer. FIG. 3A shows a QCM-D profile depicting the changes in the third frequency overtones (f3) for a range of concentrations (10, 5, 2, and 1 mg / ml) for omalizumab.

[0025] FIG. 3B shows a QCM-D profile depicting the changes in the third frequency overtones (f3) for a range of concentrations (10, 5, 2, and 1 mg / ml) for tocilizumab.

[0026] FIG. 3C shows results of viscosity measurements for omalizumab and tocilizumab for a concentration range from 40-150 mg / ml. Solid lines show the fit and the dashed lines the 95% prediction. Note that viscosity does not change up to 10 mg / ml for any of the mAbs.

[0027] FIG. 3D shows results of opalescence measurements for different concentrations of omalizumab and tocilizumab.

[0028] FIGS. 4A-B provide tables depicting viscosity measurements obtained using a RheoSense mVROC. FIG. 4A provides measurements for omalizumab. FIG. 4B provides a table depicting the viscosity measurements for tocilizumab. The reported values for the viscosity were selected based on the data quality instructions from the instrument manufacturer, with strict adherence to the criteria of R2 slope > 0.98 and %fiill scale value falling between 5% and 95%.

[0029] FIG. 5A shows QCM-D frequency plots of the loosely interacting layer for eight mAbs spanning good and poor solution behavior.

[0030] FIG. 5B shows QCM-D dissipation plots of the loosely interacting layer for eight mAbs spanning good and poor solution behavior.

[0031] FIG. 6A provides a plot of diffusion coefficient versus concentration range (1-5 mg / mL) for BSA in 10 mM, pH 4.5 acetate buffer.

[0032] FIG. 6B provides a plot of diffusion coefficient versus concentration range (1-5 mg / mL) for BSA in 10 mM, pH 6 histidine buffer.

[0033] FIG. 6C provides a plot of diffusion coefficient versus concentration range (1-5 mg / mL) for BSA in 10 mM, pH 7.4 phosphate buffer.

[0034] FIG. 7A depicts the sensitivity of diffusion interaction parameter as measured using dynamic light scattering (kD-DLS) to changes in temperature and concentration. This plot shows the average diffusion coefficient vs. concentration for a temperature ranging from 20° to 26° C with a difference of 1°C.

[0035] FIG. 7B depicts the sensitivity of kD-DLS to changes in temperature and concentration. This plot shows the average diffusion coefficient vs. temperature for a concentration ranging from 1-5 mg / ml with a 0.5 mg / ml difference.

[0036] FIGS. 8A-D demonstrate the robustness of methods of the invention, measured by spiking samples with polystyrene beads and their comparison with control using both QCM-D and kD-DLS. FIG. 8A provides results from a control QCM-D experiment. FIG. 8B provides results from a control DLS experiment. FIG. 8C provides results from a spiked QCM-D experiment. FIG. 8D provides results from a spiked DLS experiment. As can be seen, the presence of particles (impurities) did not influence the QCM- D measurement of the self-association metric whereas the kD-DLS measurements were greatly affected. FIG. 9 shows frequency changes associated with the loosely interacting layer, Aft. versus the concentration for omalizumab and tocilizumab.

[0037] FIGS. 10A-B provide thickness plots obtained from Dfind Smartfit modeling in Q Sense Dfind software. FIG. 10A is a thickness plot for adsorption from a 10 mg mb'1solution of omalizumab. FIG. 1 OB is a thickness plot for adsorption from a 10 mg mb'1solution of tocilizumab.

[0038] FIG. 11 provides plots of the diffusion coefficient vs. concentration range (1-5 mg / ml) for eight mAbs, which depict regression line slopes and intercepts that were used to calculate diffusion interaction parameters.

[0039] FIG. 12 shows a co-relation of frequency change of the third resonance harmonic, Af with dissipation change at that frequency, AD;, for eight mAbs.

[0040] FIGS. 13A-D provide overtone frequency and dissipation plots obtained using 10 mg / mL1solutions of two antibodies. FIG. 13A provides frequency plots for the overtones for omalizumab. FIG. 13B provides frequency plots for the overtones for tocilizumab. FIG. 13C shows dissipation plots for the overtones for omalizumab. FIG. 13D provides dissipation plots for the overtones for tocilizumab.

[0041] FIG. 14 shows frequency changes associated with the loosely interacting layer, Af versus the diffusion interaction parameter kD-DLS for eight mAbs.

[0042] DETAILED DESCRIPTION

[0043] Atypical experiment using QCM or QCM-D consists of three main steps: (1) obtaining a baseline frequency (or an overtone or harmonic thereof) and dissipation signal (e.g. , using buffer or vehicle); (2) contacting the sensor with a solution / suspension of molecules / particles of interest in a vehicle (e.g., buffer) to allow for adsorption of the molecules / particles on the sensor surface until the surface is saturated; and (3) rinsing with the buffer / vehicle to remove unbound molecules / particles. See, e.g., FIG. 1. During step (2), the added mass of the sensor due to adsorption produces a negative frequency shift Af, while any potential softness of the adsorbed layer produces a positive dissipation change AD, until the surface is saturated. While the term “adsorbed layer” typically refers to the layer of molecules / particles that remains on the surface after rinse, the present invention is based on the recognition that QCM-D can detect loosely interacting molecules / particles associated with the adsorbed layer, which are rinsed away in step (3).

