On the Reproducibility of Early-Stage Thermally Induced and Contact

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On the Reproducibility of Early Stage Thermally Induced and Contact-Stir Induced Protein Aggregation Curtis W Jarand, and Wayne F. Reed J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b07820 • Publication Date (Web): 18 Sep 2018 Downloaded from http://pubs.acs.org on September 18, 2018

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The Journal of Physical Chemistry

On the reproducibility of early stage thermally induced and contact-stir induced protein aggregation

Curtis W. Jarand, Wayne F. Reed*

*

Correspondence. [email protected]. Physics Dept., Tulane University, New Orleans, LA, 70118. Tel. 504-862-3185 1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract Are aggregation kinetics for a protein in given conditions reproducible?

Is aggregation

inherently deterministic, stochastic, or even chaotic? Because protein aggregation in ex vivo formulations is complex, with many origins and manifestations, the question of aggregation reproducibility for a given protein, formulation, and stressor is of both fundamental and practical significance. This work concerns temperature induced and contact-stir induced aggregation of bovine serum albumin (BSA) and a monoclonal antibody (mAbX). It assesses reproducibility via early stage aggregation rates (AR) from light scattering. ‘Global stressors’ affect the entire protein population; e.g. temperature. ‘Local stressors’ affect only a partial population at a given instant; e.g. stirring.

The instrumental error distribution (IED) allows stochasticity to be

identified for AR distributions (ARD) broader than IED. For ARD at the limit of the IED behavior is ‘minimally stochastic’ or ‘operationally deterministic’. A Stochastic Index is defined in terms of the ratio of SD of log(AR) data and SD of IED.

Thermal aggregation was

operationally deterministic for BSA and mAbX, although significant lot-to-lot variations for BSA were found. ARD from contact stir-stress was stochastic for BSA and mAb. Despite this, log(AR) decreases logarithmically with RPM. These trends may hold for other global and local stressors.

Keywords Protein aggregation, light scattering, aggregation kinetics reproducibility, stochastic, deterministic

2 ACS Paragon Plus Environment

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Introduction Protein aggregation in therapeutic drug formulations is an unfortunate and ubiquitous phenomenon.

1, 2

There are many different mechanisms and stressors for aggregation.3 The

aggregates themselves can range from dimeric and oligomeric structures, to sub-micron clusters of proteins, to micron and visible size ranges. The morphology of aggregates ranges from organized rodlike fibrils to amorphous globular structures with fractal characteristics. Many methods are used to study and characterize aggregation, including static and dynamic light scattering (SLS and DLS, respectively), size exclusion chromatography (SEC), differential scanning calorimetry and fluorescence (DSC and DSF, respectively), Thioflavin T (ThT) fluorescence, circular dichroism, Raman scattering, infrared microscopy, and many types of video imaging analyses and particle counting.4,5,6 It is difficult to predict under what formulation conditions a protein drug candidate will be stable. Early in the drug candidate screening process, quantities of protein are too scarce to screen many formulation conditions for product stability.

Later in the drug development

pipeline, there is still a question of what methods are most appropriate to characterize product stability. For these reasons, thorough study of the reproducibility of aggregation kinetics in therapeutic protein is warranted in order to 1) set confidence bounds on aggregation measurements taken from small numbers of precious samples and 2) to better understand the underlying mechanisms leading to the formation of aggregates, and 3) to determine whether reproducibility studies can be applied to the conditions under which therapeutic proteins are stored and administered. Much prior work on kinetics and reproducibility has centered on fibrillar aggregation of human disease related proteins. It has been argued that irreproducible aggregation profiles of



amyloid β is due to a stochastic nucleation event causing variation in aggregation “lag times” among nominally identical samples7, but this is contrasted by later work finding highly reproducible kinetics in amyloid β among many tightly controlled samples.8 One protocol shows examples of irreproducible aggregation which were attributed to experimental error and therefore unsuitable for analysis.9 The aggregation lag time, and observed variation in such, is manifested in nucleation limited processes.10

In microdroplet volumes, aggregate nucleation events are so rare that

stochastic behavior is observed, due to small number fluctuations, or ‘Poisson Noise’.11 In a larger volume of the same sample, the nucleation events are more likely, and the overall aggregation process can be considered deterministic.

