Structure and Dynamics in Concentrated, Amorphous Carbohydrate

7308

J. Phys. Chem. B 1999, 103, 7308-7318

Structure and Dynamics in Concentrated, Amorphous Carbohydrate-Water Systems by Molecular Dynamics Simulation C. J. Roberts and Pablo G. Debenedetti* Department of Chemical Engineering, Princeton UniVersity, Princeton, New Jersey 08544 ReceiVed: April 6, 1999; In Final Form: June 30, 1999

We report results from molecular simulations of binary aqueous solutions of the carbohydrate stereoisomers, β-D-glucose, β-D-mannose, and D-fructose over a concentration range from zero to 80 wt % carbohydrate at 300 and 270 K. It is found that increasing carbohydrate concentration has a number of striking effects on the microscopic structure and dynamics of these solutions, including (1) a percolation threshold for connected water clusters at ca. 60 wt % carbohydrate, (2) a maximum in the hydrogen bond network strength and degree of ordering, as a function of carbohydrate concentration, at ca. 29 wt %, and (3) activated or “hopping” dynamics in the translational diffusion of water due to the influence of (1) and (2). There are appreciable differences in the magnitudes of these effects as a function of sugar type for the three stereoisomers studied. The relevance of these results is discussed in the context of the efficacy of sugars in biopreservation and lyophilization applications.

I. Introduction For many pharmaceutical formulations, the majority of the nonmedicinally active components are simple carbohydrates and their derivatives such as low molecular weight polyols and saccharides, as well as high molecular weight polysaccharides.1-4 Empirically, carbohydrates or sugars are known to help stabilize biological components in aqueous solution, e.g. proteins,5 protein-lipid bilayers, and cells,3,6 particularly during the dynamic processes of drying and desiccation, when these components are subjected to significant “water stress”. These stresses are due to the large gradients and concentration changes of salts and buffers typically present at low concenterations in the initial solutions, as well as to eventual loss of hydrationlayer water molecules at very low moisture levels.5 The molecular mechanism by which particular sugars are able to stabilize and protect labile biomolecules is not fully understood, although a number of possibilities have been suggested e.g., preferential exclusion of sugars from the protein surface7 or water replacement due to the ability of carbohydrates to act as substitutes for water in the hydrogen bond network (HBN) which is essential to providing the hydrophobic driving force for stability and activity in many biological structures.3,6 For longterm storage and biopreservation applications, very low moisture conditions (i.e., approximately a few wt % water) are desired. In practice,5 these systems are brought to a “dry” state via some combination of freeze concentration of the amorphous phase and evaporative drying. The amorphous phase containing (uncrystallized) carbohydrate and water traverses a wide range of carbohydrate concentrations, typically from as low as 5 wt % to greater than 95 wt %, and thus no single stabilization mechanism would be expected to be dominant throughout the process. With a view to understanding these very complicated systems, we have used molecular dynamics simulations to study the changes in the structure and dynamics in amorphous, binary sugar-water systems as a function of concentration. Both the * Corresponding author. E-mail: [email protected].

effects of concentration from the dilute-sugar to concentratedsugar regimes and the effects of relatively small changes in sugar stereochemistry have been investigated. Previous simulation studies of the effects of stereochemistry have been confined to dilute solution.8 To the best of our knowledge, there are only two published reports of simulations of concentrated sugarwater solutions, one of which focused on estimating glass transition temperatures (Tg) in glucose-water solutions,9 while the other focused on the changes in hydration of glucose as a function of temperature in an 85 w/w % glucose solution.10 For low moisture systems ( e.g., freeze-dried, spray-dried, or evaporatively dried formulations),5 the dominant methods of stabilization are thought to be structural arrest and the consequent dramatic slowing down of diffusive processes in the amorphous solid, or glassy state in which these systems exist at ambient conditions,5,11,12 along with the idea that sugars are unusually efficient in acting as hydrogen bond (HB) replacers for water molecules.13 In the former case, the stability of the labile components relies on the system being in an amorphous, solid state so as to provide large activation barriers to diffusionmediated degradation processes (both inter- and intramolecular processes). However, it should also be noted that although the system is a glassy solid, water is able to desorb on practical time scales,14-16 indicating that water mobility is not truly arrested. In the latter case, stabilization is thought to be due to the ability of low MW carbohydrates to provide a “water-like” environment in terms of HBs even in the absence of water molecules, so that complex biomolecules, such as proteins, will not have as much of an energetic penalty for maintaining native or near-native13,17,18 structures in the anhydrous solid. This has been proposed as a hypothesis as to why R,Rtrehalose and proline are naturally occurring protectants for organisms under low-moisture conditions.6,13 In particular, there has been considerable interest in understanding what role(s) the specific stereochemistry of R,R-trehalose plays in this natural selection.19-21 The fact that water remains quite mobile in some carbohydratewater glasses (e.g., DH2O ∼ 10-10-10-8 cm2 s-1)14-16 and that

