Relating Collective Diffusion, Protein-Protein Interactions and

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Relating Collective Diffusion, Protein-Protein Interactions and Viscosity of Highly Concentrated Monoclonal Antibodies through Dynamic Light Scattering Barton J Dear, Amjad Chowdhury, Jessica J. Hung, Carl A. Karouta, Kishan Ramachandran, Maria P. Nieto, Logan R. Wilks, Ayush Sharma, Tony Y. Shay, Jason K Cheung, Thomas M. Truskett, and Keith P. Johnston Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b03432 • Publication Date (Web): 30 Aug 2019 Downloaded from pubs.acs.org on August 30, 2019

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Industrial & Engineering Chemistry Research

Relating Collective Diffusion, Protein-Protein Interactions and Viscosity of Highly Concentrated Monoclonal Antibodies through Dynamic Light Scattering Barton J. Deara, Amjad Chowdhurya, Jessica J. Hunga, Carl A. Karoutaa, Kishan Ramachandrana, Maria P. Nietoa, Logan R. Wilksa, Ayush Sharmaa, Tony Y. Shaya, Jason K. Cheungc, Thomas M. Trusketta,b and Keith P. Johnston*a a) McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712, United States b) Department of Physics, The University of Texas at Austin, Austin, TX 78712, United States c) Biophysical and Biochemical Characterization, Sterile Formulation Sciences, Merck & Co., Inc., Kenilworth, NJ 07033 USA

*200 E Dean Keeton St. Stop C0400, Austin, TX 78712 Phone: 512 471 4617 Fax: 512 471 7060 email: [email protected]

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Abstract To understand and predict the viscosities of highly concentrated monoclonal antibody (mAb) solutions, it is important to characterize the protein-protein interactions (PPI) and how they influence the possible formation of protein clusters. Herein, the collective diffusion is measured by dynamic light scattering (DLS) for solutions of three different mAbs, each with a various co-solutes to tune the PPI. The results are combined with measurements of static structure factor, (0), and self-diffusion coefficient, Ds, to understand the behavior of viscosity at high concentration. The small degree of variation in the hydrodynamic factor,

, and solvent protein friction,

, among systems with a

wide range of viscosities suggests solvent-protein interactions have a small influence on viscosity. Measurements of net PPI such as (0) and the diffusion interaction parameter,

, are predictive of high

concentration viscosity across co-solutes for a single mAb, but not for multiple mAbs. In contrast, properties that characterize the presence of clusters in solution, such as the polydispersity index from DLS,

, and the coefficient of protein-protein friction,

, exhibit stronger correlations to

viscosity.

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Introduction Monoclonal antibodies (mAbs) may be used to treat a wide variety of diseases, for example, autoimmune diseases and cancer.1-2 In order to deliver a sufficient dose by subcutaneous administration, highly concentrated (100-300 mg/mL) solutions are required.3-5 Here the separation between mAbs becomes small (1 s for pulsed field gradient nuclear magnetic resonance (PFG-NMR)), the mAb is able to exit the surrounding cage during the course of the measurement leading to more complex dynamics.47-49 The long-time self-diffusion coefficient,

is often related to viscosity through the Generalized Stokes-

Einstein (GSE) equation (1)

= where

and

are the Boltzmann constant and temperature, and

and

are the hydrodynamic

radius and effective viscosity experienced by the tracer, respectively50. If the tracer particle is much smaller than the proteins in solution,

is equivalent to the solvent viscosity,

= 0.