[0044] The QCM-D approach allows for probing frequency (f) and dissipation (D) values at multiple harmonics (n = 3, 5, . . .) of a resonant frequency in succession on the millisecond time scale. These different harmonics are typically represented by subscripts (e.g., ft. Ds) and their differences are represented in the same way (e.g., Afs, ADs). Data obtained using multiple harmonics permits modeling the experimental data in a way that can allow the extraction of meaningful parameters such as mass, thickness, density, viscosity, and storage modulus. Dixon, M.C., “Quartz Crystal Microbalance with Dissipation Monitoring: Enabling Real-Time Characterization of Biological Materials and Their Interactions” Biomol. Techniques 2008; 19: 151-158, 153. This invention is based, in part, on the discovery that the behavior of a layer of loosely interacting molecules / particles on a QCM or QCM-D sensor can provide unique and practical insights into the selfassociation of the molecules / particles, and that these analytical methods can be used to predict intermolecular or inter-particulate association (e.g., self-association) behavior in various applications in colloidal science and biotechnology. Association and self-association in this context may occur by weak, non-covalent forces such as van der Waals, electrostatic, hydrophobic, hydrogen bonding, and steric forces that can potentially contribute to the interaction of the molecules in this layer (FIG. 1), forces which also affect the colloidal stability of macromolecular and particulate systems.

[0045] In particular, this invention is based on the discovery that Afc can be correlated with the amount of molecular or particulate association (e.g., self-association) in a solution or liquid mixture. As shown in FIG. 1 and as used herein, the term Afc refers to the difference between Af\ and Afs, wherein Af\ is the change in oscillation frequency (or a harmonic or overtone thereof) compared to baseline (e.g, as determined by QCM) of a piezoelectric sensor saturated with molecules or particles and Afs is the change in oscillation frequency (or a harmonic or overtone thereof) compared to baseline of the sensor after having been washed with the vehicle (e.g. , buffer) that contained the molecules or particles of interest. Saturation of the sensor generally occurs when continued exposure of the sensor to the solution or mixture results in no further changes in oscillation frequency. Of course, because Af\ and Afs are both calculated by subtracting the sensor’s baseline oscillation frequency (or its harmonic or overtone), their difference (i.e., Afc) may be calculated by simply taking the difference between the frequency of the fully loaded (saturated) sensor (fA) and the washed sensor (fi ) . Referring to FIG. 1, Afc is the “Af loosely interacting layer”. Generally, the third harmonic or overtone of the sensor’s fundamental oscillation frequency, Afc is used for the measurements described herein.

[0046] This invention is also based on the discovery that ADc can be correlated with the amount of molecular or particulate association in a solution or liquid mixture. As used herein, the term ADc refers to the difference between ADA and ADB wherein ADA is the change in dissipation compared to baseline (e.g., as determined by QCM-D) of a sensor saturated with molecules or particles and ADB is the change in dissipation compared to baseline of the sensor after having been washed with the vehicle (e.g., buffer) that contained the molecules or particles of interest. Of course, because ADA and ADB are both calculated by subtracting the sensor’s baseline dissipation value, their difference (i.e., ADc) may be calculated by simply taking the difference between the dissipation of the fully loaded (saturated) sensor (DA) and the washed sensor (DB).

[0047] Thus, comparison of Afc and / or ADc values obtained for one protein (or values derived therefrom) with those obtained for another (or values derived therefrom) can be used as a means of assessing the proteins’ relative degrees of self-association, which in turn may be correlated to physical characteristics such as colloidal stability. The phrases “value derived therefrom” and “values derived therefrom” are used herein to encompass — but are not limited to — values mathematically derived from Afc and / or ADc measurements, such as their absolute values, their values after addition, subtraction, multiplication, or division to or by other numbers, and non-linear (e.g., quadratic, logarithmic) derivatives thereof.

[0048] One embodiment of the invention is a method of assessing molecular or particulate association (e.g., self-association), which method comprises: obtaining a first Afc for a first plurality of molecules or particles in a first mixture; and comparing the first Afc, or a value derived therefrom, with a second Afc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0049] This invention also encompasses a method of predicting behavior (e.g., phase separation, opacity, viscosity) of a solution, which method comprises: obtaining a first Afc for a first plurality of molecules or particles in a first mixture; and comparing the first Afc, or a value derived therefrom, with a second Afc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0050] In the various methods described herein, Afc may be determined by: contacting a mixture comprising a plurality of molecules or particles with a surface of a resonant material having a resonant frequency under conditions sufficient to provide a coated material comprising a first layer and a second layer of the plurality of molecules or particles, wherein the first layer is adsorbed on the surface and the second layer is loosely associated with the first layer; measuring a first resonant frequency of the coated material or a harmonic thereof; washing the coated material under conditions sufficient to remove the second layer and thereby provide a washed material; measuring a second resonant frequency of the washed material or a harmonic thereof; and calculating the difference between the first and second resonant frequencies or the harmonics thereof.

