Glycerol Mixtures

Article pubs.acs.org/JPCB

Local Minimum in Fragility for Trehalose/Glycerol Mixtures: Implications for Biopharmaceutical Stabilization Lindong Weng and Gloria D. Elliott* Department of Mechanical Engineering and Engineering Sciences, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, United States ABSTRACT: Approximately a decade ago it was observed that adding a small amount (5 wt %) of glycerol to trehalose could substantially improve the stability of enzymes stored in these glasses even though the final glass transition temperature (Tg) was reduced by ∼20 K. This finding inspired great interest in the fast dynamics of dehydrated trehalose/glycerol mixtures, leading to the observation that suppression of fast dynamics was optimal in the presence of ∼5 wt % of glycerol. It was also recognized that the fast dynamics should, in theory, be related to the fragility of these glass formers, but experimental confirmation of this hypothesis has been lacking for trehalose/glycerol mixtures or any other mixtures of this nature. In the present study a dynamic mechanical analyzer (DMA) was used to determine both the Tg and the kinetic fragility index (m) of trehalose/glycerol mixtures within the mass fraction range of 80−100 wt % of trehalose. It was found that the fragility index correlated with the mass fraction of trehalose in a nonmonotonic manner, with a local minimum between 87.5 and 95 wt % of trehalose, whereas the composition dependence of Tg was found to follow a Gordon−Taylor-like relationship, with no local minimum. The composition of 5−12.5 wt % glycerol in trehalose thus yielded a matrix that maximized the strong glass-forming contribution of glycerol, while minimizing its Tg lowering effect. This quantitative evidence supports speculation about the fragility characteristics of these mixtures that has been ongoing for the past decade. The DMA-based Tg and fragility determination method developed in this study represents a new approach for identifying optimal compositions for preservation of biologics.

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glycerol.12 Using low-frequency Raman analysis, Caliskan et al.13 found that at 200 K the quasi-elastic scattering (QES) intensity, which was used to characterize protein flexibility and local rearrangements of amino acids of lysozyme, was lower in liquid glycerol than in glassy trehalose. This was attributed to the “filling-in” role of glycerol in the free volumes between protein chains and thus the enhanced packing efficiency at low temperatures.13 Cicerone et al.14 demonstrated that adding a small amount (5 wt %) of glycerol (Tg = 190 K15) to sugar glasses (e.g., trehalose or lactose) substantially improved the stability of the enzymes horseradish peroxidase and yeast alcohol dehydrogenase by increasing the enzyme deactivation times even though the total Tg was reduced by ∼20 K compared to pure trehalose. Recent studies have revealed that the fast dynamics of sugarbased glasses strongly affect the conformational fluctuations and low-frequency vibrations of embedded proteins.11,16−18 For example, using Raman and neutron scattering spectra analyses, Caliskan et al.18 demonstrated that the dynamics of lysozyme were strongly coupled with the dynamics of the solvents glycerol and trehalose on the picosecond time scale, over a wide temperature range from 100 to 350 K. In complementary work using molecular dynamics simulation, Curtis et al.19 found that the protein dynamics were mainly influenced by the inertia of

INTRODUCTION Sugars have been widely utilized as preservatives or protectants for biological materials such as proteins and cells,1−3 as the glassy state of sugars enables suppression of cooperative, largescale molecular motions, such as structural or α-relaxation of biomolecules, at noncryogenic temperatures. The glass transition temperature (Tg), which by convention is the temperature at which the viscosity of the material reaches 1012 Pa·s (i.e., becomes physically “solid”),4 is thus an important consideration when formulating compositions for long-term storage.5,6 However, molecular motion within glasses involves a variety of relaxation dynamics covering a wide range of frequencies, ranging from atomic vibrations, motion of cages, and secondary or β-relaxation including Johari−Goldstein (JG) relaxation, to the fully cooperative α-relaxation associated with the glass transition.7 It has generally been speculated that solvent viscosity is the predominant contributor to suppressing conformational fluctuations within proteins.8,9 However, in many cases stability against aggregation, chemical degradation, and loss of enzymatic activity of proteins embedded in sugar glasses has been proven to not be directly related to viscosity, α-relaxation, or Tg, but instead has been shown to be a function of the fast, high frequency (THz) dynamics or fast β-relaxation of the solvent matrix, which occurs on the scale of picoseconds.10,11 For example, it was shown that ligand binding to myoglobin occurred at similar rates in concentrated aqueous solutions of sucrose and glycerol, even though the viscosity of the sucrose solution was ∼103−107 times higher than that of © 2015 American Chemical Society

