Separation techniques for the quantification of protein aggregates

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Vrije Universiteit Amsterdam

MSc Chemistry

Analytical Sciences

Literature thesis

Separation techniques for the quantiﬁcation

of protein aggregates

by

Debbie van der Burg

October 2017

12 ECT

Supervisor:

2

nd

_Examiner:

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Abstract

Biopharmaceuticals are an upcoming field in the pharmaceutical industry. Biopharmaceuticals consist of proteins, which have the tendency to aggregate. The presence of protein aggregates has shown to cause adverse effects and safety issues. Detection of protein aggregates is crucial in order to ensure safety, efficacy, and quality of the drug product.

For the quantification of protein aggregates, several techniques could be applied. In some cases, for example for heterogenous samples, separation is required for accurate quantification. The main challenge during protein aggregate quantification is that factors related to separation techniques could disrupt the aggregate distribution, resulting in unreliable results. These factors include dilution, shear stress, change of solvent conditions, adsorption to surfaces, and physical filtration.

This literature thesis focusses on separation techniques that could be applied for the quantification of protein aggregates without disrupting the higher order structure. These techniques include size exclusion chromatography (SEC), asymmetric flow field-flow fractionation (AF4), analytical ultracentrifugation (AUC), disk centrifugation or differential centrifugal sedimentation (DCS), capillary gel electrophoresis (CGE), and sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). The advantages, limitations, and applications of these techniques are discussed in this thesis.

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List of abbreviations

Abbreviation

Meaning

AF4 Asymmetric flow field-flow fractionation AFM Atomic force microscopy

AUC Analytical ultracentrifugation

CD Circular Dichroism

CE Capillary electrophoresis

CGE Capillary gel electrophoresis

DCS Differential centrifugal sedimentation DLS Dynamic light scattering

EM Electron microscopy

ESI Electrospray ionization

FDA Food and Drug Administration

FT-IR Fourier transform infrared

LO Light obscuration

MALS Multi angle light scattering

MALDI Matrix assisted laser desorption ionization

ME Maximum entropy

MS Mass spectrometry

NMR Nuclear magnetic resonance

OM Optical microscopy

SDS Sodium dodecyl sulfate

SDS-PAGE Sodium dodecyl sulfate polyacrylamide gel electrophoresis

SE Sedimentation equilibrium

SEC Size exclusion chromatography

SLS Static light scattering

SV Sedimentation velocity

TP Tikhonov-Phillips

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1 Introduction

Protein-based pharmaceutical products, or biopharmaceuticals, have become an important factor in the pharmaceutical industry. The availability of different classes of biopharmaceuticals, such as antibodies, hormones, and enzymes, provides useful tools in a number of treatments for human diseases. Including treatments for several types of cancer, autoimmune and inflammatory diseases, and metabolic disorders [1], [2]. Non-human proteins in biopharmaceuticals could be recognized as foreign by the immune system, and provoke an immune response. This could be dangerous for the patient. In order to reduce immunogenicity-related problems, recombinant human proteins, which are believed not to evoke an immune response, are used. Despite the high quality of biopharmaceuticals and the use of recombinant human proteins, immunogenicity remains an important concern [1]–[3]. It is a key limitation for the clinical use of biopharmaceuticals since it causes adverse events such as neutralization of endogenous protein or reduced efficacy [2], [4]. Proteins can assemble into large aggregates which do not have the same properties as the native protein. Protein aggregation is a general term for the self-association of proteins into assemblies other than the native quaternary structure [2], [3]. It is believed that protein aggregates are more easily recognized by the immune system than the native protein. It is generally recognized that the presence of aggregates is one of the main risk factors for inducing immune responses [1]–[3].

Biopharmaceuticals have proven to be effective in treating a wide range of diseases. Over the past years, the number of biopharmaceuticals has been growing. At present, about 100 different biopharmaceuticals have been approved for clinical use by the Food and Drug Administration (FDA) [5]. The presence of protein aggregates is a major drawback of the use of biopharmaceuticals and can directly be related to bioavailability, drug efficacy, shelf life, and potential negative side effects like adverse immune responses [6]. Immune responses caused by protein aggregation cause problems for both patient safety and product efficacy. Loss of efficacy is problematic for all biopharmaceuticals, especially if the product is lifesaving. Safety consequences of immunogenicity vary widely and are often unpredictable. A few safety concerns associated with immunogenicity are anaphylaxis, cytokine release syndrome, “infusion reactions”, non-acute reactions, and cross-reactivity to endogenous proteins [7].

In order to ensure safety, efficacy, and quality, the early detection and characterization of protein aggregates are critical [8]. The characterization of protein aggregates could also help

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for developing strategies for aggregation inhibition. Different techniques are utilized for the quantification and characterization of protein aggregates. Techniques such as visible or microscopic inspections, spectroscopic techniques, and light scattering techniques are often used for this purpose. These techniques do not separate the protein aggregates from the monomer species or from other analytes. Since these techniques measure an average value of all protein aggregates in solution, little information is provided about solutions containing both small and large aggregates. For these solutions, separation is required for the quantification of protein aggregates. Several separation techniques are utilized for the analysis of protein aggregates. Mobile phase and column interactions, dilution and the sample preparation required, however, could alter the protein aggregate conformation and distribution. Separation techniques could, therefore, provide unreliable results.

This literature thesis will focus on the possibilities to use separation techniques for the quantification and characterization of intact protein aggregates, without disrupting the higher order structure during analysis.

2 Protein aggregation

2.1 Pathways

Proteins consist of polypeptide chains which are folded into a three-dimensional structure. Many different types of forces are involved in protein folding. These include hydrophobic and electrostatic interactions, covalent bonding, hydrogen bonding, and van der Waals forces. The hydrophobic residues are folded to the inside of the protein, whereas the hydrophilic residues are directed to the outside of the protein. Stress conditions that upset the balance of the forces folding the protein lead to conformational change. When hydrophobic residues are directed to the outside of the protein after a conformational change, the solubility decreases and proteins tend to aggregate [9]. Various modification reactions such as deamidation, oxidation, isomerization, and peptide bond cleavage negatively affect the conformational stability. Stress conditions such as temperature fluctuations, light, shaking, and pH adjustments can induce protein aggregation during each of these stages also affect conformation stability and induce aggregation [3]. Protein aggregates can form throughout the life cycle of a drug product, including production, storage, handling and delivery of the drug product [3].