[0051] Another embodiment of the invention is a method of assessing molecular or particulate association (e.g., self-association), which method comprises: obtaining a first ADc for a first plurality of molecules or particles in a first mixture; and comparing the first ADc, or a value derived therefrom, with a second ADc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0052] Another embodiment of the invention is a method of predicting behavior of a solution, which method comprises: obtaining a first ADc for a first plurality of molecules or particles in a first mixture; and comparing the first ADc, or a value derived therefrom, with a second ADc obtained from a second plurality of molecules or particles in a second mixture, or a value derived therefrom.

[0053] In the various methods described herein, ADc may be determined by: contacting a mixture comprising a plurality of molecules or particles with a surface of a resonant material having a resonant frequency under conditions sufficient to provide a coated material comprising a first layer and a second layer of the plurality of molecules or particles, wherein the first layer is adsorbed on the surface and the second layer is loosely associated with the first layer; measuring a first dissipation value of the coated material at the resonance frequency or a harmonic thereof; washing the coated material under conditions sufficient to remove the second layer and thereby provide a washed material; measuring a second dissipation value of the washed material at the resonance frequency or a harmonic thereof; and calculating the difference between the first and second dissipation values. Dissipation is typically measured for a harmonic of the fundamental resonance frequency (e.g., fi. L. f7, f9, fn), in which case it may be referred to as AD3, AD5, and the like.

[0054] This invention also encompasses a method of comparing a plurality of liquid mixtures, which comprises: obtaining a fc and / or ADc value for each mixture, and; ranking or plotting the Afc and / or ADc values or values obtained therefrom. Generally, Afc and / or ADc may be obtained by: (a) contacting the mixture with the surface of a resonant material having a resonant frequency and a dissipation factor under conditions sufficient to provide a coated material comprising a first layer and a second layer of the polymers, wherein the first layer is adsorbed on the surface and the second layer is loosely associated with the first layer; (b) measuring a first resonant frequency or a harmonic thereof and / or a first dissipation factor of the coated material; (c) washing the coated material under conditions sufficient to remove the second layer and thereby provide a washed material; and (d) measuring a second resonant frequency or a harmonic thereof and / or second dissipation factor of the washed material; wherein Afc is the difference between the first and second resonant frequencies or their harmonics and ADc is the difference between the first and second dissipation factors.

[0055] Another embodiment of the invention encompasses a method of predicting colloidal stability of molecules in a solution or liquid mixture having a first Afc, which method comprises comparing the first Afc, or a value derived therefrom, with a second Afc, or a value derived therefrom, which second Afc has been correlated with a diffusion interaction parameter (kD-DLS), an osmotic second virial coefficient (B2), or data obtained using nanoparticle spectroscopy (e.g., AC-SINS, CS-SINS).

[0056] In particular embodiments of the invention, the molecules are polymers (e.g., synthetic or naturally occurring polymers such as DNA, RNA, proteins, or fragments or derivatives thereof). Particular proteins are antibodies or antibody fragments. In certain embodiments, the mixture is a suspension.

[0057] EXPERIMENTAL DETAILS

[0058] Materials. BSA (lyophilized powder, essentially globulin free >99%), L-histidine monohydrochloride monohydrate, and L-histidine were obtained from Sigma-Aldrich Co. (St. Louis, MO). Sodium acetate and acetic acid were obtained from Fisher bioreagents (Pittsburgh, PA), and both monobasic and dibasic potassium phosphate buffer components were purchased from EMD Millipore (Burlington, MA). All of the chemicals obtained were of reagent grade. Several mAbs, including tocilizumab, omalizumab, fremanezumab, dupilumab, cetuximab, trastuzumab, and evolocumab, were extracted from commercially available therapeutic products, and anrukinzumab was acquired from Creative Biolabs (Shirley, NY). Preparation of mAbs and BSA. The extraction and purification of mAbs from their commercialized product were performed by surfactant removal following the buffer exchange in 10 mM histidine buffer, pH 6.0. Surfactant was removed from the drug product formulations employing DetergentOUT™ Tween spin columns (G-Biosciences; St. Louis, MO), and buffer was exchanged using Vivaspin® ultrafiltration spin column with a 30 kDa molecular weight cutoff (MWCO) membrane (Sartorius, Stonehouse, U.K.). Solutions of mAbs at a concentration of 1-10 mg mL1were prepared after filtering the buffer exchanged samples using filters of pore size 0.2 pm with sterile PES syringe filter systems (Cytiva, Marlborough, MA).