Received: February 18, 2015 Revised: April 30, 2015 Published: May 8, 2015 6820

DOI: 10.1021/acs.jpcb.5b01675 J. Phys. Chem. B 2015, 119, 6820−6827

Article

The Journal of Physical Chemistry B

properties of its glassy state, for example, the characteristics of the boson peak,26,27 thereby relating the fragility of liquids with the fast dynamics of glasses. It has also been shown that at T ≤ Tg fast, conformational fluctuations occur with much higher probability in fragile glass-forming systems than in strong ones.18,28 However, to the best of our knowledge, the fragility index (m) of dehydrated trehalose/glycerol mixtures, which has attracted great interest over the past decade, has not yet been experimentally determined. Rare evidence has been found so far to prove that the suppression of fast dynamics at around 5 wt % of glycerol will correspond to a local minimum of m at this mass fraction of glycerol. For the present study a DMA protocol was developed to enable the determination of the kinetic fragility of glass formers, and experiments were then focused on trehalose/glycerol mixtures within the interesting mass fraction range of 80−100 wt % of trehalose. DMA is recognized as one of several experimental techniques including modulated differential scanning calorimetry and dielectric analysis that can be used to determine relaxation dynamics such as fragility. In this study DMA data were utilized to determine the Tg and fragility index as a function of the mass fraction of trehalose in composition with glycerol. A local minimum in liquid fragility was identified in the same composition range in which fast dynamics in the glass were shown to be maximally suppressed, thus providing experimental evidence for the coupling between these phenomena.

trehalose/glycerol glasses, with specific interactions at the protein−solvent interface playing a less significant role. Their modeling work suggested an optimal glycerol mass fraction of 12.2 wt % to achieve the highest suppression of dynamics throughout the entire protein. Dirama et al.20 proposed that the physical origin of dynamic protein−solvent coupling was actually traced to the hydrogen bonds formed between the first shell of solvent and the surface atoms of the protein and such coupling could be transferred inward by intramolecular interactions in proteins. These various investigations into the dynamic coupling between proteins and their hosting glasses drove the research focus toward a new concept wherein the protein dynamics is essentially controlled by the dynamics or relaxation on the pico- to nanosecond time scale in the hosting matrix rather than the relatively slow, cooperative α-relaxation. Subsequently, a great deal of effort was devoted to exploring the fast dynamics in various hosting matrices, especially those made of trehalose and glycerol. Using incoherent neutron scattering data to interrogate trehalose/glycerol mixtures, Cicerone and Soles10 found that the suppression of short-length scale, high-frequency dynamics (200 MHz and faster) was responsible for the stabilization of enzymes stored in these room-temperature glasses of trehalose/ glycerol. Elastic neutron scattering results showed that the glassy environment was stiffest with the 5 wt % glycerol presence, and this composition also resulted in the greatest suppression of the hydrogen-weighted mean-square atomic displacement at temperatures up to 350 K.10 Additionally the inelastic neutron scattering results showed that the QES/boson peak intensity ratio in the glass was at its minimum, and thus the glass exhibited the slowest relaxation in the presence of 5 wt % glycerol. This was observed at 100 K, as well as at room temperature (296 K).10 The experimental finding that the greatest suppression of fast dynamics occurred in 95 wt %/5 wt % trehalose/glycerol glass was also supported by the molecular dynamics simulation study conducted by Dirama et al.21 The authors found that the robust intermolecular hydrogen-bonding network in this particular composition was the most effective at suppressing protein dynamics compared to the other mass fractions,21 which was further confirmed by the inelastic neutron scattering investigation by Magazù et al.22 The study conducted by Magazù et al.22 also highlighted that, based on the peak shifts, the suppression effect of glycerol had a more marked effect on the intramolecular bending vibrations in trehalose molecules than intermolecular transitional or librational modes. The antiplasticizing role of glycerol in its mixtures with trehalose has also been investigated by dielectric spectroscopy.23,24 It was found that the secondary dielectric or fast relaxation involving small-amplitude motions throughout the entire glucopyranose rings in trehalose could be slowed down in the presence of glycerol at T ≪ Tg. These findings were consistent with the expectation that the addition of glycerol was able to make trehalose a stronger glass former in the limit of low mass fraction of the additives. Despite considerable evidence that establishes the importance of fast dynamics in trehalose/glycerol glasses used for preservation purposes, data connecting these motions to fragility have been considerably sparse. Fragility is defined as the deviation of the temperature dependence of the αrelaxation time or viscosity from Arrhenius behavior,25 and has been regarded as one of the most important factors affecting the bioprotective efficacy of the glasses.14 There is evidence that the fragility of a liquid can be embedded in the