A system of modified mass balance

equations has been developed for analysis of the prior stochastic nucleation elements in microdroplet samples11. In other theoretical work, a deterministic Hamiltonian approach has been formulated which yields exact solutions to aggregation processes and finds new conservation laws under certain conditions.12 Poor sample or experimental quality can induce significant variation. A researcher may falsely assume an aggregation process is stochastic if poor protocols are followed. Strategies to improve reproducibility of α−Synuclein fibrillation kinetics in plate reader assays were published. 13 The aggregation of α−Synuclein is typically regarded as a stochastic process, but it was found that orbital agitation and the addition of glass beads, preformed fibrils, or surfactants to samples decreased variation in the nucleation and growth rate constants.14 Aggregation of oligomeric superoxide dismutase-1 was found to be stochastic due to competing fibrillar and amorphous pathways of aggregation. The first pathway to nucleate, seen


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as a probabilistic event, dominates the rest of the process and determines the morphology of the resulting aggregates.15 It should be noted that most of the above references use ThT fluorescence as the measure of aggregation. ThT only detects the presence of medium sized aggregates, not the hundreds of nucleation intermediates, and ThT is known to alter aggregation dynamics16 17. The possible causes of stochasticity in aggregation kinetics include: i) Multiple, competing aggregation pathways, ii) Poisson-noise fluctuations: when low probability events, e.g. nucleation, are required to start aggregation, iii) variations in protein folding conformations, iv) formulation impurities, v) thermodynamic treatments used to produce the proteins; e.g. whether they have been lyophilized and reconstituted, subjected to any heat treatment, and possibly many other causes. Although the issue of kinetics and reproducibility of protein aggregation has been studied extensively regarding disease physiology, there are few published studies of the same for therapeutic protein formulations. If, under nominally identical physiochemical conditions, a given protein formulation is expected to aggregate by deterministic mechanisms, then the time resolved aggregation profiles of repeated experiments should overlay. Deterministic population balance equations have been applied to analyze mAb aggregation kinetics18,19, but the quality of repeated experiments is not reported. This work uses time resolved total intensity light scattering, also termed Static Light Scattering.

DLS was not used.

The analysis uses the initial time rate of change of the

dimensionless quantity Mw(t)/M0, where Mw(t) is the weight average molar mass of all scatterers in solution at time t after a stressor is applied. Mw(t) includes all native proteins and aggregates,



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and M0 is the molar mass of the native, unaggregated protein.

Mw(t)/M0 was previously

introduced20 and the aggregation rate (AR) defined as

AR( s −1 ) =

[

d M w (t ) / M 0 dt

]

(1) t =0

The object of this work is to assess variations that occur in AR for repeated experiments under nominally identical conditions, and to separate out experimental error from true stochastic variations in aggregation behavior. Because all measuring instruments have an Instrumental Error Distribution (IED), set by their precision, it is not possible to declare whether a measurable parameter, such as AR, is deterministic based on such measurements, as that would require infinite precision. However, if the experimental AR distribution (ARD), based on a statistically meaningful set of experiments, falls outside the IED then the aggregation process can be declared stochastic.

