Hydration Properties of α-, β-, and γ-Cyclodextrins from Molecular

ARTICLE pubs.acs.org/JPCB

Hydration Properties of r-, β-, and γ-Cyclodextrins from Molecular Dynamics Simulations Madhurima Jana and Sanjoy Bandyopadhyay* Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur - 721302, India ABSTRACT: Atomistic molecular dynamics (MD) simulations of R-, β-, and γ-cyclodextrins (ACD, BCD, and GCD) in aqueous solutions have been performed. Detailed analyses were carried out to compare the microscopic properties of water confined within the cavities of these macromolecules and in the hydration layers around them. It is noticed that reduced tetrahedral ordering of water in and around the CD molecules are associated with their restricted motions. Interestingly, unlike the translational motions, the rotational motions of cavity water molecules are found to be highly dependent on cavity dimensions. Additionally, it is found that severely hindered rotational motion of cavity water molecules is the origin of drastically restricted structural relaxation of hydrogen bonds involving those water molecules. It is demonstrated that the geometrical constraints within the cavities of the CD molecules enhance the rate of reformation of broken hydrogen bonds, thereby resulting in rapid establishment of the breaking and reformation equilibria for hydrogen bonds involving cavity water molecules.

1. INTRODUCTION Cyclodextrins (CDs) are water-soluble cyclic oligosaccharides containing a few D-glucopyranose units linked by R(1-4) glycosidic bonds.1,2 Naturally occurring CDs in general contain six, seven, or eight glucose rings, and are known as R-, β-, and γ-cyclodextrins, respectively.1 These are essentially toroidal-shaped macromolecules with a hydrophobic cavity surrounded by a hydrophilic exterior composed of primary and secondary hydroxyl (OH) groups.1,3 The wider sections of the CD molecules are formed by the secondary hydroxyl groups, while the narrower sections contain the primary hydroxyl groups. The molecular structures of the three forms of CD molecules along with a general schematic representation of a pair of glucose rings connected by a glycosidic link and the numbering scheme of the atoms are shown in Figure 1. The presence of OH groups at the exterior makes these molecules water-soluble. Due to their unique structural features, the CD molecules can efficiently trap a wide range of mostly hydrophobic guest molecules in the cavities to form inclusion complexes.4
7 Formation of such inclusion complexes provides an important means to solubilize otherwise insoluble hydrophobic molecules in aqueous media. As a result, CDs are widely used in pharmaceutical and food industries as well as in environmental science.8 Since most of the applications of CD molecules take place in aqueous solutions, an appropriate microscopic understanding of the interaction between these molecules and water and the consequent structural and dynamical correlations between them are of fundamental importance. Considering the importance of the problem, this has been an active area of research over many years. In an early work, Zewail and co-workers9,10 studied the dynamics of reactions inside the cavities of cyclodextrins on femtosecond time scales. Bhattacharayya and co-workers11
14 studied in detail the solvation r 2011 American Chemical Society

dynamics and proton transfer phenomena in different forms of CDs and their substituted forms from time-resolved fluorescence emission spectroscopy measurements. They demonstrated that the solvation dynamics of the CD molecules slow down on substitution of the OH groups of their glucose rings. Recently, they also studied the deuterium isotope effect on the solvation dynamics of coumarin 153 (C153) in methyl substituted CDs.15 The dynamics of pure and substituted R-, β-, and γ-CDs and their hydration properties in aqueous media have been investigated by Shikata and co-workers16,17 using dielectric relaxation techniques. Exchange of water between the free and bound states was identified from the obsereved relaxation modes. It is shown that the hydration states and solubility of the CDs strongly depend on the number of available OH groups. The dynamical aspects associated with these molecules in dimethyl sulfoxide (DMSO) solution have also been studied by them.17 Holm and co-workers18 recently reported the effect of substitution on the ability of BCD derivatives to form inclusion complexes from titration calorimetry measurements. Several theoretical and simulation studies are also attempted to explore different properties of the CD molecules. In an important work, the principles of molecular hydrodynamics theory (MHT) and multishell continuum model (MSCM) were employed by Nandi and Bagchi19 to demonstrate how the longtime component of the solvation of coumarin is affected within the cavity of a CD molecule. In one of the earlier works, van Gunsteren and co-workers20 simulated the experimental crystal structure of the hexahydrated form of ACD. In recent times, Pereira and Received: February 12, 2011 Revised: April 10, 2011 Published: April 21, 2011 6347