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MATERIALS AND METHODS High-purity α,α-trehalose dihydrate was purchased from Ferro Pfanstiehl Laboratories (Waukegan, IL). Glycerol was purchased from Sigma-Aldrich (St. Louis, MO), and deionized water (18 MΩ·cm) was used for all solutions. Aqueous trehalose/glycerol solutions, 20% (w/v), were prepared with the appropriate mass ratios to generate anhydrous compositions with a trehalose mass fraction (φtre) of 0.8, 0.85, 0.875, 0.9, 0.95, 0.975, and 1. Amorphous trehalose/glycerol mixtures were obtained by freeze-drying 10 mL of the aqueous solutions in a VirTis BenchTop lyophilizer (SP Scientific, Stone Ridge, NY) for 24 h. The freeze-dried samples were then temporarily stored in a desiccator over P2O5 and used within 24 h as required to avoid potential phase separation. A DMA (Q800, TA Instruments, New Castle, DE) was utilized to conduct temperature step/frequency sweep experiments on amorphous samples. A sample of the lyophilized trehalose/glycerol mixtures (10−20 mg) was loaded into a stainless steel material pocket29 (PerkinElmer, Norwalk, CT) and melted on a heating plate at 480 K to remove the last trace of moisture in the lyophilized mixtures. The anhydrous glassy state was obtained by quenching the melt on a cold steel surface (∼283 K) cooled by liquid nitrogen, and then the sample was immediately subjected to the temperature step/ frequency sweep experiment. The temperature ranges were chosen to bracket a temperature range above and below the expected Tg value as given in the literature.10 The beginning and ending temperatures are provided in Table 1. The temperature increment was 5 K with an equilibration of 5 min ahead of the frequency sweep. The oscillation frequency was swept from 20 to 0.01 Hz (i.e., 20.00, 19.00, 15.80, 12.60, 10.00, 7.90, 6.30, 5.00, 3.20, 2.50, 2.00, 1.60, 1.30, 1.00, 0.79, 0.63, 0.50, 0.40, 0.32, 0.25, 0.20, 0.16, 0.13, 0.10, 0.08, 0.06, 0.05, 0.04, 0.03, 0.02, and 0.01 Hz) at each temperature step with a displacement amplitude of 30 μm. Four samples were independently prepared and measured for each composition. 6821


