The hydration of glucose: the local configurations in sugar–water hydrogen bonds

Abstract

The hydration of a simple sugar is an essential model for understanding interactions between hydrophilic groups and interfacial water molecules. Here I perform first-principles molecular dynamics simulations on a glucose–water system and investigate how individual hydroxyl groups are locally hydrated. I demonstrate that the hydroxyl groups are less hydrated and more incompatible with a locally tetrahedral network of hydrogen bonds than previously thought. The results suggest that the hydroxyl groups form roughly two hydrogen bonds. Further, I find that the local hydration of the hydroxyl groups is sensitively affected by seemingly small variations in the local electronic structure and bond polarity of the groups. My findings offer insight into an atomic-level understanding of sugar–water interactions.

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Introduction

A detailed description of hydrogen bonds (H-bonds) is the key to understanding the properties of any H-bonded system. A perfect example is liquid water, which is held together by a three-dimensional, locally tetrahedral network of H-bonds.^1–3 From a physicochemical standpoint, an H-bond can basically be viewed as a special kind of dipole–dipole interaction or as an interaction between bond dipoles.^4,5 Hence, polar groups such as hydroxyl groups can readily form H-bonds with highly polar water molecules.

Over the last half-century, hydroxyl groups of simple sugars, or monosaccharides, have generally been assumed to mimic the locally tetrahedral character of the H-bond network in liquid water with a little distortion because they contain a fragment of a water molecule.^6–9 However, there are some computational studies suggesting that the hydroxyl groups are not as hydrated as they could potentially be.^10–12

Here I perform ab initio molecular dynamics (MD) simulations^13,14 on a glucose–water system, an essential model for molecular biology,¹⁵ to address this contradictory issue. While previous works focused on the overall hydration structure of glucose and provided many insights, the local H-bonding configurations in sugar–water H-bonds have been little addressed. My position, however, is that an accurate understanding of how individual hydroxyl groups are locally hydrated should precede a better understanding of the overall hydration structure. To put it another way, the microscopic hydration of glucose cannot be properly understood unless the local H-bonding interactions between the hydroxyl groups and water molecules are accurately understood.

Hence, my approach is entirely different from previous ones; the main objective of this work is to analyse the local interactions between the hydroxyl groups and water molecules instead of the overall hydration structure. For this reason, the present work focuses exclusively on the local H-bonding configurations and electronic properties.

By analysing the electronic and H-bonding properties, I provide a quantitative reason why the local hydration of the hydroxyl groups is not predominantly three-coordinated but roughly two-coordinated. I also show that the hydroxyl groups usually enhance the dipole moment of water molecules in the first hydration shell, but only when the groups form donor H-bonds. Together with this, my detailed analysis demonstrates that the local H-bonding properties alter more sensitively from one hydroxyl group to another than previously conceived. All this suggests that the hydroxyl groups are more incompatible with a locally tetrahedral H-bond network than previously thought.

Methods

The glucose–water system

The glucose–water system consisted of one glucopyranose molecule and 60 water molecules in a cubic supercell of side 12.54 Å (about 1 g cm⁻³ density) (Fig. 1a and 1b), with periodic boundary conditions.

Fig. 1 The glucose–water system. (a) A snapshot from an ab initio MD simulation on glucopyranose in aqueous solution. Carbon, oxygen and hydrogen atoms are represented by blue, red and white respectively. Transparent yellow and light blue represent the centres of localized Wannier functions associated with lone pairs and covalent OH bonds respectively. The molecular graphic was created by VMD.⁵⁷ (b) The drawing of glucopyranose with the numbering scheme of its carbon atoms. The wavy bond at the anomeric site (C1) indicates either the α or β anomer. (c) A localized orbital description of the electronic properties of a hydroxyl group. The colour representation is the same as in (a). To evaluate the electronic properties, I used three distances: d_LP, d_CV and d_CV–H. (The same definitions hold for water molecules.) The distance d_LP is the average distance from the oxygen atom to the two centres of the lone pair Wannier orbitals. The distances d_CV and d_CV–H are the distances from the centre of the covalent OH-bond orbital to the oxygen atom and to the hydrogen atom respectively. The molecular graphic was created by gOpenMol.⁵⁸

The number of water molecules in this system may seem small compared with the number that can readily be handled in classical force-field MD simulations. Nonetheless, this system size allows one to investigate important aspects of water molecules in the first hydration shell, as already proven by previous ab initio MD studies on simple sugars in aqueous solution with similar system sizes^10,12,16,17 or smaller.¹⁸ In fact, Stubbs and Marx performed force-field MD simulations on the hydration of glucose by changing the number of water molecules to assess the effect of the system size,¹⁶ and they found that increasing the system size has little effect on the pair correlation function between a glucose oxygen-atom and water oxygen-atoms. The study suggested that 57 water molecules are enough to study the behaviour of water molecules in the first hydration shell using the ab initio MD method.

Note that investigating the behaviour of water molecules in the second and third hydration shells is beyond the scope of the present work. Instead, my focus is exclusively on H-bonds between the hydroxyl groups and water molecules in the first hydration shell.