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Figure 1. Molecular structures of (a) ACD, (b) BCD, and (c) GCD. Schematic representation of a pair of glucose rings connected by a glycosidic link and the numbering of atoms are shown in part d.

co-workers21 investigated the conformational and solvation properties of CDs from MD simulations. The CD molecules were found to exhibit high conformational freedom in solutions with long residence times of water molecules inside their cavities. MD simulations are also used to investigate the differential solubility of these molecules in aqueous media and their conformational fluctuations.22
24 Recently, it is shown from MD simulations that the restricted orientation of coumarin 153 within the cavity of the β-CD molecule originates from its preferential solvation by a particular glucose unit of the macromolecule.25 Yamazaki and Kovalenko26 proposed a decompositional analysis method recently to study the thermodynamic properties associated with the solvation and complex formation ability of CD molecules. Recently, we studied the effects of substitution of the OH groups of the BCD molecule on the properties of water near it.27
29 In general, it is noticed that the effect of confinement within the cavity of the molecule increases with substitution of the OH groups. In this Article, we have investigated in detail the microscopic properties of water present in the first hydration layers and confined in the cavities of ACD, BCD, and GCD molecules in aqueous solutions from atomistic MD simulations. In particular, the ordering of water in and around the CDs, their translational and rotational motions, and the kinetics of hydrogen bonds formed by them are compared. The rest of the Article is organized as follows. In section 2, we provide a brief description of the setup of the systems and the simulation methods employed. The results obtained from our investigations are presented and discussed in the next section (section 3). The important findings from our study and the conclusions reached therefrom are highlighted in section 4.

2. SYSTEM SETUP AND SIMULATION METHODS Three separate simulations involving aqueous solutions of the ACD, BCD, and GCD molecules were carried out. The initial coordinates of the CD molecules were taken from the literature.30
32 Upon addition of hydrogen atoms, the molecules

were immersed in three separate cubic cells with cell lengths of 45 Å each containing well-equilibrated water molecules. To avoid possible unfavorable contacts, water molecules that were found within 2 Å of the CD molecules were removed. Finally, the systems contained 2969, 2903, and 2884 water molecules for the ACD, BCD, and GCD molecules, respectively. Initially, the temperatures of the systems were kept low, which then gradually raised to the room temperature of 300 K within a short MD run of ∼100 ps. The systems were then equilibrated at constant temperature (T = 300 K) and pressure (Pext = 0 atm) (NPT ensemble) for about 500 ps. During these periods, the cell volumes were allowed to fluctuate isotropically. At the end of these NPT runs, the volumes of the three systems attained steady values with cell edge lengths of 44.8, 44.5, and 44.4 Å for the ACD, BCD, and GCD molecules, respectively. At this point, we fixed the dimensions of the simulation cells and the conditions were changed to constant temperature (300 K) and volume (NVT ensemble). The equilibration runs were continued under NVT conditions for another 1 ns duration. This was then followed by NVT production runs of 8.5 ns duration for each of the three systems. All the simulations were carried out utilizing the Nos
e
Hoover chain thermostat extended system method,33 as implemented in the PINY-MD code.34 The reversible multiple time step algorithm, RESPA33, was used to integrate the equations of motions with a time step of 4 fs. Electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method.35 For analysis, the MD trajectories were stored with a time resolution of 400 fs. Additionally, parts of the three equilibrated trajectories (∼500 ps) were also stored under identical conditions but with a higher time resolution of 16 fs to estimate ultrafast properties. This is a standard practice to particularly study the microscopic kinetics of hydrogen bonds involving such macromolecules as described earlier.29 The potential parameters for the CDs were taken from the GROMOS force field,20 while the rigid three-site extended simple point charge (SPC/E) model36 that is consistent with the chosen force field for 6348

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Figure 2. The top (a) and side (b) views of the initial configurations of ACD, BCD, and GCD molecules. The top and side views of the corresponding representative simulated configurations are shown in parts c and d, respectively.

the CDs was employed for water. These parameters were found to reproduce fairly accurately the experimental properties of this class of macromolecules.25,37 Further details of the simulation protocols employed in this work are the same as those mentioned in our earlier works.27,29

