Glycerol Cryoprotectant Mixtures

Article pubs.acs.org/JPCB

How Heterogeneous Are Trehalose/Glycerol Cryoprotectant Mixtures? A Combined Time-Resolved Fluorescence and Computer Simulation Investigation Sandipa Indra and Ranjit Biswas* Department of Chemical, Biological and Macromolecular Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Salt Lake, Sector-III, Kolkata 700106, India S Supporting Information *

ABSTRACT: Heterogeneity and molecular motions in representative cryoprotectant mixtures made of trehalose and glycerol are investigated in the temperature range 298 ≤ T (K) ≤ 353, via timeresolved fluorescence Stokes shift and anisotropy measurements, and molecular dynamics simulations of four-point density−time correlations and H-bond relaxations. Mixtures containing 5 and 20 wt % of trehalose along with neat glycerol are studied. Viscosity coefficients for these systems lie in the range 0.30 < η (P) < 23. Measured solute (Coumarin 153) rotation and solvation times reveal a substantial departure from the hydrodynamic viscosity dependence, suggesting the strong microheterogeneous nature of these systems. Fluorescence anisotropy decays are highly nonexponential, reflecting a nonMarkovian character of the medium friction. A complete missing of the Stokes shift dynamics in these systems at 298 K but partial detection of it at other higher temperatures (shift magnitude being ∼400−600 cm−1) indicates rigid solute environments. An amorphous solid-like feature emerges in the simulated radial distribution functions at these temperatures. Analyses of mean squared displacements reveal rattling-in-a-cage motion, non-Gaussian displacement distributions, and strong dynamic heterogeneity features. Simulated dynamic structure factors and four-point correlations hint, respectively, at very long αrelaxation and correlated time scales at 298 K. This explains the long solute rotation times (∼80−200 ns) measured at 298 K. Stretched exponential decay of the simulated H-bond relaxations with long time scales further highlights the strong temporal heterogeneity and slow dynamics inherent to these systems. In summary, this work provides the first insight into the molecular motions and interspecies interaction in a representative cryoprotectant mixture, and stimulates further study to investigate the interconnection between cryoprotection and dynamic heterogeneity. However, in the “strong-fragile” scheme,7,8 both glycerol and trehalose are classified as “intermediate” glass formers. Raman spectroscopic and neutron scattering studies9−11 suggested that protein preservation time can be enhanced by making the preservative formulation a stronger glass-forming liquid. It has been observed that addition of 20 wt % trehalose into glycerol increases the Tg by ∼13 K.12,13 This modulation of Tg is 2 times smaller than that predicted by the regular solution model.13,14 Glycerol possesses an extensive H-bond network15 and a large dipole moment.16,17 The molecular dynamics of glycerol has been studied extensively by carrying out dielectric relaxation measurements at temperatures from ambient liquid to supercooled temperatures.18−24 Interestingly, experimental25−30 and computer simulation31−35 studies of aqueous solutions of trehalose have shown that trehalose has a high propensity to form H-bonds with water as well as to other

1. INTRODUCTION To survive at extreme conditions, such as at very low temperature and humidity, live cells and tissues synthesize some sugars and polyalcohols in both their inter- and intracellular fluids. These particular sugars and polyalcohols help to prevent cell damage at extreme environmental conditions and keep the integrative cell functions intact. These particular molecules are therefore termed as cryoprotectants, and the process is known as cryopreservation. Glycerol, a simple polyol, and trehalose, an alpha-linked disaccharide, are known to function as cryoprotectants. While glycerol acts as an intracellular agent, trehalose resides as an extracellular compound.1,2 The effective way to enhance preservative efficiency is antiplasticization3 that is the slowing down of large-scale molecular transport. Trehalose has been proven to be the most effective preservative among all other sugar formulations because of its high glass transition temperature (Tg = 390 K).4−6 On the other hand, glycerol is a stronger glass former (Tg = 190 K) than trehalose because its smaller size facilitates efficient packing in the glassy state. © 2016 American Chemical Society

Received: June 28, 2016 Revised: October 6, 2016 Published: October 10, 2016 11214

DOI: 10.1021/acs.jpcb.6b06511 J. Phys. Chem. B 2016, 120, 11214−11228

Article

The Journal of Physical Chemistry B

dynamic Stokes shift data suggest trehalose mediated disruption of the H-bond network of glycerol. Measured solvation and rotation times reflect fractional viscosity dependence49−56 and a sort of rotation−translation decoupling. Simulated radial distribution functions and mean squared displacements at room temperature suggest solution characteristics that resemble those in supercooled glassy systems. At the low temperature region, the inertial motion of the molecules governs the solution dynamics, whereas the diffusion controlled mechanism takes over at higher temperatures.

neighboring trehalose molecules. In this way, trehalose can obstruct the crystallization process by disrupting the tetrahedral hydrogen bond (H-bond) structure of water. Like trehalose, glycerol in aqueous solution also exhibits cryoprotective properties.36,37 There exist several reports of trehalose/glycerol binary mixtures at the glassy state.3,38−43 It has been observed that addition of a small amount of glycerol (∼2.5%) into trehalose makes the system a stronger glass former due to interspecies H-bonding.38,42,43 This antiplasticizing effect of glycerol on trehalose can significantly increase the preservation times of proteins.44−46 Despite this biological relevance and application potential, a systematic study of the structural and dynamical aspects of trehalose/glycerol cryoprotectant mixtures is still lacking. The present study is an attempt toward this direction where solution heterogeneity and molecular motions are monitored and characterized by fluorescence spectroscopic measurements and computer simulations. Cryoprotectants prevent crystallization or dehydration of biomolecules during cryopreservation. It is well-known that solvent molecules play a significant role in the crystallization of biomolecules.47,48 Therefore, an understanding of this crystallization demands a thorough knowledge of the local solution structure and the associated solvent molecular motions. A study of dynamical heterogeneity provides a microscopic view of the spatially varying molecular motions of the system under investigation. Hence, the crystallization or dehydration of biomolecules is directly connected to the spatiotemporal heterogeneity of the host solvent. The current study therefore acts as a precursor to the following questions: How does the interspecies interaction mediated new solution structure provide a favorable host for biopreservation? How do solvent molecular motions and their spatial variations affect protein preservation in such a host? How does slowing down of molecular dynamics (that is, antiplasticization) assist in retaining protein’s structure and normal functioning? Is there any connection between the extent of antiplasticization and the duration of protein preservation? A quest for insight into these questions provides the necessary motivation for studying the composition-dependent structure and dynamics of the present representative cryoprotectant system. For studying trehalose/glycerol binary systems in the solution phase at room temperature, we have chosen two different compositions: 5 and 20 wt % of trehalose in glycerol. We have found that the maximum amount of trehalose that is completely soluble in glycerol is 20 wt %. Coumarin 153 (C153) has been employed as a solute probe in the relevant spectroscopic measurements. The chemical structures of glycerol and trehalose are shown in Scheme 1. Dynamic fluorescence Stokes shift and anisotropy measurements for C153 in these trehalose/glycerol mixtures have been performed over the temperature range 298 ≤ T(K) ≤ 353. Measured