10.1021/jp9911548 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/05/1999

Structure and Dynamics in Amorphous Carbohydrate-Water Systems in some cases14 its diffusivity has only a weak temperature dependence upon cooling through Tg is interesting both scientifically and in applications. From a polymer-science approach,12 this is understood as water acting as a plasticizer. This appears to hold reasonably well22 for some low-MW carbohydratewater systems even though it is perhaps counterintuitive when one considers that in these carbohydrate-water glasses both components are of similar size. A plausible explanation may be that at very low moisture conditions the HBN among the carbohydrate molecules allows them to act as a weakly (i.e. noncovalently) bonded polymer network. With the above points in mind, it is of interest to know how low-MW carbohydrate-water solutions evolve toward a glassy state upon dehydration (in the absence of crystallization), and how differences in sugar stereochemistry affect this evolution. For most carbohydrate-water systems, crystallization of carbohydrates from concentrated solution does not occur on practical time scales, with the notable exception of mannitol.1-3 Thus, sugar-water solutions are of practical interest across the full range of sugar concentration. From the standpoint of predicting and designing formulations for preserving labile compounds and biological structures, it is desirable to have a molecular-level understanding of how the structure and molecular dynamics of carbohydrate-water solutions are affected by changes in composition and stereochemistry of the sugar molecules. As a first step toward this objective, the present study investigates these effects for binary aqueous solutions of three simple monosaccharide stereoisomers, β-D-glucose, D-fructose, and β-D-mannose, over a broad range of concentration (Cs ) 0 to 80; Cs [)] w/w % sugar) at 300 K and atmospheric pressure. For β-D-glucose, preliminary studies of the effects of temperature across this concentration range have also been done. The three sugars were selected because of their similarities in stereochemistry, and because their relatively small sizes permitted longer simulations to be performed with the available computer resources. The goals of this work are to obtain a microscopic picture of how the solution structure (as measured, for example, by pair-correlation functions) and molecular mobility change as the system moves from dilute to concentrated conditions, and as a function of sugar stereochemistry. The latter understanding is important for discerning which effects are general features of sugar-water systems, and which are sensitive to the particular sugar involved. The longer-term goals of this research are to be able to apply (relatively) simple molecular models in designing improved formulations for stabilization of labile organic and biological components. Our results fall into two categories, structure and dynamics. In terms of structure, it is found that at high concentrations the mixtures are very heterogeneous, with a transition to isolated clusters or “pockets” of water molecules between a Cs of 60 and 80, independent of sugar type. This is the same range of Cs over which water rotational dynamics were found by Girlich and Lu¨demann23 to decouple from carbohydrate rotational motion in concentrated sucrose-water solutions. Oxygenoxygen pair distribution functions also show the effects of structural heterogeneity and are sensitive to both concentration and to sugar type. This holds for both sugar-water and waterwater correlations. In terms of HBN structure, the degree of ideal, or “ice-like”, local HB structure as well as the resistance of the network to rearrangements displays a maximum at Cs ≈ 29. However, HBN lifetimes increase monotonically with concentration due to the increased solution viscosity as Cs is increased. At Cs ≈ 29 the translational motion of water molecules becomes “activated”,24-26 that is to say, it is

J. Phys. Chem. B, Vol. 103, No. 34, 1999 7309

characterized by episodic jumps across preferential distances. It is also noteworthy that this onset of activated dynamics occurs at a Cs much lower than that of the structural transition to isolated water clusters mentioned above. Carbohydrate translational motion appears to be very localized at concentrations higher than Cs ≈ 29 on the time scales of our simulations (∼10-9 s), implying25,26 that on these time scales carbohydrate molecules are not able to escape the “cages” formed by the neighboring carbohydrates; in contrast, water molecules remain quite mobile up to Cs ≈ 80, although their motion becomes activated at Cs ≈ 29, as mentioned above. These results suggest that the activated dynamics of water diffusion are due more to the effects of the carbohydrate molecules on the overall HBN in the solution than on the increased solution viscosity upon increasing Cs. The remainder of the paper is organized as follows: in section II the simulation methods are described along with the details of the model potentials used to simulate these systems; results are presented and discussed in section III; section IV provides a summary of the present study and suggests possible directions for future work. II. Simulation Methods and Molecular Model Carbohydrate-water solutions were simulated with standard contant temperature and density molecular dynamics,27 with periodic boundary conditions used to eliminate size effects.27 The combination velocity-Verlet and RATTLE28 algorithm was used to integrate Newton’s equations of motion while maintaining fixed bond lengths, with a time step of 2 × 10-15 s. Longrange (i.e., electrostatic) forces were treated using a reaction field approach.27 Only pairwise interactions were considered and a standard cutoff was applied at a distance of 7.9 Å. Carbohydrate molecules were modeled as being semirigid; bond lengths were fixed but bond angles were flexible. C, O, and H atoms were treated separately, except for hydrogen atoms covalently bonded to a carbon, which were treated with the standard unitedatom approach.2,29 Using the values reported in ref 29, each C and each O were given a Lennard-Jones (LJ) potential and a partial atomic charge, while each H that was a member of a hydroxyl group was given only a partial atomic charge. The values of the LJ parameters and partial atomic charges are given in Table 1. Torsional potentials29,30 were also applied in order to maintain 4 C1 chair conformations throughout the duration of the simulations. As noted by Franks and Grigera,2 there is no a priori need for applying torsional or bond-angle potentials. However, these more restrictive potentials were imposed so as to make comparisons between the low- and high-concentration results more straighforward through prevention of ring-flips and other large conformational changes which on the time scale of our simulations would be rare events in dilute solution (i.e. τ ∼ 10-9 s),31 but virtually nonexistent at high Cs. The SPC/E potential32 used in this work models water molecules as having a LJ site centered on the O atom (see Table 1), and three partial atomic charges: two equal positive charges centered on each of the two H atoms, and the whole of the negative charge centered on the O atom. The H atoms are each 1 Å distant from the O atom with an H-O-H intramolecular bond angle of 109.5°. Simulations were performed for binary aqueous solutions of each of three monosaccharides: β-D-glucose, D-fructose, and β-D-mannose (hereafter referred to as glucose, fructose, and mannose). They are stereoisomers of one another, their geometric differences shown with stick representations in Figure 1. Figure 1 also illustrates which hydrogen atoms are accounted

7310 J. Phys. Chem. B, Vol. 103, No. 34, 1999

Roberts and Debenedetti

TABLE 1: LJ Parameters [OLJ (kcal/mol) ) (C12/r12) (C6/r6)] and Partial Atomic Chargesa LJ Values atom type

C12 (107

CH CH2 O Owater

nm12

kcal 8.930 251 1.700 420 1.772 461 6.293 251

C6 mol-1)

kcal nm6 mol-1) 695.904 1128.960 540.630 625.500 (106

Partial Charges atom type

charge/e

CH(1) O(1) H(1) CH(2) O(2) H(2) CH(3) O(3) H(3) CH(4)

0.45 -0.65 0.40 0.25 -0.65 0.40 0.25 -0.65 0.40 0.25

atom type

charge/e

O(4) H(4) CH(5) Oe CH2 (6) O(6) H(6) Owater Hwater

-0.65 0.40 0.45 -0.40 0.25 -0.65 0.40 -0.2026 0.1013

a Numberings of CH, CH , H, and O correspond to those in Figure 2 1. Subscript e denotes enantiomeric oxygen.