3. RESULTS AND DISCUSSION 3.1. Cyclodextrin Structures. In Figure 2, we display the snapshots of ACD, BCD, and GCD molecules that best represent their average conformations as obtained from the simulations. The initial configurations obtained from the crystal structures of these molecules30
32 are also shown for comparison. Flexibility of these macrocyclic molecules in aqueous solution is evident from the figure. To visualize structural deviations of these molecules from the crystalline forms, we have superimposed several of their configurations as obtained from the simulated trajectories at regular time intervals, which are shown in Figure 3. This is done by removing the translational and rotational degrees of freedom of the selected configurations of the molecules with respect to their initial configurations. Though the overall structures of the molecules are retained in general, an increase in flexibility with the number of glucose rings is clearly evident from the ACD to the GCD molecule. We also explored whether the relative conformations of pairs of glucose rings of the CDs exhibit syn to anti transformations in aqueous solutions by monitoring the flip angles between the glucose rings.38 The flip angle is a virtual dihedral angle defined as O3(i) 3 3 3 C4(i) 3 3 3 C1(i þ 1) 3 3 3 O2(i þ 1) (see Figure 1d). It is found that, for all three CDs, the glucose rings primarily retain their syn arrangements with some occasional kinks in the flip angles. This agrees well with an earlier report on such small-sized CDs.38 To quantify the differences between the simulated structures of the three CDs with respect to their crystalline forms, we have estimated the root-mean-square deviations (rmsd) between

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Figure 3. Superposition of several simulated configurations of (a) ACD, (b) BCD, and (c) GCD molecules taken at regular intervals from the equilibrated simulation trajectories. The hydrogen atoms are not shown for visual clarity.

them. The rmsd values were calculated for all the non-hydrogen atoms of the CD molecules. The time evolution of the RMSDs and their distributions are displayed in Figure 4. It is evident that the structural deviation is minimum for ACD, and it increases with the size of the macrocyclic ring and becomes maximum for GCD. The average rmsd values have been found to be 1.39 ((0.07) Å, 1.41 ((0.14) Å, and 2.26 ((0.13) Å for ACD, BCD, and GCD molecules, respectively. It indicates that the cavity inside the ACD molecule containing six glucose rings is highly constrained. However, with an increase in the number of glucose rings, the volumes inside the cavities become relatively less constrained. Such differential flexibility of the cavities of these molecules plays an important role in controlling their abilities to form inclusion complexes with appropriate guest species. 3.2. Water Structure and Ordering around Cyclodextrins. Due to the microheterogeneous environment associated with the CDs, the regular structure and ordering of water molecules are expected to be modified by their presence in aqueous solutions. This in turn may provide important information about the role played by water in and around the CDs in controlling their properties. To explore this, we have studied the structure, ordering, and energetics of water around the three CD molecules, as discussed below. We have calculated the pairwise correlation function, known as the radial distribution function, g(r), of the water molecules with the oxygen atoms of the CDs. The calculations are carried out by averaging over all the oxygen atoms of the CDs, and the results are displayed in Figure 5. It can be seen that the distribution curves are characterized by a sharp peak corresponding to the first hydration shells of the CD molecules at around 3 Å. In addition, the presence of another peak with sufficient intensity at around 5 Å provides evidence for strong influence of the CD molecules on local structuring of water around them. No noticeable differences 6349

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Figure 4. (left) Time evolutions of the root-mean-square deviations (rmsd) of the three CD molecules with respect to their crystal structures.30
32 (right) The distributions of the rmsd values for the three molecules.

Figure 5. Pairwise correlation function, g(r), of water molecules as a function of distance from the oxygen atoms of the three CD molecules.

in water structure around the three molecules have been observed. This is expected, as the exterior of the CDs provide an identical environment and therefore perturb the local water structure around them in a similar manner. By integrating the g(r) curves up to the first minimum, it is found that there are on average about four water molecules within the first coordination shells of each of the oxygen atoms of the CDs. To further explore the influence of the CD molecules on water, we have estimated the tetrahedral ordering of water around them. This is done by measuring the tetrahedral order parameter (qtet), which is defined as39
41   4 3 3 1 2 qtet ¼ 1
cos ψjk þ ð1Þ 8 j¼1 k¼j þ 1 3

∑ ∑

Here, ψjk is the angle between the bond vectors rij and rik, where j and k are the four nearest neighbor atoms of the ith water

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Figure 6. Distributions of the tetrahedral order parameter, qtet, for the water molecules that are present in the first hydration layers (black) and in the cavities (blue) of the three CD molecules. The corresponding distribution for water in pure bulk state is also shown for comparison.