Conversely,

becomes the macroscopic viscosity, , when the tracer particle is much larger than the protein. Thus, tracer particles, ranging from approximately 100 nm to 1 µm, are often used to measure the viscosity of protein solutions.12, 51-53 However, when the sizes of the tracer and mAb are on the same order (for example when the tracer is a labelled mAb),

=0

250 mM) to target a concentration of 250 mM at high concentration as done in previous work.13 After the final concentration was achieved the pH of both solutions was verified (Table 1). The reported SLS (except for mAb4), viscosity and FCS data were previously published as mAb2 and mAb3 SLS and viscosity data can be found in work by Hung et al.,41 mAb4 viscosity data in Dear, et al.,26 and mAb2 FCS data can be found in Hung et al.58 The mAb4 SLS measurements were performed identically to those for mAb2 and mAb3 by Hung et al.41 Dynamic Light Scattering (DLS) The diffusion coefficient of the mAb in each co-solute formulation was measured by DLS using a ZetaPALS zeta potential analyzer (Brookhaven Instruments, Holtsville, NY; P = 660 nm, R = 90°, and thus

= 0.013 nm-1), with some select samples also measured on a Malvern ZetaSizer Nano ZS

(Malvern Panalytical, Westborough, MA; P = 633 nm, R = 173°, and thus samples were sterile-filtered with 0.22 T

= 0.020 nm-1). MAb

PVDF filters (Ultrafree -MC-GV, MilliporeSigma,

Burlington, MA) prior to DLS measurements (to remove dust and particulates) and measured in triplicate, where each run consisted of 4 15-second scans that were averaged together. The recorded values are the average value of all the runs and the error bars indicate the measured standard deviations. The DLS ACFs, ) * were fit using Brookhaven Instruments’ Dynamic Light Scattering software using the quadratic cumulant algorithm77 to obtain

and the polydispersity index, 7


, by Eqn. 3

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)(*) = + ,

(-

* *

+

2*

2

2

2

)

(3)

where * is the correlation time, + is the fit baseline amplitude of ) * = 0), * is the fit characteristic mean correlation time with * = (

2 -1

)

, and

2

is the variance of the inverse correlation times fit to

quantify the effect of polydispersity on the diffusion with polydispersity index,

= *2 2.78 In

addition to the quadratic cumulants the ACFs were also fit with a Gaussian distribution model (GDM) (Eqn. 4) similar to what has been previously used to fit FCS data.58, 79 * 2

( )

(4a)

]

(4b)

]

(4c)

150

)(*) = +/1 = 1 1exp - *1

+1 = ) ,

[

/150 ) , 1=1

[

ln

*1 2

() *

- 2ln (7)2

ln

*1 2

() *

- 2ln (7)2 = 1

where *1 represents 150 different pre-selected correlation times (logarithmically spaced between 1 and 10000

), which are weighted by a Gaussian distribution with weight

1.

1

was determined by fitting

the average and standard deviation of characteristic correlation times, * and 7, respectively. ) is a normalization constant determined by Eqn. 4c. Representative ACFs with both the cumulants and GDM fits at ~200 and ~10 mg/mL are reported in Fig. S2 of the supporting information for samples of all three mAbs with either 250 mM Arg or 250 mM NaCl, as well as for mAb2 with 1000 mM Im. All DLS values reported are calculated from the quadratic cumulants method, unless specifically stated otherwise. All of the low concentration

values (concentrations up to the point at which

linearly with concentration) were fit to Eqn. 580-82 to obtain

0,

and

, where

began to change nonis the slope of

0

versus concentration at infinite dilution. ( )=

0(1

The values of

(5)

+ 0

and

from Eqn. 1 using

for each mAb solution are reported in Table S1 along with the =

=0

with

=0

9

calculated

being measured by a Cannon-Fenske viscometer.26

Theory 8 ACS Paragon Plus Environment


As derived in previous work54, 63, =

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can be calculated by Eqn. 6

(1 - :)2

where

(6)

is the solvent-protein friction per mole protein per mole solvent,

of solvent, : is the volume fraction of protein and

is the molar concentration

is the gas constant. To accurately calculate the

protein volume fraction the hydration layer was included83-85 as follows: :=

; < + =

(7)