Protein aggregates are formed via a diversity of pathways depending on the environmental conditions and the initial state of the protein (native, degraded or unfolded state) [4]. The major

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pathways are aggregation through unfolding intermediates and unfolded states, aggregation through protein self-association or chemical linkage, and aggregation through chemical degradation [10]. Usually, native proteins in solution are in equilibrium with a small amount of unfolding intermediates and completely unfolded or denatured proteins. These small amounts of unfolding intermediates are suggested to be precursors for the aggregation process. This could be explained by the higher number of hydrophobic residues directed toward the outside and the larger flexibility of the unfolding intermediates. Interaction between these intermediates leads to the formation of protein aggregates. Completely folded or unfolded proteins, in contrast, do not aggregate easily since the hydrophobic side chains are either mostly buried out of contact with water or randomly scattered. Proteins can also directly associate into protein aggregates from the native state. This self-association can be caused by just electrostatic or both electrostatic and hydrophobic interactions depending on the experimental conditions. Other weak forces such as van der Waals forces could also initiate self-association. Self-association often leads to reversible aggregates, which can be precursors of irreversible aggregates. Protein aggregation could also be initiated by chemical degradations which directly crosslink protein chains. The most common cross-linking reaction the disulfide bond/exchange. Other chemical degradation pathways can also induce protein aggregation. These pathways include oxidation, dimerization, deamidation, hydrolysis, and glycation. These chemical degradations often cause changes to the physical properties of the protein, such as protein hydrophobicity or association tendency, secondary/tertiary structures, and the thermodynamic/kinetic barrier to protein unfolding [10].

Figure 1: Schematic model of protein aggregation [2].

Initially formed aggregates are small, but they gradually become larger. Proteins associate to form dimers or oligomers. The formation of oligomers could lead to the formation of larger aggregates. Linear aggregates form when proteins associate uniformly, whereas amorphous

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aggregates form by the association of proteins in a disordered manner. Eventually, the aggregates become insoluble, visible aggregates [2], [10].

2.2 Classification

Protein aggregates can be formed via a variety of pathways. This results in a wide size range and a large diversity of protein aggregates, which makes classification difficult. Protein aggregates can be categorized into several types according to their characteristics [2], [6]. At the moment, there is no unified system to define aggregates. The imprecise terms to describe aggregates leads to confusion and is a bottleneck in the comparison of results across labs and organizations. Therefore, one system to classify protein aggregates should be used. Several publications classified protein aggregates on conformation, linkage, reversibility and size [4], [11]–[13]. In the category size, aggregates are often classified as soluble aggregates, oligomers, subvisible aggregates and visible aggregates. The interpretation of this classification could lead to confusion, and therefore the quantitative classification of Narhi et al. [12] is recommended. In this quantitative classification aggregates are classified as nanometer (< 100 nm), submicron (100-1000 nm), micron (1-100 µm), and visible (> 100 µm) aggregates. Aggregates could be classified as reversible or irreversible. Reversible aggregates reverse to the lower molecular weight state when the solution condition that initiated aggregation (e.g., protein concentration, pH, temperature, or presence of a co-solute) is removed. The proteins in reversible aggregates retain their native structure except for the part contributing to the bonds. Irreversible aggregates do not reverse to the lower molecular weight state when the condition that initiated aggregation is removed [6], [12]. Aggregates that do not reverse to the monomeric state upon returning to the original solution condition, while they do return to the monomeric state upon manipulation of the solution conditions in other ways, can be classified as dissociable aggregates [12]. The conformation of the proteins in the aggregate can be classified as native or non-native. In native aggregates, the higher-order structure of the monomeric unit is largely retained. Non-native aggregates could be divided into the subcategories partially unfolded, misfolded, inherently disordered, unfolded, or amyloid. Aggregates can either be covalently or non-covalently linked. Non-covalent aggregates are formed via weak forces such as hydrophobic, electrostatic, van der Waals or hydrogen-bond mediated interactions whereas covalent aggregates are formed as a result of chemical bonds such as disulfide linkage [4], [6]. Narhi et al. [12] also added morphology as a fifth category. This category includes characteristics such as aspect ratio, surface roughness, how regular or amorphous the structure appears and whether it is a fiber or a sphere. The most common forms of aggregates observed in biopharmaceuticals are

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nanometer or small submicron, irreversible aggregates. The linkage could either be covalent or non-covalent, and they could have native or non-native conformation [11].

2.3 Influencing factors and analysis

This classification of proteins aggregates is not as black and white as it is stated. The reversibility of protein aggregates, for example, is actually a continuum of states between reversible and irreversible. The reversibility can be affected by solvent components, such as salts, sugars, organic modifiers, and other excipients, pH, temperature and time. In addition, reversible aggregates have a broad spectrum of lifetimes. For many techniques, especially for separation techniques, the time taken for measurement may be greater than the lifetime of a reversible aggregate. Therefore often only the longer-lived aggregates are detected [13].

When rapidly reversible self-association proteins are analyzed with a separation technique, there is a constant battle between separation and re-equilibration. The results then often depend on the rates of the association-dissociation reactions and the equilibrium constants, making analysis very complex. When separating protein aggregates with slower association-dissociation rates than the physical separation rate, resolved peaks often represent a dynamic mixture of multiple aggregate species instead of a pure, individual aggregate species. Separating protein aggregates with very slow association-dissociation reactions compared to the time scale of the separation results in resolved individual aggregate peaks[13].

The wide size range, the broad diversity and the changes to protein aggregates make analysis difficult. These factors impact the measurement approach and the proper interpretation of the data. It is impossible to have one analytical technique or approach that will provide complete answers, and that will work in all situation and products [13]. Many factors play a role in affecting protein aggregation, including temperature, pH, ionic strength, surface adsorption, shearing, shaking, the presence of metal ions, organic solvents and additives, protein concentration, purity and morphism, pressure, freezing and drying [14]. This means sample preparation and handling should be considered carefully. Also, analysis techniques, especially separation techniques, involve factors that can disrupt the distribution of aggregate species. These factors include dilution, change of solvent conditions, adsorption to surfaces, physical filtration or disruption, concentration on surfaces and shear [13].

The difficulty in using separation techniques is that the time taken for measurement may be greater than the lifetime of a reversible aggregate, or the measurement techniques themselves

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may destroy or create further aggregates. The latter is one of the most critical problems in analyzing protein aggregates. Therefore, it is important to use multiple, orthogonal techniques.

3 Non-separation techniques

Several non-separation techniques are frequently used for the detection of protein aggregation. These techniques often do not induce conformational changes of protein aggregates and are therefore well suited for the qualitative analysis. However, these techniques measure an average of all species in solution and therefore provide little information about samples containing both small and large protein aggregates. For completeness, a short overview of these techniques is given below.