If the ARD falls on the IED, then it can be considered ‘minimally

stochastic’, and it could even be deterministic, but this cannot be confirmed by the system. For practical purposes, for a given IED, an ARD that falls on it can be considered ‘operationally deterministic’; i.e. repeated measurements of AR fall on the IED. A technical refinement to AR is first presented via the use of a logarithmic scale to define a ‘logarithmic aggregation rate’, LAR, after which the experimental errors in light scattering instrumentation due to stray light are computed, since this is the single largest source of error controlling the IED. Then, repetitions of nominally identical experiments are carried out under temperature and contact-stir stressors and the logarithmic-ARD are analyzed based on their standard deviations (SD). The IED is estimated for the light scattering instrument used, a Stochastic Index (SI) is defined, and the results for the two proteins under thermal and contactstir stress classified as ‘operationally deterministic’ or ‘stochastic’.


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Methods Aggregation rate and logarithmic scale representation The aggregation rate was introduced as the initial time rate of change of Mw(t)/Mo (Eq 1). When there is no aggregation Mw(t)/Mo=1, when Mw(t)/Mo=2 then there are on weight-average two proteins per aggregate, etc. Mw(t)/Mo does not contain any information on the nature or breadth of the complete molar mass distribution (MMD), and additional information, such as with SEC and multi-angle static light scattering (MALS) is needed. Aggregation rates have been measured, spanning the range of 0.1 s-1 to 10-9 s-1; i.e. measured AR vary by nearly ten orders of magnitude.20 As is customary when working with quantities which vary by orders of magnitude a log scale representation for AR is now introduced, which defines logarithmic aggregation rate, LAR, as

LAR ≡ − log10 ( AR)

(2)

LAR is dimensionless, and implicitly takes AR=1s-1 as the denominator of the argument; LAR=log[AR(s-1) /1s-1]. Use of the negative logarithm makes LAR>0 for all AR1 +

./ /

B

(31)

1) ∆LAR1. The temperature precision of the Argen instrument is nominally ∆T=+/- 0.1oC. This value is used to obtain ∆LAR via Eq 27, using T=300K and γ=38,500K for BSA. It can be computed for other T and γ by Eq 27. This error is independent of cell material and whether Method I or II is used. Measurements are made with standard K-type thermocouples.

2) ∆LAR2.

Signal-to-noise ratio. The baseline S/N before stress on BSA at 1 mg/ml gives

Mw/M0=1.000 +/-0.024, which leads to ∆LAR2=0.010. A similar value is found for pure buffer. Combined in quadrature, for Mw(t)/M0 over the range of determination of AR leads to ∆LAR2=0.0140 .

3) ∆LAR3. AR determination. For thermal stress the AR slope method was always computed over the same time interval, so, since reproducible aggregation will yield reproducible slopes over the same interval, the only variation in slope is a) when pure raw data are used and b) raw data for which outlier points have been rejected. Outlier points are generally caused by sparse large particles passing through the scattering volume. When the raw data and data with outliers


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are analyzed ∆LAR3 =0.0022, for both Methods I (solvent subtract) and Method II (toluene calibration). This source of error is negligible compared to the others.

The next source of error took account of whether a) serial measurements are made on a single sample compartment (e.g. in a single sample absolute SLS instrument); intra-compartmental measurements or b) parallel measurements with the 16 compartment Argen; inter-compartmental measurements. If a flow cell were used then ~, will yield the least error from stray light. The following shows that stray light is the single largest source of error.

4aI) ∆LAR4a,I. Intra-compartment stray light variations in Method I, solvent subtraction. The variation of a sample cell was determined by inserting, removing, and re-inserting the cell into the same compartment, in the same orientation and with the same contents (1 mg/ml BSA or pure buffer) multiple times. SD for each was set to and , respectively, and the average value used in the denominator for AR in Eq 17.

Eq 17 was then used to determine ∆AR/AR,

whence ∆LAR4a,I=0.062 for glass cells, and 0.053 for PS cells.

4aII) ∆LAR4a,II. Intra-compartment stray light variations in Method II, toluene calibration. Reinsertion data for toluene gave 0.06927 +/-0.00126. Because the constant of solvent subtraction disappears when computing AR=d(Mw/Mo)/dt, the only effect left is due to the δt= 0.00126 in computing Mw, yielding ∆LAR4a,II=0.0307.