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The Journal of Physical Chemistry B Table 1. Temperature Range (from T1 to T2) Used for Temperature Step/Frequency Sweep Experiments for Each Trehalose/Glycerol Mixture

composition to cover the full temperature range under investigation. As a result, the α-relaxation time profile used for the following fitting procedure is an average of the three obtained τ(T) profiles. Several models have been proposed to relate the horizontal displacement values to temperature. In general supercooled liquids above the glass transition temperature are found to follow the Williams−Landel−Ferry (WLF) equation,34 which is given by eq 235−37

Composition φtre

φgly

1 0.975 0.95 0.9 0.875 0.85 0.8

0 0.025 0.05 0.1 0.125 0.15 0.2

T1 368 358 348 318 318 308 298

T2 K K K K K K K

423 408 403 373 368 363 348

K K K K K K K

log10(τ /τg) = −

C1(T − Tg) C2 + (T − Tg)

(2)

wherein C1 and C2 are material coefficients that can be obtained by statistically fitting the data to this model. Angell25 proposed that C1 could be a universal constant with a value of ∼16; thus, C1 was fixed as 16 for the current study.35 Since the α-relaxation time profile τ(T) follows the WLF equation at T > Tg,31 one can obtain the values of C2 and Tg by best-fitting τ(T) with the limitation of T > Tg to eq 2. At Tg, the relaxation time τg has been suggested to be 100 s, independent of the material, and this value was used as a constant for the fitting process.36,38−40 The most widely used metric for quantifying kinetic fragility is the steepness index (m) as defined by eq 3.40,41

The DMA was calibrated in single-cantilever mode at multiple oscillation frequencies using standard polycarbonate bars. Highpurity nitrogen was used as the purge gas in the experiment. The loss modulus (E″) data as a function of frequency, for a specific temperature series, can be shifted to fit a master curve using a time−temperature superposition model30 wherein a given temperature trace is shifted horizontally to coincide with the trace at a given reference temperature (Tr). This can be expressed mathematically as E″(ω, T) = E″(aTω, Tr) with aT being the horizontal shift or x-shift.30 The horizontal shift factor for each temperature series was obtained using Advantage data analysis software (V5.7.0, TA Instruments, New Castle, DE). The α-relaxation time (τ) at a given temperature under study can then be calculated using the following definition of aT τ = aT τr (1)

m=

d log10(τ ) d(Tg /T )

|T = Tg

(3)

By combining eqs 2 and 3, the fragility index is given by

where the α-relaxation time (τr) at a given reference temperature Tr can be calculated as τr = 1/ωmax, according to linear viscoelastic theory.31,32 The maximum angular frequency (ωmax, in rad/s) corresponds to the maximum loss modulus in the time−temperature superposition master curve (shown in Figure 1b). This maximum in loss modulus occurs, when, at a given reference temperature, the sample can deform or relax within the same time frame as the corresponding oscillation frequency (i.e., ωmax).33 In this study, three different reference temperatures (Tr) were chosen for each replicate of a given

m=

37

C1Tg C2

(4)

where Tg is in K.

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RESULTS AND DISCUSSION Time−Temperature Superposition Master Curve. Time−temperature superposition (TTS) is an extrapolation principle that enables the characterization of viscoelastic properties of glass formers over a wide range of time or

Figure 1. (a) The isothermal variations of the loss modulus (E″) of pure trehalose as a function of the oscillation frequency (ω, 0.06−125.7 rad/s) at each temperature step. (b) The master curve of E″ generated by shifting the curve of each temperature toward the reference trace (403 K) by an amount given by the horizontal shift factor (aT). Inset: A sketch of the single-cantilever mode of DMA. 6822