3.1 Turbidity

Turbidity is a measure of light transmitted through a sample solution [15]. Large particles, such as protein aggregates, scatter light more than smaller particles. This reduces the amount of transmitted light. Therefore, the formation of protein aggregates or particles in solution leads to an increase in turbidity. The turbidity is either quantified by determination of the loss of light of the transmitted beam or by the intensity of the scattered light at a given angle. Better sensitivity can be obtained with light scattering since only a few particles are required to detect scattered light, while a large number of particles is needed to achieve a significant reduction in the transmitted light [9]. A UV-Vis spectrometer in the wavelength range of 320-800 nm can be used to measure the transmitted light [15]. Turbidity measurements are nonspecific and do not provide information about size, concentration, or nature of protein aggregates. Nonetheless, it is highly useful for relative comparison of samples. Because of its high sensitivity for small aggregates, turbidity is capable of detecting the formation of particles in solution early during stability studies [15].

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3.2 Light scattering

Light scattering techniques are used for the sensitive detection of aggregates in solution and an estimation of the size of the protein aggregates. Light scattering can be categorized into two techniques: static light scattering (SLS) and dynamic light scattering (DLS). These two techniques provide very different characteristics of aggregates in solution [6].

Multi-angle light scattering

The most used form of SLS is multi-angle light scattering (MALS). In MALS, the intensity of the scattered light of molecules in solution is used to determine the size. When a macromolecule is irradiated with laser light, the oscillating electric field of the light induces an oscillating dipole within the molecule. This oscillating dipole will re-radiate light. The intensity of the scattered light and the molecular weight of the molecule are directly related through the Rayleigh equation. This equation could be simplified when the intensity of the scattered light is measured at a 0° angle to the incident light beam. However, at this angle the scattered light and the incident beam are indistinguishable. In MALS, the light intensity is measured at multiple angles around the molecule to build a model of the scattered light as a function of angle. This model could be used to extrapolate to a value for the scattered light intensity at 0°. The number of angles typically varies between 2 and 20 angles, where the intensity is detected simultaneously at each angle [16], [17]. Measuring at multiple angles leads to more precise estimates of molecular mass, size, conformation, and shape.

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Dynamic light scattering

Dynamic light scattering (DLS) is a non-invasive technique which uses light scattering for the analysis of the particle size. In solution, particles undergo Brownian motion. When a solution is illuminated with a laser beam, light scatters from the moving molecules. The Brownian motion imparts a randomness to the phase of the scattered light. Addition of the scattered light from multiple particles creates a changing destructive or constructive interference. This results in time-dependent fluctuations in the intensity of the scattered light [19, 20]. These time-dependent fluctuations are directly related to the rate of diffusion of the molecules, which can be determined by a correlation function. As the particles move in the solvent, the intensity graph changes and the correlation between these graphs decays. The time at which the correlation starts to decay, indicates the diffusion coefficient, which is related to the particle’s hydrodynamic radius by the Stokes-Einstein equation [19], [20]. The diffusion, however, is affected by water molecules, which may be encapsulated around the protein. Furthermore, the hydrodynamic radius depends on their shape and molecular mass. Therefore, the hydrodynamic radius may differ significantly from their true physical size and is not a reliable measure of the molecular mass.

Figure 4: Left: Intensity graph at time point zero compared with graphs at later time points. Right: Correlation curve.

An advantage of DLS is the minimal sample preparation, typically, samples can be placed in a clear glass tube or cuvette, and direct measurements can be made to assess the size distribution. The distribution is intensity weighted but can be converted to a weight weighted

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distribution or other types of distributions. In this conversion, assumptions are built in. Therefore, data should be interpreted with caution. Since the measurement is done directly on the sample, DLS is capable of following aggregation kinetics as the reaction proceeds. Nowadays, instruments are available that can perform high throughput measurements with the aid of 96-well plates. Originally scattered light is collected at a 90° angle. However, instruments that allow analysis at higher angles, or in back-scattering mode are now available, allowing analysis of relatively high concentrations or turbid samples [6].

DLS carried out in batch mode suffers from limitations as interference from dust particles, air bubbles, and other larger impurities. The data is intensity weighted, thus larger particles tend to affect the size distribution. This could be avoided using sample filtration, however, there is a risk of also removing larger aggregates. The capability to resolve various size distributions depends on the size range of interest. DLS might not be able to resolve dimer and trimers from the monomer. Turbid samples or samples with high concentrations of protein may cause a loss of intensity due to the inner filter effect [6]. Both MALS and DLS provide the average molecular mass for all molecules in solution.

3.3 Light obscuration

Light obscuration (LO) is a technique used for the analysis of micron aggregates [21], [22] and is the primary method described in the current pharmacopeias Ph. Eur. 2.9.19 and US pharmacopeia <788>. In an LO measurement, a dilute sample is drawn into the system through a syringe. The sample passes between a laser and a detector. As particles pass the laser beam, they block a part of the light, producing a ‘shadow’ on a light-sensitive detector. Using a calibration curve, the area of the produced shadow can be converted into the equivalent circular diameter of the particle [21]–[23].

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3.4 Particle counters

Aggregation could eventually lead to the formation of insoluble particles. Detection of these particles could be conducted by particle counters. Particle counters use electrical-sensing zone analysis to detect the number of particles present in a solution. This measures changes in electrical impedance of an electrolyte produced as non-conductive particles pass through a small opening between two electrodes. Each particle produces a pulse of voltage, the size of which is considered to be dependent on particle volumetric size. However, this takes no account of shape or changes in resistivity between different particles. This technique has been used extensively to count particles (1–1000 µm) in the pharmaceutical industry, especially to monitor the quality of intravenous solutions. The technique is limited by the smallest available opening between the electrodes. This sets the lower limit in the size of particles that can be counted and leads to difficulty counting particles smaller than 2 µm [9].

3.5 Microscopic techniques

For the detection of particles several microscopic techniques could be utilized.

Optical microscopy (OM) can be used to magnify visible particles up to a level where regular structures can be observed. It is a quick and easy technique for comparing samples by observing gross changes between them and by counting the number of particles seen in a specific area [9].

Electron microscopy (EM) is used to observe objects down to a few angstroms by using the shorter wavelength of the electron. Sample preparation is difficult in EM, and the conditions required are extreme. Samples are often frozen in liquid nitrogen, coated with metal vapor and observed in a vacuum. This could cause artefactual results [9].