[0059] For viscosity and opalescence measurements, the solutions of tocilizumab and omalizumab were concentrated using Sartorius centrifugal concentrators to concentrations of 150 mg mL and 80 mg mL1. respectively. The samples were then diluted to 20, 40, 60, 80, 100, and 120 mg nil for tocilizumab, and to concentrations of 20, 40, and 60 mg mL1for omalizumab. The concentrations were cross-checked by spectrophotometric measurements employing a NanoDrop™ 2000 (ThermoScientific, Waltham, MA).

[0060] BSA was dissolved in 10 mM histidine, acetate, and phosphate buffers, with pHs of 6, 4.5, and 7.4, respectively, to prepare a stock solution of 20 mg mL1and filter. The BSA solution with 10 mg mL1was diluted from the stock solution for the Flow Imaging Microscopy study. The concentration of BSA was checked by using a NanoDrop™ 2000 at 280 nm.

[0061] Quartz Crystal Microbalance with Dissipation. QCM-D measurements were performed using a Qsense™ Explorer (Biolin Scientific, Gothenburg, Sweden) and a single flow chamber with a peristaltic pump (Ismatec, Grevenbroich, Germany) at a flow rate of 10 or 150 «L min1. The temperature was maintained at 20 °C during the experiments by using the internal control system of QCM-D. Gold sensors (QSX 301) were obtained from Biolin Scientific and used to study protein adsorption. Before the experiments, the sensors were cleaned using UV / Os treatment, followed by a chemical treatment in which sensors were immersed in H2O / ammonia / hydrogen peroxide with a ratio of 5 : 1 : 1. The sensors were then rinsed with ultrapure water and cleaned again using UV / O3 treatment. The sensors were eventually washed with ultrapure water and dried under filtered air. The frequency shifts A and dissipation changes AD were measured at six overtones: i = 3, 5, 7, 9, 11, 13. The third overtone was the main frequency used herein, as other overtones gave qualitatively similar results.

[0062] QCM-D experiment consisted of a series of sequential steps of exposure and wash: (a) A reference baseline was established using the 10 mM histidine buffer, pH 6.0, unless specified otherwise. The baseline was considered stable when the values for Af, and AD did not drift more than 1 Hz and 0.2 x 10 ' per 10 min, respectively; (b) next, the protein solution was introduced into the flow cell and allowed to run to achieve maximum saturation until the frequency and dissipation values reached a steady state; (c) then, the surface was rinsed with baseline buffer until a stable plateau was reached to remove any loosely bound protein; (d) finally, the fluid path was primed with Milli-Q® water for 30 minutes to clean the system, followed by extensive flushing with sodium dodecyl sulfate (SDS) solution for the next 30 minutes. To finish cleaning the fluid path, it was rinsed again with water for 25 minutes and dried with dust-free air. The A of the loosely interacting layer was calculated by subtracting the Af of the total adsorbed protein layer at the steady state obtained in step (b) and A / of the irreversibly adsorbed layer obtained from the rinsing step (c). In order to obtain information about the thickness and mechanical properties of the adsorbed layer, the data from all overtones were modeled using the Smart Fit function of the Dfind software.

[0063] For the adsorption of BSA in different formulations, QCMD was conducted in a single and separate experiment; a concentration of 20.0 mg mL1of BSA was used and allowed to flow in different formulations, namely, acetate, histidine, and phosphate buffers with pHs of 4.5, 6.0, and 7.4, respectively. The flow rate used for this experiment was 150 pL min1. The experiment was initiated with baseline stabilization in a 10 mM acetate buffer at pH 4.5. The adsorption of BSA followed this in the same acetate buffer and subsequently in 10 mM histidine buffer at pH 6.0. Finally, there was another adsorption in a 10 mM phosphate buffer at pH 7.4 in the same experimental run. To conduct QCM-D experiments employing mAb samples, the flow rate of 10 pL min1was utilized, which allows for reaching the saturation using smaller amounts of sample. In an experiment in which omalizumab and tocilizumab were used as representatives of poorly and well-behaved mAb, respectively, the concentration range of 1, 2, 5, and 10 mg ml1was used. In the other experiments where a set of eight mAbs was used, a concentration of 10 mg ml1was employed. All measurements were performed 3 times using separately prepared samples and averages and standard deviations were calculated and presented.