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4bI) ∆LAR4b,I. Inter-compartment sample variation. 16 different sample cells with 1 mg/ml BSA were simultaneously measured in different sample compartments and then 16 measurements made on different sample cells with buffer. Eq 17 was used to obtain ∆AR/AR, whence ∆LAR4b,I=0.043 for glass cells, and 0.037 for PS cells.

4bII) ∆LAR4b,II. Inter-compartment toluene variation. This is expected to be similar for all compartments. ∆LAR4b,II=∆LAR4a,II=0.016.

Using the highest values from all these sub-categories leads to ∆LARtotal,=0.0661, Table 4.

Table 4. Sources of error expressed in terms of ∆LAR. ∆LARtotal, and ETV are shown in bold. ETV (oC) is from Eq 28 with γ=38,500K, and T=331K

Error source

T fluctuations

S/N

AR method

Stray light

Total ∆LAR

ETV °C

∆LAR

0.0180

0.014

0.0022

0.062

0.0661

0.43

While the statistics are not extensive enough to make firm assertions, the following trends were suggested by the sub-group statistics: i) There is no essential difference between serial measurements in a single compartment and parallel measurements in the 16 different compartments of the instrument used. ii) Measurements in PS cells showed measurably smaller ∆LARtotal than for glass, for both intra- and inter-compartment measurements. iii) As expected, the lowest ∆LARtotal is from Method II, using toluene calibration. The ∆LAR values measure precision of measurements, not accuracy. 34 ACS Paragon Plus Environment

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Computing the Instrumental Error Distribution (IED) of LAR using ∆LARtotal The IED is taken as a Gaussian of the form 4(^#$) =

(

789 *− g√6
1 criterion for confirming stochastic behavior. Only further repeat testing with other proteins and stressors might make clear the significance of the magnitude of SI when SI>1.

Table 5. Average SI for BSA (all lots) and mAbX for thermal and contact-stir stress

Protein

Stress

SI

SD of SI

Classification

BSA

Temperature

1.05

0.08

Operationally deterministic

mAbx

Temperature

0.6

(no subgroups)

Operationally deterministic

BSA

Contact-stir

6.4

2.2

Stochastic


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mAbx

Contact-stir

4.8

1.5

Stochastic

Lot to lot variation Use of this methodology shows there are significant variations in reproducibility among different lots of nominally identical material. Four lots of nominally identical BSA from SigmaAldrich (see Table 1) were measured at T=580C. Figure 7 shows that lots A and B give LAR within each other’s error bars, but both lot C and lot D are far outside these error bars. Hence, these variations are real and not due to experimental error, so there is stochastic variability among lots of nominally identical material. The origin of the variation is not known, but may be related to impurities, manner in which material is desiccated and otherwise handled prior to commercial distribution.

Figure 7. Lot to lot variation of LAR for nominally identical BSA.



The NIST standard mAb should, in principle, provide a reference source for the issue of kinetic repeatability and is a logical choice for further study.22 Pharmaceutical quality mAbs will also likely contain lower lot-to-lot variation than the lyophilized BSA.

Stochastic vs deterministic chaotic aggregation Deterministic chaos means that there are deterministic equations, e.g. non-linear differential equations, not probabilities (stochastics), for a trajectory, so that under totally identical starting conditions the same trajectory will be followed; in the aggregation case, if deterministic, the long term, non-linear time dependent signatures of many experiments will be identical under identical starting conditions. In a deterministic chaotic system, because of its non-linearity, very small differences in initial conditions can lead to vastly different trajectories. Very early stage trajectories for chaotic systems with tiny differences in initial conditions should be virtually identical but the divergent, chaotic nature of the trajectories emerges exponentially, or steeper, as time increases. Hence, this work, which focuses on very early phase aggregation, does not address chaotic aggregation behavior. Chaotic aggregation is potentially relevant, however, since any chaotic behavior in aggregation over longer term storage conditions of days, months, or years, could result in vastly different aggregate content for many vials of nominally identical material, among which initial conditions may be very slightly different, or which receive minutely different perturbations during their storage (e.g. a storage rack is disturbed, transient light exposure, slight thermal gradients, etc.) The subject of chaos in protein aggregation has been suggested previously.25,26 It could be interesting to make a more formal study using current formalisms and ideas for describing