molecule. Here, it is assumed that non-hydrogen atoms of the CD molecules can also act as neighboring atoms for those tagged water molecules that are present close to them. We have calculated the qtet values for water around the CDs. The calculations are carried out by separating the water molecules into two types, one involving the water molecules present in the first hydration layers of the CDs and the other involving only those that are present inside the cavities. The water molecules that are present within a shell of 4 Å thickness surrounding the CDs are considered to form the first hydration layers.27 The cavity water molecules are identified following the same approach as mentioned in our earlier work.27 It may be noted that on average 4, 8, and 11 water molecules are found within the cavities of ACD, BCD, and GCD molecules, respectively. The distributions of the tetrahedral order parameter (P(qtet)) for water present in the hydration layers and in the cavities of the three CD molecules are displayed in Figure 6. For comparison, the corresponding distribution function for pure bulk water as obtained from a separate MD simulation of SPC/ E water molecules under identical conditions is also displayed in the figure. The bimodal distribution of qtet for pure SPC/E water with the location of the higher qtet peak at around 0.75 and that of the lower one at around 0.5 as obtained from our calculations agrees well with earlier reports.42,43 A decrease in the intensity of the higher peak with a consequent increase of the same for the lower peak can be seen for water in close proximity to the CD molecules. This indicates reduced tetrahedral ordering of water present in the first hydration layers around the CDs and inside their cavities. The effect is small for the hydration layer water and is independent of the size of the CDs. On the other hand, the ordering of the cavity water molecules is found to be significantly reduced. The effect is more noticeable for the ACD molecule. Thus, it is clear that the confined environment inside the cavities prevents the water molecules from orienting themselves in a tetrahedral manner. With the degree of confinement inside the cavity of ACD being maximum, almost no ordering is noticed for the corresponding water molecules. The calculated average order parameter values (Æqtetæ) for water present in the first hydration layers and inside the cavities are listed in Table 1. It can be seen that, while the 6350

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Table 1. Average Tetrahedral Order Parameters (Æqtetæ) and the Tagged Potential Energies (ÆUTPEæ) of Water Present in the First Hydration Layers and in the Cavities of the CD Moleculesa ÆUTPEæ (kcal mol
1)

Æqtetæ system

hydration layer

cavity

hydration layer

cavity

0.535 (0.089)
23.55 (2.03)
24.67 (1.98)

ACD

0.624 (0.095)

BCD

0.621 (0.090) 0.595 (0.093)
23.55 (2.01)
25.16 (2.08)

GCD

0.620 (0.095)

bulk water

0.594 (0.095)
23.58 (2.02)
24.78 (2.07)

0.637 (0.094)


22.23 (2.05)

a

The data for pure bulk water are listed for comparison, and the values in the parentheses are the estimated standard deviations.

Figure 8. Mean square displacement (MSD) of water molecules that are present in the first hydration layers (black) and in the cavities (blue) of the three CD molecules. The MSD of water in pure bulk state is also shown for comparison.

Figure 7. Distributions of the tagged potential energy (TPE), UTPE, for the water molecules that are present in the first hydration layers (black) and in the cavities (blue) of the three CD molecules. The corresponding distribution for water in pure bulk state is also shown for comparison.

Æqtetæ values for water in the first hydration layers of the three CDs are quite close to that of pure bulk water, the values deviate more for water confined inside the cavities, with the deviation being maximum for ACD. Let us now explore whether the ordering of water molecules in and around the CDs depends on their interaction energies. For that, we have calculated the tagged potential energy (TPE), UTPE, of those water molecules that are present either in the first hydration layers or inside the cavities of the CDs. UTPE is the binding energy of a tagged water molecule and is defined as the interaction energy of that water with the rest of the system.43
45 In Figure 7, we show the distribution function, P(UTPE), for the hydration layer and cavity water molecules of the CDs. The corresponding function for pure bulk water is also included in the figure for comparison. The estimated average values, ÆUTPEæ, as obtained from the distributions are listed in Table 1. It can be seen that the presence of the CD molecules results in lowering of ÆUTPEæ values as compared to that for pure bulk water. The effect is more for the cavity water molecules. Interestingly, we notice that lowering of the tetrahedral ordering of water in and around the CDs occurs with a decrease in their tagged potential energies. This is in contrast to the normal expectation that lowering of the tagged potential energies should be associated with increased ordering of water. It

indicates that, for cyclic macromolecules like cyclodextrins, the effect of confinement plays a dominating role in controlling the ordering of water in and around them. 3.3. Water Dynamics around Cyclodextrins. The dynamics of water molecules present in the first hydration layers of the three cyclodextrins and inside their cavities are discussed in this section. Effort has been made to understand the effect of variation of the number of glucose rings of the CD molecules on the dynamics of water. 3.3.1. Translational Motion. We have measured the translational motion of the water molecules from their mean square displacements (MSD), ÆΔr2æ, defined as ÆΔr 2 æ ¼ Æjri ðtÞ
ri ð0Þj2 æ