Atomic force microscopy (AFM) utilizes a very fine stylus (5-60 nm tip radius) mounted on a short cantilever, typically 100-250 µm in length, to systematically scan across a surface of interest. As the tip moves, it interacts with any molecular features on the surface and is deflected accordingly. These signals are amplified by corresponding deflections of a laser beam reflected off the surface of the probe and are converted into height signals by photoelectric circuitry. These signals are then processed to create a digital height map of the surface, which can be presented in a number of different formats. The low spring constant (<1N/m) of the cantilever minimizes the force acted upon the surface, but this may still be too much for a biological surface, leading to damage and a distorted image of the surface. However, this can

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be overcome using an AFM in ‘tapping mode’, where the probe is not in continuous contact with the surface but instead gently oscillates up and down, as it scans. AFM can scan fields from less than 20 nm up to 150 µm, with a spatial resolution of approximately 1 nm and a height resolution of 0.1 nm [9]

3.6 Spectroscopic techniques

Structural analysis is carried out with several spectroscopic techniques. Aggregation of proteins often involve a change in the secondary structure. Characterizing the secondary structure could provide information about the mechanism of aggregation and the conformation of the protein aggregates [24]. Techniques that provide information on the secondary structure are nuclear magnetic resonance, circular dichroism, Raman spectroscopy, and Fourier transform infrared spectroscopy [11], [24]. These spectroscopic techniques make use of electromagnetic radiation to measure a quantity as a function of wavelength. The results are usually in the form of a spectrum of the response of the quantity at varying wavelengths and show an average of the entire molecular population [24].

Nuclear magnetic resonance (NMR) can provide detailed structural information about macromolecules at atomic resolution and helps to elucidate the compound’s structure. It makes use of the atoms property to absorb electromagnetic fields and radiate the energy back out at frequencies specific for the strength of the field and the atom. With NMR, the magnetic properties of atomic nuclei, such as hydrogen, are analyzed to determine different local environments [24]. The chemical shifts observed with NMR can be used to identify regions of the secondary structure of the protein [25].

Circular Dichroism

Circular Dichroism (CD) measures the difference in absorption of right-handed and left-handed circularly polarized light by chiral molecules. CD may arise from inherently asymmetric groups, such as the chiral a-carbon of the peptide bond. In the far UV spectrum (170-250 nm), the contribution of peptide bonds to CD is dominant. As the CD band position and intensity of peptide bonds depend on their conformation, far UV CD spectroscopy allows for the assessment of the secondary structure of proteins. In the near UV CD region (250-350 nm), only the aromatic residues and cystine absorb light. The near UV part of the spectrum provides information about the tertiary structure of a protein. The characterization of the secondary and tertiary structure allows the study of the conformational stability of protein [24]–[27].

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Raman spectroscopy is used to observe vibrational modes and is based on inelastic Raman scattering. Molecules illuminated by a laser, absorb a photon and transit to a virtual state between the ground state and the electronic excited state. The molecule and photon exchanged energy and the molecule emits a photon of lower energy than the absorbed photon, called Stokes-Raman scattering. When the molecule is in a vibrational state upon excitation, the photon can gain energy from the molecule, resulting in an emitted photon of higher energy. This is called anti-Stokes Raman scattering, however, the intensity of this signal is much weaker than that of the Stokes Raman since a much smaller population of the molecules is in a vibrational state. Molecular groups rich in π-electrons, such as C=C, S-S, C-S, and S-H groups, give Raman signal.

Raman spectroscopy can determine the secondary structure characteristics. Information about the secondary structure could be obtained from Raman shifts in specific spectral bands. These specific bands are the Amide I, Amide III, and the skeletal stretching mode. The Amide I band from ~1600 cm-1_{to 1700 cm-1 is mainly caused by the C=O stretch vibrations combined with a} small amount of C-N stretch vibrations. The Amide III band from ~1200 cm-1 to 1340 cm-1, is a result of the coupling of the C-N stretch and the N-H bend vibrations. The shapes of these bands change when the secondary structure changes. The N-Cα-C skeletal stretching mode, which has a band from ~930 cm-1_{to 950 cm}-1_, _{is indicative of α-helix content. Table 1} summarizes these characteristic bands.

Table 1: Correlation between Raman shift and protein secondary structure [28].

Figure 6 shows the Raman spectra of bovine serum albumin (BSA) before and after thermal stress. The characteristic bands for the skeletal stretching mode, Amide I, and Amide III are highlighted in this figure. The spectra show a clear transition from an α-helix rich structure into a β-sheet abundant structure.

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Figure 6: The Raman spectra of BSA (50 mg/mL at pH 7.4, PBS buffer), collected at 20°C and 90°C, respectively. Spectra are normalized to the phenylalanine intensity at 1004 cm-1 [28].

Raman spectroscopy can provide information about the secondary structure and provide structural information on aromatics, chromophores, and other side chains in proteins reflecting the tertiary structure. Therefore, Raman spectroscopy is well suited to monitor the transformation of native protein to protein aggregate by analyzing changes in the secondary structure or hydrophilic exposure of any side-change. It also has the ability to identify reversible and non-reversible changes by determining the presence of more disordered structures common in unfolded proteins [24], [26], [28], [29].

Fourier transform infrared spectroscopy (FT-IR) is another technique to observe vibrational modes and provides complementary information to Raman spectroscopy. Infrared spectroscopy measures absorption of light due to vibrations of the molecule in the in the range of 12500 cm-1 to 10 cm-1_{, the most commonly used range for the analysis of protein secondary structure is} 4000 to 400 cm-1_{, which is called middle IR spectroscopy. Vibrations of functional groups such} as amide groups are observed in this region [26].

In FT-IR, the absorption is measured at all wavelengths simultaneously instead of one by one. Infrared light is converted to an interferogram by an interferometer. This is usually a beam splitter which splits the infrared light in two beams. One part of the light goes to a fixed mirror, whereas the other part goes to a moving mirror. When the two beams meet at the beam splitter again, the two beams interfere with each other, resulting in the interferogram. This interferogram passes through the sample, which absorbs all different wavelengths characteristic for the proteins in it. These absorptions are subtracted from the interferogram and a variation in energy

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versus time is reported for all wavelengths simultaneously. This could be converted to a intensity versus frequency spectrum following the mathematical Fourier transform function [30]. FT-IR can also determine the secondary structure using vibrations. Figure 7 shows FT-IR spectra of salmon calcitonin (sCT) and of sCT in the presence of the metal ions Zn2+_{and Al}3+_. The spectrum of the native sCT shows a strong Amide I band at 1654cm-1_{, which is} characteristic of an α-helix conformation. The spectra of the sCT in the presence of the metal ions exhibit a broad band from 1650 cm-1_{1632 cm}-1_{, corresponding to random coil and β-sheet} formation. This conformational change indicates aggregation [31].

