Kinetics of solutions uponagitation - PNAS · Proc. Nati. Acad. Sci. USA Vol. 88, pp. 9377-9381, November1991 Applied Biological Sciences Kinetics ofinsulin aggregationin aqueoussolutions

Proc. Nati. Acad. Sci. USAVol. 88, pp. 9377-9381, November 1991Applied Biological Sciences

Kinetics of insulin aggregation in aqueous solutions upon agitationin the presence of hydrophobic surfaces

(protein stability in solution/degradation pathways/mathematical modeling)

VICTORIA SLUZKY*, JANET A. TAMADA*, ALEXANDER M. KLIBANOVt, AND ROBERT LANGER**Departments of *Chemical Engineering and tChemistry, Massachusetts Institute of Technology, Cambridge, MA 02139

Communicated by Robert A. Alberty, July 22, 1991 (received for review May 16, 1991)

ABSTRACT The stability of protein-based pharmaceuti-cals (e.g., insulin) is important for their production, storage,and delivery. To gain an understanding of insulin's aggregationmechanism in aqueous solutions, the effects of agitation rate,interfacial interactions, and insulin concentration on the over-all aggregation rate were examined. Ultraviolet absorptionspectroscopy, high-performance liquid chromatography, andquasielastic light scattering analyses were used to monitor theaggregation reaction and identify intermediate species. Thereaction proceeded in two stages; insulin stability was enhancedat higher concentration. Mathematical modeling of proposedkinetic schemes was employed to identify possible reactionpathways and to explain greater stability at higher insulinconcentration.

The stability ofprotein-based pharmaceuticals is essential forthe efficacy of conventional therapeutic preparations (1),continuous infusion pumps, and controlled release polymericdevices. Insulin aggregation, accompanied by drastic reduc-tion of biological potency and obstruction of delivery routes,creates serious problems for drug delivery systems (2-4).Although insulin aggregation has been investigated (5-16), itsmolecular mechanism remains speculative.

This study aims at elucidating the fundamental nature ofthis phenomenon using a rigorous kinetic analysis. Based onexperimental observations, a reaction mechanism was for-mulated and possible destabilizing pathways were identified.Mathematical modeling was used to verify the predictivepowers of the proposed scheme.

MATERIALS AND METHODSSolution Preparation. Bovine Zn-insulin (specific activity,

24.4 international units/mg; Zn2+ content, <0.5%) was used.Phosphate-buffered saline (PBS) (0.14 M NaCI/0.1% NaN3preservative, pH 7.4) was sterilized by filtration through a0.45-,um Millipore HV filter and degassed by sonication.Stock solutions were prepared by adding Zn-insulin to PBS;the resulting cloudy mixture was sealed with Parafflm, placedin a shaker, and gently agitated for 3 hr at 37°C. Zn-insulindissolved completely at concentrations up to 0.6 mg/ml. Thestock solutions were filtered through sterile 0.22-,m MillexGV low-protein binding filters; lower concentrations wereobtained by dilution with PBS prior to final filtration. Allglassware was rinsed with 0.01 M HCl, followed by drying at100°C. The initial concentrations of Zn-insulin solutions weredetermined by UV absorbance at 280 nm (e = 5.53mM-'cm-1).

Concentration-Dependence Studies. Air-water interface.Glass 1.1-ml HPLC vials were filled with 0.75 ml of insulinsolution, capped, sealed with Parafilm, taped horizontally to

the shaker platform, and agitated at 250 rpm and 370C. Every20 min, one vial was removed and the extent of aggregationwas determined by size-exclusion isochratic HPLC analysis[Bio-Rad's SEC-125 column; mobile phase consisting of 10%acetonitrile and 90% aqueous solution containing 0.02 MNaH2PO4 and 0.05 M Na2SO4 (pH 6.8), flow rate of 1.2ml/min, detection at 280 and 217 nm]. Insulin concentrationwas determined by peak area integration.

Teflon-water interface. Five Teflon spheres (Poly-sciences, 0.64 cm in diameter) were placed in each 12 x 75mm glass tube to provide a hydrophobic surface. Insulinsolution was added to each tube so that there was noheadspace left (and thus the only hydrophobic interactionswould occur on the Teflon surface), and the samples weresealed with Parafilm, taped horizontally to the shaker plat-form, and agitated at 80 rpm and 370C. Every 30 min, one tubewas removed from the shaker and its contents were filteredthrough sterile 0.8-,um Millex-PF filters to remove the fullyaggregated, micron-size Zn-insulin particles. The concentra-tion of Zn-insulin remaining in solution and the size distri-bution of insulin species were determined via UV absorbanceand quasielastic light scattering (QELS).QELS analysis used a Lexel argon-ion laser, with a