2. EXPERIMENTAL DETAILS AND SIMULATION PROCEDURES 2.1. Sample Preparation. Laser grade C153 was purchased from Exciton and used as received. Glycerol (≥99.5%) and D-(+)-trehalose dihydrate (≥99%) were obtained from Sigma-Aldrich and used without further purification. A measured amount of trehalose was added to a measured volume of glycerol in an airtight glass vessel. The clear solution was prepared by heating the mixture at 333 K and stirring (magnetic stirrer) for 3 h. After obtaining a clear solution, it was cooled to room temperature. A few μL of a freshly prepared solution of C153 in heptane was poured into a quartz cuvette of 1 cm optical path length. The nonpolar solvent was then evaporated by blowing hot air around the outer surface of the cuvette. Then, ∼3−4 mL of sample solution was added into the cuvette. The solution was slightly heated and stirred for some time to ensure complete dissolution of the probe. Next, the solution was allowed to cool to room temperature normally. Note that the concentration of C153 was maintained at ≤10−5 M in all the trehalose/glycerol compositions studied here. 2.2. Data Collection and Analysis for Absorption and Steady-State Fluorescence Emission Spectra. Absorption and emission spectra of C153 at different solution compositions and temperatures were recorded by UV−visible spectrophotometer (UV-2450, Shimadzu) and fluorimeter (Fluorolog-3, Jobin-Yvon, Horiba), respectively. Temperature was controlled by using Julabo and Peltier temperature controllers, respectively. The standard spectral analysis protocol was then followed to determine spectral frequencies.57−61 The typical error bar for the determined spectral frequencies was ±250 cm−1. 2.3. Data Collection and Analysis for Time-Resolved Fluorescence Emission Spectra. The time-correlated single photon counting (TCSPC) technique based on a laser system (Lifespec-ps, Edinburgh, U.K.) with a light-emitting diode (LED) producing excitation light of 409 nm was employed for time-resolved fluorescence emission measurements. The full width at half-maximum (fwhm) of the instrument response function (IRF) (measured at the magic angle using water and 409 nm excitation light) was ∼75 ps. The fluorescence emission decay was collected using an emission band-pass of ≤2.0 nm. All the measurements were recorded using a Peltier temperature controller with an accuracy in the temperature measurements of ±1 K. 2.4. Analysis for Dynamic Stokes Shift Measurements. For dynamic Stokes shift measurements, typically 17−18 emission intensity decays were collected at the magic angle (54.7°) at equally spaced wavelengths across the steady state emission spectrum of C153 in solution. Subsequently, the established protocol was followed to generate the time-resolved emission spectra (TRES) from these intensity decays.57,61−65

Scheme 1. Schematic Representations of (a) Glycerol and (b) α,α-Trehalose

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The Journal of Physical Chemistry B The time-dependent solvation of the laser-excited probe was then followed by constructing the normalized spectral or solvation response function57 ν(t ) − ν(∞) S(t ) = ν(0) − ν(∞)

Table 1. Measured Temperature-Dependent Viscosity (η) and Density (ρ) of Trehalose/Glycerol Mixtures at Different Trehalose Concentrations (CTre) Considered

∫0

∞

dtS(t ) =

∫0

ρ (g/mL)

0

298 313 333 353 298 313 333 353 298 313 333 353

861 273 82 33 937 298 89 36 2258 631 167 61

1.2570 1.2478 1.2347 1.2187 1.2664 1.2569 1.2440 1.2310 1.2971 1.2877 1.2747 1.2587

∞

20

U = [ ∑ krij(rij − rij0)2 ] + [ ∑ k θijk(θijk − θijk0 )2 ] bonds

+[ dt ∑ [ai exp( −t /τi)] = i

∑ aiτi

∑ torsions

angles

k ϕijkl[1 + cos(nϕijkl − δ)]]

⎤ ⎡ ⎧ ⎡ 12 ⎛ σij ⎞6 ⎤ qiqj ⎫ ⎪⎥ ⎢ ⎪ ⎢⎛ σij ⎞ ⎥ ⎬⎥ + ⎢∑ ⎨4εij⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥ + r ⎝ rij ⎠ ⎦ 4πε0rij ⎪ ⎢⎣ i < j ⎪ ⎭⎥⎦ ⎩ ⎣⎝ ij ⎠

i

where ai and τi are the amplitudes and time constants obtained from the multiexponential fits and ∑i ai = 1. 2.5. Data Collection and Analysis for Rotational Anisotropy. For the measurements of rotational anisotropy decay, r(t), time-resolved emission intensities were collected at the wavelengths corresponding to the peak maxima of the steady-state fluorescence emission spectra.68,69 Emission intensities were collected at three different positions of the emission polarizer: magic angle (54.7°), parallel [I∥(t)], and perpendicular [I⊥(t)] with respect to the polarization of the excitation light. Subsequently, the standard analysis procedure63,66,68,70 was followed to construct the r(t) decays as follows:

(4)

For glycerol, the relevant expression is given by U = [ ∑ krij(rij − rij0)2 ] + [ ∑ k θijk(θijk − θijk0 )2 ] bonds