Figure 7: FT-IR spectra of native sCT and sCT aggregates in the presence of Zn2+_{and Al}3+_{ions [31].}

FT-IR yields information on the secondary structure and conformational changes of proteins as well as intermolecular interactions. FT-IR can be applied on both liquid and solid samples. Analysis of highly aggregated samples is also possible with FT-IR [26].

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4 Separation techniques

Analyzing protein aggregates is challenging because of the unknown nature of the formed aggregates, the wide size range, and the concentration range [3], [26]. The choice of the technique is commonly governed by the size and the characteristics of the aggregates. Without prior knowledge about the size and characteristics of the aggregates, several techniques with different principles should be combined to obtain as much information as possible [6].

For a lot of separation techniques, it is impossible to quantify and characterize intact protein aggregates, without disrupting the higher order structure during analysis. Factors associated with separation techniques, such as shear stress, dilution, and incompatible mobile phases, change the aggregate conformation. In reversed phase liquid chromatography, for example, the mobile phase will denature the protein. Hence, only the primary structure can be analyzed. Techniques that could be utilized for the determination of intact protein aggregates and their advantages and limitations are discussed in this chapter.

4.1 Size exclusion chromatography

Size exclusion chromatography (SEC) is a widely used analytical technique for the detection and quantification of most types of nanometer (<100 nm) and small submicron (100 – 1000 nm) aggregates. SEC separates protein aggregates on basis of their hydrodynamic radius. The column is filled with spherical porous particles with a controlled pore size. The column acts as a sieve where smaller molecules penetrate deep into the pores and therefore take a longer path through the column, whereas larger molecules are unable to enter the pores and therefore move more quickly. Consequently, small molecules will elute later than large molecules. The analytes are separated on the basis of molecular size differences, rather than by their chemical properties. The separation is ideally without any adsorption. A calibration curve, based on proteins or polymers of known molecular weight, could be used to determine the molecular weight of an unknown analyte [6], [26], [32], [33]. The concentration of the eluting protein is often monitored using a spectrophotometric, refractive index, or a light scattering detector [6], [26]. Typical column dimensions are 30 cm column length and 4.6-8 mm inner diameter. Various particles of 3-20 µm with different pore sizes are commonly used. The analysis time when using this commonly used columns is 15 – 50 min [33].

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Figure 8: Illustration of a SEC separation. Left: small molecules can penetrate further into the pores of the porous bead than the larger molecules, and therefore take a longer path. Right: SEC chromatogram with the protein aggregate eluting before the larger monomer peak.

SEC analyses are often used in routine analysis where high throughput is desired. In order obtain high throughput analysis, short analysis times are required. Since there is no retention, all analytes elute before the total void volume. Decreasing the analysis time in SEC could, therefore, be achieved by reducing the column size and increasing the flow rate. Decreasing the column length, however, proportionally reduces the number of theoretical plates. The main difficulty in achieving both high speed and high resolution in SEC is the slow mass transfer of the analytes between the interstitial space and the pore space. This mass transfer could be increased by increasing the temperature. The column performance in SEC could be described according to the following relationship:

H = 3.5 · d

_p

+ 1.3

(1+k)DM u

+ 0.6

k (1+k)2 dp2 DM

u

(Eq 1)

where H is the plate height, dp is the particle diameter, k is the retention factor, DM is the

molecular diffusion coefficient and u is the mobile phase linear velocity. Resolution between the aggregates and the native protein could be enhanced by reducing the particle size. Figure 9 shows an H-u plot of the estimated impact of the particle size and the mobile phase temperature on the column performance [33].

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Figure 9: Theoretically expected impact of the particle size and mobile phase temperature on column performance. (For the calculations, a 50 kDa protein was assumed) [33]

The packing material for SEC columns can either be silica, with or without surface modification, or cross-linked polymeric packings with an hydrophobic, hydrophilic, or ionic character. For the analysis of protein aggregates, modified silica packing is mostly used. In order to prevent non-specific interactions, silica is often modified with diol functional groups to neutralize the acidic surface of the silanol groups. Several hydrophilic cross-linked packings have also been developed for the separation of biopolymers. Most of these packings are proprietary hydroxylated derivatives of cross-linked polymethacrylates [33].

The appropriate pore size can be selected with the size of the protein and its aggregates to be separated. All particles larger than the largest pores in the stationary phase elute first with the interstitial volume. Smaller molecules elute in order of decreasing size. An example of pore sizes appropriate for different molecular weight ranges is given by Agilent in Table 2. If the proteins elute near the intestinal volume, a smaller pore size should be considered, whereas a larger pore size should be considered if the protein elutes near the total void volume.

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Table 2: Pore sizes appropriate for molecular weight ranges [34]

Since separation in SEC is not based on retention, large pore volumes are required to obtain appropriate selectivity. Therefore generally, columns with 30 cm column length and 6 – 10 mm inner diameter are employed. Recently narrow bore column with 4.6 mm inner diameter and 15 cm column length are available. These columns offer similar separation power as standard columns while shortening the analysis time by a factor 3-4. For complex samples, high resolution separation is required. The resolution of a SEC column is directly proportional to the square root of the column length. For complex samples, long columns are required which can be obtained by joining multiple columns in series [33].

Although it is a straightforward technology, SEC analysis has a number of limitations. This limitation must be addressed in order to draw valid conclusions. The column can act as a filter, larger protein aggregates either elute with the void or accumulate on top of the column or pre-column. SEC involves significant dilution of the sample, potentially dissociating reversible aggerates. The range of molecular mass that can be separated, the dynamic range, is limited. Choosing a pore size for good separation of monomer and dimer often means that all species larger than trimer or tetramer are unresolved. This is inversely related to resolution. A less important limitation is that SEC cannot reliably measure the true molecular mass. Calibration curves of retention time versus molecular weight are constructed using globular molecules. Therefore, the elution position does not only depend on the molecular weight of the analyte, but also on its shape. Since the shape of protein and aggregates could vary (e.g., globular, rod-like or flexible chains), their hydrodynamic radius, rather than their molecular weight is determined [35]. Therefore, a calibration method that relates the hydrodynamic radius to its elution volume is required. An example of such a calibration method uses the linear relationship between ln(RH)

and ln(1-KD), where RH is the hydrodynamic radius of the analyte and KD the partition coefficient,

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radius based calibration curve. In the molecular weight based calibration curve, the dimer and trimer do not fall on the curve, suggesting they are not spherical. However, both dimer and trimer fall on the calibration curve when hydrodynamic radii are measured.

Figure 10: SEC calibration curves generated with small proteins ranging from ribonuclease A to thyroglobulin (unfilled symbols). A: Molecular weight based calibration curve. B: Hydrodynamic radius based calibration curve. Filled symbols represent antibody dimer and trimer [35].