?> + ; < + =

where ; is the protein mass and < is the volume of dry protein per mass (set to 0.7407 mL/g for this study),85 is the volume of water per mass (set to 1 mL/g), ?> is the total volume of unbound water, and = is the mass of hydration in terms of the mass of bound water per mass of protein). The value of = was set to 0.7 g/g for this study, which is higher than the 0.4 g/g previously used for BSA,85 because mAbs likely have more bound water than BSA due to their larger surface per volumes. Furthermore, this value produces : similar to those in previous studies.32, 41, 58, 86 Dividing the numerator and denominator of Eqn. 7 by 1 ml yields :=

(8)

< +=

At infinite dilution where : = 0 and (0) = 1, 0

=

=

9

where 9

9

(9)

=0

9

is the solvent-protein friction per mole solvent per mole protein at infinite dilution (with = 0@+),

=

and

9

is the hydrodynamic radius of the particle at infinite dilution.

Combining Eqns. 2, 6, and 9 shows that (0) =

is described by the Stokes-Einstein equation

(1 - :)2

= 0

9

= 0@+

can be directly related to

(1 - :)2

=

0

and :. (10)

Alternatively self-diffusion coefficients are related to both protein squared,

,

and protein-protein friction per mole

, as previously derived54, 63 (11)

+


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where

is the molar concentration of protein. At infinite dilution Eqn. 11 simplifies to Eqn. 9 as both

and

equal

0.

Assuming that

+

=

@+ at concentrations greater than zero

converts Eqn. 11 into the GSE equation (Eqn. 1). Combining Eqn. 6 and Eqn. 11 yields the following relation between =

and

+

(1 - :)2

=

. (1 - :)2 1

Previous studies have either assumed =

9

and

follows GSE yielding

(12) = 0, yielding the friction ratio, =

= 1,64, 87 or assumed that

=0

.54

The data will be compared to analytical expressions for hard sphere (HS) solutions. HS structure factors, (0) , hydrodynamic factors, (0) , normalized self-diffusion coefficients, and

9 0

, are

calculated from the Carnahan-Starling (Eqn. 13)49, the empirically determined Eqn. 1488 (which is shown to match simulations of (0) 89 - 90 in Fig. S3), and the Van Blaaderen (Eqn. 15)91, respectively. The normalized collective diffusion coefficients of hard spheres,

9 0

, is calculated by Eqn.

16 which comes from combining Eqns. 2, 13 and 14 as follows: (1 - :)4

(0)

= (1 +

(0)

= (1 - :)6.55

(13)

:)2 + :3(: - 4)

(14)

(1 - :)3

9 0

( ) 0

(15)

= 1 + '&0: + 2:2 + 3:3 = (1 - :)2.55[(1 + :)2 + :3(: - 4)]

(16)

Results and Discussion Collective Diffusion We begin with the results of

from DLS at low concentration to approximate the strength of

mAb PPI through kD 6, 9, 13, 15, 24, 34, 92. In Fig. 2, 0

the kD of each mAb solution was determined by fitting

0

versus concentration at low concentration using a weighted linear least squares minimization (further



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details can be found in the supporting information). The concentration range for the fit was limited to concentration values less than the point at which the change in

0

began to deviate from linear behavior.

For mAb2 and mAb3, in Figs. 2A and 2B respectively, the mAb diffusion is faster (higher

) for

solutions with Arg and Im (particularly 1000 mM Im) relative to those with NaCl or Lys. This order matches that of relative viscosities,

C,

(Fig. S4 and Table 1) which are lowest for Arg and Im at a given

mAb concentration. The 250 mM Arg and NaCl solutions for each of these mAbs, and the more viscous mAb4, are presented in Fig. 2C. The

values still loosely follow the order of viscosity, as the

larger for NaCl relative to Arg solutions. Furthermore, the

is

values increase from mAb2 to mAb3 to

mAb4 (for relative viscosity ;+D > ;+D( > ;+D )as presented in Table 1. In Fig. 3 the measurements of of the mAb solutions