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chaotic systems.27,28 Study of long term, non-linear SMSLS time dependent aggregation signatures might be one approach. Hence, it has been assumed in this work that measurable variations in series of LAR measurements that fall outside of the IED are due to stochastic, not chaotic effects.

The

stochastics can result from different probability distributions of local stressors, such as irregularities in stir bar or scattering cell surfaces, varying details of a stir bars motion, impurities in the liquid or adsorbed to the cell, and even thermal irregularities or gradients that may occur across the scattering cell from the heating surfaces at its edges. The fact of large lot-to-lot stochastic variation of nominally the same material is perhaps one of the most disconcerting factors found in this work.

Conclusions A Stochastic Index, SI, has been proposed, given by Eq 32. If SI≤1 for a series of measurements then the process is operationally deterministic. For SI>1 the process is stochastic. Repeat experiments of BSA and mAbX aggregation under a variety of temperatures, contact-stir rates, and different scattering cell materials were carried out and it has been demonstrated that temperature stress produces operationally deterministic aggregation in the early phase for both proteins. However, significant lot-to-lot stochastics in LAR for BSA indicate large lot-to-lot variation of stability for nominally identical materials, even though aggregation is repeatable within a given lot of material. Contact-stir stress is clearly stochastic for both BSA and mAbX. Within the broad error bars, LAR decreases logarithmically with RPM for both proteins. The behavior shows up most



clearly when RPM span at least two orders of magnitude; in this work 10-2,000 RPM was covered. While mAbX is orders of magnitude more thermally stable than BSA (figure 1), BSA is measurably more stable against contact-stir stress than mAbX. This suggests that comparative studies of thermal and stir stability among different proteins and formulations could be valuable. For a given pair of proteins or formulations, A and B, the order of thermal A/B stability may not be the same as contact-stir A/B stability. This could impact development and formulation, since candidates with good thermal stability may not have good contact-stir stability, and vice versa. It is suggested that contact-stir can be used as a sort of ‘battering ram’, a means of drastically stressing protein candidates during discovery and formulation, as a fast-fail test of their ability to withstand mechanical stress. In this study temperature stress is a global stressor that affects all proteins simultaneously and leads to a population of aggregates whose masses increase in time in a way that is operationally deterministic. In contrast, the aggregation kinetics of contact-stir stress are demonstrably stochastic. Contact-stirring is a local stressor and only affects molecules in the vicinity of the stir bar at any given time and produces a very small mass fraction of very large particles. Many factors may lead to the stochastic behavior, such as the microscopic contact area for any given stir bar/sample cell, stir bar surface morphology irregularities, stir bar spin trajectory, relatively small number of proteins affected at any time (‘Poisson noise’), etc. Application of this approach to a wide variety of proteins under different formulations and stressors, for which many types of aggregation mechanisms can come into play, may determine whether or not general statements concerning operational deterministic early phase aggregation kinetics are possible. Other global stressors, in addition to temperature, include


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radiation, ultra-sound, formulation conditions, and possibly shaking. Shear stress in tubular or capillary flow might be considered semi-global, since there is a different shear rate affecting proteins at different distance from cylindrical walls. Local stressors can include different means of pumping – peristaltic, syringe-driven, piston based- as well as filtering, and contact with different surfaces.

Acknowledgments Partial support for this work came from NSF EPS-1430280 and Louisiana Board of Regents. The authors thank Daniel J. Rees for additions to the Introduction and careful proofreading of the text

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