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The Journal of Physical Chemistry B frequencies that are inaccessible with a given instrument at a particular reference temperature. Based on the TTS principle, the DMA can be used to perform a temperature step/frequency sweep experiment over an experimentally convenient frequency range. The viscoelastic spectrum over a wider range of frequencies can then be obtained by generating the master curve. Figure 1a displays the isothermal variation of the loss modulus (E″) for one of the four replicates of pure trehalose as a function of frequency (ω), at each temperature step. As described in the previous section, the isothermal viscoelastic response of the sample was recorded as a function of frequency, which was varied from 20 to 0.01 Hz (i.e., 125.7 to 0.06 rad/s). To generate the master curve of E″ (as seen in Figure 1b), the curves in Figure 1a corresponding to each temperature were shifted horizontally to overlap with the reference 403 K trace. The magnitude of this shift (aT) is shown in Figure 2, as a

Figure 3. Temperature dependence of the α-relaxation time (τ, mean ± SD) for the trehalose/glycerol mixtures of representative compositions (80 wt %, 85 wt %, 90, 95, and 100 wt % of trehalose). The WLF curves were obtained by best-fitting 4−7 data points at the high temperature end of the average τ(T) to acquire the highest goodness of fit (R2 > 0.99).

of temperature. The three resulting τ(T) profiles were averaged to generate the average τ(T) profile for each experimental replicate. The resulting τ(T) profiles for each of the four experimental replicates were then averaged to generate the τ(T) profile for each composition, as shown in Figure 3. By best-fitting 4−7 data points at the high temperature end of the average τ(T) profile (shown in Figure 3) to eq 2, we obtained WLF curves which have a high goodness of fit (R2 > 0.99). It is evident from Figure 3 that the best-fit curve given by the WLF equation begins to deviate from the data points in the vicinity of Tg where log10(τ/τg) is in the range of ∼0−2, which is in agreement with the literature.46,47 For the determination of m, the values of C2 and Tg were obtained by best-fitting 4−7 data points at the high temperature end of the average τ(T) profile for each replicate of a given composition to eq 2 to acquire the highest goodness of fit (R2 > 0.98). Since four replicates were analyzed for each composition, four sets of values of C2 and Tg were obtained as listed in Table 2, which were used to calculate the fragility index (m) (in the form of mean ± SD) with eq 4 as shown in Figure 4. Fragility and Glass Transition Temperature. The fragility index (m) of the dehydrated trehalose/glycerol mixtures is given in Figure 4. The values of m predicted by the molecular dynamics simulations21 and the prediction results based on the simple additive mixing rule (mgly = 5340,48 and mtre = 115.2) were also presented in this figure. Due to the lower fragility of glycerol, it was expected that the addition of glycerol to trehalose would decrease the fragility of the final mixture. However, the m(φtre) profile deviated significantly from the curve predicted based on the additive mixing rule. Specifically, the value of m of the 87.5, 90, and 95 wt % trehalose samples had clearly lower values than additive mixing would predict. Further addition of glycerol beyond 12.5 wt % yielded results that were in alignment with additive mixing predictions. The fragility index of 87.5 wt % of trehalose was found to be statistically lower than that of 85 wt % trehalose (p < 0.01) while the fragility index of 95 wt % of trehalose was statistically

Figure 2. Horizontal shift factors (aT) for the temperature series in the case of Figure 1. The reference temperature was 403 K in this figure; thus, log10 aT = 0.

function of temperature. The position of the primary peak of E″ in the master curve characterizes the α-relaxation frequency and thus the α-relaxation time at the reference temperature. In fact, the complete time−temperature superposition principle comes with both horizontal (aT) and vertical (bT) shifts, with bT = Trρr/(Tρ) where ρ is the density of the material.42,43 Since the vertical shift factors are largely empirical with very little theoretical validity44,45 and the density of the trehalose/glycerol mixture at the series of temperatures under study is unavailable, we did not perform the vertical shifts in our study. Therefore, the slight mismatch seen in Figure 1b is mainly due to the absence of vertical shifts. Figure 3 shows examples of the α-relaxation time profiles of trehalose/glycerol mixtures of 80−100 wt % of trehalose as a function of temperature, which represent the average of the four replicates for each composition. For each replicate three different reference temperatures were selected to generate three master curves; therefore, three sets of horizontal-shift factors were obtained. Each of the three sets of horizontal-shift factors were then used to obtain a relaxation time profile as a function 6823


