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20 February 2014 Literature Thesis Sedimentation Velocity Analytical Ultracentrifugation (SV-AUC) for characterizing protein aggregates and contaminants in therapeutic proteins The elaboration of mathematical relations behind SV-AUC theory AUTHOR(S) : Lam, S. SUPERVISORS : dr. W. Th.Kok (Universiteit van Amsterdam)
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Page 1: Sedimentation Velocity Analytical Ultracentrifugation (SV-AUC) … · Sedimentation Velocity Analytical Ultracentrifugation (SV-AUC) for characterizing protein aggregates and contaminants

20 February 2014

Literature Thesis

Sedimentation Velocity Analytical Ultracentrifugation

(SV-AUC) for characterizing protein aggregates and

contaminants in therapeutic proteins

The elaboration of mathematical relations behind SV-AUC theory

AUTHOR(S) : Lam, S.

SUPERVISORS : dr. W. Th.Kok (Universiteit van Amsterdam)

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Literature thesis S. Lam

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MSc Chemistry

Analytical Sciences

Literature Thesis

Sedimentation Velocity Analytical Ultracentrifugation

(SV-AUC) for characterizing protein aggregates and

contaminants in therapeutic proteins

The elaboration of mathematical relations behind SV-AUC theory

by

S. Lam

February 2014

Supervisor:

dr. W.Th. Kok

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Table of context

Table of context 5

Abstract 6

1. Introduction 7

2. Protein aggregates and contaminants 9

3. Sedimentation Velocity Analytical UltraCentrifuge (SV-AUC) 11

3.1 Sedimentation velocity versus sedimentation equilibrium 11

3.2 Principle of the AUC 12

3.3 Principle of sedimentation boundary modeling (Lamm equation) 16

3.4 Sedimentation coefficient 18

3.5 Apparent sedimentation coefficient 18

4. Instrumentation 20

4.1 Analytical ultracentrifuge 20

4.2 XLA 23

4.3 XLI 24

4.4 Ordering 24

4.5 Application of the AUC 25

5. Analyses and approach 26

5.1 Apparent sedimentation coefficient distribution g*(s) analysis 26

5.2 Sedimentation coefficient distribution c(s) analysis 27

5.3 Therapeutic product related impurities (contaminations) 28

5.4 Approach and interpretation of the applications 28

6. Applications 31

6.1 Comparison between c(s) and g(s*) analyses 31

6.2 c(s) distribution with low aggregation levels 32

6.3 Therapeutic monoclonal antibodies homogeneity 33

6.4 Fluorescence detection 35

7. Conclusion 36

8. Discussion 36

References 37

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Abstract

Sedimentation velocity analytical ultracentrifugation (SV-AUC) is one of the classical

techniques for the study of protein aggregates and contaminations in therapeutic drugs (i.e.

monoclonal antibodies). Monitoring the sedimentation of proteins in the centrifugal field

allows the characterization of the sedimentation behavior of the particles in the solution,

without any interaction with matrix or surface. The sedimentation behavior and the rate of

sedimentation are described by the sedimentation velocity (SV) analysis.

The current thesis focuses mainly on the determination of the homogeneity and the

detection of small levels of soluble species (e.g. dimer, trimer, and so on). However, the

overload of new advancements, complex computational theories and large data sets make it

difficult for the protein scientists to gain sufficient expertise to apply AUC to their research

problems. Therefore, this thesis will initially explain the basic principle of SV-AUC, followed

by the modeling of the sedimentation boundaries obtained with this technique.

The two modeling analyses c(s) and g(s*) supported by the computational programs SEDFIT

and DCDT+, respectively, provide (apparent) sedimentation coefficient distributions. These

distributions are similar to chromatograms and are therefore easily to be interpreted.

However, c(s) and g(s*) analyses are slightly different, because c(s) includes diffusion while

g(s*) does not. After comparison, c(s) analysis was selected to continue with other

measurements, because it has a more improved resolution and sensitivity compared to g(s*)

analysis.

SV-AUC using c(s) analysis enables to determine the homogeneity of different types of

therapeutic proteins. It is also possible to detect small aggregates at low concentration levels.

A breakthrough for this SV-AUC will be the incorporation of the fluorescence detection into

account next to the currently used absorbance and interference detection, because the

sensitivity of fluorescence detection is much higher. This makes detecting low concentrated

aggregates and contaminants in strongly diluted samples possible.

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1. Introduction

In pharmaceutical chemistry studies, proteins (e.g. monoclonal antibodies[ 1 ]) are an

important division of therapeutic drugs[2]. In order to obtain therapeutic drugs, complex

reaction mechanisms are generally carried out between proteins from a particular biological

mixture. However, the same proteins can appear in different forms (e.g. misfolded,

denaturated and degraded) because the weak interactions and disulfide bonds that hold the

sensitive protein molecules together can be easily disrupted by stresses during purification,

storage or processing. The stresses[3] can be caused by several factors such as: hydrophobic

surfaces, elevated temperature, a change in pH, high shear, (hydrophobic) surface

adsorption, and the removal of water and high protein concentrations.

In general, a structural alteration in protein's structures often leads to protein

aggregation[1],[2],[4]. Protein aggregation is related to protein physical degradation and a

decrease of immunogenicity[2],[5],[6]. Therefore protein aggregates can have a negative

influence on the therapeutic drugs and also activate adverse resistant reactions to the drug.

Due to the complexity of protein's characteristics (i.e. various reactive chemical groups and

weak three-dimensional structures), it is however, practically impossible to develop a

therapeutic drug consisting of solely a pure native form of the protein.

In clinical research, maintaining the appropriate efficacy and safety of the therapeutic drug

ensures the quality of the therapeutic product. Because there are no clear guidelines or

agreed-upon approach in pharmacopoeia to ensure the quality[4] of the product. It is

imperative to have a control of the amount of protein aggregates, contamination and

homogeneity of the therapeutic protein. Consequently, characterization and identification

of protein aggregates and contaminants of the product is essential to eventually understand

the degradation pathways affecting proteins and the goal of an extensive repertoire of

analytical methods. Once the degradation pathways are discovered, the quality of the

therapeutic drug can be improved. Furthermore, therapeutic products are often

contaminated with host-cell-protein or non-protein particles besides the protein aggregates,

such as silica particles and leachates. These contaminations can lead to an expansion of

protein aggregates, which results in a serious damage to the product.

Moreover, protein aggregation has become a significant problem in the biopharmaceutical

industry due to its medical association with over 40 human diseases[7] (e.g. Alzheimer’s,

Parkinson's, Huntington's, prion and type II diabetes). Since protein aggregation has so

much impact on the characteristic of (therapeutic) protein drugs, it is necessary to measure

the amount of protein aggregation and comprehend the nature of protein structures to

understand the protein aggregation conditions.

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It should be noted that protein aggregates can be divided into different categories according

to solubility, reversibility, size and type of bonding[8]. The details of protein aggregates will

be discussed later in this thesis.

In this literature thesis, the selected analytical technique to characterize, identify and

quantify protein aggregates and contaminants is sedimentation-velocity analytical

ultracentrifugation (SV-AUC[9],[10],[11]). AUC actually has two modes (the sedimentation

velocity and sedimentation equilibrium modes[ 12 ],[ 13 ],[ 14 ]), but in this paper only

sedimentation velocity (SV)[15] measurements will be discussed. SV is more commonly used,

because it is a more time-saving and wider applicable method compared to the

sedimentation equilibrium mode. SV-AUC is selected to determine protein aggregation and

contaminants in therapeutic products because 1) SV-AUC has a typically measuring size

range[16] of 1.0 nm - 110 nm for protein aggregates, monomers and oligomers and 2) sample

destruction is not necessary due to its matrix- and column-free approach. The principle,

applicability and performance of SV will be discussed in chapters 2 and 3.