ð2Þ

where ri(t) and ri(0) are the position vectors of the oxygen atom of the ith water molecule at time t and at t = 0, respectively, and the averaging is carried out over different time origins with the tagged water molecules. The results are shown in Figure 8 along with that of pure bulk water. Restricted translational motions of water in the hydration layers and inside the cavities of the three CDs can be easily seen from the figure. The degree of restriction is more for the cavity water molecules due to confinement. Similar behavior was observed earlier for water in and around BCD derivatives.27 It is noticed that water present in the hydration layers of the three CDs exhibits an almost similar translational mobility. Interestingly, similar uniformity is also noticed among the cavity water molecules. Thus, the cavity dimension of a CD molecule does not seem to have any noticeable effect on the translational motions of water confined within it. 3.3.2. Rotational Motion. The presence of macromolecules like CDs is expected to influence the rotational motion of water in and around them. We have investigated the rotational motions of hydration layer water and cavity water molecules for the three CDs. This is done by measuring the reorientational dynamics of the electrical dipole μB of the tagged water molecules. μB is defined as the vector connecting the oxygen atom of the tagged water molecule to the center of the line connecting the two hydrogen atoms. The time evolution of μB can be estimated by measuring the dipole
dipole time 6351

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Table 2. Average Reorientational Time Constants (Æτμæ) of Water Present in the First Hydration Layers and in the Cavities of the CD Moleculesa Æτμæ (ps) system

hydration layer

cavity

ACD

17.31

127.07

BCD

16.44

51.70

GCD

15.06

bulk water a

Figure 9. Reorientational time correlation function of the water dipoles, Cμ(t), for water molecules that are present in the first hydration layers (black) and in the cavities (blue) of the three CD molecules. The corresponding function for water in pure bulk state is also shown for comparison.

correlation function (TCF) Cμ ðtÞ ¼

^i ð0Þæ Æ^ μi ðtÞ 3 μ ^i ð0Þæ Æ^ μi ð0Þ 3 μ

ð3Þ

where μ^i(t) is the unit dipole moment vector of the ith water molecule at time t. The angular brackets denote that the averaging is carried out over the tagged water molecules at different reference initial times. The results are displayed in Figure 9. Consistent with the translational motions, the rotational motions of water around the CDs and inside their cavities are also found to be restricted. Again, due to confinement, the effect is more for the cavity water molecules. The effects of the CDs on the rotational motions of hydration layer water molecules are similar, which is in agreement with their translational motions (see Figure 8). However, note the significant heterogeneity in the rotational motions of water present in the cavities of the three molecules. It is apparent that, due to increase in confinement with decrease in the cavity size of ACD, the rotational motions of water present in its cavity are drastically hindered. Interestingly, we notice that the translational and rotational motions of water confined within the cavities are affected in a nonuniform manner. Rotational motion, being faster, is found to be more sensitive to the degree of confinement. This is an interesting observation which to the best of our knowledge is the first such attempt where differential effects of confinement on translational and rotational motions of water within the cavities of the CD molecules are investigated. As reported in our earlier work,27 we have fitted the decay curves with triexponentials, and estimated the amplitude-weighted average reorientational times (Æτμæ) of water molecules, as listed in Table 2. It is found that, while compared to water in the bulk phase the hydration layer water molecules take about 3
4 times longer to reorient themselves, the cavity water molecules take more than an order of magnitude longer time to do so. Besides, sudden enhancement of rotational confinement of water in the cavity of ACD is reflected in the corresponding Æτμæ value that is about 3 times longer than that for the cavity water of the GCD molecule.

45.96 4.57

The Æτμæ value for pure bulk water is listed for comparison.