Figure 2. State diagram showing the T and Cs values of the simulation points (filled symbols). For reference, estimates from an empirical Gordon-Taylor34 form of Tg (Cs) for glucose-water (solid curve), mannose-water (dashed curve), and fructose-water (dot-dashed curve) are included. The experimental data needed to construct these curves are the Tg and ∆cp at Tg for the anhydrous carbohydrates and for water. The carbohydrate data was taken from Roos;22 amorphous solid water data was used for ∆cp35 (and references therein); the Tg for the SPC/E model of water was estimated from simulations.36

TABLE 2: System Sizes and Compositions

Figure 1. Stick representations of the different stereochemistries of the sugars simulated in this work, showing the numbering of C atoms.

for explicitly in the simulations. Only β anomers were used as it would unnecessarily complicate comparisons between sugars to consider mixtures of isomers in the same system in this initial study. For each of these systems a series of simulations was performed, spanning the range Cs ) 0-80, at constant temperature. Near-isobaric conditions were maintained in all simulations by choosing a density at each composition that gave approximately the same pressure along an isotherm. It proved sufficient to employ the experimental values of the densities33 for glucose-water solutions at STP as a function of composition. For consistency of comparison between simulations with different sugars, the same densities as a function of composition were used for all three sugar-water systems simulated. The simulated pressures fall on an isobar of approximately -100 bar; taking into account the statistics of pressure fluctuations in the simulations, this is practically indistinguishable from atmospheric pressure since fluctuations in p on the order of 100 bar over times on the order of hundreds of time steps are typical in NVT MD simulations such as the one performed here.27 This notwithstanding, the differences between the simulated and experimental pressure do not significantly affect the findings we report here, as they rely on the system being on an isotherm and isobar which lies near to conditions at which the systems become glassy. As shown in Figure 2, we estimate this to be the case by comparison of the state points for our simulations

Cs (wt %)

density (g cm-3)

box length (Å)

no. H2O molecules

no. sugar molecules

0 4 29 60 80

1.000 1.000 1.164 1.287 1.468

19.55 19.50 19.30 20.01 22.41

250 238 200 135 80

0 1 8 21 32

to the empirically calculated curves for the glass transition temperature as a function of sugar concentration at 1 bar, noting that the Tg curves are expected to be only weakly dependent upon pressure (see, e.g. Chapter 4 in ref 35). The number of molecules and the system size for each state point was the same for each of the three sugar-water systems, and is given in Table 2. An essential consideration in these simulations is the generation of an initial configuration for each state point, and the elimination of any artifacts that may result from this initialization, especially at high sugar content. The following initializaton protocol was followed. For the 29-80 wt % glucose solutions the initial state was a system of 48 glucose molecules in their crystalline arrangement,37 with atoms given random initial velocities scaled such that the average kinetic energy of the system increased to 450 K where it was held for a duration of 300 ps to randomize the system. Taking the ending configuration, a number of glucose molecules were selected from uniformly distributed positions within the simulation box and each was replaced with 5-6 water molecules oriented randomly. The number of such replacements was chosen so as to give the desired weight percent in the resulting configuration (see also Table 2). The system was then expanded with appropriate rescaling of the center-of-mass positions of the molecules to a density of 0.5 g cm-3. At this point the system was quenched to a local energy minimum by simulation for 300 ps at a thermostated temperature of 0 K. The resulting configuration was then heated to 400 K before being cooled to 300 K and continuously compressed over 500 ps to reach the final density corresponding to the experimental value at 1 bar for that composition.33 The resulting configurations were noted by visual inspection (i.e. using a standard three-dimensional graphics rendering software package) to be isotropic, or as

Structure and Dynamics in Amorphous Carbohydrate-Water Systems


Figure 3. Ow-Ow radial distribution functions for each of the three types of sugar-water solutions at Cs of (a) 4, (b) 29, (c) 60, and (d) 80 at 300 K. The curve for pure water (SPC/E) is included as a reference in each panel. The same legend applies to all four panels.

isotropic as can be expected considering the system sizes needed to allow the simulations to be feasible (cf. Table 2). For fructose and mannose, the same protocol was followed, except that rather than start from crystal structure data for fructose or mannose, after the stage where the pure glucose system had earlier been melted at 450 K from the glucose crystal, the glucose molecules were then transformed to fructose or mannose molecules. The remainder of the procedures were analogous to that for glucose. For the dilute systems (Cs ) 0, 4), all that was required was to start with an initially ordered array of 250 water molecules at 1 g cm-3, heat it to 400 K, cool to 300 K, and in the case of the Cs ) 4 solutions to then insert a single sugar molecule in a random orientation and systematically remove any water molecules with significant overlaps (i.e., those which resulted in large repulsive forces which would have rendered the numerical integration algorithm unstable). Each of the systems was prepared as above, then equilibrated at 300 K for a minimum of 300 ps, followed by an ensembleaveraging or production period of between 500 and 2000 ps, depending upon the concentration. Systems were considered to be equilibrated when the internal energy and pressure each reached plateau values over at least 150 ps and water molecules diffused more than ca. one molecular diameter (e.g. 4-6 Å). All results are from the production parts of the simulation runs, with configurations collected every 0.2 ps. Additional, shorter runs were also used to collect configurations every 0.010 ps for use in analyzing the dynamics over the full range of accessible time scales (10-14-10-9 s).