Another possibility for the determination of the molecular weight is the use of a multi angle light scattering detector. This allows for the accurate determination of the average molecular weight of the eluting aggregates without the use of calibration standards [6].

A final limitation is the nonspecific protein binding to the column stationary phase, this often causes an underestimation of aggregate quantity [33], [35], [36], modification of the aggregate conformation [33] and distribution [35], abnormal elution positions [33], [36], [37], and undesirable changes in peak shape and chromatographic resolution [32], [33]. Proteins interact with the stationary phase through electrostatic and hydrophobic interactions. If the protein aggregate and the stationary phase are of the same charge, repulsion could prevent the aggregate from entering the pores and decrease elution time. If the protein and the stationary phase are of opposite charge, adsorption could increase elution time. Hydrophobic interactions also lead to increased elution times [33]. A new column has a greater tendency to bind proteins. Also, low protein concentrations often have a low recovery [32], [36]. An ideal and robust method should lead to identical result regardless of how long the column has been used, and the protein recovery should be independent of the amount of protein loaded [32], [36]. Protein adsorption can be avoided by using the right column and mobile phase composition, for

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example, the addition of various co-solvents to the mobile phase can suppress the electrostatic and hydrophobic interactions [32], [33], [36]. To reduce hydrophobic interactions, some organic modifiers could be used [33]. However, the addition of organic modifiers could alter the protein aggregate distribution. Electrostatic interactions are commonly reduced by increasing the ionic strength or salt concentration of the mobile phase, increasing the concentration of a counter ion, adjusting the pH of the mobile phase to a value close to the isoelectric point of the protein, or addition of additives in the mobile phase. It should be considered that high concentrations of counter ions in the mobile phase can lead to increased hydrophobic interactions. It is good practice to use buffered mobile phases with an ionic strength of 50-200 mM. A commonly used additive is arginine, which reduces the possible interactions with the stationary phase by binding to the protein, leading to an improvement in protein aggregates quantitation and peak shape. Figure 11 shows the SEC chromatographic profiles of recombinant human basic fibroblast growth factor in the presence and absence of arginine. Although the addition of arginine could improve the separation, it should be noted that arginine shows significant UV absorbance at wavelengths below 220 nm, and could, therefore, reduce the sensitivity [33].

Figure 11: SEC chromatographic profiles of recombinant human basic fibroblast growth factor (bFGF) in 0.2 M NaCl (A) and 0.2 M arginine (B). There is little resolution in the separation of bFGF (arrow) from the salt in when no arginine is added to the mobile phase, while baseline resolution is observed after addition of arginine [33].

Ryosuke Yumioka et al. [36] tested the effect of the use of arginine in the mobile phase. Two new identical columns were used for this study. All experimental conditions, except for the buffer, were equal. Mouse monoclonal antibody containing 4-5% of soluble aggregates was analyzed

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with both buffers. Figure 12 shows the results for the NaCl and the arginine buffer. The measured aggregate content was significantly higher for the arginine buffer than for the NaCl buffer. For both buffers, the first injections underestimated the aggregate content of ~4%, in the later injections, the arginine buffer resulted in a more reliable value. The arginine buffer also showed a better resolution between the monomer and the dimer [36].

Figure 12: Effects of repeated injection on the recovery of aggregates with NaCl and arginine buffer. The aggregate content of ten subsequent injections of mouse monoclonal antibody is plotted against the run number [36].

Ryosuke Yumioka et al. also tested the effect of the loaded amount of sample by injecting 20-fold different amount of the mouse monoclonal antibody. Injections of 1 and 20 mg were compared. When using the NaCl buffer, the method gave an aggregate content of 4.4% for the 20 mg injection and only 1.1% for the 1 mg injection. When using the arginine buffer, the method gave an aggregate content of 5.7% for the 20 mg injection and 4.1% for the 1 mg injection [36]. This is a great improvement. This experiment showed the importance of the buffer; an arginine buffer gives a more reliable and consistent result than a NaCl buffer, especially for low loading amounts.

Although SEC is mostly used to analyze irreversible nanometer and small submicron aggregates, it can also be used to characterize the reversibility of aggregates. The behavior of reversible aggregates depends on the equilibrium and the interaction with the column, since this is affecting the profile of the eluting peaks, SEC can be used to characterize protein self-association. Protein aggregates can associate and dissociate in the column, the interconversion between the two species can be slow, intermediate or fast. The peak profile can determine the rate of interconversion. For slow interconversion, the column separates the associated species on the time scale of the experiment, meaning the species elute as distinct peaks. For rapid

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interconversion, the species rapidly re-equilibrate and the peaks will not be resolved. For the intermediate case, some separation, as well as asymmetry in the eluting peak, is expected. This three cases could be distinguished by injecting solutions of different initial protein concentration at various flow rates. For example, flow rates do not affect the distribution of the species for rapid interconversion, whereas for intermediate or slow interconversion, the flow rate will have an effect [6].

Supplementary information about the protein structure of monomers and aggregate species could be obtained simultaneously with conventional SEC analysis by additional fluorescence detection and the post column addition of a fluorescent dye. The dye interacts with hydrophobic residues, usually directed to the inside of the protein. After protein unfolding, hydrophobic surfaces become exposed and fluoresce intensity increases, enabling the detection of conformation changes [38].

The main advantage of SEC is the mild elution conditions that allow for the characterization of the protein with minimal impact on the conformational structure and the local environment [33]. Additional advantages of SEC are its ease of use, relatively high throughput, the equipment and columns are readily available, and it is often relatively simple to validate with high resolution, precision, and accuracy [6], [32]. Furthermore, the mobile phase can be varied to characterize and monitor reversibility of aggregates. SEC allows for both sizing and quantification of protein aggregates. Separation and detection in the range of 5 to 10 kDa can be achieved. In addition, the method requires little sample preparation, often the samples can be injected directly without any modification, except for occasional dilution [6].