⎡ +⎢ ∑ ⎢⎣ torsions +

angles

{

V1 V (1 + cos φ) + 2 (1 − cos 2φ) 2 2

V3 (1 + cos 3φ) 2

⎤ ⎥ ⎥⎦

}

⎡ ⎧ ⎡ ⎤ 12 ⎛ σij ⎞6 ⎤ qiqj ⎫ ⎪⎥ ⎢ ⎪ ⎢⎛ σij ⎞ ⎥ ⎜ ⎟ ⎜ ⎟ ⎨ ⎬ + ⎢∑ 4εij⎢⎜ ⎟ − ⎜ ⎟ ⎥ + ⎥ r ⎝ rij ⎠ ⎦ 4πε0rij ⎪ ⎢⎣ i < j ⎪ ⎩ ⎣⎝ ij ⎠ ⎭⎥⎦

I (t ) − GI⊥(t ) I (t ) + 2GI⊥(t )

η (cP)

5

(2)

r (t ) =

T (K)

(1)

where ν(t) denotes some measure of the time-dependent frequency (first moments in the present study) of the fluorescence emission spectrum of the laser-excited dye dissolved in that medium. ν(0) is the emission frequency of the time zero spectrum and ν(∞) the emission frequency after the solvent relaxation is complete.66 Because of insufficient resolution, ν(0) for the present study was estimated by using the literature method.67 The average solvation time, ⟨τs⟩, was then obtained analytically by time integrating the multiexponential functions that adequately describe the measured S(t) as follows ⟨τs⟩ =

CTre (wt %)

(5)

Here, the intramolecular bonded interactions consist of harmonic terms for bond stretching (bond length, rij; equilibrium bond length, r0ij; bond force constant, krij), angle bending (bond angle, θijk; equilibrium bond angle, θ0ijk; angle force constant, kθijk), and torsional potential defined over cosines of the dihedral angle ϕijkl (multiplicity, n; phase shift angle, δ; torsional force constant, kϕijkl). In the OPLS-AA potential, V1, V2, and V3 denote the coefficients of the Fourier series and φ is the torsional angle. The nonbonded interactions are included via Lennard-Jones (LJ) and Coulomb interactions. The potential well depth, van der Waals radius, and distance between atoms are symbolized by εij, σij, and rij, respectively. The parameter q represents the partial charge of the atom, and ε0 denotes the static dielectric constant. LJ interactions between unlike atoms are calculated via Lorentz−Berthelot combining rules.74 2.8. Simulation Details. Simulations were carried out with a total of 512 molecules in a cubic box with periodic boundary conditions employing the DL_Classic_1.975 package. As the system was highly viscous, the following method was adopted

(3)

Here, G is the geometric factor which was obtained by tail matching the intensity decays I∥(t) and I⊥(t). 2.6. Viscosity and Density Measurements. Solution densities were measured by using an automated density-cumsound analyzer (DSA 5000, Anton Paar). Viscosity coefficients of the solutions were measured by an automated microviscometer (AMVn, Anton Paar). Measured viscosity coefficients (η) and densities (ρ) are provided in Table 1. 2.7. Force Field. We have performed simulation studies using the GLYCAM0671 force field for trehalose and the OPLSAA72 force field for glycerol. Note that the modified partial charges for various atomic sites of glycerol are used here.73 The partial charges and Lennard-Jones parameters of both of the models of trehalose and glycerol are provided in Tables S1 and S2 of the Supporting Information. The total potential energy expression employed for trehalose is as follows: 11216


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how this fast dynamics gets coupled to the structural diffusion. The relaxation of continuous H-bond lifetime is calculated by the time-correlation function, SHB(t),85−87

to reach the properly equilibrated configuration. First, the system was heated up to 500 K via a step-up process with a step of 100 K in the NVT ensemble. Subsequently, the system was cooled down to the desired temperature via a step-down process with the same temperature gap. Next, the system was equilibrated in the NPT ensemble for 2 ns to achieve the experimental density. Subsequently, a 2 ns equilibration run followed by a 50 ns production run was performed in the NVT ensemble using the Nosé−Hoover thermostat76,77 with a relaxation time of 0.5 ps for calculating different structural and dynamical properties. Equations of motions were solved by the Verlet−Leapfrog algorithm74 with a time step of 1 fs. The Ewald summation technique74 and the SHAKE algorithm78 were employed, respectively, for electrostatic interactions and to constrain all bonds involving the hydrogen atoms.

SHB(t ) =

C HB(t ) =

(13)

4. RESULTS AND DISCUSSION 4.A. Spectroscopic Measurements. 4.A.1. Absorption and Steady-State Emission Spectra: Temperature Effects. Figure 1 shows representative temperature-dependent absorption and emission spectra of C153 at 20 wt % trehalose concentration in trehalose/glycerol mixture. Figure 2 depicts the temperature dependence of spectral peak frequencies (ν) in these cryoprotectant mixtures at three different trehalose concentrations. Note the temperature dependence of absorp-

(7)

3⟨Δr 4(t )⟩ −1 5⟨Δr 2(t )⟩2

⟨h(0)h(t )⟩ ⟨h⟩

where reformation of the H-bond after breakage is allowed and counted. This reformation can be with another molecule which has diffused into the nearest neighbor region after the H-bond with the initial partner has been broken. CHB(t) is, therefore, associated with the structural relaxation. The average structural H-bond relaxation time, ⟨τHB C ⟩, can be obtained by time integrating CHB(t).