III. Results and Discussion (i) Structure. We begin by showing the effects of concentration and sugar type on the time-averaged structure in solution, as measured by radial distribution functions (RDFs). In general, the RDF for two (atomic) species i and j gives the local density of an atom of type j at given distance from an atom of type i, normalized by the corresponding number density in the bulk solution.38 In Figure 3, the water oxygen-water oxygen (OwOw) RDF is shown for each type of sugar solution as Cs increases from 4 to 80. A key feature to note is that these correlation functions, which do not directly involve sugar molecules, are strongly influenced by relatively minor structural differences between the three sugars, and that this effect is seen at all Cs > 4. The features which appear to be independent of sugar type are the large first peak associated with hydrogen bonding (cf. RDFs for pure water which are included in each panel of Figure 3), and the trend that the second and third neighbor peaks become less pronounced and broader as Cs increases until about 60, at which point the trend reverses, with water structure developing longer-ranged correlations that differ appreciably from the behavior seen at low Cs. Thus there is an initial water destructuring with increasing Cs (i.e., a disruption of the radially averaged ordering found in pure water). This effect reaches a maximum extent in the vicinity of Cs ) 60. At still higher Cs there is a restructuring of water molecules, with only the first neighbor shell retaining a structure similar to that of low Cs systems.



Figure 4. O3-Ow radial distribution functions as a function of sugar type and concentration. O3 is the O atom covalently bonded to C3 ( cf. Figure 1). The legend key, and the concentration corresponding to each figure panel are the same as in Figure 3.

The other type of atomic pair correlation functions studied here are On-Ow RDFs, where n ) 1, ..., 6 labels the oxygen atoms of a given carbohydrate using the standard convention2 (see also Figure 1). Similar to the Ow-Ow RDFs, these are very sensitive to sugar type as well as concentration. Figure 4 shows a series of curves analogous to those in Figure 3, but for O3-Ow correlations. The O3-Ow RDFs were chosen because the intramolecular environment around the O3 atom changes little when considering the different sugars (see Figure 1). Figure 4 shows trends similar to Figure 3, except that at the lowest Cs major differences already exist between the O3-Ow RDFs for the different sugars in the second and higher neighbor shells. Additionally, there is a distinct difference in the second neighbor peak(s) between fructose and the other two sugars. The O3Ow RDF for fructose clearly shows a bifurcation of the second peak, implying at least two different preferred distances for water molecules relative to the O3 atom. It is expected that with much longer simulation runs the minor fluctuations or fine structure in the RDF curves would be smoothed. However, the differences in the positions and heights of the of the major peaks mentioned above should remain, as the RDF’s shown in Figure 4 represent averages over 105 values for each discretized value of the radial position. The major difference in stereochemistry between fructose and the other two sugars is that the CH2OH(6) group is bonded to C(1) rather than C(5). Thus the pronounced differences in the second peak(s) may be due to additional

TABLE 3: HB Statistics for Sugar Solutions as a Function of Concentrationa sugar

4 wt %

29 wt %

glucose mannose fructose

1.93, 0, 1.7, 1.93 1.94, 0, 2, 1.93 1.95, 0, 1.5, 1.95

1.83, 0.1, 0.95, 1.82 1.84, 0.12, 1.12, 1.82 1.75, 0.08, 1.48, 1.70

sugar glucose mannose fructose water a

60 wt %

80 wt %

1.06, 0.13, 1.13, 0.85 0.66, 0.36, 0.475, 0.403 1.05, 0.14, 0.92, 0.9 0.73, 0.27, 0.62, 0.425 1.01, 0.13, 0.83, 0.99 0.66, 0.3, 0.53, 0.375 〈nHB〉 ) 1.96 (pure water, 300 K)

wc ww Entries are given in the format 〈nHB〉, 〈ncc HB〉, 〈nHB〉, 〈nHB 〉.

volume in the vicinity of C(5) which is available near fructose molecules but not near mannose or glucose molecules in aqueous solution. HB statistics are another useful measure of structure in aqueous solutions. Table 3 gives the HB statistics for each of the three sugar-water systems as a function of concentration. The nomenclature used is as follows: 〈nHB〉 is the average number of distinct HBs per molecule in the system, 〈ncc HB〉 the average number of carbohydrate-carbohydrate HBs per carbohydrate molecule, 〈nwc HB〉 the average number of water-carbohydrate HBs per carbohydrate molecule, and 〈nww HB 〉 the average number of water-water HBs per water molecule. In this work, a geometric HB definition9,29 is used. Two oxygen atoms are considered to be hydrogen-bonded if they (1) do not belong to

Structure and Dynamics in Amorphous Carbohydrate-Water Systems

Figure 5. (a) Distribution of the number of water-water HBs in which a water molecule participates, nwHB, as a function of Cs for glucosewater solutions. The numbers on the curves are the glucose weight percentages, Cs. The 4 wt % curve is not shown as it is not resolvable versus the pure water curve on the scale of this figure. (b) Distribution of nwHB for 29 wt % glucose solution (circles), and its contributions from water molecules involved in only ww HBs (squares, curve labeled w) and from water molecules involved in a wc HB (triangles, curve labeled c).

the same molecule, (2) have an interatomic separation RHB e 3.4 Å, and (3) their O-H‚‚‚O bond angle is 180° ( ∆HB, where we have used ∆HB ) 20°. Our results do not change qualitatively if we relax or tighten these bounds for RHB ((0.1 Å) or ∆HB ((10°), and our conclusions are independent of the small quantitative changes that arise from using different values of RHB or ∆HB. The results in Table 3 show little dependence on sugar type, with the same trends for all three types of sugar-water solution wc cc of decreasing 〈nHB〉, 〈nww HB 〉, and 〈nHB〉, and of increasing 〈nHB〉 with increasing Cs. Similar measures of the HBN structures in these systems are presented in Figure 5. Figure 5a shows p(nwHB), the probability of finding a water molecule involved in nwHB ()0,...,5) HBs, including ww and wc bonds, as a function of Cs for glucose solutions. Figure 5b shows p(nwHB) for the 29 wt % glucose solution as well as the analogous curves for water molecules involved in only water-water HBs, and for water molecules involved in a HB with a sugar molecule. The latter two curves are defined as the chance of finding that a given water molecule of that type (e.g. involved in only ww HBs) is involved in nwHB HBs. Note that these latter two curves by their