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Table 2. Values of C2 and Tg (mean ± SD) obtained by Best-Fitting the First 4−7 Data Points at the High Temperature End of the τ(T) Profile to eq 2 for Each Composition φtre

1

0.975

0.95

0.9

0.875

0.85

0.8

C2 Tg (K)

54.1 ± 2.9 388.8 ± 0.6

58.8 ± 2.6 376.0 ± 2.1

69.1 ± 2.5 368.1 ± 2.5

68.6 ± 2.9 344.9 ± 2.6

64.0 ± 1.2 339.5 ± 5.7

54.1 ± 1.7 327.2 ± 2.4

54.7 ± 2.0 310.8 ± 1.0

Dirama et al.,21 based on molecular dynamics simulations, predicted fragility index values in the form of F to be 1.88, 1.17, 1.42, 1.19 for trehalose/glycerol mixtures ranging from 100 wt % to 85 wt % of trehalose in a 5 wt % step, respectively, and 0.81 kJ/(mol·K) for pure glycerol. These values can be converted to m values of 98.10, 61.05, 74.10, 62.10, and 42.27 using the relation m = F/(2.305R) where R is the gas constant.21,25,28 Although the molecular modeling prediction of m is found to be quantitatively different from our experimental results as seen in the inset of Figure 4, a local minimum of m was observed at 95 wt % of trehalose which is very close to our experimental observations. Moreover, based on neutron scattering data, Magazù et al.52 proposed that glycerol affected the fragility of the sugar in a nonmonotonic manner, suggesting a minimum at a glycerol mass fraction of 2.5 wt %. Curtis et al.19 proposed, based on molecular dynamics simulation, an optimal glycerol mass fraction of 12.2 wt % to generate the strongest inertial effect of the bulky glass and thus the maximum suppression of protein dynamics. While the optimal ratio of glycerol to trehalose reported in this study and those in the literature are not exactly the same, they are all in general agreement, especially given the wide range of probing techniques, the different properties under investigation, and the various levels of resolution of mass fraction in each of the studies. From the perspective of fragility, we have demonstrated that the addition of a small amount of glycerol can decrease the fragility of trehalose much more significantly than a simple additive mixing rule would predict. Figure 5 displays a classic fragility plot that indicates the strong−fragile pattern characterizing the temperature dependence of the α-relaxation time (τ) of supercooled liquid compositions of trehalose/glycerol. The temperature dependence of τ described by the Arrhenius law τ = τg exp(EA/T), where EA = mTg ln 10,40 was shown in the inset of Figure 5 as dashed lines. The m = 16 line represents the theoretically smallest fragility index characterizing the strongest liquid. Since the fragility indicates the deviation of the temperature dependence of τ from the Arrhenius behavior,25 the m = 16 line is identical to the one predicted by the Arrhenius law as seen in the inset graph. Among the seven mass fractions investigated in this study, we found that the supercooled 90 wt %/10 wt % trehalose/glycerol liquid was the strongest composition, showing the smallest deviation from the corresponding Arrhenius law (e.g., log10 τWLF − log10 τArrhenius = 0.45 at Tg/T = 0.96). Pure trehalose was found to be the most fragile liquid with the largest deviation (e.g., log10 τWLF − log10 τArrhenius = 0.92 at Tg/T = 0.96). In contrast to the m(φtre) profile, the mass fraction dependence of Tg was found to be monotonic as seen in Figure 6. The plasticizing role of glycerol was demonstrated by the fact that the glass transition temperature was gradually decreased with a continuous addition of glycerol to trehalose. The Tg determined in this study, which corresponded to an αrelaxation time of 100 s, was found to be in good agreement with the calorimetric results reported in the previous study.10 In Figure 6, we presented the Tg curve calculated by the Fox