The ab initio MD method

All the ab initio MD simulations were performed using CPMD code.^13,14,19 The electronic structure calculations were carried out in the framework of the Kohn–Sham formulation of density functional theory (DFT).^20,21 The gradient-corrected BLYP functional was used.^22,23 The valence–core interactions were treated by norm-conserving pseudopotentials by Goedecker, Teter and Hutter, which give the optimal efficiency in numerical calculations when plane waves are used as a basis set.²⁴ Only the Γ point was used to sample the Brillouin zone. The Nosé–Hoover chain thermostat method^25,26 was used to control the ionic temperature at about 300 K; and after this stage (about 3 ps), microcanonical simulations were then performed for data collection (6 to 10 ps; for more detail, see Table S1 in the ESI†). The trajectories were sampled every ten steps, and the maximally localized Wannier functions^27,28 were also computed after every ten steps.

Conformations

Carbohydrates generally have the potential to form multiple conformational families in aqueous solution. In this regard, simulating carbohydrates is a great challenge from a theoretical and computational standpoint—and this is especially true of ab initio MD simulations. In fact, in previous ab initio MD simulations on glucose in aqueous solution, conformers are relatively limited.¹⁰

I performed seven simulations on the α anomer and seven on the β anomer, where the three staggered hydroxymethyl rotamers were taken into account. (Note that the aim of this study is not to explore fully the conformational space of glucose in aqueous solution.) These hydroxymethyl rotamers are usually characterized by the O5–C5–C6–O6 torsion angle (see Fig. S1 in the ESI†). The computational details of the simulations on the conformers are summarized in Table S1 in the ESI.† The results of the conformations in the hydroxymethyl group are summarized in Table S2 in the ESI.†

Data analysis

Since my main objective was to understand the basic differences between water–water H-bonds and sugar–water H-bonds, the differences in the local hydration structure among the conformers were beyond the scope of this work. When I calculated the electronic, the structural and the H-bonding properties, the data were first averaged for each simulation, and then they were again averaged over all the simulations.

This procedure may seem to be a slightly simplified approach, since individual conformers exist in different population ratios; however, the procedure is still considered reasonable if the following points are taken into account. First, since some of the population ratios remain uncertain both experimentally and theoretically (e.g. the population ratios of hydroxymethyl rotamers are still somewhat controversial¹⁷), it would be inappropriate to add such uncertainty into the subsequent analysis. Second, the length of each simulation is unavoidably limited because of the high computational cost. Therefore, (i) the differences in the electronic properties of the hydroxyl groups among the conformers are difficult to assess accurately; (ii) each MD trajectory may not necessarily represent all the features of the hydration structure of individual conformers.

Because of all this, in the present context averaging over the simulations with equal weighting is considered to be practical. This procedure nonetheless allows the sampling of a variety of configurations in which individual hydroxyl groups were hydrated in different ways; it still ensures the statistical reliability for my main objective.

I also computed the dipole moments of water molecules in the first hydration shell using the method of maximally localized Wannier functions.^27,28 (The averaging procedure was the same as I described above.) The dipole moments of water molecules were obtained using the following numbers of electronic configurations of water molecules: (i) water molecules forming acceptor H-bonds with the hydroxyl groups, about 474 000 configurations; (ii) water molecules forming donor H-bonds, about 579 000; (iii) water molecules that form H-bonds with water molecules, about 4 960 000; (iv) water molecules that form H-bonds with the individual hydroxyl groups, about 93 000–98 000 each.

A localized orbital approach

In modern ab initio MD simulations, the method of maximally localized Wannier functions, a localized orbital approach, plays an important role.²⁷ This approach makes it possible to study the electronic properties of hydroxyl groups of glucose intuitively and accurately, even if the molecule is surrounded by water molecules (Fig. 1a). In this localized orbital picture, the chemical bonding of a hydroxyl group that is mainly relevant for H-bonding can be described by three localized orbitals: two lone pair orbitals (the acceptor side) and one orbital associated with the covalent OH-bond (the donor side) (Fig. 1c). I carefully investigated the two sides.

Results and discussion

The acceptor side

General aspects. I began by analysing the acceptor side, and the analysis suggested that the hydroxyl groups form weaker acceptor H-bonds than water molecules. To evaluate the electronic properties on the acceptor side, I calculated the average distance from the oxygen atom to the centres of the lone pairs (d_LP) (Fig. 1c). Then I compared this distance with that of bulk water molecules.²⁹ The average distance d_LP in the hydroxyl groups shrank by 3.2% (0.010 Å) to 0.322 Å from that in the water molecules, 0.332 Å. To put it simply, the shrinkage can be viewed as a lesser ability to attract positively charged species compared with the oxygen side of water molecules (this point will be discussed in detail later on).

How much does that shrinkage affect the local configurations on the acceptor side? To answer this question, I plotted the number of acceptor H-bonds (N_acc) as a function of d_LP (Fig. 2a). Since the anomeric carbon (C1) is bonded to two oxygen atoms and is thereby located in a chemically different environment (Fig. 1b), I divided the data into two subgroups: one consisting of the data points from O2, O3, O4 and O6 (Fig. 2a, open circles), and the other from O1 (Fig. 2a, closed triangles). The correlation coefficient of the former was 0.87, whereas that of the latter was 0.88. In either case, N_acc was highly correlated with d_LP [the correlation coefficient for the whole data set was 0.84 (Fig. 2a, solid line)]. The results demonstrate that the shrinkage of d_LP is a good measure of how weakly the hydroxyl groups form acceptor H-bonds.