The presence of heterogeneity can then be quickly checked by calculating the translational non-Gaussian (NG) parameter, α2(t), and the new non-Gaussian (NNG) parameter, γ(t), as follows80,81 α2(t ) =

(12)

where H(t) = 1 if the tagged pair of molecules, for which h(0) is calculated, remains continuously H-bonded until time t, or else zero. SHB(t) describes the probability that a tagged pair of molecules remains continuously H-bonded up to time t, and approaches zero when H-bonding between them breaks down for the first time. The average continuous H-bond lifetime, ⟨τHB S ⟩, is then obtained via a time integration of SHB(t). The coupling of structural diffusion to the H-bond fluctuations is described by the structural H-bond relaxation function, CHB(t), defined as85−87

3. SIMULATION DATA ANALYSES: STATISTICAL MECHANICAL RELATIONS The translational self-diffusion coefficient (D) of a particle moving in a fluid can be calculated from the mean squared displacements (MSDs) of center-of-mass position vectors ri(t) as follows 1 ⟨|Δr(t )|2 ⟩ = ⟨∑ |ri(t ) − ri(0)|2 ⟩ (6) N 2 with ⟨|Δr(t)| ⟩ denoting the MSD. Subsequently, D has been calculated from the simulated ⟨|Δr(t)|2⟩ at long time as follows:79 ⎡1 ⎤ D = ⎢ (⟨|Δr(t )|2 ⟩)⎥ ⎣ 6t ⎦t →∞

⟨h(0)H(t )⟩ ⟨h⟩

(8)

N where ⟨Δr 2 (t)⟩ = ⟨N −1 ∑ i=1 |Δr(t)| 2 ⟩ and ⟨Δr 4 (t)⟩ = N ⟨N−1∑i=1 |Δr(t)|4⟩ with Δr denoting the single particle displacement. Δr(t) = ri(t) − ri(0). The NNG parameter γ(t) is linked to the MSD as follows81

γ (t ) =

with

1 1 ⟨Δr 2(t )⟩ 3 Δr 2(t )

1 Δr 2(t )

=

1 N

N

∑i = 1

1 |Δr(t )|2

−1 (9)

.

The temporal correlation among relaxing particles is then obtained via the four-point dynamic susceptibility, χ4(k, t), from the fluctuations of the self-intermediate scattering function, Fs(k, t),82−84 χ4 (k, t ) = N[⟨Fs(k, t )2 ⟩ − ⟨Fs(k, t )⟩2 ]

(10)

where Fs(k, t ) =

1 N

N

∑ ⟨cos k·[ri(t ) − ri(0)]⟩ i=1

Figure 1. Temperature-dependent absorption (upper panel) and emission (lower panel) spectra of C153 in a trehalose/glycerol mixture at 20 wt % trehalose concentration. Representations are color-coded. Note that “trehalose” has been denoted by “Tre” in this figure and others to avoid clutter.

(11)

Because these mixtures are H-bonded systems, an investigation into the H-bond fluctuation time scales may provide information regarding the fast dynamics at the local level and 11217


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different trehalose concentrations are presented. Note the λexdependent emission spectra have been recorded at 298 and 353 K for these mixtures. Clearly, νem and Γem show the strongest λex dependence for the mixture with 20 wt % trehalose at 298 K, which considerably weakens upon raising the temperature to 353 K. 4.A.2. Solvation Dynamics: Temperature Dependence. Representative time-resolved emission spectra (TRES) of C153 in the solution containing 20 wt % trehalose at ∼333 K are shown in the upper panel of Figure 4. The difference between

Figure 2. Temperature-dependent absorption (upper panel) and emission (lower panel) spectral frequencies of C153 in trehalose/ glycerol mixture at three different trehalose concentrations (0, 5, and 20 wt %). Trehalose concentrations are color-coded.

tion peak frequencies is weaker than that of emission frequencies, although they (absorption and emission) show opposite temperature dependence. This is because blue-shift in absorption spectra reflects the temperature-induced decrease of medium polarity (in terms of static dielectric constant); for emission, in contrast, red-shift with temperature indicates solute emission arising from better solvent-relaxed configurations at successively higher temperatures. Similar opposing temperature dependence of solute absorption and emission spectra has also been observed in amide/electrolyte deep eutectics.88 The spatial heterogeneity aspect is subsequently investigated in Figure 3 where excitation wavelength (λex) dependence of emission frequency (νem) and spectral full-width-at-halfmaximum (Γem, fwhm) of C153 in these mixtures at three

Figure 4. Synthesized time-resolved emission spectra (TRES) of C153 at different time slices from the experimentally obtained decays collected at the magic angle (54.7°) of the emission polarizer in a trehalose/glycerol mixture with 20 wt % trehalose in the solution at 333 K. The TRES shown (upper panel) are at the following time intervals after solute excitation: 0, 20, 100, and 2000 ps. The time evolution of the first moment frequency, ν(t), is shown in the middle panel, and the widths Γ(t) are shown in the lower panel. The difference in the short time behavior of Γ(t) at three different compositions is also shown.

the first moment frequencies of the reconstructed time-zero spectrum and the spectrum at t = ∞ is found to be ∼600 cm−1, which is ∼30% less than the estimated “true” dynamic Stokes −1 shift (νSS est = 840 cm ) for C153 in this solution. The shift in emission frequency with time for this composition and temperature is shown in the middle panel. Time-dependent widths, presented in the bottom panel, reflect irregular change at the initial times for pure solvent glycerol as well as for trehalose/glycerol solution. The use of broader time resolution in the present experiments and the consequent poor fits to the time-resolved data points at the initial times may be a reason for this irregular time dependence. However, Γ(t) reaching a

Figure 3. Excitation wavelength (λex) dependence of emission frequency (νem) and spectral width (Γem) of C153 at different trehalose concentrations at ∼298 K (open symbols) and ∼353 K (filled symbols). 11218


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setup, and as a result, the fast solvation response (which could be nearly the full response at 298 K) is completely missed. Solvation response functions, S(t), measured at three different compositions of trehalose/glycerol solutions at ∼333 K are shown in the upper panel of Figure S4 (Supporting Information), whereas the lower panel of the plot shows temperature-dependent S(t) at 20 wt % trehalose solution. Single and biexponential fit parameters to these response functions are summarized in Table 2. Note the average

plateau with time is an observation made already for a variety of systems.51,52,57,89 Another feature to note in this context is the complete missing of the Stokes shift dynamics in the trehalose/glycerol mixture at 20 wt % trehalose at 298 K by the present measurements. This is interesting because this composition at 298 K forms a highly viscous solution with η ∼ 23 P (see Table 1) in which one expects to detect the diffusive solvation component by the temporal resolution accessed (∼90 ps) here. However, the intensity decays at three representative wavelengths (480, 550, and 630 nm) shown in the upper panel of Figure 5 suggest no rise component at the red wavelength (630