Brookhaven apparatus consisting of a goniometer and a128-channel digital correlator and signal processor, whichincorporated a computer. Measurements were made at 488nm, at a 900 scattering angle. The latter was particularlyuseful for observing Rayleigh scatterers (i.e., particles muchsmaller than the wavelength A). Nonaggregated insulin mol-ecules behaved as Rayleigh scatterers, since the hexamer's5-nm diameter was much smaller than A. The presence ofpeaks at diameters >50 nm was verified at 1350, wherescattering contributed by dust and rotational diffusion wasminimized (17). For each sample, light-scattering measure-ments were accumulated during 5-min intervals to reducerandom signal noise and ensure a stable baseline. The ex-perimentally determined autocorrelation function g(t) wasused to obtain the size-distribution function G(F) using in-verse Laplace transform algorithms nonnegatively con-strained least squares and CONTIN (of Provencher) (17, 18).Adsorption Studies. To examine insulin (initial concentra-

tion, 0.6 mg/ml) adsorption to glass and Teflon, samplescontaining 10 Teflon spheres were agitated at 160 rpm and370C overnight. Fully aggregated samples were removed,aliquots from each test tube were centrifuged, and insulin inthe supernatants was assayed using absorbance at 280 nm.Precipitated pellets were resuspended in 8 M urea andincubated at 370C for 6 hr. Glass vials and Teflon sphereswere rinsed twice with distilled water, and the spheres weretransferred to glass vials containing 8 M urea and placed inthe shaker. Urea (8 M) was also added to each original tubewhich was then capped and shaken for 6 hr. Insulin concen-

Abbreviation: QELS, quasielastic light scattering.tTo whom reprint requests should be addressed.

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trations were determined using absorbance at 280 nm (e = 6.0mM-1-cm-1 for Zn-insulin in 8 M urea).Computer Simulations. Mathematical modeling of putative

reaction pathways was accomplished by simultaneous solu-tion of a set of differential equations describing insulininteractions with the Teflon-water surface and protein-protein interactions in solution. The dynamics of insulinaggregation were simulated using the STELLA II softwarepackage. A fourth-order Runge-Kutta method was used forintegration (19).

RESULTSOur experimental system was designed to achieve rapid andreproducible aggregation under controlled conditions. Ele-vated temperature, mechanical stresses, and presence of ahydrophobic surface mimicked the destabilizing conditionspresent in many drug delivery systems. We investigated theeffects of insulin concentration, agitation rates, and hydro-phobic interactions on the kinetics of insulin aggregation.Once the reaction began, insulin solutions became increas-

ingly cloudy, and micron-sized agglomerates settled whenagitation stopped. Only one peak-for native, monomericinsulin-was observed by HPLC analysis throughout theexperiment, suggesting that insulin's self-association wasdisrupted by dilution and column-packing interactions.

Concentration Dependence of Insulin Aggregation. Kineticstudies in which the initial insulin concentrations were variedin the presence of air-water (Fig. LA) and Teflon-waterinterfaces (Fig. 1B) showed similar behavior. Initially, therewas a flat period of stability, followed by a sloping portion,indicating insulin depletion due to aggregation. This charac-teristic shape was observed at all concentrations, in thepresence of either air or Teflon.

Control of the air-water interface was difficult due tobubble formation and foaming; consequently, the air-waterinterface was replaced with a Teflon-water interface tofacilitate characterization and modeling of surface interac-tions. Like air, Teflon is inert and hydrophobic; thus protein-surface interactions at the Teflon-water interface resembledthose at the air-water interface present in shaken vials (andin diabetes injection therapy systems). In a portable pump,

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air can be eliminated, but insulin solutions are still in contactwith solid hydrophobic surfaces. In our system, the Teflonspheres mimicked these destabilizing interactions (at solid-liquid and liquid-gas interfaces) and provided the necessaryagitation.The comparison of insulin half-lives in solution revealed

greater stability at higher concentration. Similar results werereported previously (12, 20), but no explanation was pro-posed for this anomalous behavior. In general, aggregationprocesses are kinetically controlled, with rates ofaggregationproportional to protein concentration (21, 22).