Fig. 2 The electronic and H-bonding properties of the acceptor side of the hydroxyl groups. (a) The number of acceptor H-bonds (N_acc) is plotted as a function of the distance d_LP. For the definition of d_LP, see Fig. 1c. The criteria used for an H-bond are O_A⋯H ≤ 2.4 Å and the O_A⋯H–O_D angle > 120°, where O_A and O_D–H are an H-bond acceptor and an H-bond donor respectively. An individual data point represents the average values for N_acc and d_LP from a hydroxyl group in a simulation; hence, the plot consists of 70 data points (5 hydroxyl groups; 14 simulations). In this plot, the data are divided into two subgroups: one consists of the data points from O2, O3, O4 and O6 (open circles) and the other from O1 (closed triangles). The least-squares lines for the subgroups are shown by the dashed and the dotted lines respectively. The solid line is the least-squares line obtained using all the data points. (b) The site-dependent differences in the shrinkage of d_LP: (A) OH1; (B) OH2; (C) OH3; (D) OH4; (E) OH6; (F) bulk water molecules (denoted by the dashed curve).

This seemingly small shrinkage of d_LP plays a key role in the local H-bonding configurations on the acceptor side. As the distance d_LP shrinks from 0.34 to 0.32 Å, the number N_acc roughly decreases from 2 to 1 (Fig. 2a, solid line); that is, a 6% shrinkage of d_LP leads to a 50% drop in N_acc. This is basically due to a contact-like character of H-bonding interaction that is turned on when lone pairs touch a hydrogen atom of a water molecule but is turned off as soon as the contact is broken.³⁰ In the language of hybridization, one could say that upon the shrinkage of d_LP, the lone pairs of the hydroxyl groups have more s character and less p character than those of a water molecule.³¹

To be more precise, however, H-bonding originates from various kinds of physical interactions; it is a complex interaction that can arise from electrostatic interactions (or electrostatic plus polarization interactions), charge transfer, exchange repulsion and dispersion.^4,32 That said, there are basically two ways to view H-bonding.³³ On the one hand, H-bonding is attributed to purely electrostatic interactions or electrostatic plus polarization interactions; on the other hand, H-bonding is considered to be stabilized largely by charge transfer—the interaction between a lone pair orbital of one molecule and an antibonding covalent orbital of another.^33,34

Because of such complex nature of H-bonding, its precise definition remains a matter of debate,^32–38 and quantifying how much each of the above components contributes to a given H-bond is an intricate task in general. There is also a report suggesting that the component which is dominant for a given H-bonded system alters from one species to another.³⁹ Hence, a straightforward, single explanation for why the acceptor side of the hydroxyl groups forms weaker H-bonds would probably be difficult.

Nevertheless, I point out three physical interactions that are presumably relevant to the lesser ability of the hydroxyl groups to form acceptor H-bonds. For one thing, the lesser polarity of the O–C bonds perhaps contributes to a weaker electrostatic attraction. For another thing, the shrinkage of d_LP is considered to have more direct effects; it probably leads to (i) a decrease in the local polarization between the oxygen nucleus and the lone pairs and (ii) a decrease in the overlap of lone pair orbitals of the hydroxyl groups and antibonding OH orbitals of water molecules (i.e. a decrease in the charge transfer), resulting in a lesser energetic stabilization.^33,34

All this may still sound like a chicken-and-egg situation: does a decrease in the number of acceptor H-bonds merely result in a decrease in d_LP? Or does a decrease in d_LP fundamentally cause a decrease in the number of acceptor H-bonds?

One way to answer this question is to consider the difference between a water molecule and a hydroxyl group from a chemical standpoint. An oxygen atom of a water molecule can pull the bonding electrons equally from both sides; however, an oxygen atom of a hydroxyl group cannot. This is because the electronegativity of carbon is slightly larger than that of hydrogen, and thus the oxygen atom can no longer pull the OH bonding electrons from the carbon-side as easily as from the hydrogen-side.

With this in mind, it seems easier for the oxygen atom to pull the lone pairs toward itself than to pull the bonding electrons. My analysis suggests that this is actually the case. The main reason is that, as can be seen from Table 1 (and as will be discussed later in the analysis on the donor side), the oxygen atom in a hydroxyl group usually fails to pull the OH bonding electrons effectively (on average only a 0.2% decrease). Instead, to compensate for the “loss” of electrons, the oxygen atom tends to pull exclusively the lone pair electrons toward itself (a 3.2% decrease), which results in the shrinkage of d_LP. All this suggests that the hydroxyl groups are less hydrated because of the shrinkage of d_LP.

Table 1 The electronic and H-bonding properties of the hydroxyl groups of glucose in aqueous solution^a

	The acceptor side		The donor side
Hydroxyl group	d LP /Å (%)	N acc	d OH /Å (%)	d CV /Å (%)	d CV–H/Å (%)	N dnr
a In the columns for dLP, dOH, dCV and dCV–H, values in parentheses are the deviations (%) from the corresponding values for water molecules in the liquid. [In the case of dCV–H, in evaluating the deviations (%) I used dOH−dCV≈dCV–H.] For the definitions for dLP, dCV and dCV–H, see Fig. 1c. In my calculations, the electronic and structural properties of water molecules in the liquid were the following: dLP, 0.3324 Å; dOH, 1.0106 Å; dCV, 0.5102 Å. Nacc and Ndnr are the average number of acceptor H-bonds and that of donor H-bonds respectively. For the criteria for H-bonding I used, see Fig. 2 caption. In short, the results indicate weaker acceptor H-bonds and stronger donor H-bonds of the hydroxyl groups than water–water H-bonds. The table also shows that the average number of H-bonds per hydroxyl group is 2.083.
OH1	0.3144 (−5.40)	0.928	1.0195 (+0.88)	0.5039 (−1.24)	0.5171 (+3.05)	0.967
OH2	0.3225 (−2.97)	1.166	1.0126 (+0.20)	0.5112 (+0.18)	0.5031 (+0.22)	0.918
OH3	0.3245 (−2.35)	1.267	1.0123 (+0.18)	0.5105 (+0.06)	0.5034 (+0.30)	0.943
OH4	0.3196 (−3.86)	0.987	1.0127 (+0.21)	0.5107 (+0.09)	0.5035 (+0.33)	0.917
OH6	0.3280 (−1.32)	1.395	1.0130 (+0.24)	0.5096 (−0.12)	0.5047 (+0.60)	0.935
Average	0.3218 (−3.18)	1.147	1.0140 (+0.34)	0.5092 (−0.20)	0.5064 (+0.90)	0.936