4.2 Asymmetric flow field-flow fractionation

Asymmetric flow field-flow fractionation (AF4) is a size-based separation technique. AF4 is a one-phase chromatography technique. Separation is achieved within a thin channel, formed by an impermeable upper plate and a permeable bottom plate separated by a spacer with a typical thickness of 100 – 500 µm. The flow in the AF4 is split in two parts with flow regulators or an extra pump. One part is the carrier flow that moves in axial direction towards the outlet and detector. The other part is the cross flow, which is perpendicular to the carrier flow. The sample is injected into the channel. The analytes are moving under the influence of these two flows. The laminar carrier flow is driving the analytes towards the outlet of the channel, whereas the perpendicular cross-flow is forcing the analytes to accumulate at the semipermeable bottom plate. An ultra-filtration membrane with a typical size barrier of 10 kDa covers the bottom plate

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to prevent the sample from penetrating the channel. Diffusion of the molecules creates a counteraction motion: analytes diffuse back to the center of the channel. The laminar carrier flow has a parabolic flow profile, the stream moves faster in the center of the channel flow than is does closer to the edges. Depending on their diffusion coefficients, analytes reach a certain height in the channel. Smaller particles have higher diffusion rates than larger particles and reach an equilibrium position higher up in the channel. At a higher position, the laminar carrier flow is faster, therefore smaller particles are being more rapidly transported along the channel than larger particles. Consequently, small particles elute before the larger ones [3], [39], [40].

Figure 13: Schematic illustration of an AF4 channel [39].

An AF4 experiment could basically be divided into three steps: sample injection, sample focusing, and elution. The analytes are separated in the elution step. During sample injection and focusing, the in-going flow enters the channel from both the inlet and the back and of the channel. This is concentration the analytes in a narrow banc near the entrance of the channel. After injection, a set focusing time will further concentrate the analytes. After the focusing step, the elution starts. The in-going flow now only enters the channel from the inlet and is split in the carrier and the cross flow. During elution, the cross flow continuously forces the particles against the accumulation wall, and diffusion causes the analytes to move back to the center of the channel. The further the analytes diffuse to the center, the faster they will elute [41], [42]. The focusing time should be optimized for every application. When the focusing time is too short, the sample band is wider than necessary, compromising resolution. When the focusing time is too long, smaller particles might be lost. Due to the focusing step, limitations regarding overloading are minimized [42].

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Figure 14: Illustration of an AF4 separation and elution process. A) injection of molecules onto the AF4 channel. B) focusing (concentration) of analytes prior to analysis. C) elution, starting with the ending of the focusing flow and the particles moving down the channel. D) separation of small and large particles over time as they move down the channel [41].

The retention in AF4 only relies on the flows and the diffusion coefficient, which makes it easy to determine the molecular weight based on the retention. With some approximations, the elution time can be calculated as:

t

_R

=

w2

6D_i

h (1 +

F_C

F_OUT

)

(Eq 2)

where w is the height of the channel (the thickness of the spacer), Di the diffusion coefficient of

the component, Fc the cross flow and Fout the carrier flow. The size can be determined form the

diffusion coefficient with the Stokes-Einstein equation [42].

Elution times depend on the flow ratio (Fc/Fout), and the spacer height. Elution times do not

depend on the length or width of the channel. Of course, also the peak width is of importance. With a simplified equation, the standard deviation σt of a peak of a monodisperse compound

can be calculated as:

σ

_t

= 0.82

w u_C

· {ln (1 +

F_C F_OUT

)}

1/2 (Eq 3)

where uc is the cross flow velocity. This formula only contains instrumental parameters, implying

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The elution time depends on the flow ratio, and the peak width depends on both the flow ratio and the cross flow velocity. To obtain efficient separations, the system should run at flow rates as high as possible. In Figure 15 the flow ratio is kept constant, while the flow rates are varied. Due to the constant flow rates, the elution times are equal. With higher flow rates, the separation efficiency increased. It should be considered that there are limitations related to a high cross flow, such as the high pressure, the possibility of the channel to leak, possible loss of smaller analytes through the membrane, and possible adsorption when analytes are forced into the pores [42].

Figure 15: Effect of the flow rates on the separation efficiency in AF4. Separation model proteins with a flow ratio of 2.5, with (a) Fc = 1.5, Fout = 0.6 mL/min; (b) Fc = 2.5, Fout = 1.0 mL/min [42].

Figure 16 shows the correlation between the cross flow intensity and resolution of a separation of human serum albumin (HSA) containing ~10% of dimer and larger aggregates. When no cross flow is applied, monomer and aggregates are not separated. With higher cross flows, the analytes are forced against the accumulation wall, sample elution is prolonged and analyte fractionation is performed [43].

Figure 16: Fractionation of HSA at different AF4 separation conditions. Note the correlation between increasing cross flow strength and prolonged elution time/resolution power [43].

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The high cross flow rate could potentially immobilize higher molecular weight aggregates on the ultra-centrifugation membrane. This higher molecular weight aggregates could be eluted by decreasing the cross flow after elution of the separated smaller aggregates. Figure x shows the analysis of the human serum albumin sample with 0% and 75% cross flow intensity. The 75% cross flow is reduced to 0% after 20 minutes; this enables the detection of the higher molecular weight aggregates. Now monomer (66.9 kDa), dimer (133.8 kDa), trimer (204 kDa), and aggregates >106_{Da can be analyzed. Flow programming enables a broad dynamic size range} to be separated [43].

Figure 17: Fractogram of HSA using 0% and 75% cross flow intensities. Reducing the cross flow from 75% to 0% after 20 minutes [43].

AF4 separates protein aggregates ranging from a few nanometers to a few micrometers diameter [3], [26], [44], [45]. The open channel without stationary phase reduces shear and mechanical stress on the proteins, making it a gentle technique. The broad dynamic separation range, together with the open channel without stationary phase or packing material make this technique very suitable for the analysis of protein aggregates. Another great advantage is the wide choice of carrier liquid, allowing the sample to be analyzed in the formulation buffer [44]. This reduces changes to the aggregate structure due to the matrix. A few examples of the successful analysis of aggregates with AF4 are the analysis of BSA aggregates [46], submicron IgG aggregates [45], [47], oat globulin aggregates [48], and the analysis of aggregates in egg yolk [44].

Although AF4 is a gentle technique, several steps in AF4 could potentially affect delicate or weakly bound protein aggregates. Bria et al. [40] tested the effects of carrier fluid, syringe shear

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stress, focusing and dilution on aggregate stability. When the sample is loaded into the injection valve, shear can be experienced which influences the protein aggregate distribution. After injection, the sample is focused at the beginning of the channel by two opposing flows, prior to fractionation. This focusing step concentrates the sample, the concentration at the accumulation wall could be increased by 10-100 fold. This increase in concentration can lead to aggregation and/or increased membrane interactions if excessively long focusing times are used. When the focusing flow is turned off, the sample components are transported along the length of the channel. During separation, analytes can experience shear and dilution which is inherent to separation techniques in general. This can cause dissociation of aggregates. Compared to SEC, shear rates are orders of magnitude lower in AF4. Because shear stress is less predominant in AF4, loosely bound aggregates stay intact during analysis when no focusing and cross-flow are used. Sample dilution is dependent on separation conditions and channel dimensions, in contrast to SEC, sample dilution does not necessarily increase along the length of the channel. Most dilution occurs when the analytes at the accumulation wall leave the channel through the channel outlet. All parts during separation are associated with either dilution, concentration or shear stress and may affect non-covalent protein aggregates. The carrier fluid seemed to have a significant impact on aggregate stability, almost complete and partial dissociation was observed in two different buffers. Although shear stress did not affect the AF4 results, altered aggregate size distributions were observed in samples exposed to shear stress analyzed by DLS. However, increased focusing times did not change the aggregate distribution. Aggregates partially dissociate to smaller aggregates species during separation. Low molecular weight aggregates are more likely to dissociate in the buffer and during separation than high molecular weight aggregates [40].