definitions do not include the nwHB < 1 portion of p(nwHB). The same trends are observed at other concentrations, and very similar curves to those in Figure 5, a and b are found for mannose and fructose (not shown). Figure 5a shows that increasing Cs shifts p(nwHB) to lower values of nwHB, to the extent that at 80 wt % glucose over half of the water molecules are on average not involved in any water-water HBs. Note, however, that these curves shift uniformly to higher nwHB if we use a less stringent HB definition (data not shown), so the absolute values of nwHB are not so important as the changes with Cs. From Figure 5b, we see that water molecules that HB with a sugar molecule tend to participate in more HBs than do water molecules that are hydrogen bonded only to other water molecules. This point will be revisited later, when discussing HB dynamics and water mobility. A more sensitive measure of the network structure of HBs is the distribution of O‚‚‚O‚‚‚O angles (p(θOOO)) for triplets of hydrogen-bonded molecules. Figure 6 shows p(θOOO) for OwOwOw. There are a number of striking features associated with the changes in these curves with Cs as well as with sugar type. First, the p(θOOO) curves show that as fructose concentration increases to 29 wt % (Figure 6a) p(θOOO) becomes closer to the “ideal” distribution, even compared to pure water at the same temperature. The OOO angle in the ideal or perfectly tetrahedral HBN in water is 109.5°, which is indicated with an arrow in each of the panels of Figure 6. Note in particular that the Cs ) 29 curve (Figure 6a) does not include a shoulder at low θOOO such as is evident in the Cs ) 0 and 4 curves. This effect is independent of sugar type. As Cs is increased further (Figure 6b) p(θOOO) narrows about a θOOO of ca. 115° and particularly in the Cs ) 60 solutions has increasing contributions from highly distorted geometries, e.g. increased shoulders at θOOO ≈ 140°. This effect is also seen for all three types of carbohydrate-water solutions, though the magnitudes of the contributions from shoulders, and of the shift of the central peak to θOOO > 109.5° does depend on the sugar type (Figure 6c). These results imply that the HBN structure evolves from being water-like at low Cs, to even closer to “ideal” at intermediate Cs, to highly distorted at high Cs. A similar effect has also been suggested by experimental and computational studies of alcoholwater,39 alcohol-lysozyme-water,40 and acetonitrile-water41 solutions, with an inferred transition from a water-dominated HBN to a solute (alcohol or acetonitrile)-dominated HBN at a composition around 30 wt % solute.39,41 Note also that the results shown in Figures 2 and 3 support this picture of a structural evolution as sugar concentration increases. Another useful measure of solution structure is the probability distribution of an arbitrarily chosen water molecule being a member of a water cluster of a particular size (i.e., number of water molecules). This distribution p(xH2O) is the chance of choosing an arbitrary water molecule and finding it is a member of a water cluster of size xH2O, with xH2O ) (number of water molecules in the cluster)/(number of water molecules in the simulation box). A water cluster here is defined as the set of water molecules that are connected to each other by an unbroken path of nearest-neighbor water molecules. Thus, as xH2O f 1 we have essentially a single percolating water cluster, and xH2O appreciably less than 1 indicates regions of nearest-neighbor (nn) water molecules which are disconnected from other groups of nn water molecules. Figure 7 shows p(xH2O) for mannose solutions. These change from having a percolating water cluster (for all Cs less than ∼60) to having a number of isolated groups of water molecules (and no percolating water clusters) at some Cs e 80. The same behavior is seen between 60 and 80 wt % sugar in the fructose and glucose solutions (data not shown).



Figure 7. Water cluster distribution in mannose-water solutions at Cs ) 60 (circles) and 80 (diamonds). p(xH2O) is the probability that a water molecule is a member of a water cluster of size xH2O, with xH2O equal to the ratio of water molecules in the cluster to water molecules in the simulation box. The dashed line is included as a guide to the eye to illustrate that p(xH2O) is a single-valued function. The scatter in the data reflects the quality of the statistics attainable from ∼103 configurations saved and analyzed for a typical nanosecond simulation.

TABLE 4: Water Diffusion Coefficients as a Function of Cs and Sugar Type

Figure 6. Distribution of θOOO, the angle formed by a triplet of hydrogen-bonded water molecules, as a function of Cs in fructose solutions. The arrow in each figure panel indicates the value of 109.5°, corresponding to the OOO angle in a perfect tetrahedral network. (a) OwOwOw distributions for Cs ) 0, 4, and 29, (b) OwOwOw distributions for Cs ) 60 (broken curve) and 80 (solid curve), (c) OwOwOw distributions for Cs ) 80 for different sugars.

Note that the data for Cs ) 60 show that water molecules are either part of the percolating cluster or they form small clusters (n e 3). Larger, but nonpercolating, clusters are not found. These results suggest a description of concentrated carbohydrate solutions as structurally heterogeneous (see section I). In the remainder of this section the results for the translational mobility and HBN dynamics in sugar-water solutions are presented, which show how the structural heterogeneity is coupled with

sugar type

T (K)

Cs (wt %)

DH2O (10-7 cm2 s-1)

water glucose glucose glucose mannose mannose mannose fructose fructose fructose water glucose glucose

300 300 300 300 300 300 300 300 300 300 270 270 270

0 4 29 60 4 29 60 4 29 60 0 4 29

258 ( 3 180 ( 8 10.7 (.7 1.8 (.2 150 ( 5 15.3 (.6 2 (.1 180 ( 5 6.2 (.5 1.6 (.3 170 ( 10 62.5 ( 7 1.8 (.5

heterogeneous dynamics,25 and how this evolves as Cs increases. Such changes in dynamics may occur in a nearly isothermal drying process. (ii) Dynamics. Diffusion coefficients for water, DH2O, were calculated at each state point from the mean square displacement vs time, 〈r2(t)〉, averaged over all water molecules. The slope of 〈r2(t)〉 at large t is related to DH2O by27 d〈r2(t)〉/dt ) 6DH2O. The values of DH2O are given in Table 4. Values for Cs ) 80 are not reported because the 〈r2(t)〉 curves for those solutions did not reach a linear regime at the largest t sampled in the simulations (∼10-9 s). Diffusivities were also calculated at 270 K for glucose solutions. The results in Table 4 can be summarized as follows: (1) DH2O shows appreciable quantitative differences as a function of sugar type at each value of Cs; (2) qualitative trends are the same for all sugar solutions, i.e., DH2O decreases by ca. a factor of 2 as Cs increases from 0 to 4, and decreases by an order of magnitude upon each successive increase in Cs from 4 to 29 to 60; (3) the 270 K data for glucose shows that DH2O is increasingly sensitive to T with increasing Cs, e.g. DH2O (300 K)/DH2O (270 K) ≈ 1.5, 3, and 10 for Cs ) 0, 4, and 29, respectively. Part of the value of these results is a confirmation that simulations of this scale are able to provide reasonable estimates of DH2O (Cs) and measurable differences for different sugars. For reference, the most recent experimental values for DH2O in glucose-D2O solutions, as measured using deuterium