Interfacial and Agitation Dependence of Insulin Aggrega-tion. Insulin aggregation occurred only when agitation andhydrophobic surfaces were present. Stationary samples (at370C) containing air-water or Teflon-water interfaces andsamples agitated in the absence of hydrophobic surfaces(37TC, no headspace, Teflon spheres replaced by borosilicateglass beads) exhibited no aggregation after 2 weeks. Adsorp-tion studies indicated that only a minute amount of proteinwas lost to the solid surface: typically, the precipitate con-tained 95.5% of the original insulin, 4.4% adsorbed to the 10Teflon spheres (12.67 cm2), and 0.1% adsorbed to the glassculture tubes (28.3 cm2 per tube).The effects ofhydrophobic interface on insulin aggregation

showed that when the number of Teflon spheres was dou-bled, the induction period was shorter and the slope (or rateof aggregation) was steeper (Fig. 1C). Similar results wereobtained when the agitation rate was doubled (Fig. 1D).These observations highlighted the importance of insulininteractions with the hydrophobic interface and the role ofmass transfer and/or mechanical stresses in aggregation.QELS Analysis. QELS [a noninvasive technique (23, 24)]

was used to monitor the changes in particle size distributionduring insulin aggregation (Fig. 2). Since QELS has lowresolution (17), the uncertainty about the intermediate spe-cies' shape made it impossible to determine their diameterwith >10% accuracy; thus only estimates of insulin species'weight distribution were obtained. Initially, only native in-sulin molecules were present, as reflected by the peak at 5 nm(Fig. 2A). Due to the small size of the insulin monomer andthe small differences in the hydrodynamic diameters ofmonomers, dimers, and hexamers, it was difficult to distin-

20

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FIG. 1. Concentration profiles of Zn-insulin aggregation upon shaking at 370C. Computer simulations are depicted by solid lines. (A)Air-water interface studies: insulin solutions in glass vials shaken at 250 rpm at initial concentrations of 0.6 (v), 0.3 (-), and 0.1 mg/ml (-). (B)Teflon-water interface studies: 5-ml insulin samples (with 5 Teflon spheres) shaken at 80 rpm at initial concentrations of 0.6 (A), 0.4 (c), and0.2 mg/ml (A). (C) Effects of Teflon surface area with 5 (c) and 10 spheres (o). (D) Effects of agitation rates at 80 (o) and 160 rpm (o). Eachpoint is the average of three experiments, with error bars representing standard deviation from the mean.

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FIG. 2. QELS analysis of insulin aggregation upon shaking. Insulin samples (0.6 mg/ml) containing 10 Teflon spheres were agitated at 80rpm and 370C. Relative scattering intensities (% of total) are plotted versus the diameter of the particle responsible for scattering. These sizedistribution histograms were generated using the program CONTIN. (A) Initial conditions. (B) Three weeks without shaking. (C) One hour ofshaking. (D) Twenty-one hours of shaking.

guish among these species. Following 1 hr of agitation in thepresence of Teflon, a second peak appeared (Fig. 2C),corresponding to particles of -150 nm in diameter (whichmade up <0.01% by weight of total protein in solution). Thisbimodal distribution was observed for the remainder of theexperiment: even in an almost fully aggregated solution, anative and an intermediate peak were observed (Fig. 2D).Thus, there were three species of insulin present: nativemolecules (monomers, dimers, hexamers) represented by thepeak at 5 nm; fully aggregated micron-size particles (>800nm) filtered out prior to analysis; and stable intermediatesrepresented by the peak at 170 ± 20 nm. Neither intermediatespecies nor aggregation was observed in control samples thatwere incubated at 370C with 10 Teflon spheres for 3 weekswithout shaking (Fig. 2B). Note that the intermediate speciesappeared before aggregation could be detected by othermeans (e.g., concentration changes or visible turbidity).Hence, the initial stages of aggregation involved relativelyfew destabilized molecules, and the intermediate speciesapparently facilitated subsequent aggregation.

Protein-Protein Interactions in Insulin Aggregates. HPLCanalysis of the redissolved aggregates revealed only onespecies, equivalent in size to the insulin monomer. Thechromatogram was indistinguishable from that of freshlyprepared insulin solutions, indicating absence of fragmenta-tion and the noncovalent nature of aggregation, as suggestedpreviously (12, 25).

MODEL FORMULATION AND DISCUSSIONIt has been suggested that insulin is destabilized by adsorptionat hydrophobic interfaces (air-water or water-pump materi-als) (15, 26) and that the initial step is nucleation-i.e.,formation of small intermediate aggregates that serve as pre-cursors to large precipitates (26). These elements alone, how-ever, fail to describe insulin aggregation behavior: a successfulkinetic scheme must predict the biphasic nature of the timecourse and greater insulin stability at higher concentration[which previously has been attributed only to the concentra-tion-dependent self-association equilibrium (15, 26)].