The SV-AUC is able to provide extension information on protein aggregates and

contaminants when supported by complex computational and internet resources. The

corresponding software programs SEDFIT[17] and DCDT+[22] are used to model sedimentation

data. Boundary modeling of the data based on non-linear least-squares regression includes

the mathematical relations of Lamm's equation[18],[19],[20] (transport-differentiation) and

Stafford[21] (time-derivative[22],[23]) method. Additionally, the two size distribution analyses

that will be discussed and partly compared in this paper are: 1) continuous sedimentation

coefficient distribution c(s) Lamm equation model (using SEDFIT program) and 2) apparent

sedimentation coefficient distribution[20] g*(s) (using DCDT + program).

The complex computational theories make it extremely difficult for protein (bio)scientists to

gain sufficient expertise to apply this modern technique to their research problem and to

manage the interpretation of the measured results. Therefore, this thesis will first explore

the (underlying) mathematical theory behind the SV-AUC to gain more knowledge of the

application of this analytical technique.

The major aim of this paper is to gain a greater understanding of the difficult mathematical

relation and principle of SV-AUC for the characterization of protein aggregates and

contaminations in therapeutic drugs. The methodology of SV-AUC is certainly not trivial,

because this can provide sufficient information to assist protein scientists to link with

different type of research with respect to therapeutic drugs, proteins, protein complexes

and protein aggregates.

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2. Protein aggregates and contaminants

When a protein binds to other copies of the same molecule they can oligomerize[24]. This

chemical process occurs between a few monomers and forms dimers, trimers or tetramers.

As the composition has exceeded four monomers, oligomer becomes polymer.

The advantageous feature to explore protein oligomerization is that due to these subunits

interactions the activity of the protein becomes concentration dependent and is therefore

beneficial for functional control. Proteins are not only occupied with self-associated

interactions[24], but also hetero-associated interactions[25],[26]. The latter occurs when the

protein interacts with other molecules. If protein interacts with other protein it forms a

protein complex[27] and is considered as a protein interacting system. The interactions

between two different proteins play an important role in various diseases.

Therapeutic drugs composed of protein mixtures are considered as an increasingly medically

important class because they are associated with over 40 human diseases (e.g. Alzheimer,

Parkinson etc.). Due to the sensitive bindings of proteins, they can be easily influenced by

stress factors. The stress factors (i.e. hydrophobic surfaces, elevated temperature, a change

in pH, high shear, surface adsorption, the removal of water and high protein concentrations)

interfere the protein structures and result unfolding or misfolding of the protein. This

occurrence of protein physical degradation regularly appears in therapeutic proteins.

Structurally changing of proteins forms cause a strong tendency of the protein to aggregate

during storage, processing and manufacturing. Protein aggregation has become a major

concern in pharmaceutical industry over the last decades, mainly due to unclear guidelines

or agree-upon approach in pharmacopoeia. Therefore it is crucial to characterize, quantify

and identify protein aggregates in therapeutic drugs.

Furthermore, it is important to characterize protein aggregates because once the

aggregation process has been started, protein aggregates are able to accumulate.

Accumulation of protein aggregates results an increase of misfolding proteins. According to

the mechanism of aggregation, the presence of contaminants accelerates the accumulation

of protein aggregates. These contaminants are often non-protein (e.g. silica particles), host

protein materials or an unfolded form of the protein product itself. The pathway of the

mechanism of aggregation from a product in presence of contaminants is likely to form

soluble oligomers as shown in Figure 2A pathway 1. These soluble oligomers then become

larger aggregates. In case the damaged protein contaminates with the native protein

(original protein), the pathway is slightly different (Figure 2A pathway 2). Accordingly,

pathway 2 leads to partial unfolding caused by soluble oligomers interacting with the native

protein. These partially or fully unfolded proteins may aggregate with other contaminants or

even incorporated into an existing aggregate nucleus to form larger aggregates. The latter

phenomenon is the major reason causing an accumulation of protein aggregates.

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Chemical modification (e.g. oxidation and deamidation) and stress (e.g. elevated

temperature and shear) are mostly the causes of damaged proteins. Minimizing protein

aggregation from these two mechanisms requires homogeneity in the therapeutic product,

therefore the determination of homogeneity is essential.

Figure 2. The pathway of the mechanism of aggregation from a product in presence of contaminants[2]

A third pathway occurs according to the mechanism of protein aggregation for self-

associating systems, which are dependent on low pH, temperature and solvent composition.

The native antibody is taken as an example for the illustration of the self-associating system

(Figure 2 B). This system refers to the formation of aggregates (oligomers) by native

antibodies. Acid stability takes a major role in aggregation of therapeutic monoclonal

antibodies, because both low-pH elution from a protein-A affinity column and viral

inactivation are involved during the purification process. These processes result in partially

unfolded monomers. The unfolded monomers associate with damaged monomers at low pH

and form protein aggregates.

The content of reversible aggregates changes with the total protein according to the law of

mass action. In principle, reversible aggregates will dissociate completely when the

therapeutic protein will be highly diluted in contrast to irreversible aggregates. These

irreversible oligomers are a concern to the therapeutic protein because they do not

dissociate at high dilution. Moreover, reversible aggregates can easily become irreversible

and thus the self-associating proteins aggregation is another pathway for accumulation. To

prevent the cause of this type of aggregates accumulation by self-associating proteins,

reversible aggregates have to be minimized. Therefore, quantitative determination of

content and characteristics of protein aggregate are required.

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3. Sedimentation Velocity Analytical UltraCentrifuge (SV-AUC) 3.1 Sedimentation velocity versus sedimentation equilibrium

To explain the basic principle of analytical ultracentrifuge (AUC[28],[29]) it should be noted that

this technique can be divided into two modes of operation: sedimentation equilibrium (SE)

and sedimentation velocity (SV). The former is used to obtain thermodynamic properties and

the latter to obtain hydrodynamic properties. Thermodynamic properties[30] are interesting

for characterization of reversible associations and hydrodynamic properties[35] are more for

general determinations. This thesis only focuses on SV, because this is a faster, more general

and wider applicable method than SE. It is worth noting that it is still often recommended to

carry out sedimentation equilibrium mode to complement SV. Furthermore, SV and SE are

based on the same principle.

The selection of which method (sedimentation velocity or sedimentation equilibrium) is

strongly dependent on the type of interaction (static or dynamic). Static interactions are very

slowly reversible or irreversible, whereas dynamic interactions are rapidly reversible on the

time scale of the experiment. Slowly reversible associations cannot physically separate

different states of association during the whole measurement and are commonly studied by

the sedimentation equilibrium (SE) method. An example of this low-speed experiment is

shown in Figure 3 (b). This figure shows the equilibrium between sedimentation and

diffusion of a 65 kDa single species.

Figure 3. Basic concepts in analytical ultracentrifugation (AUC). (a) Sedimentation velocity (high-speed) experiment with

elapsed time intervals of 5 minutes. (b) Equilibrium (low-speed) experiment with elapsed time intervals of 4 hours. The red

line represents the final gradient, which is a close approximation to sedimentation equilibrium. [15]

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In contrast to dynamic interactions, static associations make it possible to physically

separate and characterize different states of association (e.g. individual oligomers). Static

associations are mostly studied by the sedimentation velocity (SV) method. This method is

shown in Figure 3 (a). Furthermore, the principle of the AUC technique is valid for both SV

and SE methods and will be explained in the next chapter.

3.2 Principle of the AUC

The principle of AUC is based on three forces that act on the particle (m) : sedimentation

force (Fs); the opposing directional forces: buoyant force (Fb) and frictional force (Ff). A

schematic sketch of a particle with a constant velocity (u) experiences in a solution during

centrifugation is illustrated in Figure 4.