To reduce sample loss, the membrane has to be chosen carefully. The cut-off range and the membrane-protein interaction significantly affect sample loss and recovery. Membrane-protein interactions are most prominent at high cross-flow conditions, selecting low absorption membranes such as regenerated cellulose, often minimizes this problem. For better separation, the membrane must be thin, smooth, flat, and free of creases [49]. In order to ensure a gentle separation as well as a high resolution, a programmed cross-flow could be useful [44], [45]. AF4 can be combined with similar detectors as for SEC, such as UV, refractive index, fluorescence and light scattering detectors [3]. Advantages of AF4 are the lack of stationary phase, which reduces shear and mechanical stress and interaction with the sample, the little sample preparation required, the wide choice of carrier liquid, allowing the use of the formulation

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buffer, and the large separation range from a few nanometers to a few micrometers diameter. Disadvantages are the dilution and concentration effects during the measurement which could influence the separation or alter the aggregates. Also, solution viscosity and potential interactions of the analyte with the membrane can influence the separation [26].

4.3 Centrifugation

Another separation technique to analyze protein aggregates is centrifugation. Centrifugation techniques separate analytes in suspension by their particle size or density using sedimentation. The hydrodynamic radius and density can be calculated using Stokes’ law. Two types of centrifugation are commonly used for the separation of proteins: analytical ultracentrifugation and disk centrifugation [26].

4.3.1 Analytical ultracentrifugation

Analytical ultracentrifugation (AUC) is a separation technique based on mass, size and shape. It is one of the most important methods to study interactions of macromolecules under physiological conditions and is able to study both weak and strong interactions [50]. In AUC a sample is centrifuged, separating analytes from the liquid. Analytes are separated from the liquid at different times, according to their density. Larger analytes are separated more quickly than smaller analytes. This provides an indication of the molecular weight and the diameter of the analyte [51]. The analytes are monitored in real time by optical absorbance or interference systems. This enables precise observations of the behavior of analytes undergoing sedimentation [52]. With AUC, little to no sample preparation is necessary and nearly any type of analyte can be investigated over a wide range of concentrations and in a diverse variety of solvents. This enables the characterization of aggregates in relevant solutions such as their formulation buffer [3], [4], [52]. At high protein concentrations, dilution might be required to prevent unreliable molecular weight determinations due to non-ideality [4]. The impact of dilution on reversible aggregates needs to be considered carefully. Results obtained by AUC are not dependent on comparison standards and do not rely on assumptions concerning shape [9], [24], [26]. AUC is able to analyze aggregates over wide size range from 1 kDa to over 2 GDa [24]. AUC is suitable for small protein aggregates up to 2000 kDa, the technique seems to be unsuitable for particles larger than 100 nm due to scattering effects and rapid sedimentation of large particles which will hinder detection. Approaches which use reduced centrifugation speed to analyze protein particles are being developed [26].

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A major advantage of AUC is the possibility to quantify protein aggregates, while formation or disruption of aggregates as a result of sample preparation, dilution or matrix effects is limited. Disadvantages are the often poor reproducibility and difficulty of assigning the limit of detection or quantification, the lengthy run time, and the requirement of highly specialized operators [3], [24]. Regular calibration and intensive maintenance of the system are required. Still, AUC has some strong advantages over SEC or AF4 such as the absence of interactions with columns or membranes, therefore AUC can be used as a qualitative orthogonal method for SEC or AF4. It can, for example, be used to verify that no aggregates potentially present in a sample are missed by SEC or AF4 [3].

There are several methods for characterization of heterologous protein-protein interactions including sedimentation velocity, sedimentation equilibrium, tracer sedimentation equilibrium and analytical band sedimentation. They all provide different information. Mostly used are sedimentation velocity (SV), which provides information about the size and shape of the molecule and sedimentation equilibrium (SE) which provides information regarding the molar mass, association constant, stoichiometry, and solution nonideality [4], [52].

Figure 18: Diagram of sediment velocity and sediment equilibrium AUC [24].

Sedimentation equilibrium

Dynamic associations which are reversible on the time scale of the experiment cannot be physically separated. These interactions are in an equilibrium that depends on the total protein concentration. The method of choice for these dynamic interactions is sedimentation equilibrium AUC [50]. In SE-AUC the sample is centrifuged at moderate speed to deplete all proteins from the region close to the center of the rotor. The centrifugal force produces a concentration gradient across the cell. The sedimentation is counteracted by diffusion of the analytes, resulting in a thermodynamic equilibrium between diffusion and sedimentation. The analyses

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distribute in an exponential. The concentration distribution at equilibrium only depends on the molecular mass and is measured by absorbance or refractive index detection while the sample is spinning. Furthermore, the overall distribution of monomers and self-associating aggregates will also be in equilibrium and, therefore, reflects the higher molecular weight of the associated states and their proportion in the sample [50], [53].

The exponential distribution can be seen in Figure 19 which shows the data from a monomer↔dimer↔tetramer reversibly associating system. Figure 19 b shows the fit as a sum of three exponentials and Figure 19 a shows the distribution of residuals for the fit. Figure 19 c shows the distribution of species as a function of the total monomer concentration

Figure 19: Equilibrium sedimentation data for a mutant VL domain of REI. a) distribution of residuals, b) fit of the data as a sum of three exponentials, c) derived distribution of species as a function of the total monomer concentration [50].

The information of the concentration profile significantly increases with larger column heights. However, the time taken to attain results is proportional to the square of the height of the solution column. A typical experiment requires between one and two days to perform [24]. Sedimentation velocity

For the characterization of protein aggregate interactions of static nature, sedimentation velocity is the method of choice [50]. Sedimentation velocity is the most used mode in AUC. In a SV-AUC experiment, the sample is centrifuged at high speed (50,000-60,000 rpm). The centrifugal force is larger than in SE-AUC and rapidly forces the proteins away from the center of the rotor,