In solution, insulin monomer is in equilibrium with morestable dimers and hexamers (27). The hexamer's conforma-tional stability (28-30) makes it an unlikely candidate fordenaturation at hydrophobic surfaces. Dimer unfolding at theTeflon-water interface also can be discounted: one of themonomer's two hydrophobic regions is involved in dimerformation (31), thereby stabilizing its tertiary structure.Thus, of the three insulin species, the monomer is the mostlikely to denature at a hydrophobic interface. Note that wheninsulin's self-association was eliminated (Zn-free insulin in0.1 M Tris/60% ethanol, pH 7), aggregation rates increasedwith increasing concentration (25), implying that the mono-mer initiated precipitate formation. Insulin denaturation athydrophobic interfaces (14, 32) and adsorption to Teflon andother surfaces have been reported (33).Based on observed insulin aggregation kinetics, formation

of a stable intermediate species, and importance of interfacialinteractions, we propose the following mechanism (Fig. 3):dimers and hexamers reversibly adsorbed to the Teflonsurface without undergoing denaturation; however, less sta-ble monomeric species partially unfolded upon adsorption.The unfolded species either snapped back to their nativeconformation (most likely event) or combined with otherunfolded species, initiating nucleation (the formation of in-termediate aggregates of 170 nm in diameter). The smallerintermediates (U2, U3, etc.) were short-lived transients: theycontinuously combined and fell apart and interacted onlywith other unfolded species. Once a critical size was reached,the intermediates had enough surface area for stability andstarted reacting with native molecules. The slow formation ofthe 170-nm stable intermediates explained the lag time: nosignificant aggregation was observed until a population ofnucleating species was established.

Increased stability at higher concentration (when a largerproportion of insulin was oligomeric) was due to occupationofthe Teflon surface by dimers and hexamers, which reducedthe surface available to unfold the monomer. As insulinconcentration increased, so did the monomer concentration.In the absence of dimer and hexamer adsorption onto Teflon,higher insulin concentrations would result in more rapid

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Kdjmer Khexamer6N <========> 3N2 <========> N6

K adsorptionN2 + I <=========> N2I

KadsorptionN6 + I <=========> NI

k unfoldN + I ======> U + I

k refoldU ======> N

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FIG. 3. Kinetic scheme used to model Zn-insulin aggregationupon shaking in the presence of a Teflon-water interface. N, nativespecies; U, unfolded molecules; I, interfacial sites; K, equilibriumconstants; k, rate constants. Kdenaturation = kunfold/krefold.

aggregation, as denaturation rate depended on concentra-tions of monomers and interfacial sites (Table 1). To reducethe driving force at higher concentration, the number ofdestabilizing sites (leading to denaturation and subsequentnuclei formation) had to be reduced. One way to accomplishthis, given a fixed surface area, was for the more stablespecies to occupy interfacial sites without undergoing con-formational changes.Most kinetic and thermodynamic parameters were taken

from the literature: Kdimer = 1.1 X 105 M-1 (27), Khcxamer =

2.89 X 108 M-2 (27), Kadsorption = 1.20 x 10' M1 (33), andKdenaturation = 1.20 x 105 M-1 (34). Rate constants of nucleiformation (ku-association and ku-dissociation) and of the subse-quent aggregation (kawgrgation) were fitted to the concentrationprofile at 0.6 mg/ml, 80 rpm, 37°C, with five Teflon spheres.These parameters, which remained unchanged during thesubsequent computer simulations, had to be internally con-sistent: kuassiation had to be at least an order of magnitudegreater than kawgg.tion, so that prior to reaching the stablecritical size unfolded monomers would be much more likelyto interact with each other than with native species. QELSsuggested that the critical size necessary for stability of theintermediate species is on the order of 100 molecules [basedon insulin monomer's diameter of =2 nm (31)]. To shorten thecomputation time, the number of association steps needed toreach the critical size was limited to 10. This simplificationdid not change the curve shape but meant that the fitted

FIG. 4. Results of sensitivity analysis. (A) Effects of Kdimer oninsulin aggregation profiles: model value (A) and model value plus (o)or minus (o) 10%o. (B) Effects of Kdnwuow on insulin aggregationprofiles: model value (A) and model value plus 150%o (n) or minus 50%o().

parameters were not the actual rate constants. Since theabsolute values of these parameters could not be determinedindependently, this modified reaction mechanism led to qual-itative predictions about trends in insulin aggregation behav-ior.The unfolding and refolding at the hydrophobic interface

were assumed to be a pseudo-equilibrium process, sinceintramolecular changes occur on a much shorter time scalethan bimolecular interactions (35). The concentration ofdenatured monomers was based on the equilibrium constantKdenaturation for insulin unfolding and refolding in the absenceof destabilizing interactions (34). To simulate the effects ofagitation (mass transport to the interface) and the presence ofa hydrophobic surface, Kdenaturation at 80 rpm was arbitrarilyincreased by an order of magnitude. When the agitation ratewas doubled, Kdenaturation was also doubled, in proportion tothe increase in the mass transfer coefficient and in sheardenaturation rate.