Figure 4. Schematic sketch of particle in solution during centrifugation[28]

As illustrated in Figure 4, Fb and Ff are working at the opposite direction of Fs, therefore the

two forces have negative signs. The sedimentation force has to be much stronger than the

sum of the two opposite forces to let the particle sediment towards the bottom of the vial.

Fs can only be stronger when the particle is subjected to the gravitational field, since the

strength of Fs is fully dependent on the applied gravitational field. After applying a

gravitational field the particles basically migrate away from the axis of spin based on their

masses. The sedimentation force is proportional to the mass difference between fluid (m0)

and particle (m)with the corresponding equation the gravitational acceleration of the

particle(ω2r) can be determined with AUC.

Sedimentation force : Fs = ω2r(m - m0) (1a) Where: ω square of angular velocity r distance of particle from the axis of rotation m mass of particle - m0 mass of the fluid that is displaced by the particles

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The frictional force exists because there is more than one particle in a solution. Basically

when many particles are continuously moving in the solution, the particles are moving along

each other. Thus, it does not matter which direction a specific particle is moving there is

always frictional force between the particles. The corresponding equation for this force:

Frictional force : Ff = -f .u (1b) Where: f frictional coefficient u velocity of the particle

Particles with different sizes sediment with different velocities. The large particles sediment

faster toward the bottom than smaller particles. Additionally, there is a flux diffusion force

or diffusion flux (Jr) that opposes the sedimentation force. Fick's laws of diffusion describe

the movement of the number of molecules from high concentration crossing an area per

time to low concentration regions. The diffusion flux Jr is used to quantify how fast the

diffusion process occurs. The description of diffusion process is described by equation 2a.

Diffusion flux :

(2a)

Where: C Concentration of protein r radius -D diffusion coefficient

The negative sign of the diffusion coefficient (-D) is to cancel the negative concentration

difference, dC (Clow-Chigh), because diffusion occurs from high concentration to low

concentration.

The principle of diffusion flux (force) according to Fick's first law of diffusion is illustrated in

Figure 5A, where the concentration (C) of the particles (y-axis) is plotted against the radius

direction, r-direction (x-axis). The start position (r1, blue dotted line) divides the molecules

into two different (low and high) concentration levels (two solid horizontal lines). Different

end positions are denoted as ri (i = 1, 2,...,n). As two radius positions are selected the radius

and concentration differences, dr (rn -r1) and dC (Cn - C1), respectively are measured. This

resulted the calculation for the gradient dC/dr, which is equal to the slope of a particular

(red) point on the concentration profile.

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Figure 5 A Principle of diffusion flux (Fick's first law) Figure 5 B Diffusing atoms towards r-direction

[31] Diffusion is a mass transfer process from high concentration to low concentration over a

certain direction with different positions (r1, r2, r3...rn). This direction indicates the

movement of particles toward a specific position in the vial and is expressed in radius (r) or r-

direction (Figure 5B).

By combining equation 2a with the illustration in Figure 5A, we observe proportionality

between the diffusion fluxes along direction r with the concentration gradient dC/dr. The

principle of AUC is supported by the sedimentation and diffusion terms. Thus, to describe a

better association between diffusion flux and sedimenting particles, the sedimentation term

( has to be added to the flux equation[32] (equation 2a). The extended diffusion

flux equation including sedimentation term is shown as follows:

Flux :

(2b)

Where: C Concentration of protein r radius -D diffusion coefficient sω2r velocity or u

Jr : diffusion flux

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Fick's diffusion flux equation is only functional for a solution in an ideal infinite cell. In an

ideal infinite cell the concentration of species and the radius are linear related. However, for

real finite sector cells with experimental conditions the concentration distribution is not an

ideal infinite cell to any further extent. A normally used finite sector cell in SV-AUC

experiments is displayed in Figure 6.

Figure. 6 Finite sector cell/cup for analytical ultracentrifuge

[33]

In Figure 6, where the ω is denoted as the rotational axis and r refer to the radius from spin-

axis to the cell. In addition, the meniscus is a curved surface formed by the surface tension

between the liquid and the cup. In contrast to ideal infinite cells, finite sector cells provide

non-linear sigmoid distribution as shown in Figure 7. The inset of this figure shows

distributions over different times. This means that the concentration is not only dependent

on the radius distance, but is also dependent on the time.

Figure 7. The illustration of concentration distribution with centrifugation, frictional and diffusion force. The inset is distributions measured over different times.[34]

Even though equation 2b is not the most appropriate formula for describing the true

relationship between sedimentation and diffusion because the time variable is neglected, it

still describes the basic principle of the particle's behaviors undergoing sedimentation and

diffusion. This Fick's equation can be adjusted to a Lamm equation solution, which includes

the time variable. The diffusion flux equation according to Fick's first law is therefore

considered as the kernel of this upgraded and corrected Lamm equation solution.

r

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3.3 Principle of sedimentation boundary modeling (Lamm equation) The Lamm equation solution is obtained by combining the partial derivatives of the two

dependent variables: time (t) and radius (r). The purpose of partial derivatives is holding one

variable constant while changing the second dependent variable. The Lamm equation

solution is shown in equation 5a and it shows the evolution[i] of the concentration

distribution variations of molecules in a centrifugal field as a function of time with the two

competing processes: diffusion (

(r,t)) and sedimentation terms ( (r,t)).

Lamm equation solution:

(5a)

Where: r radial position (r,t) concentration of solute as function of time and radial position ω square of angular velocity s sedimentation coefficient

The Lamm equation solution is convenient because it can be directly applied on the raw data

for direct boundary modeling. In practice, the concentration distributions ( from this

Lamm equation solution are denoted as continuous distribution c(s) or apparent

sedimentation coefficient distribution g*(s).

Furthermore, Lamm equation solution is based on the mass transport process theory[34],[35]

and was used for the modeling of concentration distributions in SV-AUC experiments in this

study. To explain the principle of mass transport theory, sinusoidal functions are used to

simulate the motion of particles in AUC. Although the particles in AUC do not behave

sinusoidal, but this assumption makes it easier to explain this theory.

So let's assume the waves of the sinusoidal functions have a constant speed (velocity). If we

measure the magnitude of the waves on arbitrary positions, the magnitude will be changing

at every turn. Same is true for measuring the magnitude on different times, because then

the magnitude will be varying as well.

This mass transport theory can be used for AUC, because 1) the molecules are continually

moving away from the spin axis of the cell (r) with a constant diffusion speed and 2) the

magnitude of the sinusoidal functions varies at different times even the same radial area

(between r1 and r2) is holding the same. This phenomenon of sinusoidal functions based on

the principle of mass transport theory is illustrated in Figure 8. Where, the magnitude of the

sinusoidal waves is replaced by the concentration of the molecules (y-axis). It should be

noted that the real sedimentation data are not sinusoidal functions, but sigmoid functions.

i Evolution = The progress of different subpopulation of molecules during sedimentation.

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Therefore sinusoidal waves shown in Figure 8 (left) are only for the clarification of the

principle of the mass transport theory. The raw data generated from AUC are s-shape

boundaries (sigmoid functions). The principle of the mass transport theory is applicable for

the sigmoid functions/sedimentation boundaries that are measured over times (Figure 8

(right)).

The concentration is plotted against the radius/radial position (x-axis). The radial area is

between the two vertical red lines. The black line refers to the original sinusoidal function on

t = 1 and the black dotted line is the same sinusoidal function measured at a later time (t = 2).

Figure 8. (left) Principle of mass transport using sinusoidal waves. (right) transport equation applied to Sedimentation

boundaries (raw data)[10]

.