Figure 4. Variation of fragility index (m) as a function of trehalose mass fraction (φtre). The blue solid line represents the fragility profile predicted by an additive mixing rule.

lower than that of 97.5 wt % trehalose (p < 0.01). Therefore, it is clear that there is a statistically significant local minimum in fragility within the range 87.5−95 wt % of trehalose compared to its surrounding mass fractions, even though the values of m within this range were not statistically different. This deviation implies that a preservative matrix that has the characteristics of a strong glass former due to the presence of a small amount of glycerol and inherits a relatively high glass transition temperature from the pure trehalose can be formulated within the range of 87.5−95 wt % of trehalose. The slowing down of fast dynamics due to strong hydrogen-bonding interactions upon the addition of a small amount of glycerol to trehalose was suggested to be responsible for the decreased fragility.10,18,19,21,22,49 The fragility of a liquid has been observed to be correlated with the intensity of the fast relaxation normalized to the boson peak intensity.28 In other words, the normalized intensity is high in fragile glass formers and low in strong ones.50 The inelastic neutron scattering results given by Cicerone and Soles10 observed that the QES/boson peak intensity ratio was minimized in the presence of 5 wt % glycerol at 100 and 296 K, indicating that this mixture was the least fragile, which is in agreement with our m(φtre) profile. Moreover, the fragility index of anhydrous trehalose was determined to be 115.2 ± 6.3 in this study, in good agreement with the literature value of 107 ± 3 determined previously using dielectric measurements.38 To further validate the fragility determination method by DMA, we also obtained the fragility index of pure sucrose (98.1 ± 0.9) which is consistent with the literature values reported by Wang et al.41 (98−100) and Cassel51 (100 ± 5). 6824


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trehalose and glycerol as well as their differences in size and shape.53 1 − φtre φ − tre Tg = Tg,gly Tg,tre (5) Tg =

(1 − φtre)Tg,gly + kφtreTg,tre (1 − φtre) + kφtre

(6)

Implications for Biopharmaceutical Stabilization. We compared the hydrogen-bonding lifetime (τHB) profile reported by Dirama et al.21 and the slow β-relaxation (JG relaxation) time (τβ) reported by Anopchenko et al.23 with the fragility index obtained in this study, as seen in Figure 7. The lifetime of

Figure 5. Fragility plot: the strong−fragile pattern that characterizes the temperature dependence of α-relaxation time of supercooled trehalose/glycerol liquid mixtures. Note that only representative compositions were displayed for clarity purposes.

Figure 7. Coincidence of the local minimum of fragility found in this study and the local maximums of hydrogen-bonding lifetime and βrelaxation time reported in the literature. (a) The fragility index (m) profile; (b) the hydrogen-bonding lifetime (τHB) profile reported by Dirama et al.;21 (c) the β-relaxation time (τβ) profile at 297 K reported by Anopchenko et al.23

the hydrogen bonds formed between trehalose and glycerol molecules at 300 K was found to be the longest at 90 wt % of trehalose. On the other hand, the lifetime of the hydrogen bonds formed among trehalose molecules reached its local maximum at 95 wt %. The hydrogen-bonding lifetime could be an indicator of the strength of the interacting network existing in the mixture.6 The extended hydrogen-bonding lifetime implies a stronger interacting network. Therefore, it is proposed that the strongest interacting network should exist in the composition between 90 and 95 wt % of trehalose as demonstrated in Figure 7b. Since the JG relaxation is the precursor of α-relaxation,7 we can observe a good match between the τβ and m, with both reflecting the characteristics of α-relaxation dynamics. Specifically, the maximum of τβ at 90 wt % of trehalose, which represents the locally most suppressed βrelaxation dynamics, was in agreement with the local minimum of the average m at 90 wt % of trehalose, which represents the strongest glass former.