Insulin concentration at the Teflon-water interface wasdetermined from insulin adsorption isotherms (33). The num-ber of interfacial sites occupied by insulin molecules wasbased on the hexamer cross-sectional area of 2000 A2; thus6.3 x 1012 protein molecules could occupy a 0.64-cm (diam-eter) Teflon sphere.

Results of computer simulations of insulin aggregation at aTeflon-water interface and experimentally determined con-

Table 1. Simulation of monomer denaturation rate (proportional to free monomer [N] and interfacial site [I]) with andwithout dimer and hexamer adsorption to Teflon

[I] x [N] withMonomer [N], Teflon surface [I] [I] x [N] without adsorption, adsorption,

Zn-insulin, molecules per ml after adsorption,* sites-molecules per m12 sites-molecules per m12mg/ml (x 1015) sites per ml (x 1011) (x 1028) (x 1027)0.6 9.32 6.56 2.95 6.120.2 5.93 13.6 1.87 8.06

*Teflon surface before protein adsorption was 3.16 x 1012 sites per ml; interfacial site concentration after adsorption wascomputed as (initial Teflon surface area)/{1 + KadsrPtion([dimer] + [hexamer])}.

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centration profiles are presented in Fig. 1. Fig. 1B illustratesthe effects of concentration on insulin aggregation. Duringthe computer simulations, all kinetic and thermodynamicparameters and the Teflon surface area were kept constant:the only parameter that changed was the number of insulinmolecules present in the beginning of each experiment.Simulations of varying the Teflon-water interface predictedthe induction period decrease, the steeper slope when theTeflon surface was doubled (Fig. 1C), and the increasedaggregation rates with more vigorous agitation (Fig. iD).

Sensitivity analysis was performed on the model's kineticand thermodynamic parameters. None of the perturbationschanged the kinetic profiles' shape-i.e., the initial period ofstability, followed by a slightly sigmoidal curve (Fig. 4).However, the induction period duration, the slope steepness,and relative durations of the two phases of the aggregationreaction did change.

Since the fitted parameters ku-association and kagggion dif-fered only by an order of magnitude, it was impossible tosignificantly change one without compromising the internalconsistency ofthe proposed mechanism. However, as long asthese constants remained within the specified order of mag-nitude range, it was possible to test model sensitivity to suchvariations. Changes in ku-association affected induction periodduration and curve slope. These effects would have beenmuch less pronounced ifthe size ofthe intermediate had beenon the order of '100 molecules.The contribution ofdimer and hexamer formation to overall

insulin stability was examined by varying equilibrium con-stants for self-association. Results indicated that the extent ofdimerization directly affected insulin stability, since this wasthe main route for decreasing monomer concentration. Themodel assumption that dimers and hexamers experienced noconformational changes upon interfacial interactions impliedthat hexamerization played a minor role in increasing solutionstability. At higher concentration-where the hexamer be-comes the dominant species-one would expect a greaterstabilizing effect arising from hexamer formation.

Finally, the agitation-dependence studies and sensitivityanalysis pointed to the importance of Kdenaturation, whichcontained information about mass transport to the solid-liquid interface, shear effects, and destabilizing surface in-teractions. Although variations in Kdenaturation did not changethe concentration profiles' shape, they affected inductionperiod duration and steepness ofthe aggregation curve slope.The sensitivity analysis provided additional insights into

the nature of the aggregation processes, because it allowed aseparate evaluation of contributions of different pathways tothe instability pattern. This analysis identified the pathwaysmost sensitive to perturbations and hence could be used topropose ways to mitigate destabilizing interactions.

In closing, the experimental observations led to a minimalmodel (a kinetic scheme containing the fewest number of stepsrequired to adequately describe system dynamics), which wasused to simulate insulin aggregation. This model could beexpanded to take into account additional destabilizing path-ways, and, with further study, it may be used to predict effectsof stabilizing agents on the aggregation behavior, to choosestability-enhancing conditions, and to design additives aimedspecifically at blocking unfavorable interactions.

This work was supported by National Institutes of Health Grant

26698 and by the Biotechnology Process Engineering Center atMassachusetts Institute of Technology.

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