The distance of the migration is expressed in radius (cm). Like mentioned before, the

observed area is hold constant between r2 and r1. As shown in the picture the concentrations

of the solid line at t=1 and the dotted line at t=2 are different, where t=1 is at a previous

time than t=2. Figure 8 (left) shows different concentration at the same area on different

times, which reflects the underlying (mass) transport of the Lamm equation. The theory that

is illustrated in Figure 8 (left) is very useful for real sedimentation boundaries data (Figure 8

right), because the principle according to the mass transport theory is the same.

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3.4 Sedimentation coefficient The motion of the sedimentation boundary as a function of time is typically used to

determine the sedimentation coefficient (s)[36],[37], diffusion coefficient (-D) and homogeneity.

Diffusion coefficient was already explained in the previous section, but the sedimentation

coefficient is a new introduced parameter derived from the Lamm equation solution. This

parameter is important because it characterizes the protein's or protein aggregate's

behaviors undergoing the sedimentation process using boundary sedimentation velocity.

The equation of sedimentation coefficient according to Svedberg theory is given as follow:

Sedimentation coefficient :

(6a)

Where: a centrifugal acceleration u velocity ω square of angular velocity or angular momentum

Sedimentation coefficient is expressed in Svedberg unit (S)[17],[38] or 10-13sec and is the

velocity of the particle per unit gravitational acceleration. To keep it simple and not going

into details of physics is actually an intuition of centrifugal acceleration from AUC. It is

important to know that the velocity of a molecule in a centrifugal field depends on the

physical properties of the molecule. Molecules with different properties will have a different

velocity in a centrifugal field. Sedimentation coefficient does not solely depend on the

acceleration but more on the properties of the particles and the medium that the particles

are suspended in. The physical properties that the sedimentation coefficient is associated

with are: molecular weights (only significant for single molecules), shapes, sizes and

densities.

3.5 Apparent sedimentation coefficient Sedimentation coefficients (s) can also be determined for each individual radial point instead

of a specific boundary area (between r1 and r2). This is called an apparent sedimentation

coefficient (s*)[17],[39] and is dependent on the position, time and rotor speed. This parameter

is determined by the differential apparent sedimentation coefficient distribution g*(s)

method. This method will be discussed in chapter 5.1.

For the calculation of the apparent sedimentation coefficient, the boundary has to be

equally divided into boundary parts. Subsequently, the boundary parts will be cumulative

ranked in an ascending order. For cumulative ranking the maximum is set on 1 (or 100%

percentile) and the minimum is set on 0. Accordingly, the cumulative distribution ranges

from 0 to 1 or (0% - 100%). The plateau concentration is the maximum concentration that

has reached the saturation absorbance level. The corresponding radius of this maximum is

the plateau radius (rp). The minimum of this distribution is the radius at meniscus (rm).The

calculation of the apparent sedimentation coefficient is shown in equation 6b.

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Apparent sedimentation coefficient

(6b)

Where: ω square of angular velocity or angular momentum t time ri/rp boundary fraction rp radius at plateau ri radius that is taking from the cumulative distribution

As shown in equation 6b, a boundary fraction is calculated by ri/rp (i = 0.1, 0.2,...,1). The

illustration of this theory for estimating the apparent sedimentation coefficient g*(s) is

shown in Figure 9.

Figure 9. Cumulative distribution of sedimentation boundary to determine the apparent sedimentation coefficient (s*). This

graph with boundary fraction as the y-axis is plotted against radius (x-axis)40

.

A shown in Figure 9, the boundary fraction can be selected by choosing any individual radius

point ( ) and divide it by rp to calculate the apparent sedimentation coefficient s*. For

example, if the selected radius is at the plateau concentration (rp), the calculated boundary

fraction is then rp/rp (r11/r11) which results 1 as shown in Figure 9. If the selected

concentration is at the meniscus (rm/rp, r1/r11) it is 0. The mobility of a particle at a specific

time corresponds to a sedimentation coefficient. Since the relation can be written as: ln(ri/rp)

= s*ωt, this relation can be better illustrated with Figure 10. The apparent sedimentation

coefficient s* is the slope of the sedimentation boundaries that are measured over time.

Figure 10. The illustration of calculating the apparent

sedimentation coefficient s*.[36]

slope = s*

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4. Instrumentation

4.1 Analytical ultracentrifuge The AUC[41] is able to rotate at speeds up to 60,000 rpm, which creates a centrifugation force

of up to 250,000 g. This strong g-force is required to sediment small particles (i.e. proteins,

protein aggregates and contaminants). There are two types of analytical ultracentrifugation

that is introduced by Beckman Coulters Optima Instruments, the XLA and XLI. The difference

between the two AUC are the optics. XLA has UV and visible absorption optics and XLI has

integrated absorbance and interference optics. The detection optics XLA or XLI are normally

installed at the same AUC centrifuge. Accordingly, the selection in mode has to be initially

selected for XLA or XLI. The AUC from Optima with XL-A and XL-I optics is shown in Figure 11.

Figure 11. The Optima™ XL-A and the Optima XL-I analytical ultracentrifuges

[42].

Although the optics are based on different principles in detection, same sector-shaped

centrifuge cells are used for both XLA and XLI. These sector-shaped centrifuge cells are

covered by quartz or sapphire to make optical detection possible. Double sector

centerpieces are commonly used, where the one sector is filled with the sample solution and

the second sector can be used as reference cell to correct for high absorbance background of

the solvent (Figure 12 A). For a triple-sector centerpiece for six channels (Figure 12 B), three

solution/solvent pairs can be measured. The columns are shorter with a speed limitation and

are commonly used for sedimentation equilibrium (SE) analysis (this is not discussed in this

report of sedimentation velocity). For sedimentation velocity analyses a double-sector

centerpiece is mostly chosen to obtain a sedimentation boundary.

Figure 12. sector-shaped centrifuge cells/centerpieces: (A) Double sector for SV experiments (B) Triple sector for SE experiments

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A complete assemble of the analytical ultracentrifuge cell including the double-sector

centerpiece is shown in Figure 13.

Figure 13. Assembly of the double-sector analytical ultracentrifuge cell. A) Assembly of window assemblies.

B) Stacking centerpiece and window components. C) Cell housing[43]

.

The technique of loading solutions into double-sector centerpiece (shown in Figure 13)

requires a rigorous level of technical attention, because sample cell components are often

very expensive and to achieve an optimum working condition. Sample cells hold a sectored

centerpiece sandwiched between two window components (Figure 13 A and B). The contact

between centerpiece and window assemblies must be as tight as possible to prevent leaking

and breakage during the rotating speeds up to 60.000 rpm and under high vacuum.

Reference solution and sample are loaded into the centerpiece bottom and upper sectors,

respectively. After placing in a cell-housing with screw-ring and washer (Figure 13 C), the

cells are precisely aligned into a titanium rotor so that the optical detection systems scan

both (protein) sample and reference solution in the same radial path mid-line.

The absorbance or interference that is measured for the protein is dependent on the

position of the centerpiece. Since the AUC is set on a very high speed, the positions of the

meniscus (top) of both solvent/reference and sample are important to recognize at which

radius from the meniscus the species are measured. As shown in Figure 14 A - D, varying

time of sedimenting species provide different plots. The plots are raw data of absorbance (y-

axis) versus radius (x-axis).

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Figure 14. (A-D) Sedimentation plots of different times of sedimenting species.[46]

XLA[44] has UV and visible absorption optics and XLI[45] has integrated absorbance and

(Schlieren or Rayleigh) interference optics (Figure 15). Schlieren optics[34] measures the

refractive index gradient and is normally used for molecules that do not have (sufficient)

chromophores to use photoelectric absorbance. The refractive index gradient is directly

proportional to the concentration gradient; therefore the Schlieren readout can be used to

determine the concentration of protein solutions. Rayleigh interference optic is more

sensitive than Schlieren optic, so for modern AUC the Rayleigh optics are used. Rayleigh

optic has a higher refractive index, due to their light source (i.e. monochromatic light, laser).