3.4. Hydrogen Bond Time Correlation Functions. In aqueous media, the CD molecules are capable of forming hydrogen bonds with water. These molecules can modify the regular water
water (WW) hydrogen bonds by forming CD
water (CW) hydrogen bonds.29 Lifetimes of the CW hydrogen bonds are expected to control the hydration properties of the CDs. Here, we investigate the dynamics of hydrogen bonds by calculating suitable time correlation functions (TCFs). For that, it is first necessary to set appropriate criteria to define hydrogen bonds. Generally, one uses either a geometric46
48 or an energetic49
52 criterion to define hydrogen bonds. Here, we have employed the same geometric criteria to define CW and WW hydrogen bonds as described in our work.29 We then calculate the intermittent (C(t)) and continuous (S(t)) hydrogen bond TCFs, which are defined as52,53

CðtÞ ¼

Æhð0ÞhðtÞæ Æhð0Þhð0Þæ

ð4Þ

SðtÞ ¼

Æhð0ÞHðtÞæ Æhð0Þhð0Þæ

ð5Þ

and

The variable h(t) is defined to be unity if a particular pair of sites (CW or WW) are hydrogen bonded at time t; otherwise, it is zero. On the other hand, H(t) is unity when the tagged pair of sites remain continuously hydrogen bonded from time t = 0 to time t; otherwise, it is zero. Thus, by definition, C(t) takes into account possible breaking and reformation of hydrogen bonds at intermediate times due to recrossing of the barrier separating the bonded and the free states, as well as the long-time diffusive behavior of the tagged species. Therefore, the function C(t) provides information about the overall relaxation time scales of hydrogen bonds. The function S(t), on the other hand, describes the probability that a hydrogen bond once formed between two sites at t = 0 remains bonded at all times up to t. Thus, S(t) provides a direct measure of the lifetime of a particular hydrogen bond. All the calculations presented below are carried out by averaging over different types (CW or WW) of hydrogen bonds that are formed at different time origins. We have calculated the functions CCW(t) for the CW hydrogen bonds formed between the CD molecules and water and CWW(t) for the WW hydrogen bonds formed between the water molecules. Once again, the calculations involving the hydration layer water and cavity water molecules are carried out separately, as shown in Figure 10. For comparison, the function CWW(t) for pure bulk water is also included in the figure. It is found that, irrespective of whether the water molecules involved in CW 6352

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Table 3. Average Relaxation Times of Intermittent CW WW (ÆτCW C æ) and WW (ÆτC æ) Hydrogen Bond TCFs for Water Present in the First Hydration Layers and in the Cavities of the CD Moleculesa ÆτCW C æ (ps) system

hydration layer

cavity

hydration layer

cavity

ACD

51.00

170.21

5.96

156.14

BCD

45.21

77.67

5.82

44.11

GCD

44.61

75.34

5.78

bulk water a

Figure 10. (a) Intermittent time correlation function, CCW(t), for the hydrogen bonds formed between the glucose rings and water molecules that are present in the first hydration layers (black) and in the cavities (blue) of the three CD molecules. (b) The corresponding function, CWW(t), for the hydrogen bonds formed among the first hydration layer or cavity water molecules of the three CDs. The function for water in the pure bulk state is also shown for comparison.

hydrogen bonds are present in the first hydration layers surrounding the CDs or confined inside their cavities, the relaxation of the function CCW(t) is always slower than that for the WW hydrogen bonds in pure bulk water. Such restrictions are more drastic when the cavity water molecules take part to form CW hydrogen bonds. These results are consistent with the restricted motions of the corresponding water molecules, as discussed before (see Figures 8 and 9). Interestingly, due to the identical environment, the effect is almost similar for CW hydrogen bonds formed by the hydration layer water molecules of the three CDs. However, the differential degree of confinement of water within the cavities is reflected in the relaxation pattern of the corresponding decay curves. It is noticed that, with change in cavity size, a correlation exists between the restricted rotational motions of water confined in the cavities and the overall relaxation of the corresponding CW decay curves. Increasingly hindered rotational motions of cavity water with decrease in cavity size result in drastic slowing down of the decay of CCW(t) involving the cavity water of the ACD molecule. We have estimated the average relaxation times (ÆτCW C æ) by fitting each of the decay curves with a sum of three exponentials, which are listed in Table 3. We find that the average times required for the CW hydrogen bonds formed by the hydration layer water molecules of the CDs to relax are 7
8 times longer than that for pure bulk

ÆτWW C æ (ps)

31.58 6.52

The ÆτWW C æ value for pure bulk water is listed for comparison.