[0064] Viscosity Measurements. Viscosity measurements were performed at 20 °C employing m-VROC (RheoSense, San Ramon, CA) and processed using the instrument’s control software. The rheometer is based on measuring an accurate pressure drop employing an array of pressure sensors of the microfluidic chip. Viscosity measurements were performed for varying concentrations of tocilizumab (1, 2, 5,10, 20, 40, 60, 80, 100, and 120 mg mL ' ) and omalizumab (1, 2, 5, 10, 20, 40, 60, and 80, mg mL ). Each concentration was tested at different shear rates (100, 200, 500, 1000, 2000, and 3000 1 / s). The measurement at higher shear rates was impossible for some higher concentrations due to pressure increase beyond the capacity of the system, and therefore, the results of the lower shear rates were reported. It is noteworthy that the viscosity values (reported in centipoise [cP]) were not shear rate dependent in the measured range. For the measurements, an A05 chip with ID 22RA05100657 was used. 300 pL of the samples was filled in the glass syringe, and three measurements were performed for each concentration. Out of 300 pL. 100 pL was used for each measurement, the first of which was ignored to minimize the potential errors associated with imperfect initial filling of the sensor cell. The accurate viscosity determinations were considered based on the “Min Slope Fit Rsqrd” values above 0.98 and % full-scale value between 5 and 95% using shear rates 100, 200, 500, 1000, 2000, and 3000 s ' .

[0065] Flow Imaging Microscopy. The particle size distribution of micrometer-sized particles was measured using an 8000 series FlowCam (Yokogawa Fluid Imaging Technologies, Scarborough, Maine). The measurement was conducted with a 10x objective lens, an FOV80 flow cell, and a sample volume of 300 pL at a flow rate of 150 pL min1. Samples were captured at 5 pm to the nearest neighbor and imaged using thresholding parameters of 20 for both dark and light pixels at a rate of 20 frames per second. The instrument was autofocused using the NIST 15 pm polystyrene bead standard (Duke Standards, Fremont, CA) before measuring the samples. The flow cell was flushed between the measurements with ultrapure water, SDS 1%, and an alkaline-based reagent to warrant a clean flow cell. The number and size of the subvisible particles in the range of 1- 100 pm were determined and plotted per size categories (>1, >2, >5, and >10 pm) in different formulations.

[0066] To assess the colloidal stability of BSA formulations, BSA samples were prepared at a concentration of 10 mg ml1in acetate, histidine, and phosphate buffers with pH values of 4.5, 6.0, and 7.4, respectively. The samples were then incubated at 5 °C for 5 days. After the incubation period, duplicate samples were taken and analyzed for subvisible particles using flow imaging microscopy.

[0067] Opalescence Measurements. The experiment involved measuring the light scattering signal of tocilizumab solutions (with concentrations of 10, 20, 40, 60, 80, 100, 120, and 150 mg mL ') and omalizumab solutions (with concentrations of 20, 40, 60, and 80 mg ml1) using a SpectraMax M5 spectrometer (Molecular Devices, San Jose, CA). To perform this, 200 pL of each sample was added in triplicate to a Coming 96-well clear UV-transparent flatbottom microplate (Coming, Inc., New York, NY) and measured in the 340-360 nm range. The baseline subtraction with a histidine buffer was performed for each measurement. A measure of the opalescence of mAb samples was obtained by using the mean optical density with 5 nm increments, which was calculated as the average of three separate sets of measurements.

[0068] Diffusion Interaction Parameter by DLS. Dynamic light scattering (DLS) studies were performed in a 96-microwell glass-bottom sensoplate microplate (Greiner Bio-One, Monroe, NC) using a DynaPro Plate Reader II (Wyatt, Santa Barbara, CA). The stock solution of mAbs (10 mg mL ' ) was diluted to a concentration range of 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5 mg mL1concentrations in 10 mM histidine buffer, pH 6.0. For the loading of samples, 80 pL of samples were added in triplicates for each mAb concentration. Next, 10 acquisitions were measured for a duration of 5s at 20 °C using an autoattenuated laser wavelength of 825 nm. Dynamics software version 7.8 (Wyatt Technology, Santa Barbara, CA) for fitting the data with a cumulant model was utilized for data analysis. The kD-DLS representing an average of three measurements for each mAb was calculated in units of mL g1as a ratio of linear regression slope to the intercept from the plot of diffusion coefficient versus the concentration of mAbs.

[0069] Robustness Studies. For robustness studies, the effect of impurities and temperature variation on the mAb samples was evaluated. For determining the effect on trastuzumab, samples with concentrations from 1 to 5 mg mL1were spiked with 1 pm polystyrene microspheres to reach a final concentration of 2.0 million particles mL Next, a set of three measurements were conducted at 20 °C to analyze the trastuzumab sample using QCM-D and DLS techniques. The loosely interacting layer was evaluated using A / in QCM-D, while the kD-DLS value was determined by DLS through linear regression with the trastuzumab concentration as an independent variable. The average A / and kD-DLS values and their standard deviations from three separate measurements using separately prepared samples were calculated and are presented.

[0070] DLS studies were carried out to investigate the effect of temperature on kD-DLS as kD measurements require several DLS measurements at different concentrations of the protein, and therefore, the risk of having slightly different temperatures in each measurement is high. The study examined the effect of temperature (seven temperatures 20.0 to 26.0 °C) on the diffusion coefficient of tocilizumab at all concentrations ranging from 1 to 5.0 mg mL Studies were performed for three sets of separately prepared samples, and the kD-DLS value was determined by fitting a linear regression as described above.