Table 2. Fit Parameters to the Measured TemperatureDependent Solvation Response Functions, S(t), for C153 in Trehalose/Glycerol Mixtures at Three Different Trehalose Concentrations, CTre CTre (wt %)

T (K)

0

298 313 333 353 298 313 333 353 298 313 333 353

5

20

τ1 (ps)

a2

τ2 (ps)

⟨τs⟩ (ps)

0.24 0.24

49 34

1.00 0.76 0.76 1.00

345 178 100 44

345 147 84 44

0.40 0.84 0.73

67 66 35

0.60 0.16 0.27

227 238 143

163 94 64

0.48 0.44 0.87

78 39 68

0.52 0.56 0.13

455 167 909

274 111 177

a1

solvation time (⟨τs⟩) becomes slower upon addition of trehalose into glycerol as η of the medium (Table 1) increases. ⟨τs⟩ shortens with the increase of temperature because η decreases with temperature. Interestingly, when the temperature is increased from 333 to 353 K at trehalose concentration CTre = 20 wt %, ⟨τs⟩ becomes longer. Following our study of alcohol/water binary mixtures,64,92−94 it may be assumed that this binary mixture probably undergoes a structural transition at higher temperature via breakage of the collective H-bond network, allowing the slow diffusive modes to carry out a sizable portion of the total solvation energy relaxation. Further study is required to examine this conjecture and estimate the relative contributions of the diffusive and collective solvent intermolecular modes to the Stokes shift dynamics in these cryoprotectant mixtures. Table 3 summarizes the temperature-dependent dynamic Stokes shift magnitudes observed and estimated67 in these mixtures. Note the missing percentage is the maximum for pure glycerol at 298 K. Glycerol is known to form an extensive Hbond network at room temperature.95−97 A high viscosity (η ∼ 9 P) of glycerol at 298 K ensures sluggish solvent relaxation, allowing the fast collective intermolecular solvent modes to overwhelmingly dominate the solvation energy relaxation. Consequently, the present measurements have failed to detect the dominant portion of the total solvation response. Interestingly, the missing percentage decreases with the increase of temperature. Increase of temperature leads to disruption of the H-bond network, ensuring increased participation of the solvent diffusive modes to carry out the solvation energy relaxation. As a result, the missing percentage has been found to decrease with the increase of temperature. Data in Table 3 also suggest that addition of trehalose in glycerol decreases the missing percentage. Here, the H-bond structure breaking ability98,99 of trehalose comes into play,

Figure 5. Representative fluorescence intensity decays of C153 at 20 wt % trehalose concentrations in a trehalose/glycerol mixture at three different wavelengths of emission spectrum: blue, middle (close to the peak maximum), and red at ∼298 K (upper panel) and ∼353 K (lower panel). Representations are color-coded. Experimental data are shown by circles, whereas solid lines represent fits through the experimental data. The inset shows the same experimental data but on a short time scale to better visualize decay/rise at the blue and red wavelengths.

nm). Data presented in the inset on a shorter time scale and fit parameters in Table S3 (Supporting Information) confirm this. In contrast, the red wavelength decay at 333 K (η ∼ 1.7 P) clearly shows both the rise and decay components. Given that rise and decay components at the red wavelength and decay components only at the blue wavelength are considered as a hallmark of Stoke shift dynamics, absence of these features in the most viscous solution among the systems studied here is somewhat unexpected. The probable reason for such an observation could be that, in such a high viscous solution (∼23 P), solvation energy relaxation occurs mainly via the solvent inertial modes, leaving a tiny fraction to be carried out by the slow solvent diffusion. The trehalose/glycerol system contains several −OH groups which participate in the collective solvent intermolecular vibrations and librations. These collective modes are known to participate in the polar solvation energy relaxation at the subpicosecond regime.90,91 Unfortunately, such a fast response cannot be detected by the present 11219


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Figure 6 compares the measured ⟨τr⟩ values with those predicted by the modified Stokes−Einstein−Debye (SED)

Table 3. Temperature-Dependent Dynamic Stokes Shift Magnitudes and Missing Components (in Percentage) for C153 in Trehalose/Glycerol Mixtures at Different CTre CTre (wt %)

T (K)

ΔνObs (cm−1)

ΔνEst (cm−1)

missing (%)

0

298 313 333 353 298 313 333 353 298 313 333 353

352 599 604 539

1175 1192 1109 1022

70 50 46 47

594 637 618

1093 1072 990

46 41 38

482 603 452

727 840 1053

34 28 57

5

20

Figure 6. Variation of the measured average rotational times, ⟨τr⟩, for C153 (symbols) in trehalose/glycerol cryoprotectant mixtures with temperature-reduced viscosity, η/T. Predicted values of ⟨τr⟩ from the SED relation using the stick and slip (solid lines) boundary conditions are also shown.

which reduces the contribution of the collective solvent modes involving the H-bond network. Note the same disruption of the H-bond network by trehalose leads to better structural packing in the binary mixture, increasing the solution viscosity (see Table 1). 4.A.3. Solute Rotation and Effects of Temperature: Viscosity Coupling. Rotational dynamics of C153 has been measured at different CTre values in the temperature range 298 ≤ T (K) ≤ 353 to explore the solute−solvent coupling in these bioprotectant mixtures. Representative r(t) decay of C153 in solution with CTre = 20 wt % at 313 K is shown in Figure S5 (Supporting Information) along with the biexponential fit parameters. Note the pronounced nonexponential character of this r(t) decay and the widely different time constants (20 ps and ∼23 ns). This strong nonexponential character has been found in other r(t) decays collected here as well, except for those at 298 K. Fit parameters summarized in Table 4 reflect

relation, τr = Vηf C/kBT, with V = 248 Å3 for C153 (solute volume), f = 1.71 (solute shape factor), and C = 1 (stick boundary condition) or 0.24 (slip boundary condition).51,68 kBT is the Boltzmann’s constant times the absolute temperature. Table S6 (Supporting Information) summarizes the predicted slip and stick rotation times. It is interesting to note in Figure 6 that for all these systems ⟨τr⟩ follows the slip prediction except at 298 K where the stick boundary condition governs the solute rotation. This transition from slip to stick boundary condition is quite abrupt: for a lowering of solution temperature by 15 K on going from 313 to 298 K, ⟨τr⟩ lengthens by a factor of ∼15−20 while the temperaturereduced viscosity, η/T, increases by a factor of ∼3−4 only. This suggests hindered rotation of C153 which might have originated from solute caging in a cavity created by the Hbond network in glycerol and glycerol/trehalose mixtures at the lowest temperature studied. Scheme 2 provides a pictorial