water. On the other hand, due to confinement, the CW hydrogen bonds formed by the cavity water molecules require more than an order of magnitude longer time to relax. It may be noted further that enhanced confined environment within the cavity of ACD results in a ÆτCW C æ value more than twice longer than the corresponding values for the BCD and GCD molecules. It is apparent from Figure 10b that the CD molecules do not have any noticeable influence on the relaxation of the WW hydrogen bonds formed among the water molecules present in the hydration layers around them, which is evident from the corresponding average relaxation times (ÆτWW C æ) (see Table 3). However, the relaxation pattern of CWW(t) for the WW hydrogen bonds formed between the cavity water molecules is found to be significantly influenced due to confinement. The degree of such influence strongly depends on the cavity dimensions. The results are consistent with those of CW hydrogen bonds formed by the cavity water molecules (see Figure 10a) as well as with their hindered rotational motions due to geometrical constraints. It is found that, while the WW hydrogen bonds formed between the water molecules inside the cavities of BCD and GCD relax on a time scale of 5
7 times longer than that for pure bulk water (see Table 3), the corresponding relaxation time for the cavity water of ACD is more than an order of magnitude longer. Further, relatively higher restricted environment for water inside the cavity of the ACD molecule is evident from the corresponding ÆτWW C æ value that is about 5 times longer than that for water confined in the cavity of the GCD molecule. It may be noted that the time scales listed in Table 3 are consistent with that reported earlier for BCD derivatives.27 We show the relaxation of the function SCW(t) for the CW hydrogen bonds in Figure 11. The corresponding function SWW(t) for the WW hydrogen bonds formed either among the hydration layer water or the cavity water molecules is also shown in the figure along with that for pure bulk water. Rapid initial decay of S(t) as compared to C(t) can be easily seen. This arises because fast vibrational and librational motions of the hydrogen bonded sites primarily contribute to the relaxation of S(t), whereas relatively slower translational and rotational motions contribute to the relaxation of C(t). It is found that, compared to pure bulk water, the function SCW(t) relaxes slowly for all cases, thereby indicating longer CW hydrogen bond lifetimes. We have again estimated the average hydrogen bond lifetimes (ÆτCW S æ and ÆτWW S æ) by fitting the decay curves as mentioned earlier. The values are listed in Table 4. It is noticed that the ÆτCW S æ values for the CW hydrogen bonds are about 3
8 times longer than that for WW hydrogen bonds in pure bulk water. By definition (eq 5), S(t) provides information about the breaking of hydrogen bonds. 6353

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Table 4. Average Relaxation Times of Continuous CW WW (ÆτCW S æ) and WW (ÆτS æ) Hydrogen Bond TCFs for Water Present in the First Hydration Layers and in the Cavities of the CD Moleculesa ÆτCW S æ (ps) system

hydration layer

cavity

hydration layer

cavity

ACD

4.30

2.00

0.44

1.15

BCD

5.32

2.68

0.48

0.64

GCD

4.50

3.60

0.47

bulk water a

Figure 11. (a) Continuous time correlation function, SCW(t), for the hydrogen bonds formed between the glucose rings and water molecules that are present in the first hydration layers (black) and in the cavities (blue) of the three CD molecules. (b) The corresponding function, SWW(t), for the hydrogen bonds formed among the first hydration layer or cavity water molecules of the three CDs. The function for water in the pure bulk state is also shown for comparison.

Hence, its relaxation should depend on the strength of the hydrogen bonds. We have calculated the average interaction energy between a water molecule and the particular glucose unit of the CD ring with which it is hydrogen bonded. It is found to be around
7.5 kcal mol
1 for the three CDs, which is lower than the average WW hydrogen bond energy of
4.6 kcal mol
1 in pure bulk water. It may be noted that the CW hydrogen bond energy as obtained from our calculation agrees well with that reported for hydrogen bonds between glucose molecules and water.54,55 Therefore, it is clear that water present in and around the CDs forms stronger hydrogen bonds with the glucose rings with longer lifetimes. A heterogeneous relaxation behavior of SCW(t) is once again observed for the cavity water molecules of the CDs, with the degree of heterogeneity being less pronounced than that noticed for the function CCW(t) (see Figure 10). Interestingly, it is noticed that the relative relaxation patterns of the function SCW(t) for the CW hydrogen bonds formed by the hydration layer water and that formed by the cavity water are exactly opposite to that observed for the function CCW(t). In contrast to CCW(t), the function SCW(t) involving the cavity water molecules relaxes faster than that involving the hydration layer water. We find that the average time taken for overall structural relaxation of the CW hydrogen bonds formed by the cavity water of a CD molecule is longer than that formed by the