Structure and Dynamics in Amorphous Carbohydrate-Water Systems NMR at 300 K for Cs ) 40 and 75, are 40 × 10-7 and 5 × 10-7 cm2 s-1, respectively.42 Finally, as will be apparent below, estimates of DH2O at Cs g 80 from simulations on time scales of 10-9s as were performed here will necessarily miss the contributions from the qualitatively different long-t diffusive motions which are important in the highest Cs solutions. Calculation of water diffusivities in such systems will require much longer simulations. Values of Dcarbo as a function of Cs are not shown because the time scales of our longest simulations are not sufficient for the sugar molecules to diffuse over distances greater than their molecular diameters (i.e. ∼6-8 Å, the approximate distance from O(4) to O(1)). Instead, we observed that the 〈r2〉 vs t plots for the carbohydrate molecules (data not shown) appeared to attain Einstein behavior within about 500 ps; however, the maximum values of 〈r2〉 were only on the order of 4-5 Å at the longest times (∼2 ns). This was particularly evident in the systems with Cs > 29. At long times (t ∼ 2 ns), however, the 〈r2〉 curves exhibited a plateau. This is the type of behavior observed in simulations of a deeply supercooled liquid binary mixture of unequally sized particles.26 This behavior can be interpreted as being due to a fast diffusion on relatively short time scales (here, on the order of 0.1-1 ns) which reflects Brownian motion of each sugar molecule within a “cage” of its neighboring sugar molecules. The true, or long-time diffusion coefficient can be measured only over time scales on which cooperative rearrangments of the cages can occur; typically, this rearrangement occurs over times which are several orders of magnitude longer than the time scales for fast diffusion.26 This indicates that the present simulations are at best just beginning to probe such time scales for the carbohydrates in the high-Cs solutions. Water molecules, on the other hand, remain quite mobile up to a Cs of 80. As mentioned above, it was not possible to obtain good enough statistics in nanosecond-long simulations to report reliable values of DH2O in the 80 wt % solutions. Nevertheless, it was possible to observe heterogeneous water diffusion under these conditions. The term heterogeneous25 is sometimes used to refer to diffusion processes that have a heterogeneous distribution of characteristic length and time scales, due to the increasingly cooperative particle rearrangements needed for appreciable translational motion to occur in deeply supercooled liquid and glassy systems.25,43 This is consistent with the suggestion that in concentrated carbohydrate solutions water molecules diffuse on long time scales by “hopping”15,20 over preferential jump distances, ∆r. Such a hopping or jump type of diffusion has been observed spectroscopically in sugar-water solutions of Cs up to ∼40.15,20 This is demostrated in the present case by plotting the van Hove self-correlation function Gs(r,t),38 which is defined so that 4πr2dr Gs(r,t) is the probability that a given (water) molecule has translated a distance r ( (dr/2) in a time t. Figure 8 shows Gs(r,t) for water molecules as a function of Cs in fructose solutions. Panels a-c show the evolution of Gs(r) with time for Cs ) 29, 60, and 80, respectively. In each panel, a typical short-time Gs(r) profile for water is included as a reference. The full Gs(r,t) for Cs ) 0 and 4 are not included as they all have the same qualitative profile as the reference water curve and so do not show heterogeneous dynamics, which appear as secondary peaks in Gs(r,t) at large r. The secondary peaks indicate that there are preferential distances over which water molecules will translate, relative to the simple, gradually broadening unimodal distribution expected from simple Brownian motion in a uniform medium,38 and as observed in pure water at short times. Note the incipient appearance of a


Figure 8. van Hove self-correlation functions for water in fructose solutions at Cs ) 29 (a), 60 (b), and 80 (c). The short-time curve for pure water is included for reference. Note the plateau at long times for Cs ) 29 which, at Cs ) 80, develops into secondary peaks. These are indicative of “hopping”.

secondary peak at Cs ) 29, as evidenced by the plateau in Gs. Thus, we see jump-type diffusion across a wide spectrum of sugar concentrations. As mentioned above, the occurrence of “hopping” is expected in deeply supercooled liquids in which macroscopic translational mobility becomes strongly influenced by the need for highly cooperative molecular rearrangements.43 The same behavior was observed for all three sugar-water systems. Finally, we consider the time correlation function for HBN rearrangements fHB(t). In analogy with earlier work,41 fHB(t) is defined as the chance that a HB (water-water, water-


Figure 9. HBN time correlation functions as a function of Cs for fructose solutions at 300 K. The inset shows the temperature dependence of the short-time decay of fHB for pure water at 1.0 g cm-3.