0

0

are extended to high concentration up to ~250 mg/mL. For all

initially decreases with concentration, but then plateaus around ~125 mg/mL up

to the highest concentrations measured (250 mg/mL), as has previously been seen for mAbs up to 150 mg/mL with high ionic strength.37 This behavior is vastly different from HS behavior (dashed lines in Fig. 3). This indicates that mAb diffusion is strongly affected by interactions beyond those of hard spheres, such as short-range attractions, including dipole interactions, and solvation contributions. As observed for

for a given mAb, higher values of

0

at the plateau (recorded in Table 1) corresponded

closely with the relative viscosities, but the differences between samples are larger at high concentration. It should be noted that high concentration DLS measurements could possibly be affected by multiple scattering93-94 which would cause the reported

0

to be higher than the true value.95-96 The effects of

multiple scattering were addressed by performing a few experiments in the back scattering mode at 173° in the Malvern Zetasizer Nano ZS instrument, where multiple scattering is reduced. As discussed further in the supporting information (Fig. S5), the effect of multiple scattering is relatively small as the measured values of

0

only vary by ~10%. The low degree of multiple scattering is consistent with the

small turbidities (Fig. S6), with 0.98 with the

slopes. Therefore, any trends seen comparing

slope to other properties in Table 1 are essentially the same using 7 slopes (data not shown). Table 1. List of physical properties measured for each mAb solution. Previous studies reported the values for J@K

,41 and J@K

+L

;GH1IG

( ) ;; +

,

.26

Cosolute (mM)

pH

C at 200 mg/ mL

50 NaCl 250 Arg 250 NaCl 250 Im 250 Lys 1000 Im 50 NaCl 250 Arg 250 NaCl 250 Im 250 Lys 250 Arg 250 NaCl

5.38 5.30 5.35 5.92 5.43 6.32 5.30 5.39 5.40 6.14 5.58 6.05 6.08

58 27 59 30 50 13 143 43 156 73 113 70 498

MN

410 135 555 143 500 125 mg/mL)

(0) at 200 mg/mL

0.44 0.57 0.39 0.55 0.41 0.84 0.51 0.61 0.38 0.56 0.39 0.42 0.17

0.21 0.14 0.27 0.18 0.24 0.12 0.16 0.12 0.13 0.15 0.17 0.15 ---

-0.14 ± 0.07 3.59 ± 0.05 -1.43 ± 0.11 0.80 ± 0.07 -1.46 ± 0.85 6.20 ± 0.16 -0.94 ± 0.77 -1.41 ± 0.22 -3.10 ± 0.13 -2.37 ± 0.26 -2.22 ± 0.44 -0.77 ± 0.35 -9.16 ± 1.03

;GH1IG

( ) ;; +

6.56 0.01 5.86 3.04 7.75 250 mM. Higher magnitudes indicate better correlations, while negative values suggest an inverse relationship, such as when attraction is strong

is lower, but viscosity is higher. Correlations are determined from values in Table 1.