Table 4. Fit Parameters to Temperature-Dependent Rotational Anisotropy (r(t)) Decays for C153 in Trehalose/ Glycerol Mixtures at Different CTre CTre (wt %)

T (K)

0

298 313 333 353 298 313 333 353 298 313 333 353

5

20

a1

τ1 (ps)

0.31 0.20 0.21

20 20 20

0.49 0.23 0.21

20 20 20

0.33 0.29 0.37

20 41 26

a2

τ2 (ns)

⟨τr⟩ (ns)

1.00 0.69 0.80 0.79 1.00 0.51 0.77 0.79 1.00 0.67 0.71 0.63

82.18 8.09 2.65 0.96 96.95 8.99 2.96 1.01 229.5 23.15 5.34 1.53

82.18 5.55 2.12 0.76 96.95 4.60 2.29 0.80 229.5 15.45 3.82 0.98

Scheme 2. Pictorial Representation of Caging of C153 in the Matrix of Trehalose/Glycerol Binary Mixture

representation of such a caging of C153 in these media. This idea of solute-caging implicitly assumes solute distribution in solution environments that relax at different rates, rendering a coupling between ⟨τr⟩ and η/T that may deviate from the hydrodynamic prediction, ⟨τr⟩ ∝ (η/T)p, with p = 1. The coupling between the measured ⟨τr⟩ and η/T is illustrated in the upper panel of Figure 7 where the viscosity dependence of rotation times is shown in a double logarithmic fashion along with a linear fit to the measured data. A similar fit generated by using the measured C153 rotation times in several

this general trend. Such a nonexponential behavior of r(t) indicates the non-Markovian nature of the underlying frictional response and may arise from the heterogeneous nature of the medium.68,100 At 298 K, rotation of C153 in these solutions appears to be extremely slow as the average rotation time (⟨τr⟩) lies in the ∼100−200 ns range. Such a slow rotation of C153 has been observed earlier for ionic deep eutectics101 and lowtemperature ionic liquids.102 Data in Table 4 also indicate that ⟨τr⟩ increases with the increase of solution viscosity. 11220


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Figure 7. Viscosity coupling of solute rotation and solvation times (⟨τr⟩ and ⟨τs⟩, respectively) for C153 in trehalose/glycerol mixtures. Measured rotation times (upper panel) and solvation times (lower panel) are denoted by symbols. Fits through these data to the expression, log⟨τx⟩ = log a + p log(η/T), are represented by lines with respective p values indicated. For a comparison, fits (dashed lines) through suitable data for C153 in several ionic liquids (from ref 101) are also shown. Figure 8. Site−site radial distribution function, g(r), between oxygen atoms of glycerol, O(G)−O(G), at three different concentrations of trehalose (three panels) as a function of distance r at temperatures of ∼298 K (red) and ∼353 K (green).

ionic liquids103 is also shown for a comparison. Note the fit to the cryoprotectant mixture data produces p = 1.32 which suggests significant deviation from hydrodynamic viscosity dependence, a result qualitatively similar to what has been observed for C153 rotation in ionic liquids (p = 1.16). Measured rotation times for C153 in dioxane/water mixtures also exhibit a substantial departure from the hydrodynamic predictions.104 This deviation from hydrodynamics for a variety of systems that differ wildly in solute−medium interactions suggests a strong role for solution structure and molecular packing around the rotating solute in these media. Interestingly, average solvation times in these cryoprotectant mixtures exhibit fractional viscosity dependence (lower panel) with p = 0.53 which resembles closely the finding for Stokes shift dynamics in (acetamide/propionamide + lithium perchlorate) deep eutectics.88 Note that fractional viscosity dependence of diffusive time scales is a common occurrence in deeply supercooled liquids,51,89,105,106 and is explained in terms of medium dynamic heterogeneity (spatially varying solvent relaxation rates). Next we present results from our simulation studies on solution structure and dynamics, and provide a microscopic explanation for what we have observed from our steady-state and time-resolved spectroscopic measurements. The validity of the force field used for glycerol has been checked via a comparison between the simulated and experimental densities (Table S7, Supporting Information). 4.B. Simulation Results: The Microscopic View. 4.B.1. Solvation Structures: Radial Distribution Functions. The distribution of the oxygen atoms of glycerol, O(G), is shown in Figure 8 via the simulated radial distribution function (RDF), g(r), at three different compositions of trehalose/ glycerol mixtures at ∼298 and ∼353 K. Note the first peak in these simulated RDFs appears at a distance (∼2.7 Å) very similar to that observed for different water models at ambient conditions.107,108 In addition, the height of the first peak is qualitatively similar to what has been observed for LennardJones systems at liquid-like densities.79 The peak height also

does not change upon addition of trehalose but decreases to some extent as the solution temperature is increased from 298 to 353 K. What is striking in Figure 8 is the appearance of a shoulder at ∼5 Å in the second peak. Interestingly, such a shoulder in the oxygen−oxygen RDF has been found earlier for ice in both simulations107 and experiments.109 RDF simulated for amorphous solids also shows a similar splitting-cumshoulder in its second peak.110 All of these suggest that probably a solid-like character appears locally in neat glycerol and in these mixtures at these temperatures. This local solidlike character then naturally explains the observed extremely sluggish solute rotation and complete missing of the Stokes shift dynamics in these media at 298 K. With a rise in temperature, this local solid-like character develops higher mobility (as indicated by the decrease of the first peak height of the RDF)111 which, in turn, allows increased participation of the slow diffusive solvent modes to the solvation energy relaxation. Next, we explore the composition-dependent trehalose− glycerol interaction by tracking the intra- and interspecies oxygen−oxygen radial distribution functions. In the left panels of Figure 9, the RDFs between trehalose oxygen atoms, O(T)− O(T), at 298 and 353 K are shown, while those between trehalose oxygen and glycerol oxygen atoms, O(T)−O(G), are displayed in the right panels. Several peaks appear in the O(T)−O(T) RDF because of the presence of different −OH groups at different positions in a trehalose molecule. At 5 wt % trehalose concentration, the intensity of the peaks of the O(T)−O(T) RDF is ∼3 times greater than that at 20 wt % trehalose concentration. This suggests, like in dilute aqueous solutions of tetramethyl urea,112,113 aggregation among trehalose molecules at low concentrations in glycerol. Upon 11221