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This is the reason why my argument is unlikely to be a chicken-and-egg situation. Certainly, the degree to which a hydroxyl group is hydrated can cause an increase or decrease in d_LP for a short period of time. However, in the long run, the decrease of d_LP causes the decrease in the number of acceptor H-bonds. That is, I suggest that the decrease in d_LP is not the accidental result of the simulations, but the main cause of the decrease in the number of acceptor H-bonds.

Now, given that the average distance d_LP in the hydroxyl groups was 0.322 Å, the results indicate that on average an individual hydroxyl group of a monosaccharide does not form two acceptor H-bonds, but forms only about one acceptor H-bond (Fig. 2a). Actually, in my simulations, the average number of acceptor H-bonds per hydroxyl group was 1.15, and the average number of H-bonds per hydroxyl group was 2.08 (see Table 1). The feature of this kind was in fact observed in previous classical¹¹ and ab initio^10,12 MD studies on monosaccharides, but the reason for it has long been elusive. Now my result gives a quantitative reason for why the local hydration of hydroxyl groups of a monosaccharide is roughly two-coordinated.

Site-dependent differences. A more detailed analysis showed that how weakly these hydroxyl groups form acceptor H-bonds (i.e. how much d_LP shrinks) depends on where they are attached (Fig. 2b and Table 1). Being shorter by 1.3%, or 0.004 Å, than that of bulk water molecules, the distance d_LP in O6 was the longest (0.3280 Å) (Fig. 2b, curve E); and the distance d_LP in O3 was the second longest (0.3245 Å) (Fig. 2b, curve C). On the other hand, the distance d_LP in O4 was the second shortest (0.3196 Å): it shrank by 3.9%, or 0.013 Å (Fig. 2b, curve D). The distance d_LP in O1 was the shortest (0.3144 Å): it shrank by 5.4%, or 0.018 Å (Fig. 2b, curve A).

Predictably, these agreed with the results of the number N_acc. O6 formed the greatest number of acceptor H-bonds (1.40), followed by O3 (1.30), and O4 and O1 formed less than one acceptor H-bond (0.99 and 0.93). All this suggests that O6 is the best H-bond acceptor, followed by O3, and that O1 is the poorest acceptor, followed by O4.

I note that subtle variations in the O–C bond polarity in the hydroxyl groups probably play an additional role in determining these local H-bonding configurations via a kind of dipole–dipole interaction. Since H-bonding can be regarded as a special case of dipole–dipole interaction,⁵ an H-bond between the acceptor side of a hydroxyl group and the donor side of a water molecule can be viewed as an interaction between an O–C bond dipole and an O–H bond dipole. In this respect, how weakly the individual hydroxyl groups form acceptor H-bonds not only results from subtle variations in the shrinkage of d_LP, but may also be affected by those in the O–C bond dipoles.

Generally speaking, bond polarity arises when a pair of electrons is shared unequally by two atoms of a covalent bond; hence, measuring how unequally the electron pair is shared by the two atoms is the key to understanding the bond dipole.

A simple and quick way to estimate this unequal sharing is to calculate a ratio, the O–WFC distance/(the O–WFC distance + the WFC–C distance), where WFC denotes the centre of the covalent C–O bond orbital. Since the electronegativity of the O atom is larger than that of the C atom, the ratio is smaller than 50%. As a general rule, the closer to 50% the ratio is, the less polar the O–C bond will be; in other words, the smaller the ratio is, the more polar the O–C bond will become.

I calculated the ratio for each O–C bond. The ratio for the C6–O6 bond was the smallest (38.34%), whereas that of the C1–O1 bond was the largest (38.79%). More specifically, the order of the ratio magnitudes was as follows: C6–O6 (38.34%) < C3–O3 (38.49%) < C2–O2 (38.66%) ≈ C4–O4 (38.68%) < C1–O1 (38.79%). This order agrees with that of the number of acceptor H-bonds, N_acc (see Table 1). At the same time, I found that the correlation between the ratio and N_acc was in the middle range (−0.53). Hence, subtle variations in the O–C bond polarity in the hydroxyl groups probably play an intermediate role.

Where do the site-dependent differences come from? Why does the degree to which d_LP decreases depend on the individual sites? To understand this, let me take a closer look at two cases: O1 and O6. To start with, I explain the case of O1 because the anomeric site is a special case. Unlike other carbon atoms, C1 is bonded to two oxygen atoms, rather than one. This makes C1 relatively electron-poor compared with other carbon atoms; therefore, O1 cannot effectively pull the bonding electrons from C1. To compensate for this, O1 pulls its lone pairs more strongly toward itself, which leads to the largest decrease in d_LP (Table 1). This explains why d_LP in O1 is the shortest, and that results in the smallest number of acceptor H-bonds.