[0071] Comparative Statistical Analysis. To compare the novel metrics of the loosely interacting layer with kD-DLS, Af was calculated for the loosely interacting layer of the antibodies tested at a concentration of 10 mg ml1employing QCM-D. This value was then correlated with kD-DLS for the mAbs used in the concentration range of 1-5 mg mL1. The average of three measurements using separately prepared samples was taken for each mAb by both methods. To evaluate the rank order correlation between Af and kD-DLS, Spearman’s correlation coefficient was utilized. The Pearson correlation coefficient was also calculated for comparing Af and AD with the kD-DLS values. Additionally, the average relative error for both metrics was calculated to determine the reliability of the metrics.

[0072] RESULTS AND DISCUSSION

[0073] Assessment of Protein Self-Association and Colloidal Stability. To test the relationship between the self-association metric from the loosely interacting layer with colloidal stability of protein formulations, experiments were conducted to measure the Af associated with the loosely interacting layer for bovine serum albumin (BSA), in different buffers (acetate, histidine, and phosphate buffers) with pH values of 4.5, 6, and 7.4, respectively. BSA was used as a model protein in this proof-of-concept study to assess self-association by performing adsorption studies for the protein in different formulations in a single run.

[0074] In the initial experiment, a single run was performed which started with the flow of BSA in acetate formulation to achieve a baseline coating of the surface with BSA. Subsequently, another cycle of BSA in acetate and a rinse with acetate buffer was performed resulting in the largest loosely interacting layer (Af = -60 Hz) of BSA (FIG. 2A). At this stage, Af associated with the irreversibly adsorbed layer remained unchanged. Upon replacement of the buffer with histidine buffer, a shift in the Af of the irreversibly adsorbed layer was observed that had to do with the extent of swelling of the adsorbed layer in the buffer. The following run of BSA in histidine formulation and rinse with a histidine buffer resulted in the return of the signal to the baseline in histidine and revealed an intermediate loosely interacting layer in histidine (Af = -53.9 Hz). Finally, and similarly, a later run involving the flow of phosphate buffer, followed by a BSA in phosphate formulation and rinse with a phosphate buffer exhibited the smallest loosely interacting layer of BSA (Af = - 47.6 Hz). Clearly, the Af values of the loosely interacting layer were highest in the acetate formulation, which was confirmed when separate experiments were performed for each buffer (FIG. 2A and FIG. 2C).

[0075] Studying the interaction of molecules in one experiment versus separate experiments may provide advantages in terms of the usage of proteins and the duration of the experiments. Considering that the irreversibly adsorbed amount may be influenced by the type of buffer, the experiments were initiated with BSA in acetate buffer, which gives the largest stability of the system. The observation can be attributed to the fact that BSA, which has an isoelectric point (pl) of about 4.7, is uncharged when formulated in acetate buffer and experiences no major electrostatic repulsion between its molecules, although aggregation is influenced by multiple factors including conformational stability, interfacial, and other stresses in addition to colloidal stability.

[0076] An assessment of the kD-DLS values for the BSA in three formulations revealed that the lowest kD-DLS was associated with acetate buffer in line with Af values that suggest the highest self-association for this buffer (FIG. 6A-C). Colloidal stability studies were performed by storing the BSA in three buffers at 5 °C for 5 days, following which the number of subvisible particles in the micrometer size range was quantified by flow imaging microscopy (FIG. 2B). BSA prepared in acetate formulation formed the most subvisible particles, while the least number of subvisible particles was found in the phosphate formulation, in line with the Af values from QCM-D. This correlation indicates the potential of the selfassociation metric obtained by QCM-D in assessing interactions between molecules and predicting the colloidal predictive of the formation of subvisible particles.

[0077] Prediction of Solution Behavior. To understand the correlation between QCM-D metrics and the solution behavior of mAbs, a QCM-D experiment was conducted using omalizumab and tocilizumab, a poorly and a well-behaving mAb, respectively, for a range of concentrations (1-10 mg mL1). Interestingly, in the case of omalizumab, a distinct and large loosely interacting layer was detected for all concentrations (FIG. 3 A, FIG. 9, FIG. 13 A, and FIG. 13B), whereas this layer was absent or considerably smaller in the case of tocilizumab (FIG. 3B, FIG. 9, FIG. 13C and FIG. 13D). At a concentration of 10 mg ml1, the Af of the loosely interacting layer for omalizumab was -89.62 Hz, while for tocilizumab, it was -28.15 Hz, and similar trends were observed for all frequency overtones and dissipations (FIGS. 13A-D). The thickness of the layers obtained from modeling of the data are shown below in Table 1 (see also FIGS. lOA and 10B).

[0078] Table 1 These data corroborate the Af observations, suggesting that dissipation and thickness may also be used as metrics for self-association.