A major advantage of refractive index optics is that they are not interfered by high

absorbance background of the solvent.

Figure 15. Comparison of the data obtained from the (a) schlieren, (b) XLI interference, (c) XLA absorbance optical

systems[34]

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4.2 XLA The light source of XLA is a xenon lamp which is projected from a 1 mm circular aperture

which enables to produce 3-dimensional graphs. The light will pass a toroidal diffraction

grating for aberration correction, because the first-order light efficiency is intensified in the

ultraviolet (UV) range by ion bombardment. Hence, the chromatic stray light[ii] will decrease.

The grating is also rotated by a precision gear train to select or scan a wavelength in the

range of 200 nm and 800 nm with a nominal band pass of 2 nm (slit).

Light emerging from the grating collides on the 8% reflector and when the light reached the

reflector it reflects back to a solid-state detector. As a result, the intensity of light incident

on the sample in the cell assembly will be monitored by the detector. This intensity and the

transmitted intensity that are measured by the photomultiplier (PM) tube are used to

normalize the variation in the light intensity emitted from the lamp.

This normalization is necessary, because the reference and the sample sectors in the cell are

measured separately and simultaneously. Due to XLA is a dual-beam instrument it can

diverge absorbance from the reference half of the dual cell and the sample of the other half

even the distance between the dual cells is within 1 cm and the speed is 60.000 RPM (Figure

16).

Figure 16. Schematic description of XLA[34]

ii Chromatic stray light = light that has a chromatic abbreviation, which means that there is a failure of a lens to focus all colors to the same

point due to dispersion of the light (different refractive indices for different wavelengths).

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4.3 XLI The light source of XLI is a a laser diode light source which sends out monochromatic light,

which passes through two fine parallel slits. A schematic depiction of XLI is shown in Figure

17. When the light beams have passed through the slits and two sectors they undergo

interference when combined with a condenser lens to yield a band of alternating light and

dark “fringes.” When the refractive index in sample section is higher than in reference, the

sample wave is slower relatively compared to the reference wave. This causes a vertically

shift of the positions of the fringes to the concentration difference at a reference point.

Furthermore, if the concentration of the reference point, crF, is known, the concentration at

any other point can be obtained with the following equation:

Concentration sample : cr = crF +aΔj (7)

Where: Δj vertical fringe shift a constant relating concentration to fringe shift

Figure 17. Schematic description of XLI[34]

4.4 Ordering The XLA and XLI analytical ultracentrifuges can be ordered on the website of

www.Beckmancoulter.com. Unfortunately, the price is unknown on the site, but by ordering

it is possible to find that out. The experts of AUC at Merck in OSS Netherlands estimate the

price of approximately >1.0 million. Compared to mass spectrometers (200-800 K) AUC is

much more expensive.

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4.5 Application of the AUC A frequently used experiment for analytical ultracentrifuge (AUC) is the sedimentation

velocity (SV) experiment. This method is carried out at very high speeds (40.000 - 60.000

rpm) and the measurement takes 1 - 3 hours, depending on what kind of experiment is in

progress. The high centrifugal force rapidly causes the migration of the proteins towards the

bottom of the sector and forms a sedimentation boundary. The concentration distribution

across the cell at various times and radius during the experiment is measured while the

sample is rotating. It measures the sedimentation rate at which the molecules migrate in

response to the centrifugation force in AUC. This sedimentation rate provides information

about:

sedimentation coefficient s-value

boundary shape of the proteins

Isotherm of the weight-average s-value

differential distribution coefficient of the molecules

Sedimentation velocity is particularly valuable for:

Detection of aggregate(s) in protein samples and also quantify the concentration of

the aggregate(s)

Verify the homogeneity of a sample

Establish the native state of a protein, monomer, dimers and so on.

Measure the size distribution in samples, small/large molecules only or mixture of

small and large molecules.

Study the formation of complexes between proteins (antigen-antibody complex or

receptor-ligand complex)

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5. Analyses and approach

5.1 Apparent sedimentation coefficient distribution g*(s) analysis The apparent sedimentation coefficients can be estimated from sedimentation boundaries.

This can also be done for sedimentation boundaries over different measured times. The

envision of the DCDT+ approach is shown in Figure 18.

Figure 18. An envision of the chronological steps (1-4) to obtain g(s*) distribution that is derived by time derivative dcdt method.

[36]

Consequently, a collection of many s* is obtained and resulted s* distributions (step 2). By

performing the Lamm equation solution on the s* distributions, the normalized dc/dt

distribution was calculated (step 3). After simulating the dc/dt distribution, the apparent

sedimentation coefficient distributions g*(s) were obtained (step 4). Similar to a

chromatogram, the area under each peak gives the total concentration of species.

Apparent sedimentation coefficient distribution g(s*) considers the migration of boundary

and reflects the boundary shape. Even though this analysis is based on the Lamm equation

solution, this equation has to be adjusted. This is because the Lamm equation assumes

dealing with diffusing species, whereas g*(s) is assuming to have non-diffusing species. The

adjusted and converted equation derives the modeling of g*(s) distributions (shown in

Figure 19).

Lamm-equation Differential distribution of non-diffusing species

Figure 19. The conversion of a differential distribution of non-diffusing species for modeling g*(s) from Lamm-equation

modeling.

Conversion

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Where, r is radius; t is time; s is sedimentation coefficient; D is diffusion coefficient; and is

residual. Figure 18 shows the direct boundary model where the solution of single species of

the Lamm-equation is replaced by the theoretical sedimentation profiles of

non-diffusing species . The measured sedimentation profile, absorbance or

interference profiles are given as c(r,t). The measured profiles are modeled as an integral

over the differential concentration distribution c(s) for Lamm equation and sedimentation

coefficient distribution g*(s) for the converted equation. The converted apparent

distribution is assumed to have no diffusion (D (s) = 0).

A major drawback of g*(s) analysis is the low resolution and sensitivity of the sedimentation

coefficient distributions for mixtures of species with different sizes; This is typically caused

by neglecting the diffusion process. To solve this drawback, a differential sedimentation

coefficient analysis was taken into account for this study. In contrast to g*(s), this c(s)

analysis includes diffusion. In this paper, these two analyses will be compared with each

other for the determination of protein aggregates and contaminants. The principle of the c(s)

analysis will be explained in the following paragraph.

5.2 Sedimentation coefficient distribution c(s) analysis The c(s) distribution is used to calculate a sedimentation distribution of species taking into

account their diffusion and is based on the Lamm equation solution (equation 5a). This

method is computationally the most complex approach, yet it has the potential for

improving resolution and sensitivity in respect to g*(s). For simple and fast measurements,

g*(s) is still the recommended analysis for modeling the data.

Because the use of numerical solutions of the Lamm equation, it has no constraints in the

data set that can be considered for analysis. Additionally, this is the most general

sedimentation approach with respect to size range for the distribution. However, there are

some key assumptions made in this technique in the form of statistical and experimental

prior knowledge, which must be properly adjusted to avoid wrong interpretation of results:

(1) The strategy uses hydrodynamic prior knowledge (weight-average frictional ratio) to

estimate the extent of diffusion for each species and 2) validation of prior assumptions is

necessary.

An example of the differential sedimentation distribution c(s) that is plotted against the

sedimentation coefficient which was determined by the mathematical data analysis program

SEDFIT is shown in Figure 18 B. Because this program makes use of the Lamm equation

solution, the distribution of sedimentation coefficient vs. c(s) (Figure 20 B) links with the

direct sedimentation boundaries modeling results (Figure 20 A). This modeling is done by

statistical criteria involving the (non-linear) least squares method.