On the other hand, C6 is relatively electron-rich compared to other carbon atoms since it is bonded to two hydrogen atoms. Because of this, O6 can pull the bonding electrons relatively easily from C6. Thus, O6 does not have to pull its lone pairs as tightly as other oxygen atoms do, which leads to the smallest decrease of d_LP (Table 2). This explains why d_LP in O6 is the longest; and that results in the largest number of acceptor H-bonds.

Table 2 The ability of the individual hydroxyl groups to form stronger donor H-bonds: the oxygen–oxygen distance (Å) and the dipole moments of water molecules forming acceptor H-bonds with the individual hydroxyl groups (Debye)

Hydroxyl group	R(OD⋯OW)^a/Å	μ ^b/Debye
a OD denotes the oxygen atom of the donor side of a hydroxyl group OD–H; and OW denotes an acceptor oxygen atom of a water molecule. b Dipole moments of water molecules that formed acceptor H-bonds with the individual hydroxyl groups.
OH1	2.7891	3.153
OH2	2.8638	2.996
OH3	2.8438	3.026
OH4	2.8484	3.086
OH6	2.8374	3.149

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These are two examples but in general, since individual glucose carbon atoms are in different chemical environments, the O–C local bond dipoles are slightly different from each other. That is, the unequal sharing of the electron pair along the C–O bond slightly alters from one hydroxyl group to another, which in turn affects the degree to which d_LP decreases. All this contributes to the local H-bonding configurations on the acceptor side.

The donor side

General aspects. After I worked on the acceptor side, I analysed the donor side. In general, the more the positively charged bare proton is exposed and the more the covalent OH-bond orbital shifts toward the oxygen atom, the more strongly the donor side forms H-bonds. To quantify this, I calculated the distances from the centre of the covalent OH-bond orbital to the hydrogen atom (d_CV–H) and to the oxygen atom (d_CV) (Fig. 1c). In short, the longer d_CV–H and the shorter d_CV, the better H-bond donor a hydroxyl group becomes.

The results indicated that the hydroxyl groups form stronger H-bonds than bulk water molecules. The average distances d_CV–H stretched by 0.9% from that of bulk water molecules, and the distance d_CV shrank by 0.2% (but see below). Also, the average OH distance (d_OH) stretched by 0.3% (Table 1). This suggests that the bare protons of the hydroxyl groups tend to be more exposed than those of water molecules.

Site-dependent differences. As I did on the acceptor side, I investigated the site-dependent differences in the ability to form donor H-bonds. The OH1 distance was the longest (1.0195 Å): it stretched by 0.88% (0.0089 Å) from that of bulk water molecules. The OH6 distance was the second longest: it stretched by 0.24%. Consistently, the distance d_CV in OH1 was the shortest (0.5039 Å), followed by that in O6 (0.5096 Å) (Fig. 3, curves A and E): they shrank by 1.24 and 0.12% respectively from that of bulk water molecules (0.5102 Å). These probably indicate an increase in the charge-transfer interactions.⁴⁰ As a result, the OH1 and OH6 bonds increased their polarization and their protons were more exposed to lone pairs of surrounding water molecules. In the other hydroxyl groups, however, the d_CV stretched only marginally (Table 1). There were no striking differences among OH2, OH3 and OH4 (Fig. 3, curves B to D), yet I found that the distance d_CV–H in OH2 was slightly shorter (Table 1). The results suggest that OH1 is the best H-bond donor, followed by OH6, and that OH2 is a slightly poorer donor.

Fig. 3 The electronic properties of the donor side of the hydroxyl groups. Shown are the individual distributions of the distance d_CV: (A) OH1; (B) OH2; (C) OH3; (D) OH4; (E) OH6; (F) bulk water molecules (denoted by the dashed curve). The average value for the distance d_CV of bulk water molecules is also indicated by the dotted line. For the definition of d_CV, see Fig. 1c. The distance d_CV in OH1 and that in OH6 are both shorter than that of bulk water molecules, indicating stronger donor H-bonds of these groups than those in the bulk. On the other hand, though their distributions are broader than that of the bulk, the maximum values for OH2, OH3 and OH4 are almost equal to that of the bulk. The results indicate that OH1 and OH6 are stronger H-bond donors than OH2, OH3 and OH4.

Another way to characterize how strongly the donor side forms H-bonds is to calculate the oxygen–oxygen distance. I calculated the distance R(O_D⋯O_W), where O_D denotes the oxygen atom of the donor side of a hydroxyl group O_D–H and O_W is an acceptor oxygen atom of a water molecule. The distance R(O1_D⋯O_W) was the shortest (2.7891 Å), followed by R(O6_D⋯O_W) (2.8374 Å) (Table 2); they are shorter by 0.071 Å and 0.023 Å respectively than the distance R(O⋯O) in the liquid (2.8601 Å).

Consistently, the distributions of R(O_D⋯O_W) for the individual hydroxyl groups suggest that OH1 and OH6 are better H-bond donors (Fig. 4). Further, the results show that the distributions for OH1 and OH6 are significantly asymmetrical (Fig. 4, curves A and E), which indicates that water molecules were strongly attracted to the donor side of OH1 and OH6. In general, the shorter the overall oxygen–oxygen distance, the stronger the charge transfer.³³ Hence, all this suggests that the charge-transfer interaction probably plays a role in these stronger H-bonds.