Figure 10. Effect of sugar stereochemistry on fHB(t) at 300 K.

carbohydrate, or carbohydrate-carbohydrate) which was intact at some arbitrary time t0 is intact at a later time t0 + t, independent of whether the bond broke at any intermediate time. This is quite different from the distribution of HB lifetimes and is defined in this manner so as to capture the requirement that multiple bonds must break in order for a molecule to be able to diffuse in a fluid which forms (transient) bond networks.44 For purposes of calculating fHB, each bond is distinguishable and is labeled by the atoms involved in the O-H‚‚‚O structure. An example of fHB(t) as a function of Cs for fructose solutions is presented in Figure 9. Very similar results were also found for the mannose and the glucose solutions. It can be clearly seen that there is an oscillatory short-time decay in fHB, followed by a long-time decay which has very strong Cs dependence. The short-time oscillations correspond to librational motions in which individual bonds are broken and remade a number of times, but molecules do not translate sufficiently far in the interim to prevent re-formation of some of the original bonds. This behavior is primarily due to the water-water HBN (cf. Figure 11), the water-carbohydrate bonds showing much faster shorttime decay. This behavior is also readily apparent in pure water and becomes more pronounced at lower temperatures as shown in the inset to Figure 9. Similar results from a study of individual HB kinetics in pure water were reported by Luzar and Chandler.45 The intermediate- and long-time decays of fHB are of more relevance from the perspective of water mobility,


Figure 11. Contributions to fHB for 60 wt % fructose solutions (filled circles) from ww HBs (triangles), cc HBs (open circles), and wc HBs (asterisks). The inset shows the analogous plot for the 29 wt % fructose solution. The temperature is 300 K.

heterogeneous dynamics, and HBN strength in carbohydratewater solutions, and the remainder of this section will focus on this important aspect of HBN dynamics. The intermediate-time (t ∼ 10-13-10-11 s) decays of fHB for Cs g 29 (see Figure 9) show plateaus before finally decaying to zero at much longer t, while for Cs < 29 there is a rather rapid, monotonic decay with no plateau after the initial oscillations. The long-time decay persists to longer t with increasing Cs as is expected since contributions to fHB from the much less mobile carbohydrates become increasingly important with increasing Cs. Perhaps the most remarkable feature of Figure 9 is that as Cs increases the plateau value of fHB has a maximum value at 29 wt %, and then diminishes upon further increase in Cs. This indicates that increasing Cs initially increases the intermediate-time stability of the HBN up to a maximum before reducing it at higher Cs, which is consistent with what is shown in Figure 6 via p(θOOO). The same qualitative trends were observed with all three sugars, with small but appreciable differences in the plateau values of fHB; an example of this is shown in Figure 10. The maximum in the intermediate-time HBN stability inferred from Figures 9 and 10 is also qualitatively consistent with deuterium NMR experiments of sucrose-water solutions23 in which water’s rotational relaxation time was found to have a maximum at approximately 60 w/w % sucrose. Above this sucrose concentration, water’s rotational motions were found to decouple from those of the sucrose molecules.23 It is useful to consider the contributions to fHB from waterwater (ww), water-carbohydrate (wc), and carbohydratecarbohydrate (cc) hydrogen bonds. This is shown in Figure 11 for the 60 and 29 wt % (inset) fructose solutions. Note from Table 3 that in the 29 wt % solution essentially no cc hydrogen bonds were observed during the simulation and thus no cc contribution to fHB was calculated. It is seen from Figure 11 together with Table 3 that the dominant contribution to fHB is from the ww hydrogen bonds. Additionally, the ww and the cc portions of the HBN are quite resistant to rearrangements on intermediate time scales, and the ww contributions in particular show many short-time bond breaking and re-forming events. In contrast, the wc contribution decays much more rapidly. This has a number of implications. First, the much lower plateau value for fHB of wc bonds shows that these bonds are less stable than either the ww or cc bonds. Second, the lack of short-time oscillations in fHB from wc bonds suggests that water molecules are more mobile in the vicinity of carbohydrate molecules. The

Structure and Dynamics in Amorphous Carbohydrate-Water Systems lack of short-time oscillations indicates that these water molecules remain mobile enough not to be involved in multiple bond breaking and re-forming events before diffusing away. Recall from Figure 5 that water molecules involved in HBs with carbohydrates tend to have higher 〈nHB〉. So the lower plateau values or fast decay of short-time oscillations in the wc contribution to fHB suggests that a HB between water and carbohydrate weakens the remaining HBs in which the water molecules participates. Finally, the cc contributions to the HBN show the highest intermediate-t plateau values and the longest overall decay times, although at Cs ) 60 cc contributions are only beginning to become significant (e.g. at Cs ) 60 the fraction of bonds which are cc bonds is less than 0.02 in all three sugar-water systems). This suggests an evolution of the HBN from one that is dominated by ww contributions at low and intermediate Cs to one dominated by cc contributions at high Cs. It is also important to emphasize that there are appreciable quantitative differences in HBN structure and resistance to network rearrangements at intermediate t and Cs between different sugar stereoisomers (cf. Figure 10). This suggests a way in which different sugar stereoisomers can have different efficacies as “water-replacers” in that their influence on the HBN, its structure, stability, and kinetics can differ appreciably with only minor changes in sugar stereochemistry.46 IV. Summary Using MD simulation, binary solutions of water and three stereoisomeric monosaccharides have been been studied from the dilute to concentrated regimes. There are dramatic effects on solution structure and dynamics caused by increasing sugar concentration, including (1) a transition from water-like HBN at low Cs to a hybrid, more tetraherally structured and stable HBN at intermediate Cs, to sugar-dominated HBN at high Cs; (2) “caging” of water molecules by carbohydrates, with a percolating water cluster appearing only for Cs < ca. 60 wt % sugar; (3) highly cooperative, “jump” diffusion of water molecules at Cs as low as 29 caused by a combination of (1) and (2). The qualitative effects are the same for all three sugarwater systems, but their magnitudes are sensitive to sugar type, presumably via the differences the sugar stereochemistries impose on the HBN topology. The present work is an initial study of the effects of moisture content and carbohydrate stereochemistry on the physical chemistry of binary carbohydrate-water solutions. These systems are analogous to those commonly employed in the pharmaceutical and food science industries. The aim of this work is to gain fundamental, molecular-level understanding of the changes in structure an dynamics that occur in carbohydratewater solutions as a function of temperature, water content, and carbohydrate type. The long-term goal is to aid in the rational design and formulation of commercially relevant systems for specific freeze-drying and long-term storage applications in the food and pharmaceutical industries. Future work will encompass both experiments and further simulations. The experiments include small-angle neutron scattering (SANS) and time-of-flight inelastic neutron scattering (TOF), in collaboration with the NIST Center for Neutron Research, of binary sugar-water solutions, in an effort to verify the structural transitions to isolated water clusters at Cs > 60 and the onset of “activated” dynamics at Cs ≈ 29 as seen thus far in the simulations; and deuterium NMR measurements in concert with simulations of very low moisture (Cs ∼ 95-99) systems in order to characterize water mobility and molecular