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Figure 9. Site−site radial distribution function, g(r), between oxygen atoms of trehalose, O(T)−O(T) (left panels), and oxygen atoms of glycerol and trehalose, O(T)−O(G) (right panels), at 5 wt % trehalose and 20 wt % trehalose concentrations as a function of distance r at temperatures ∼298 K (red) and ∼353 K (green).

Figure 10. Simulated mean squared displacement, ⟨|Δr(t)|2⟩ (upper panel), and non-Gaussian parameter, α2(t) (lower panel), for the center of mass of glycerol as a function of time, t, in pure glycerol and in trehalose/glycerol mixtures at 5 wt % trehalose and 20 wt % trehalose at 298 and 353 K. In the lower panel, vertical lines are drawn to show the time corresponding to the peak maximum of α2(t), τNG, and the horizontal line indicates the τNG value (∼0.2) for homogeneous hot liquids. Trehalose concentrations are color-coded. Note the simulated MSDs for C153 dissolved in the mixture at 20 wt % trehalose and 298 K are also shown (pink) in the upper panel.

increasing the trehalose concentration to 20 wt %, the intensity of the O(T)−O(T) RDF decreases. This suggests increased dispersion of trehalose molecules into glycerol at higher concentrations. However, the O(T)−O(G) RDF intensity remains insensitive to this increase of trehalose concentration. This can be explained as follows. In the present simulations, a total of 512 molecules is considered in which only 7 and 33 trehalose molecules are required to prepare trehalose/glycerol binary mixtures at 5 and 20 wt % trehalose concentrations. This means an increase from ∼1 to ∼6% in the number of trehalose molecules (with respect to a total of 512), and this change is not sufficient to induce substantial modification in the intensity of the O(T)−O(G) RDF. 4.B.2. Mean Squared Displacements: Cage-Rattling and Temperature Effects. With the above structural characterization, we next investigate the mobility of the molecules in these systems at 298 and 353 K. Simulated mean squared displacements (MSDs), ⟨|Δr(t)|2⟩, for the center of mass (COM) of glycerol at different mixture compositions are shown in Figure 10 (upper panel) as a function of time, t. These MSDs, particularly the ones at 298 K, exhibit tα dependence with α possessing three different values: (i) at initial time, α = 2, reflecting inertial motion, (ii) at intermediate time, α < 1, indicating the subdiffusive regime, and (iii) at long time, α = 1, settling finally into the diffusive regime. Such a complex tα dependence is a characteristic of supercooled glassy systems and has also been observed in ionic glasses and ionic liquids.114−116 Note the MSDs at 298 K do not reflect appreciable displacement for the diffusing particle over a substantial period of time (∼100 ps from the beginning). This represents rattling of a particle in a cage where the particle has to wait sufficiently long until the cage breaks via structural relaxation. The mobility of the diffusing glycerol molecule is quite sluggish as the root mean squared displacement (RMSD) after 10 ns is ∼1 Å at 298 K which is nearly an order of magnitude less than that at 353 K. In addition, we have found that the diffusion coefficient (D) obtained from the center-ofmass MSDs for glycerol is ∼3 times smaller than that from the MSDs of the oxygen atoms of the −OH groups in this molecule. As viscosity decreases with temperature, the duration

of cage-rattling reduces, allowing the particle to settle into the diffusive mode relatively early. This is the reason for the MSDs at 353 K not showing cage-rattling as prominently as those at 298 K. Simulated MSDs for C153 dissolved in the mixture containing 20 wt % trehalose at 298 K, shown in the upper panel, also indicate rattling-in-a-cage motion and extremely slow COM diffusion. Application of the Stokes−Einstein relation with the stick boundary condition77 leads to a COM −8 diffusion coefficient (DC153 cm2 s−1 for C153 at T ) of ∼2.4 × 10 57 298 K (with molecular diameter 7.8 Å and solution viscosity ∼2.3 P). This value of DC153 suggests, via the relation77 Δr2 = T C153 6DT t, a diffusive displacement of ∼3.3 Å in 8 ns. The simulated MSDs, however, show a displacement of ∼0.8 Å in 8 ns which is ∼4 times smaller than that predicted by the hydrodynamics. Such a small displacement strongly supports solvent caging of C153 as viewed in Scheme 2 and suggests substantial reduction of viscosity-regulated Brownian motion for C153. This observation also explains, although indirectly, long rotation times for C153 in these mixtures at lower temperatures (shown in Figure 6). Note the evidence for solute and solvent cage-rattling suggests the presence of multiple relaxation time scales, reflecting the microheterogeneous nature of these systems. The λex-dependent fluorescence emission measurements (Figure 3) and the breakdown of hydrodynamics in describing the experimentally observed viscosity dependence of the average solute solvation and rotation times (Figure 7) correlate well to this inherent microscopically inhomogeneous character of these systems. The simulation results presented below provide further support to this view. 4.B.3. Dynamic Heterogeneity: Inheritance of Slow Time Scales. The non-Gaussian (NG) parameter, α2(t), which tracks the deviation from the Gaussian distribution of displacements, 11222


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Table 5. CTre-Dependent τNG, τNNG, τα, and τ4 Values from Simulations of Trehalose/Glycerol Mixtures at 298 and 353 K τNG (ns)

τNNGa (ns)

τα (ns)

τmax (ns) 4

CTre (wt %)