Fig. 4 The distributions of the distance R(O_D⋯O_W). O_D denotes the oxygen atom of the donor side of a hydroxyl group O_D–H; and O_W denotes an acceptor oxygen atom of a water molecule in the first hydration shell for the individual hydroxyl groups: (A) OH1; (B) OH2; (C) OH3; (D) OH4; (E) OH6. The results show that the distributions for OH1 and OH6 are significantly asymmetrical, indicating that water molecules were strongly attracted to the donor side of OH1 and OH6. The dashed line indicates the average distance in the liquid waterR(O⋯O).

The order of R(O_D⋯O_W) was as follows: R(O1_D⋯O_W) < R(O6_D⋯O_W) < R(O3_D⋯O_W) < R(O4_D⋯O_W) < R(O2_D⋯O_W); this order is basically consistent with that of the d_CV–H distance (Table 1) and with that of the dipole moments of water molecules forming acceptor H-bonds with the hydroxyl groups (Table 2; see also the next subsection for more detail). On the other hand, this order did not agree perfectly with that of the number of donor H-bonds, N_dnr (Table 1). This is probably because the criteria for H-bonding is generally arbitrary. Nonetheless, considering all the available data presented here, the relative strength of the individual hydroxyl groups to form donor H-bonds is considered to be the following order: OH1 > OH6 > OH3 ≈ OH4 > OH2.

The dipole moments of interfacial water molecules

Calculating the dipole moment of water molecules in the first hydration shell is another important way to investigate sugar–water H-bonds and to clarify my findings. Thanks to the method of maximally localized Wannier functions, today we can do such calculations more easily and accurately than ever before because the electronic contribution to the dipole moment is directly computed from the electronic structure within DFT calculations.⁴¹

The results suggested that the dipole moment increases only when water molecules act as H-bond acceptors, which in turn supports the idea that the hydroxyl groups form stronger donor H-bonds. The average dipole moment of water molecules forming acceptor H-bonds with the hydroxyl groups increased by 2%, or 0.060 Debye (Fig. 5a, solid line), from that of the bulk, 3.026 Debye (Fig. 5, dashed line). By contrast, the average dipole moment of water molecules forming donor H-bonds decreased marginally by 0.2%, or 0.006 Debye, but remained almost unchanged (Fig. 5a, dotted curve) (the average dipole moment of bulk water molecules agrees well with a previous ab initio MD study⁴¹). This is consistent with another previous ab initio MD study on ribose in aqueous solution.¹²

Fig. 5 The dipole moments of water molecules in the first hydration shell. (a) The dipole moments of water molecules forming acceptor H-bonds (solid curve) and donor H-bonds (dotted curve) with the hydroxyl groups are compared with that of the bulk (dashed curve). The former shows a 2% increase compared with that of the bulk, whereas the latter does not. This suggests stronger donor H-bonds of the hydroxyl groups. (b) The dipole moments of water molecules forming acceptor H-bonds with the individual hydroxyl groups: (A) OH1; (B) OH2; (C) OH3; (D) OH4; (E) OH6. When water molecules form acceptor H-bonds with OH1 or OH6, the dipole moment rises by 4%, or 0.125 Debye, from that of the bulk (indicated by the dashed line). The result is consistent with that shown in Fig. 3 and 4.

Let me take a closer look at the mechanism of the enhancement. There are two major origins that can affect the dipole in the system. One is how weakly or strongly the acceptor or donor side of the hydroxyl groups can interact with water molecules. As I have already shown, the acceptor side and the donor side of the hydroxyl groups interact more weakly and more strongly respectively with water molecules than bulk water molecules.

The other is how sensitively the dipole moment of a water molecule responds to a local change of its molecular dipole. To understand quantitatively which side of a water molecule (the donor side or the acceptor side) more directly influences its molecular dipole moment, I calculated correlation coefficients between the absolute value of the dipole moment and some of the electronic or structural parameters, using 4.96 × 10⁷ electronic configurations of bulk water molecules. The parameters I chose were the following: the LP–O–LP angle (where LP denotes the centre of a lone pair orbital); the CV–O–CV angle (where CV denotes the centre of a covalent OH bond); the H–O–H angle; the distance d_LP; the distance d_CV; and the OH distance d_OH.

The correlation coefficients for the above parameters were the following: the LP–O–LP angle, −0.44; the CV–O–CV angle, −0.08; the H–O–H angle, −0.29; d_LP, 0.73; d_CV, −0.53; d_OH, 0.40. (The averaging procedure was the same as described in the Methods.) Hence, the distance d_LP is highly correlated with the absolute value of the dipole moment, followed by the distance d_CV. Since d_LP is associated with the enhancement of the dipole on the acceptor side whereas d_CV is associated with that on the donor side, a simple physical explanation of this is that lone pairs can move more easily than a hydrogen atom does and thus can respond more sensitively to surrounding positively charged species. This in turn means that a local change on the acceptor side has a more direct effect on the dipole moment.

All this explains why the dipole moment responds sensitively to a subtle increase in the exposure of the protons of the hydroxyl groups. When water molecules act as H-bond donors, the dipole moment remains almost unchanged because (i) hydroxyl groups form weaker acceptor H-bonds and (ii) the dipole moment correlates less highly with the distance d_CV. On the other hand, when water molecules act as H-bond acceptors, the dipole moment increases more readily because (i) hydroxyl groups form stronger donor H-bonds and (ii) the dipole moment correlates highly with the distance d_LP.