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Figure 20 A. direct sedimentation boundaries modelling

[9] Figure 20 B. c(s) versus sedimentation coefficient (s) [9]

Figure 20 B shows profiles similar to a chromatograms and the relative (loading)

concentration can be assessed by the area under the curve with different s-values. The c(s)

analysis is a frequently selected analysis for the determination of protein aggregates in

therapeutic drugs. In this paper, this analysis will be partly compared to the g*(s) analysis,

which provides apparent sedimentation coefficient distributions. The g*(s) analysis also

provides profiles that are similar to chromatograms, yet this analysis differ from c(s) analysis

because g*(s) analysis is based on a different principle.

5.3 Therapeutic product related impurities (contaminations) Proteins are macromolecules that are composed of amino acids. In this report it will mainly

discuss about protein aggregates and contaminating species. The contaminants are normally

present in the protein mixtures in small size and amount. Small species have sizes below

50kD and large proteins (aggregates) have sizes above 50kD. Generally, the SV-AUC method

can achieve several distributions (in this study, i.e.: c(s) and g(s*)) to characterize different

protein mixtures. The characterization of these protein mixture in this literature thesis

focuses on reactions containing contaminations, with emphasis on specific factors such as: 1)

homogeneity of the product and 2) detecting small soluble oligomers (e.g. dimers, trimers,

etc.), while comparing c(s) and g(s*) analyses.

5.4 Approach and interpretation of the applications Heterogeneous interactions are defined as interactions in which two (or more) reactants (A

and/or B) from mixtures containing two species (like protein A and B), reversibly form a

complex with a specific stoichiometry. Examples of such interactions would follow

association schemes like A + B ⇔ AB; A + 2B ⇔ AB 2 ; AB + B ⇔ AB 2 ; etc. Self-association

reversible system or multiple reactions are slightly different than heterogeneous interactions

and can be written as: (A + A + B ⇔ A2), where the concentration from one component

affects the concentration of the other component.

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The homogeneity of (protein) products can be determined by SV-AUC. The c(s) distribution

from a certain protein product, shown in Figure 21 will be expected.

Figure 21. Full c(s) distributions of the protein that contains 4.7 % dimer, 1.8% trimer, 1.1% tetramer and 0.7% low mass contaminant, where the percentage is based on the total protein. Inset: Enlarged c(s) distributions to show the low mass contaminant at 2S

[46].

Figure 21 shows a heterogeneous system, because we observe the amount of species

sedimenting at different rates, which are expressed in sedimentation coefficients (S).

In contrast to normal reversible systems, self-association proteins are more complex. This

system occurs when the protein has an intramolecular binding with itself and this dimer,

trimer, tetramer, etc. (Figure 22). Figure 22. Ultracentrifugation c(s) distribution analyses of full-length Factor H and three fragments. (A-C) The monomer is denoted by 1, the dimer by 2, and so on, where the c(s) is the y-axis and sedimentation coefficient is the x-axis. It can be noticed that SCR-1/5 forms only monomer (a), SCR-6/8 forms monomer and a small amount of dimer (b), and SCR-16/20 forms almost equal amounts of monomer and dimer (c). (D) shows the full-length Factor H, boundary scans measured at 5.92 mg/mL and 0.17 mg/mL are shown in red and the boundary fits are shown in black. (F) The five c(s) analyses for Factor H between 0.17 mg/mL (bottom) and 5.92 mg/mL (top) revealed the monomer and a series of oligomers labeled from 2 to 7.

[47]

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This type of system makes it looks like the monomer has a higher concentration and is

typically an occurrence of self-associating systems. Because when macromolecules associate

with itself, the molecular weight increases. Consequently, the sedimentation coefficient will

increase with increasing concentration.

In Figure 22 D the perturbations show the existence of more rapidly sedimenting species.

Figure 22 F shows that above a certain concentration of Factor H (about 10 % - 15 %), Factor

H will be dimeric if no other factors influence the equilibrium and this results the appearance

of peak number 2 at every measurement that is shown in Figure 22 F, while other oligomers

(numbers 3 - 7 ) vanish at some measurement series and present in other series.

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6. Applications

6.1 Comparison between c(s) and g(s*) analyses Small species that do not participate in the self-association system are called contaminations.

In the presence of 20% contamination in the self associating protein system, the

sedimentation coefficient distributions c(s) and g*(s) are determined. These sedimentation

coefficient distributions are shown in Figure 23 , where sedimentation coefficient

distribution, either c(s) or g(s*) (y-axis) is plotted against s-values (x-axis). To provide more

clarity for the graphs, g(s*) has an offset of 0.4.

Figure 23. Sedimentation coefficient distributions c(s) from simulated data of the self associating protein system in presence of a 20% contamination with a smaller species(of loading concentration) not participating in the association (mw = 50000 kDa and s = 3S). The normalized distributions at concentrations of 0.2 µM (solid line), 2.0 µM (dashed line) and 20.0 µM (dotted line). For comparison the same concentrations with the representing lines of the g(s*) distributions are also calculated and for clarity an offset of 0.4 is chosen for g(s*)

[48].

The 20% contamination with a smaller species is visible at 3S (Figure 23). Since these smaller

species do not take part of the association with the protein, the sedimentation coefficient of

this contamination is not dependent on the concentration of the protein. As a result,

disregarding the concentration level of the protein (e.g. 0.2 µM (solid line), 2.0 (dashed line)

or 20 µM (dotted line)), the contaminating species holds it sedimentation coefficient at 3S.

The second peaks after the peaks at 3S referring to the protein itself. As we can see here is

that, unlike the 20% contamination, the variation in concentration of the protein caused

sedimentation coefficient shift to the larger side with increasing concentration.

According to the theory and the observation from Figure 23, we see that the resolution of

g(s*) distributions are much weaker than c(s) distributions. This is because the diffusion is

not taken into account for g(s*), whereas for c(s) analysis it is. Therefore, g(s*) analysis is

also purely used for reflecting the sedimentation boundary shape and not really useful for

detecting low concentrated contaminants, like this measurement.

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6.2 c(s) distribution with low aggregation levels Previous results showed that c(s) analysis has improved the resolution of the peaks in

respect to g(s*) analysis in presence of contaminating species. Since, c(s) analysis is more

improving in separating peaks from the mixture, I have decided to continue with only the c(s)

analysis. Normally, in several studies it claimed that the c(s) analysis is not an appropriate

method to detect low aggregation levels or minor aggregates due to the dependency on

both size and shape. The detection of low aggregation levels is therefore a challenge for the

c(s) analysis. To test whether it is possible to use the c(s) analysis to detect low level

aggregates, three different proteins: an antibody, an FC-fusion protein and a cytokine were

measured by the SV-AUC using the c(s) analysis. Each protein with high levels of (10% - 20%)

aggregation was blended into a sample with very low aggregation levels, these results are

shown in Figure 24.

Figure 24. Representation of c(s) distributions using the SV-AUC method for A) Antibody, B) Fc-fusion protein and C cytokine.

For each protein a degraded sample with high levels of aggregation (10% - 20%) was combined into a sample with low

aggregation levels[49]

.

Figure 24 shows a clear separation between the first two peaks for all three proteins

(antibody, Fc-fusion protein and cytokine). The first peak is the monomer and the second

peak is typically a dimer peak, because the sedimentation rate is similar to the monomer

(result not shown). The third peaks for all three proteins present, refer to the contaminants.

It can be demonstrated that it is possible to perform c(s) analysis on different type of

proteins to separate and identify low aggregation levels.