[0079] The viscosity of tocilizumab and omalizumab formulations were the same across all of the low concentration samples (up to 10 mg ml1). while omalizumab showed a much higher viscosity at high concentration formulations (FIG. 3C, FIG. 4A and FIG. 4B). Depending on the type of mAb, at an intermediate concentration in the range of about 20-40 mg ml1, where the high number of molecules in solution brings them in close proximity to each other, the viscosity of the samples started to increase exponentially. (As used herein, the term “about” means ± 5 percent of the indicated value(s) or range.)

[0080] Fitting of the viscosity data points in this range (FIG. 3C) revealed that the viscosity value would increase to around 90 cP for 100 mg ml1omalizumab, whereas it would still be under 4 cP for tocilizumab, making the former a challenging mAb in terms of solution behavior and development of high-concentration formulations. These data clearly suggest that metrics based on characteristics of the loosely interacting layer at relatively low concentrations can predict the solution behavior of proteins. In particular, these findings indicate that at concentrations below 10 mg ml1, where the viscosity of the formulation remains similar or unchanged, the loosely interacting layer is different based on the intrinsic properties of the protein. Furthermore, the optical density of the high-concentration formulation was also measured as an indicator of opalescence, and it was comparable for both tocilizumab and omalizumab (FIG. 3D).

[0081] Comparison of QCM-D and kD-DLS Metrics. Metrics of the loosely interacting layer were compared with kD-DLS data for eight mAbs, spanning good, intermediate, and poor solution behavior. The kD-DLS values were calculated by measuring the diffusion coefficient values as a function of mAb concentration at 20 °C (FIG. 11). The characteristics of the loosely interacting layer were determined for all mAbs at 10 mg nil1concentration and terms of Af and AD were observed to be correlated (FIGS. 5 A and 5B; FIG. 12). Most important, a strong rank order correlation between kD-DLS and Af for the loosely interacting layer was observed with Spearman’s correlation coefficient of = 0.809, as shown below in Tables 2 and FIG. 13.

[0082] Table 2 A summary of the statistical analysis of correlations between Af and kD-DLS, as well as AD3 and kD-DLS, is provided below in Table 3.

[0083] Table 3

[0084] CC = Correlation Coefficient.

[0085] A strong correlation was observed in all cases, and this correlation is statistically significant in three out of the four comparisons (significance level of 0.05). Overall, Af shows a stronger correlation with kD-DLS compared to AD3.

[0086] These data show a strong positive monotonic relationship between results obtained using the method of this invention and those obtained with kD-DLS. The relationship between the two methods is statistically significant, further indicating the parameters of the loosely interacting layer as metrics of selfassociation. It is noteworthy that the experimental conditions used (e.g. , mAb in 10 mM histidine buffer pH 6 without any other excipient) have been commonly used for kD-DLS measurements, and the strong rank order correlation suggests that the Af for loosely interacting layer could serve as an alternative to kD- DLS in potentially predicting the solution behavior of the mAb molecules. In this regard, kD-DLS values are independent of the concentration, whereas the A / values reported herein are associated with the concentration of 10 mg mL

[0087] Evaluation of Robustness of DLS and QCM-D Metrics. DLS measurements are highly sensitive to the presence of impurities, including protein aggregates, which may be common in mAb formulations, particularly for self-associating mAbs, and to variations in temperature. Therefore, in the last part of this study, reliability and robustness studies were conducted to effectively compare and evaluate the QCM-D-based method with kD-DLS. The effect of temperature was investigated by measuring the diffusion coefficient in the range of 20-26 °C at mAb concentrations employed for kD- DLS measurements (1-5 mg mL1). These studies indicated that the average change in diffusion coefficient for variation in temperature by 1 °C was 1.40 x 10scm2s ' as compared to an average of 5.76 x 10 'cnf s ' for 0.5 mg ml1of mAb concentration (FIGS. 7A and 7B). These results confirmed that kD- DLS measurements are sensitive to temperature variation. Sensitivity to temperature is particularly important because kD-DLS calculation requires multiple measurements at several concentrations. In this regard, plate-based DLS systems such as the one employed in this study provide a more efficient and uniform temperature control for kD-DLS assessment. Moreover, the QCM-D metric is measured in a single measurement in a well -controlled flow chamber with minimal temperature variations.

[0088] Next, to mimic the potential presence of particulate impurities such as aggregates and external impurities like dust in samples, 1 pm polystyrene microspheres were spiked into the mAb solutions, and their effect on kD-DLS and Af measurements was evaluated. It was found that the presence of impurities did not affect the Af values of the loosely interacting layer while it significantly changed the kD-DLS value and made it difficult to obtain reliable diffusion coefficient values as shown by the broadened 95% confidence interval prediction bands (FIGS. 8A-D). Therefore, the characterization of self-associating mAbs poses significant challenges due to their inherent propensity for aggregation, which can render conventional techniques such as DLS unreliable. It is noteworthy that in the QCMD measurements, while the presence of particles may influence the total frequency shift observed before or after rinsing, the loosely interacting layer remains unaffected, with the Af of the loosely interacting layer staying constant. This observation from the spiked polystyrene bead experiment underscores the robustness of the loosely interacting layer as a metric for self-association, even in the presence of impurities and / or aggregates. All publications (e.g., patents and patent applications) cited above are incorporated herein by reference in their entireties.