A further investigation revealed that the enhancement depends on which hydroxyl group the water molecules form acceptor H-bonds with. More specifically, water molecules forming acceptor H-bonds with OH1 or OH6 mainly accounted for the enhancement. The dipole moments of these water molecules rose by 4%, to 3.15 Debye, showing the greatest increase (Table 2 and Fig. 5b, curves A and E). On the other hand, the dipole moment of water molecules forming acceptor H-bonds with OH2 decreased slightly by 1%, to 2.996 Debye (Table 2 and Fig. 5b, curve B). When water molecules formed acceptor H-bonds with OH3 or OH4, the dipole moment remained almost unchanged but increased marginally (Fig. 5b, curves C and D). The results agree with the localized orbital analysis on the donor side of the hydroxyl groups (Fig. 3) and the oxygen–oxygen distance (Table 2).

Accuracy of plane-wave DFT calculations

At this point, I should mention the basic accuracy of plane-wave DFT calculations. The accuracy of plane-wave DFT calculations within the Car–Parrinello MD (CPMD) method is a fundamental issue, and several studies have been dedicated to this subject.^42–45 In general, the performance of the plane-wave DFT calculations depends on different computational details. Examples of these are the length of simulations, the choice of the exchange–correlation functional, initial configurations, the cell size, the pseudopotential approximation, cut-off energy, the fictitious electronic mass, the system on which simulations are performed, and so on. In the following, I particularly mention the system size and the exchange–correlation functional.

Effect of the system size. To my knowledge, there is one report that addressed the influence of the cell size. Kohlmeyer systematically studied how the cell size affects the structural and dynamical properties.⁴² The study suggests that the cell size has little effect on the two main peaks of the pair correlation function of liquid water, and that 64 water molecules are sufficient for the converged main peaks.

Grossman et al. pointed out that the influence of the cell size is relatively minor compared with the choice of the fictitious mass.⁴³ In addition, the cell size probably has little effect on the centres of the maximally localized Wannier functions,⁴¹ which indicates that the electronic properties and the dipole moments are relatively reliably discussed. Considering all this, the cell size appears to have little or only a small effect, at least on the electronic and H-bonding properties.

Furthermore, I want to mention current practices in CPMD simulations of aqueous systems. In 1993, a CPMD simulation was performed on a system consisting of 32 water molecules in a cubic cell.⁴⁶ 10 years later, CPMD studies of liquid water are still performed mostly on a system consisting of 32 or 64 water molecules in a cubic cell.^43–45

CPMD simulations were also performed on the hydration of the smallest organic molecules such as uracil,⁴⁷ribose¹² and glucose,^16,17 and the number of water molecules was 60 or smaller. As I already wrote earlier, this system size nonetheless allows us to investigate important aspects of water molecules in the first hydration shell. While this point needs to be handled in the future, at present using this kind of system size is the most practical way to investigate the H-bonding properties between glucose and water reasonably in atomic detail.

Plane-wave DFT calculations. In plane-wave DFT calculations, structural properties such as bond distances (in my case, those in Table 1) tend to be overestimated; and O⋯O distances may depend on many technical and computational factors mentioned above. One of the important factors is likely to be the choice of the exchange–correlation functional.^44,45 Nonetheless, I believe that the main findings will probably not significantly change, at least on a qualitative level. Let me give some explanations in the following.

First, while studies suggest that care should be taken when one uses the BLYP functional, these works are mainly concerned with the first peak in the pair correlation function and the dynamic properties.^42–45 In this paper, however, I mainly discuss the electronic and H-bonding properties. While I sometimes discuss the structural properties, my focus is not on the dynamic properties such as the self-diffusion coefficient or the mean-square displacement. The above studies are of great importance, but their findings are not necessarily relevant to my main objective.

Second, whether or not an H-bond network is overstructured is considered relatively irrelevant to the behaviour of the dipole moment of individual water molecules. Thus, the main findings in my analysis on the dipole moment of water molecules will remain unchanged, at least on a qualitative level.

Third, the trend shown in Fig. 2a is likely to remain unchanged, regardless of different computational details within the framework of the CPMD methodology. That being the case, this still suggests that the H-bonding properties are sensitive to seemingly small changes in the electronic and structural parameters, if a contact-like character of H-bonding interaction is taken into account.

Fourth, while the BLYP functional tends to make the first peak in the pair correlation function sharper,^44,45 the coordination number does not significantly change. This is mainly because the coordination number is an accumulated property. With this in mind, my suggestion that the acceptor side is less hydrated than previously thought is likely to hold. Several computational points being addressed, in the next subsection I will discuss how the hydroxyl groups are locally hydrated.

The microscopic hydration of glucose: how the hydroxyl groups are locally hydrated

Before I discuss and characterize how glucose is hydrated in atomic detail, I briefly mention the local structure of liquid water. The local structure of the first coordination shell of a water molecule in the liquid has been under intense scrutiny for the past three years. Recent X-ray absorption and X-ray Raman experiments together with theoretical calculations challenged the traditional view, i.e. the view that water is a locally tetrahedral liquid. According to the report, most water molecules in the liquid form only two H-bonds: one strong donor and one strong acceptor.⁴⁸ That report being published, several studies addressed this issue, and a number of computational studies still supported the traditional view.^2,49–52

In particular, a recent ab initio MD study showed that available experimental data and its first-principles calculations of X-ray absorption spectra are consistent with the conventional picture of a locally tetrahedral character of the liquid.² Considering all this, although many structural aspects may remain subject to debate, in the present work I regard water as a locally tetrahedral liquid.