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6.3 Therapeutic monoclonal antibodies homogeneity Protein aggregation is a major problem for therapeutic proteins like monoclonal antibodies

(MAb), because it can affect the stability of these products. Therefore the homogeneity of

these proteins were tested by using SV-AUC (c(s) analysis). Two types of MAb: MAb-a and

MAb-b were measured at standard conditions of 20C and after heating. Heating is one of the

methods to deliver stress to the antibodies. The results for antibody MAb-a and MAb-B are

shown in Figure 25 and Figure 26, respectively.

Figure 25. Left: SV-AUC analysis of approximately 0.5 mg/ml monoclonal antibody MAb-a, at 50.000 rpm, and 20C in 50 mM Tris-HCl, 0.1 M NaCl, pH 7.5. Right: SV-AUC analysis of the same antibody from the left after heating. A) Raw sedimentation boundaries and B) sedimentation coefficient distributions c(s) derived from A)

[5].

As shown in Figure 25, the higher the molecular weight of antibodies means that the moving

boundaries for antibodies are less broadened by diffusion and the separation is more

improving. This is an important reason why it is necessary to mathematically resolve so

many components and detect peaks present at levels of only a few tenths of a percent (low

levels aggregates).

This MAb-A antibody starts off with a higher aggregate content of 5.7% (sum of aggregates %

at 9.57 S, 12.1 S and 16.0 S). After heating, the MAb-a sample becomes quite heterogeneous

(materials are sedimenting at different sedimentation coefficients).

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Figure 26. Left: SV-AUC analysis of approximately 0.5 mg/ml monoclonal antibody MAb-b, at 50.000 rpm, and 20C in 50 mM Tris-HCl, 0.1 M NaCl, pH 7.5. Right: SV-AUC analysis of the same antibody from the left after heating. A) Raw sedimentation boundaries and B) sedimentation coefficient distributions c(s) derived from A)

[5].

Figure 26 on the left shows that the monomer of antibody MAb-b has a sedimentation

coefficient of 6.63 S and accounts for 95.7% of the total sedimenting solutes. The species at

9.13 S and at 11.6 S, which accounts for 3.1% and 1.1% off the total, are probably a dimer

and trimer (results not shown). In this experiment the parameters such as shape, size and

sedimentation rate were unfortunately not taken into account, therefore the dimer and

trimer can only be empirically assumed that they present.

After the sample was subjected to heat stress (Figure 26 right), it shows a decrease to only

56.2 % of the monomer. Additionally, at least eight peaks of aggregates are detected. The

most prominent aggregate peaks at 9.90, 12.7, 15.1, 17.3, and 20.2 S fall very close to the

positions expected (relative to monomer) for dimer, trimer, tetramer, pentamer, and

hexamer based on model hydrodynamic calculations (results not shown).

Interestingly the distributions of aggregates formed by the two antibodies MAb-a and MAb-b

are different even though heat stress produced about 50% total aggregate for both.

Additionally the results of both antibodies showed that after heating they both are having a

heterogeneous system.

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6.4 Fluorescence detection The more recent additional detection with fluorescence extends the flexibility of analytical

ultracentrifugation with respect to the existing absorbance and interference detectors

dramatically. It is claimed that fluorescence detection gives a strong improvement of the

applicability of AUC compared to the two former detection modes[59].

Earlier in this report absorbance and interference detections are discussed, because these

detections are commonly used. Fluorescence detection complements these two detections,

because it allows AUC analysis for strongly diluted solutions. An example of the titration of

Alexa-488 labeled, goat anti-mouse lgG into a fixed concentration of mouse lgG in 100 mM

KCl 20 mM Tris pH 8, 0.1 mg/ml ovalbumin is shown in Figure 27. The sedimentation

coefficient distributions c(s) of the presence (dotted lines) and absence (solid line) of a fixed

concentration mouse lgG to different concentrations of Alexa-488 labeled lgG.

Figure 27. Titration of Alexa-488 labeled goat anti-mouse lgG into a fixed concentration of mouse lgG in 100 mM KCl 20 mM

Tris pH 8, 0.1 mg/ml ovalbumin. For each concentration of Alexa-488 labeled lgG in presence (dotted line) or absence (solid

line) of a fixed concentration mouse lgG, a c(s) distribution has been determined. The data have been normalized on every

c(s) distribution[48]

.

The labeled Alexa-488 lgG without mouse lgG (dotted lines) are fixed on the peak position of

6.8 S, which is consistent of being a monomer. The complex formations of labeled Alexa-488

lgG and mouse lgG (solid lines) shift to higher s-values. Interestingly, when labeled Alexa-488

lgG is in a high concentration with mouse lgG (red line, 70 nM), the peak of the complex

formation has shifted (back) to a lower s-value. This indicates that the antibody is in excess

in the solution. The shifts in s-values indicate that low-concentration sample compounds in

complex mixtures can be determined due to the high sensitivity and selectivity of

fluorescence detection.

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7. Conclusion

Protein aggregation is often a major problem for therapeutic proteins. Contaminants (such

as: non-protein, host cell protein materials or damaged form of the protein product itself)

often lead to accumulation of protein aggregates. The formation of protein aggregates can

cause serious damage to the therapeutic product; therefore experiments are carried out to

determine the homogeneity of the product and to detect small soluble oligomers. The

experiments were performed by the sedimentation velocity ultracentrifugation (SV-AUC).

The selected sedimentation distribution analyses for modeling the raw sedimentation

moving boundaries data are: c(s) and g(s*). These two analyses were supported by the data

analysis programs: SEDFITfor c(s) and DCDT+ for g(s*). The former analysis includes diffusion,

whereas the latter analysis does not. By comparing c(s) and g(s*) analyses (Applications from

6.1) I observed that the resolution and sensitivity of c(s) is more improving due to direct

fitting of sedimentation profiles with Lamm equation modeling, which includes diffusion

process. Thus after comparison I have decided to continue with solely the c(s) analysis for

the next experiments.

From the results obtained with SV-AUC and c(s) modeling I can conclude that:

1) It is possible to detect low levels aggregates (small soluble oligomers) in different type of

therapeutic proteins.

2) Homogeneity or heterogeneity of therapeutic antibodies can be properly characterized.

Overall, it can be concluded that the SV-AUC is a very useful technique in characterizing and

detecting protein aggregates in the size range of SV-AUC 1.0 nm - 110 nm (typically

measuring range for protein aggregates, monomers and oligomers) and compared to other

techniques this is a non-destructive method because it has a matrix- and column-free

approach.

8. Discussion

Fluorescence detection has a higher selectivity than absorbance and interference and is

therefore able to detect low concentration (highly diluted) species in complex protein

mixtures by observing the shifts in s-values.

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References 1 Rosenberg AS. Effects of protein aggregates: an immunologic perspective. The AAPS journal 2006;8(3):501-07.

2 Arakawa T, Philo JS, Ejima D, Tsumoto K, Arisaka F. Aggregation analysis of therapeutic proteins, part 1.

Bioprocess International 2006;4(10):32-42. 3 Byeong S, Herhenson S. Practical approaches to protein formulation development. Practical approaches to

protein formulation development. in "Rationale Design of stable protein formulations-theory and practice" (J.F. Carpenter and M.C. Manning eds.) Kluwer Academic/Plenum publishers, New York, pp. 1-25 4 Arakawa T, Philo JS, Ejima D, Tsumoto K, Arisaka F. Aggregation analysis of therapeutic proteins, part 2

Analytical ultracentrifugation and dynamic light scattering. Bioprocess International 2007;4(10):36-47. 5 Guidance for Industry Immunogenicity Assessment for Therapeutic Protein Products, U.S. Department of

Health and Human Services Food and Drug Administration. Center for Drug Evaluation and Research (CDER). Center for Biologics Evaluation and Research (CBER) 2013 6 Schellekens H. Factors influencing the immunogenicity of therapeutic proteins.