Figure 6. Variation of Tg of the trehalose/glycerol mixtures as a function of the trehalose mass fraction (φtre) together with literature values.10

equation (see eq 5). 53 Note that the glass transition temperature of glycerol is 190 K and that of trehalose is 388.15 K.15,53 The experimental Tg(φtre) profile showed a slight deviation from the predicted values within the mass fraction range interested in this study. To describe this deviation, we also obtained the Gordon−Taylor relationship (see eq 6)53 for the trehalose/glycerol mixtures, with a coefficient k = 0.4066 (R2 = 0.9956), which yielded a good representation of the data. The observed negative deviation from the Fox prediction is proposed to originate from the strong interactions between 6825


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future investigations to identify superior stabilizing compositions.

From the perspective of the definition of fragility, we can examine the case of heating a glass through the Tg. By responding to the thermal perturbation, a stronger glass former (e.g., 90 wt %/10 wt % trehalose/glycerol in this study) will maintain the structure it has as a glass and exhibit a gradual change from a glass to a liquid. But a fragile glass former (e.g., pure trehalose) will change abruptly even with a small deviation from the glass transition temperature (as illustrated in Figure 5 in terms of τ variation at a given Tg/T). From the perspective of biopharmaceutical stability, resistance of the matrix to external perturbations such as thermal or mechanical stress would be desired. We can also examine the circumstance of cooling a liquid through Tg. Strong liquids are good glass formers that resist crystallization. Fragile liquids are generally poor glass formers that can be pushed into a glassy state only by using extreme manufacturing techniques such as fast cooling rates. From the perspective of convenience of preparation of preservation compositions with the same or similar Tg, strong glass-forming materials would be desired. The relaxation dynamics of sugar-based glass-forming compositions are significantly affected by the intra- and intermolecular interactions that comprise the bulky matrix. It has been suggested that fragility is embedded in the properties of the materials in its normal liquid, supercooled liquid, and glassy states, including the fast dynamics, JG relaxation, as well as cooperative α-relaxation.50 This study demonstrates this correlation in trehalose/glycerol compositions that have been shown to be highly effective for protein stabilization. The DMA approach to determine fragility could be used to identify other combinations that are likely to be very beneficial for protein stabilization. In other words, the fragility index can be used as an indicator of the macroscopically invisible molecular interactions that are ultimately an important parameter to guide formulation of the preservative matrix for biopharmaceuticals.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +1-704-687-8365. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by Grant #5R01GM101796 from the National Institutes of Health. DMA measurements were carried out at the Materials Characterization Laboratory (MCL), a multiuser research facility supported in part by the Energy Production and Infrastructure Center (EPIC) at the University of North Carolina at Charlotte.

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REFERENCES

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CONCLUSIONS The combination of trehalose and glycerol has received considerable attention in recent years as a desirable formulation for extending the shelf life of biopharmaceuticals such as proteins. Despite this interest, important fundamental information about the fragility behavior of these compositions has been missing in the literature. The fragility profile has been suggested to be one of the most important factors contributing to the bioprotective efficacy of amorphous matrices. In this study, we determined the fragility index (m) and Tg of dehydrated trehalose/glycerol mixtures by applying the time− temperature superposition principle to relaxation data obtained by DMA. The composition dependence of Tg was found to follow a Gordon−Taylor-like relationship, representing the traditional plasticizing role of glycerol. However, it was found that the fragility index correlated with the mass fraction of trehalose in a nonmonotonic manner, with a local minimum between 87.5 and 95 wt % of trehalose, implying an antiplasticizing, glass strengthening function of glycerol. The composition of 5−12.5 wt % glycerol in trehalose has been shown to be of great importance in biopharmaceutical formulation. This study demonstrated that this concentration level of glycerol leads to the greatest improvement in fragility, without a large degree of Tg suppression, an optimization of characteristics that are highly desirable in a glass to ensure stability of embedded labile materials. The DMA protocol used to determine fragility in this study should prove useful for 6826


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