Two previous pictures of the hydration of simple sugars. The classic picture of the hydration of monosaccharides is that hydroxyl groups of a monosaccharide are well compatible with a locally tetrahedral network of H-bonds with a little or no distortion. This classic picture originally comes from a consideration of a possible compatibility between the hexagonal ice structure and the chair structure of a monosaccharide. It was suggested in the late 1950s and in the early 1960s that the hydration of a monosaccharide could be an ice-like structure.^6,7 This assumption, however, has one difficulty: although hexagonal ice is a tetrahedrally ordered array, liquid water is rather a thermally fluctuating, disordered network of H-bonded water molecules. Hence, it is unclear whether or not the assumption of this compatibility is relevant.

Later on, classical^9,53 and ab initio¹⁰ MD studies pointed out that this picture based on an ice-like lattice is irrelevant, and, in fact, demonstrated computationally that there is no clear evidence for such an ice-like structure. Since then, computational studies focused instead on the stereochemical or topological aspects associated with the molecular structures of monosaccharides.^9,53 This anisotropic-structuring picture rather emphasizes that the hydration structure varies from one monosaccharide to another.

This picture has important aspects in itself; however, the classic picture still has an appealing point. There is a similarity between the OH bond in a hydroxyl group and that in a water molecule. That is, a hydroxyl group has a fragment of a water molecule. Thus, it could be reasoned that hydroxyl groups of a monosaccharide are highly compatible with a locally tetrahedral network of H-bonds with a little or no distortion.

Logically speaking, describing an overall structure around a monosaccharide from the viewpoint of the molecular structure is one thing, but analysing how individual hydroxyl groups are locally hydrated is another. In this sense, the two pictures described above are not so mutually exclusive as one might think. Actually, while the anisotropic-structuring picture emphasizes that the hydration of monosaccharides can be distorted by their molecular structures one way or another, it also assumes that individual hydroxyl groups remain highly compatible with a locally tetrahedral structure of H-bonds.⁹ Hence, in either picture, the compatibility of the hydroxyl groups with a locally tetrahedral network has been directly or indirectly assumed.

Microscopic, detailed picture. As I mentioned in the beginning of this paper, however, some computational works suggest that hydroxyl groups are less hydrated than they could potentially be.^10–12 Where does this contradiction come from? One of the reasons is that detailed information about the local configurations in glucose–water H-bonds has been missing over the years. That is why the present work focuses on the local H-bonding configurations, instead of the overall hydration structure. In other words, a detailed understanding of how the hydroxyl groups are locally hydrated is considered to be a prerequisite for discussing the overall hydration structure.

The results of the present work suggest that the hydroxyl groups are less hydrated (on average, 2.08 H-bonds per hydroxyl group) and rather more incompatible with a locally tetrahedral network of H-bonds than previously thought. On average, glucose formed 11.15 H-bonds with water molecules in the first hydration shell; it formed 4.68 donor H-bonds and formed 6.47 acceptor H-bonds (in which the average number of acceptor H-bonds for the ring oxygen was 0.73). (However, I note that these numbers can alter to some extent or other, depending on the definition of H-bonding.)

Further, my analyses on the acceptor and the donor sides suggest that the local H-bonding configurations vary more specifically and sensitively from one hydroxyl group to another than previously conceived (Fig. 2, 3 and 4). My analyses provide detailed knowledge about how glucose is locally hydrated: (i) the anomeric site (OH1) is the best donor, but the poorest acceptor among the hydroxyl groups; (ii) OH2 is a slightly poorer donor; (iii) OH3 is a better acceptor; (iv) OH4 is a poorer acceptor; and (v) OH6 is the best acceptor and a better donor as well.

Such detailed knowledge could lead to a deeper understanding of (i) diverse roles of oligosaccharides composed of glucose units, (ii) the transport of glucose across membranes,⁵⁴ and (iii) (solvent-assisted) chemical reactions or molecular recognitions that involve sugars.

Conclusions

In conclusion, the present study suggests that the hydroxyl groups form roughly two H-bonds: one weaker acceptor H-bond and one stronger H-bond, with different variations that are sensitive to individual chemical environments of the groups. To my knowledge, such detailed analysis has been missing from virtually all previous works for about 50 years.

The analysis points to a breakdown of a locally tetrahedral character at the sugar–water interface and thereby explains why, though being hydrophilic and polar, hydroxyl groups of simple sugars are less hydrated and more incompatible with a locally tetrahedral network of H-bonds than previously thought. Rather, the present study implies that the local H-bonding arrangements around monosaccharides (and perhaps those around oligosaccharides) are far more complex and substantially different.¹² This aspect, for example, is considered responsible for the unusual dynamic properties of sugar–water solutions.^55,56

A fundamental implication of this study is that a locally tetrahedral network of H-bonded water molecules is perhaps delicately maintained by the unique electronic structure and molecular dipole of the water molecules; and this work shows that, because of a contact-like character of H-bonding interaction, the local configurations in sugar–water H-bonds are likely to be affected by seemingly small changes in the local electronic structure and bond polarity of the hydroxyl groups. The present work provides valuable insights into carbohydrate chemistry, molecular biology and interactions between hydrophilic groups and interfacial water molecules.

Acknowledgements

All the ab initio MD simulations were performed on the Hitachi SR8000 supercomputers of the University of Tokyo.

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Footnote

† Electronic supplementary information (ESI) available: Table S1, computational details; Table S2, the conformational properties of the hydroxymethyl groups in my ab initio molecular dynamics simulations; Fig. S1, three staggered hydroxylmethyl rotational conformations; Fig. S2, the dipole moment of water molecules in the first hydration shell. See DOI: 10.1039/b708719e

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