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1 2 3 Correlation of all Data 4 J@K +L at / 0 at (0) at C at ;GH1IG 5 ** J@K ** 200 200 125 200 MN 22 (>125 ;; + Slope 6 mg/mL mg/mL*** mg/mL**** mg/mL) mg/mL* 7 C at 200 1.00 0.93 -0.67 -0.82 -0.74 -0.04 0.97 0.76 0.88 1.00 1.00 8 mg/mL 9 1.00 -0.82 -0.87 -0.85 0.09 0.94 0.75 0.92 0.99 0.97 MN 10 1.00 0.87 0.86 -0.10 -0.66 -0.48 -0.78 -0.79 -0.92 11 1.00 0.88 -0.32 -0.69 -0.72 -0.82 -1.00 -0.94 22 12 / 0 13 1.00 -0.55 -0.67 -0.80 -0.78 -0.97 -0.92 (>125 14 mg/mL) 15 (0) at 200 1.00 0.03 0.52 0.16 0.97 1.00 16 mg/mL* 17 ;GH1IG ** 1.00 0.80 0.71 0.93 --18 ;; + 19 J@K ** 1.00 0.51 0.95 --20 1.00 0.35 0.89 Slope 21 at 200 1.00 --22 mg/mL*** 23 J@K +L at 24 1.00 125 25 mg/mL**** 26 *Does not include mAb4 with 250 mM NaCl 27 **Does not include any mAb4 data 28 ***Only includes 3 mAb solutions all with mAb2 (250 mM Arg, 250 mM NaCl, and 1000 mM Im) 29 **** Only includes 3 mAb solutions (mAb2 with 250 mM Arg, mAb4 with 250 mM Arg and mAb4 with 250 mM NaCl) 30 31 As can be seen in Table 3, the parameters that best correlate with viscosity are and the 32 average aggregation number, J@K +L . J@K +L was determined from SAXS structure factor data at 125 33 34 mg/mL that were fit with 12-bead coarse grained molecular dynamics simulations.26 Since both of these 35 36 properties were only measured for three high ionic strength systems (all with mAb2 for ), it is not 37 38 yet fully known if they are better indicators of viscosity than the other measurements. However, because 39 40 they are directly influenced by the presence of clusters in solution there is reason to hypothesize that 41 42 they might be better indicators than , 22, 0 or (0), as many studies suggest that the presence of 43 44 clusters in mAb solutions elevate viscosity.7-10, 26, 39, 41 Recently mAb solution viscosities were related to 45 46 the cluster size distribution.11 Furthermore, this concept has been extended for cluster size distributions 47 from 12-bead model simulations that were fit to SAXS data.26 The is a measure of friction that is 48 49 directly affected by the presence of these clusters,63 and is thus strongly related to viscosity. The J@K +L 50 51 contains direct information about the size of clusters and is influenced not only by the net PPI in 52 53 solution, but also by the presence of specific local anisotropic short ranged attraction.26, 98 Alternatively, 54 55 properties based solely on , including (0), 22, and for the most part 0 (since (0) is mostly 56 57 58 25 59 ACS Paragon Plus Environment 60

( )

( )

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similar for the studied mAbs, Fig. 5) and

, are primarily indicative of net PPI. Computational studies

of mAbs,26 and other systems27, 103 have shown that large differences in cluster formation can occur between systems with the same net value of attraction. Specifically, mAbs with large but relatively weakly attractive regions form far fewer clusters in solution than those with small but strongly attractive regions.26 Furthermore, measures of net PPI can often be correlated strongly with viscosity for a given mAb13, 41 (as seen in Table S4 for correlations of just weakly interacting mAb2 solutions), but less strongly across mAbs (such as in Table 3), especially when nonuniform local attraction is prevalent on particular beads.13, 15, 41 It should also be noted that compared to the other techniques included in Table 3, the measurements of

is somewhat more unwieldy as it requires high concentration

measurements by DLS, SLS and FCS. It should be noted that

could also potentially be measured

by shear rheology given an accurate molecular viscoelasticity model for proteins since viscosity is a measurement of the friction coefficient on the molecular level as suggested by Einstein’s fluctuation dissipation theorem104. After

and J@K

the slope of the linear fit to

+L

the properties that best correlate with high concentration viscosity are and the oligomer ratio from SLS,

;GH1IG

( ) ;; +

. Both of these properties are

correlated more strongly with viscosity than the conventional low concentration properties The

and

22.

is a direct measurement of polydispersity from the presence of clusters in solution which

explains the strong correlation with viscosity. The oligomer ratio and average cluster size from SLS, J@K

, were calculated for the mAb2 and mAb3 systems in a previous study,41 and are determined from

fits of an interacting hard sphere model30-32, 105 (IHS) to the excess Rayleigh ratio, which is directly related to (0),41 across a wide range of mAb concentrations. The IHS model attributes the changes in concentration-dependent scattering to the formation of reversible oligomers, such that the scattering intensity at a given concentration corresponds to weighted contributions from a distribution of monomer, dimer and a characteristic higher order oligomer of fit aggregation number, M. The oligomer ratio is the mass fraction, ,, of the higher order oligomer divided by the sum of mass fractions of the monomer and dimer, while the J@K

is the average mass-based cluster size /1 = '9 9M(,11 . Even though (0) at a given

concentration is only indicative of net PPI, the cluster size distributions are related to (0) (or excess Rayleigh ratio) over a wide concentration range through the IHS model, which is affected by more than simply net PPI.26, 28, 41, 105 For example, for the same net PPI (0) has been shown to change more with 26 ACS Paragon Plus Environment