Nephrology Dialysis Transplantation 2005;20(suppl 6):vi3-vi9. 7 Fang Y, Gao S, Tai D, Middaugh C R, Fang J. Identification of properties important to protein aggregation using

feature selection. BMC Bioinformatics 2013, 14:314 8 McPherson G. Beyond the speed of light (scattering), Bioprocess international april 2012

9 Krayukhina E, Uchiyama S, Nojima K, Okada Y, Hamaguchi I, Fukui K. Aggregation analysis of pharmaceutical

human immunoglobulin preparations using size-exclusion chromatography and analytical ultracentrifugation sedimentation velocity. Journal of Bioscience and Bioengineering Volume 115, Issue 1, January 2013, Pages 104–110 10

Lebowitz J, Lewis M.S, Schuck P. Modern analytical ultracentrifugation in protein science: A tutorial review. Protein sci. 2002 September, 11(9); 2067 - 2079. 11

Mittal V, Lechner M.D. Size and density dependent sedimentation analysis of advanced nanoparticle systems. Journal of Colloid and Interface Science Volume 346, Issue 2, 15 June 2010, Pages 378–383 12

Schuck P. On the analysis of protein self-association by sedimentation velocity analytical ultracentrifugation. Anal Biochem. 2003;320:104–124. 13

Laue TM. Sedimentation equilibrium as a thermodynamic tool. Methods Enzymol. 1995;259:427–452. 14

Van Holde K.E., Baldwin R. L., J. Phys. Chem. 62 (1958) 734 15

Howlett G.J, Minton A.P, Rivas G. Analytical ultracentrifugation for the study of protein association and assembly. Volume 10, Issue 5, October 2006, pages 430-436. 16

Zolls S, Tantipolphan R, Wiggenhorn M, Winter G, Jiskoot W, Friess W, Hawe A.Particles in therapeutic protein formulations, Part 1: Overview of analytical methods. Journal of pharmaceutical sciences, 2011

18

Dam J, Velikovsky C.A, Mariuzza R.A, Urbanke C, Schuck P. Sedimentation Velocity Analysis of Heterogeneous Protein-Protein Interactions: Lamm Equation Modeling and Sedimentation Coefficient Distributions c(s). Biophysical Journal Volume 89 July 2005 619–634

Page 38: Sedimentation Velocity Analytical Ultracentrifugation (SV-AUC) … · Sedimentation Velocity Analytical Ultracentrifugation (SV-AUC) for characterizing protein aggregates and contaminants

Literature thesis S. Lam

38

19

Zhao H, Balbo A, Brown P.H, Schuck P. The boundary structure in the analysis of reversibly interacting systems by sedimentation velocity, Methods 54 (2011) 16–30 20

Schuck P. Size-Distribution Analysis of Macromolecules by Sedimentation Velocity Ultracentrifugation and Lamm Equation Modeling. Biophysical Journal Volume 78 March 2000 1606–1619 21

Walter F, Stafford III. Boundary analysis in sedimentation transport experiments: A procedure for obtaining sedimentation coefficient distributions using the time derivative of the concentration profile. Analytical biochemistry 203, 295-301 (1992). 22

Stafford W. F., ‘Method for obtaining sedimentation coefficient distributions’ in Harding S. E., Rowe A. J.,Horton J. C., Analytical ultracentrifugation in biochemistry and polymer science. The royal society of chemistry, Cambridge (1992) 359.

23 Stafford W. F., Boundary analysis in sedimentation transport experiments: a procedure for obtaining

sedimentation coefficient distributions using the time derivative of the concentration profile. Anal Biochem.

1992, 203 (2); 295 - 301

24

Schuck P. Sedimentation Analysis of Noninteracting and Self-Associating Solutes Using Numerical Solutions to the Lamm Equation. Biophysical Journal Volume 75 September 1998 1503–1512 25

Schuck P. On the analysis of protein self-association by sedimentation velocity analytical ultracentrifugation. Analytical Biochemistry 320 (2003) 104–124 26

Schuck P. Diffusion-deconvoluted sedimentation coefficient distributions for the analysis of interacting and non-interacting protein mixtures. Chapter for “Modern Analytical Ultracentrifugation: Techniques and Methods ” (D.J. Scott, S.E.Harding, A.J. Rowe, Editors) The Royal Society of Chemistry, Cambridge (in press) 27

Balbo A, Minor K.H, Velikovsky C.A, Mariuzza R.A, Peterson C.B, Schuck P. Studying multiprotein complexes by multisignal sedimentation velocity analytical ultracentrifugation. University of California, Berkeley, CA, November 11, 2004 28

Ralston G; Introduction to Analytical Ultracentrifugation, Beckman Coulter Inc. Fullerton, US. 29

Lloyd P.H. Optical Methods In Ultracentrifugation, Electrophoresis, and Diffusion; Clarendon Press, Oxford 1974 30

Mücke N et al.: Molecular and Biophysical Characterization of Assembly-Starter Units of Human Vimentin. J Mol Biol. 2004 Jun 25;340(1):97-114. 31

Lecture: Introduction to material science for engineers chapter 5. University of Tennessee 32

Serdyuk I.N, Zaccai N.R, Zaccai J. Methods in Molecular Biophysics: Structure, Dynamics, Function. Cambridge University press. May 14, 2007. Edition 1. 33

Roberts R. lecture 6. http://www.its.caltech.edu/~ch24/lecture6.pdf 34

Moore J.D. Introduction to partial differential equations, May 21, 2003 35

Lenstra A. Lecture Math for HLO bachelor, 2013 36

http://www.analyticalultracentrifugation.com/sedfit_help_analytical_zone_centrifugation.htm

Page 39: Sedimentation Velocity Analytical Ultracentrifugation (SV-AUC) … · Sedimentation Velocity Analytical Ultracentrifugation (SV-AUC) for characterizing protein aggregates and contaminants

Literature thesis S. Lam

39

37

http://www.ap-lab.com/sedimentation_velocity.htm 38

Schuck P. Determination of the sedimentation coefficient distribution by least-squares boundary modeling. Biopolymers. 2000 Oct 15;54(5):328-41. 39

van Holde, K. E. and W. O. Weischet. Boundary Analysis of Sedimentation Velocity Experiments with Monodisperse and Paucidisperse Solutes. Biopolymers, 17 (1978); 1387-1403 40

Demeler, B. and K. E. van Holde. Sedimentation velocity analysis of highly heterogeneous systems. Anal. Biochem. 2004, Vol 335 (2); 279-288 42

https://www.beckmancoulter.com 43

Cole J.L, Hansen J.C. Analytical Ultracentrifugation as a Contemporary Biomolecular Research Tool. J Biomol Tech. 1999 December; 10(4): 163–176. 44

Demeler B, Saber H. Determination of Molecular Parameters by Fitting Sedimentation Data to Finite-Element Solutions of the Lamm Equation. Biophysical Journal Volume 74 January 1998; 444–454 45

MacGregor I.K, Anderson A.L, Laue T.M. Fluorescence detection for the XLI analytical ultracentrifuge. Biophysical Chemistry 108 (2004) 165–185 46

http://www.ap-lab.com/sedimentation_velocity.htm 47

Perkins S.J, Nan R, Li K, Khan S, Miller A. Complement Factor H–ligand interactions: Self-association, multivalency and dissociation constants. Immunobiology 217 (2012) 281–297 48

Laue T. Analytical ultracentrifugation: a powerful ‘new’ technology in drug discovery. Drug Discovery Today: Technologies, Vol 1, No.3, 2004; 309-315. 49

Gabrielson J.P Arthur K.K. Measuring low levels of protein aggregation by sedimentation velocity. Methods 54 (2011); 83–91


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