Claims

CLAIMSWhat is claimed is:

1. A method of assessing molecular or particulate association, which method comprises: obtaining a first Afc for a first plurality of molecules or particles in a first liquid mixture; and comparing the first Afc, or a value derived therefrom, with a second Afc obtained from a second plurality of molecules or particles in a second liquid mixture, or a value derived therefrom.

2. The method of claim 1 wherein the association is self-association.

3. A method of predicting behavior (e.g., phase separation, opacity, viscosity) of a liquid mixture (e.g., a solution), which method comprises: obtaining a first Afc for a first plurality of molecules or particles in a first liquid mixture; and comparing the first Afc, or a value derived therefrom, with a second Afc obtained from a second plurality of molecules or particles in a second liquid mixture, or a value derived therefrom.

4. The method of claim 3, wherein the behavior is viscosity.

5. The method of claim 1 or 3 wherein each Afc is determined by: contacting a mixture comprising a plurality of molecules or particles with a surface of a resonant material having a resonant frequency under conditions sufficient to provide a coated material comprising a first layer and a second layer of the plurality of molecules or particles, wherein the first layer is adsorbed on the surface and the second layer is loosely associated with the first layer; measuring a first resonant frequency of the coated material or a harmonic thereof; washing the coated material under conditions sufficient to remove the second layer and thereby provide a washed material; measuring a second resonant frequency of the washed material or a harmonic thereof; and calculating the difference between the first and second resonant frequencies or the harmonics thereof.

6. A method of assessing molecular or particulate association, which method comprises: obtaining a first ADc for a first plurality of molecules or particles in a first liquid mixture; and comparing the first ADc, or a value derived therefrom, with a second ADc obtained from a second plurality of molecules or particles in a second liquid mixture, or a value derived therefrom.

7. The method of claim 6 wherein the association is self-association.

8. A method of predicting behavior of a liquid mixture (e.g., a solution), which method comprises: obtaining a first ADc for a first plurality of molecules or particles in a first liquid mixture; and comparing the first ADc, or a value derived therefrom, with a second ADc obtained from a second plurality of molecules or particles in a second liquid mixture, or a value derived therefrom.

9. The method of claim 8, wherein the behavior is viscosity.

10. The method of claim 6 or 8, wherein each ADc is determined by: contacting a liquid mixture comprising a plurality of molecules or particles with a surface of a resonant material having a resonant frequency under conditions sufficient to provide a coated material comprising a first layer and a second layer of the plurality of molecules or particles, wherein the first layer is adsorbed on the surface and the second layer is loosely associated with the first layer; measuring a first dissipation value of the coated material at the resonance frequency or a harmonic thereof; washing the coated material under conditions sufficient to remove the second layer and thereby provide a washed material; measuring a second dissipation value of the washed material at the resonance frequency or a harmonic thereof; and calculating the difference between the first and second dissipation values.

11. A method of comparing a plurality of liquid mixtures, which comprises: obtaining a Afc and / or ADc value for each mixture, and; ranking or plotting the Afc and / or ADc values or values obtained therefrom.

12. The method of claim 11, wherein for each liquid mixture Afc and / or ADc are obtained by: a) contacting the liquid mixture with the surface of a resonant material having a resonant frequency and a dissipation factor under conditions sufficient to provide a coated material comprising a first layer and a second layer of the polymers, wherein the first layer is adsorbed on the surface and the second layer is loosely associated with the first layer; b) measuring a first resonant frequency or a harmonic thereof and / or a first dissipation factor of the coated material; c) washing the coated material under conditions sufficient to remove the second layer and thereby provide a washed material; and d) measuring a second resonant frequency or a harmonic thereof and / or second dissipation factor of the washed material; wherein Afc is the difference between the first and second resonant frequencies or their harmonics and ADc is the difference between the first and second dissipation factors.

13. A method of predicting colloidal stability of molecules in a solution or liquid mixture having a first Afc, which method comprises comparing the first Afc, or a value derived therefrom, with a second Afc, or a value derived therefrom, which second Afc has been correlated with a diffusion interaction parameter (kD-DLS), an osmotic second virial coefficient (B2), or data obtained using nanoparticle spectroscopy (e.g., AC-SINS, CS-SINS).

14. The method of any of the preceding claims, wherein the molecules are polymers.

15. The method of claim 14, wherein the polymers are DNA, RNA, or proteins.

16. The method of claim 15, wherein the proteins are antibodies or antibody fragments.

17. The method of any of the preceding claims, wherein the mixture is a suspension.

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