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concentration for 12-bead models (representing mAbs) with small strong attraction sites on particular beads than for those with large weak ones.26 Additionally, Fig. S8 specifically demonstrates that the change of (0) with concentration is consistent with the trend in viscosity (mAb4 > mAb3 > mAb2). In terms of practicality both the

and the oligomer ratio only require a single type of measurement

(DLS and SLS, respectively), but determining the oligomer ratio involves more complicated calculations and requires many measurements to accurately determine the curvature of the Rayleigh ratio versus concentration. Conclusions In this work, the dynamic behavior of three mAbs was tuned with co-solute formulations and examined and characterized using DLS up to 250 mg/mL. The

determined at low concentrations with

DLS correlates loosely with the high concentration viscosity across multiple mAbs and co-solute systems, as has been seen previously.13, 15 As the protein concentration increases to ~125 mg/mL, reaches a plateau. Thus,

0

0

does not follow GSE, as it is additionally affected by the osmotic

compressibility (equivalent to (0)), and the solution micro-viscosity, which is intermediate between the solvent and solution viscosities. The plateau values correlate well with viscosities across multiple cosolute systems for a given mAb, but not across multiple mAbs. However, the best predictor of viscosity across multiple mAbs obtained solely from DLS is the

at high concentration, which characterizes

the decay times from diffusion of monomer and small reversible oligomers. The interpretation of the DLS data was more informative upon adding complementary static measurements by SLS,41 or SAXS26 as well as measurements of properties, including

,

,

from FCS58 to obtain a broad set of

. For example, the effects of thermodynamic and hydrodynamic

interactions on the observed diffusive behavior could be delineated. The variations in combining

0

from DLS and

, obtained by

from SLS,41 were small among systems at a given mAb concentration,

as these properties followed HS behavior. The values of the hydrodynamic property

were similar

despite variations in the thermodynamic PPI and widely different viscosities, as seen previously for silica particles with varying amounts of depletion attraction.97 Upon combining from DLS, the

and friction ratio (

-1

from FCS and

) could be determined. These properties were correlated


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strongly with the aggregation number of clusters as characterized by the J@K

+L

, J@K

,

;GH1IG

( ) ;; +

and

, as well as the viscosity. Thus, the results extend previous work in which viscosities of mAb

solutions were directly related to the presence of clusters, as characterized by structure factors via simulations of SAXS data,26 and even more specifically, the cluster size distributions.11, 26 In contrast, properties related to net PPI strength, such as

0

,

,

22,

and

are only loosely correlated with high

concentration viscosities as they do not capture cluster properties that depend upon the specific strength and location of the attractive regions on the mAbs.26 Acknowledgements The authors gratefully acknowledge Merck Sharp & Dohme Corp., a subsidiary of Merck & Co., Inc., Kenilworth, NJ, USA, Pfizer Inc. and the Welch Foundation (F-1319 and F-1696) for their financial support. The authors are particularly grateful to Dr. Chuck Ekert. The emphasis that Chuck placed on molecular understanding and molecular thermodynamics were very much appreciated for this study by his academic son KPJ and the academic grandchildren. Furthermore, the influence of Chuck on Pablo Debenedetti benefitted this work through TMT. What is it good for? Hopefully more stable proteins in therapeutics and improved protein delivery to aid human health. Supporting Information Comparison of DLS and SLS data for samples prepared using dialysis vs centrifugal diafiltration, representative fits to DLS ACFs, representative turbidities,

,

model comparisons, viscosity data and corresponding model fits, data, and additional correlation values are supplied as

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