environment of in simple as well as commercially relevant formulations. Longer simulations of the systems studied in this work as well as new simulations of water-disaccharide, waterpolyol, and ternary water-sugar-sugar systems will be performed. Finally, analysis of the HBN in this work has been performed only in terms of geometric measures; future work will extend this to also include energetic measures. Acknowledgment. P.G.D. gratefully acknowledges the financial support of Merck & Co., Inc., the U.S. Department of Energy, Division of Chemical Sciences, Office of Basic Energy Research (Grant DE-FG02-87ER13714), and the donors of the Petroleum Research Fund, administered by the American Chemical Society. C.J.R. acknowledges the National Science Foundation for a Graduate Fellowship. References and Notes (1) Franks, F.; Hatley, R. H. M.; Mathias, S. F. Biopharm 1991, 4, 38. (2) Franks, F.; Grigera, J. R. Water Science ReViews 5; Franks, F., Ed.; Cambridge University Press: Cambridge, U.K., 1990; Chapter 4 and references therein. (3) Cleland, J. L., Langer, R., Eds. Formulation and DeliVery of Proteins and Peptides; ACS Symposium Series 567; American Chemical Society: Washington, DC, 1994. (4) Oksanen, C. A.; Zografi, G. Pharm. Res. 1990, 7, 654. (5) Franks, F.; Hatley, R. H. M. In Stability and Stabilization of Enzymes; van den Tweel, W. J. J., Harder, A., Buitelaar, R. M., Eds.; Elsevier Science Publ.: New York, 1993. (6) Crowe, J. H. Anhydrobiosis; Dowden, Hutchinson, and Ross: Stroudsburg, PA, 1973. (7) Xie, G.; Timasheff, S. N. Protein Sci. 1997, 6, 211, 222. Arakawa, T.; Timasheff, S. N. Biochemistry 1982, 21, 6536. (8) Galema, S. A.; Howard, E.; Engberts, J. B. F. N.; Grigera, J. R. Carbohydr. Res. 1994, 265, 215. Grigera, J. R. J. Chem. Soc., Faraday Trans. 1 1988, 84, 2603. (9) Caffarena, E.; Grigera, J. R. Carbohydr. Res. 1997, 300, 51. (10) Caffarena, E.; Grigera, J. R. Carbohydr. Res. 1999, 315, 63. (11) Angell, C. A. Science 1995, 267, 1924. (12) Levine, H.; Slade, L. J. Chem. Soc., Faraday Trans. 1 1988 84, 2619. (13) Carpenter, J. F.; Prestrelski, S. J.; Anchordoguy, T. J.; Arakawa, T. Formulation and DeliVery of Proteins and Peptides; ACS Symposium Series 567; American Chemical Society: Washington, DC, 1994; Chapter 9. (14) Aldous, B. J., Franks, F.; Greer, A. L. J. Mater. Sci. 1997, 32, 301. (15) Tromp, R. H.; Parker, R.; Ring, S. G. Carbohydr. Res. 1997 303, 199. (16) Parker, R.; Ring, S. G. Carbohydr. Res. 1995, 273, 147. (17) Remele, R. L.; Stushnoff, C.; Carpenter, J. F. Pharm. Res. 1997, 14, 1548. Pretrelski, S. J.; Arakawa, T.; Carpenter, J. F. Arch. Biochem. Biophys. 1993, 303, 465. (18) Desai, U. R.; Osterhout, J. J.; Klibanov, A. M. J. Am. Chem. Soc. 1994, 116, 9420. (19) Magazu, S.; Maisano, G.; Middendorf, H. D.; Migliardo, P.; Musolino, A. M.; Villari, V. J. Phys. Chem. B 1998, 102, 2060. Magazu, S.; Maisano, G.; Migliardo, P.; Middendorf, H. D.; Villari, V. J. Chem. Phys. 1998, 109, 1170. Magazu, S.; Migliardo, P.; Musolino, A. M.; Sciortino, M. T. J. Phys. Chem. B 1997, 101, 2348. Wang, G. M.; Haymet, A. D. J. J. Phys. Chem. B 1998 102, 5341. (20) Magazu, S.; Maisano, G.; Migliardo, P.; Musolino, A. M.; Villari, V. Philos. Mag. B 1998, 77, 655. Magazu, S.; Maisano, G.; Majolino, D.; Migliardo, P.; Musolino, A. M.; Villari, V. Prog. Theor. Phys. Suppl. 1997 126, 195. (21) Bonanno, G.; Noto, R.; Fornili, S. J. Chem. Soc., Faraday Trans. 1998, 94, 2755. Donnamaria, M. C.; Howard, E. I.; Grigera, J. R. J. Chem. Soc., Faraday Trans. 1994, 90, 2731. (22) Roos, Y. Carbohydr. Res. 1993, 238, 39. (23) Girlich, D.; Lu¨demann, H.-D. Z. Naturforsch. 1994, 49c, 250. See also: Girlich, D.; Lu¨demann, H.-D.; Buttersack, C.; Buchholz, K. Naturforsch. 1994, 49c, 258. Girlich, D.; Lu¨demann, H.-D. Z. Naturforsch. 1993, 48c, 407. (24) Sastry, S.; Debenedetti, P. G.; Stillinger, F. H. Nature 1998 393, 554. (25) Yamamoto, R.; Onuki, A. Phys. ReV. Lett. 1998, 22, 4915. (26) Kob, W.; Andersen, H. C. Phys. ReV. E 1995 51, 4626. (27) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, UK,1987. (28) Andersen, H. C. J. Comput. Phys. 1993, 52, 24.

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Structure and Dynamics in Concentrated, Amorphous Carbohydrate

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