T = 298 K

T = 353 K

T = 298 K

T = 353 K

T = 353 K

T = 298 K

T = 353 K

0 5 20

2.40 0.90 2.50

0.04 0.04 0.50

>10 6 >10

0.07 0.13 1.60

0.18 0.24 0.60

9 6 >10

0.18 0.25 1.50

For compositions where the corresponding DH profiles are not complete within the simulation run, the related time scales (τNNG and τmax 4 ) are shown as longer than 10 ns.

a

is one of the quantities that routinely characterize the dynamic heterogeneity (DH) of a system. For homogeneous systems, α2(t) is nonmonotonic in time with zero at both the inertial (initial time) and hydrodynamic regimes (long time) and a peak value of ∼0.2 at the intermediate time.114,117 α2(t), calculated by using eq 8 for the systems studied at 298 and 353 K, are shown in the lower panel of Figure 10. α2(t) being greater than 0.2 for these systems even at 353 K reflects the microheterogeneous character of these systems. Expectedly, this DH feature is relatively more pronounced at 298 K. Notice in this panel that not only are the peak values of α2(t) higher at 298 K than those at 353 K but they also appear at longer time scales at the lower temperature. In addition, both the peak heights and peak times are composition dependent. Interestingly, these peak time scales (τNG) are in the nanosecond regime at 298 K while those at 353 K are much faster and lie in the 0.03−0.5 ns range. The presence of another DH time scale slower than τNG can be traced by monitoring the new nonGaussian (NNG) parameter, γ(t), shown in Figure S8 (Supporting Information). Note, although the full profile of γ(t) at 298 K is not captured in the present simulations due to high viscosity, the trend suggests γ(t) peak-times (τNNG) would be ≥5 ns at this temperature for these systems. Values of τNG and τNNG at 298 and 353 K summarized in Table 5 then naturally explain the emergence of slow time scales in the dynamic Stokes shift and fluorescence anisotropy measurements of these systems. Such a correlation between DH time scales and slow solvation time scales has also been discussed earlier for ionic liquids118 and cycloether/water binary mixtures.104 4.B.4. Self-Dynamic Structure Factor and Four-Point Dynamic Susceptibility: Correspondence between α-Relaxation Times and Correlated Time Scales. Self-dynamic structure factors, Fs(k, t), of glycerol in both the presence and absence of trehalose have been calculated by using eq 11 in the limit of the nearest neighbor wavenumber (kσ → 2π, with σ being the diameter) and are presented in the upper panel of Figure 11. Note the nearest neighbor structural relaxations in these systems are so slow that not more than 40% of the total Fs(k, t) decay could be achievable at 298 K in the 10 ns timewindow employed here. The e−1 decay times (the time by which ∼63% of the total decay is complete) can be traced at 353 K and are marked by bullet points. These e−1 times are identified as the α-relaxation times,119,120 τα, and lie between ∼0.2 and 0.6 ns for these systems at 353 K. Note τα is the longest for the mixture at 20 wt % trehalose concentration and follows the viscosity of these solutions. The importance of τα arises from its correspondence with the time scale during which density fluctuations at two different space and time points, δρ(r1, t1) and δρ(r2, t2), in a system remain correlated.119,120 This correlated time scale may be estimated from the four-point dynamic susceptibility, χ4(k, t), via monitoring the fluctuations in Fs(k, t) and is discussed below.

Figure 11. Simulated decays of the self-dynamic structure factor, Fs(k, t) (upper panel), and four-point dynamic susceptibility, χ4(k, t) (lower panel), for the center of mass of glycerol at the nearest neighbor wavenumber (kσ → 2π) at different trehalose concentrations in trehalose/glycerol mixtures at 298 and 353 K.

Simulated χ4(k, t) at the nearest neighbor wavenumber are presented in the lower panel of Figure 11 for these systems at 298 and 353 K. Notice χ4(k, t) obtained at 353 K shows a nice nonmonotonic time-profile with a clear maximum which shifts successively to longer times as the trehalose concentration in the solution (and hence solution viscosity) increases. The time at which the peak for χ4(k, t) appears is denoted as the correlated time, τmax 4 , and is expected to be in the time scale similar to τα. τmax values summarized in Table 5 confirm this 4 correspondence for these systems at 353 K. As observed previously for other DH features, the full profile for χ4(k, t) at 298 K could not be captured within the 10 ns window employed in the present work, although the simulated data clearly suggest that τmax 4 at 298 K are much longer (∼10 ns and longer) than those at 353 K. Broad band dielectric spectroscopy (BDS), quasi-elastic neutron scattering (QENS), and pulsedfield gradient nuclear magnetic resonance (PFGNMR) measurements are a few spectroscopic techniques that can be employed to confirm the presence of such slow time scales in these systems. Note all the DH features at 353 K, where the diffusive motion is well-set within the simulation time-window, suggest the trehalose/glycerol mixture at 20 wt % trehalose concentration is the most heterogeneous among the systems considered here. This corroborates well with the excitation 11223


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structural H-bond lifetime, ⟨τHB C ⟩, for glycerol is ∼3500 times longer than that for ambient water, although the corresponding viscosity ratio is ∼900. An inspection of Table S10 shows that a slow time scale in the range ∼15−36 ns dominates the CHB(t) relaxation at 298 K. The presence of such a long time scale has already been hinted at by the DH indicators such as γ(t) and χ4(t) simulated at 298 K. In addition, these time scales explain the overwhelming domination of the collective H-bond network in the Stokes shift dynamics and very long solute rotation times in these media at 298 K.

wavelength dependence of fluorescence emission results presented in Figure 3. 4.B.5. H-Bond Relaxation Dynamics: Reflection of Heterogeneity and Signature of Slow Time Scales. The microheterogeneous nature of these systems is further explored by examining the H-bond relaxation dynamics at 298 and 353 K. Both continuous (SHB(t)) and structural (CHB(t)) H-bond relaxation dynamics have been monitored for glycerol−glycerol pairs in the absence and presence of trehalose. The geometric conditions97 adopted in the present study for defining a Hbond between two glycerol molecules are as follows: (i) the distance between two O atoms must be

Glycerol Cryoprotectant Mixtures

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