ÆτWW S æ (ps)

0.83 0.63

The ÆτWW S æ value for pure bulk water is listed for comparison.

corresponding hydration layer water, but the average survival time of the CW hydrogen bonds involving cavity water can be shorter than that involving the hydration layer water molecules. In addition, the effect of the cavity dimension on the relaxation pattern of SCW(t) is also found to be opposite to that observed for CCW(t). It can be seen that, though the ÆτCW C æ value for the cavity water of ACD is more than twice longer than that for the GCD molecule, the ÆτCW S æ value is about twice shorter for the cavity water of ACD. Thus, the effects of confinement within the cavities of the CDs on the two functions CCW(t) and SCW(t) are opposite to each other. We noticed in our earlier work27 that the substitution of the OH groups of a CD molecule has a similar contrasting effect on these two TCFs involving CW hydrogen bonds. Thus, our present findings along with that reported earlier suggest that any change in the degree of confinement in the cavities of the CD molecules affect the functions CCW(t) and SCW(t) in a differential manner. This is an important observation which may have important consequences in the propertie of this class of macromolecules. Let us explain the origin of such differential behavior. Since reformation of broken hydrogen bonds is included in CCW(t), the relative motions of water within the cavities play an important role in determining its relaxation behavior. As already discussed, highly restricted motions of water confined in the cavity of the ACD molecule result in extremely slow relaxation of the function CCW(t). On the other hand, the function SCW(t) provides information about the survival time of a CW hydrogen bond since its formation. With hydrogen bonds being directional in nature, proper geometrical orientations of the sites are important for their survival. The highly restricted environment inside the cavity of ACD prevents water molecules from orienting appropriately to form CW hydrogen bonds with the glucose rings. This results in shorter lifetimes of these bonds inside the cavity of ACD as against those formed by water in the cavities of BCD and GCD molecules. It is apparent from Figure 11b that relaxation of SWW(t) for WW hydrogen bonds among water molecules present either in the hydration layers or inside the cavities is affected differently as compared with pure bulk water. For the hydration layers, SWW(t) relaxes slightly faster with shorter WW hydrogen bond lifetimes than that for pure bulk water, while the reverse is the case for the cavity water molecules (see Table 4). Such heterogeneities in and around the three CDs is an interesting observation, which we believe is related to the differential orientational constraints for a pair of water molecules to remain hydrogen bonded in the hydration layers and inside the cavities of these macromolecules. However, this requires further investigation. 6354

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molecules with the glucose rings of the three CDs, as shown in Figure 12. The corresponding functions NWW(t) for WW hydrogen bonds formed either among the hydration layer water or the cavity water molecules are also shown in the figure. In addition, the result obtained for pure bulk water is included for comparison. It is evident that both the functions NCW(t) and NWW(t) involving water in and around the CD molecules relax significantly more slowly than that observed for pure bulk water. This provides direct evidence of a rigid arrangement of water in and around the CDs which agrees well with the relaxation patterns of the corresponding intermittent hydrogen bond TCFs (see Figure 10). Expectedly, the effect is more severe for the hydrogen bonds involving the cavity water molecules due to confinement. The effect is maximum for ACD, as its cavity dimension is the smallest among the three forms. We now attempt to estimate the microscopic kinetics of breaking and reformation of hydrogen bonds in and around the CD molecules. As proposed by Luzar and Chandler,46,56 such kinetics can be described as B h QF

ð7Þ

where B is the bound state with two tagged sites hydrogen bonded to each other and QF is the quasi-free state in which the hydrogen bond is broken but the two sites remain as nearest neighbors of each other. As per the definitions, C(t) and N(t) correspond to the populations of B and QF states, respectively, that can interconvert among themselves according to eq 7. If k1 and k2 are the breaking (forward) and reformation (backward) rate constants, then we can write a simple rate equation as Figure 12. (a) Time-dependent probability that a CW hydrogen bond formed between a glucose ring and a water molecule present either in the first hydration layer (black) or in the cavity (blue) of a CD molecule is broken but the tagged water molecule remains in the vicinity (i.e., within RH) of the site. (b) The corresponding function for a WW hydrogen bond formed between a pair of first hydration layer or cavity water molecules of a CD molecule. The results for water in the pure bulk state are also shown for comparison.

3.5. Diffusion and Hydrogen Bond Dynamics. The dynamics of hydrogen bonds in aqueous solutions of macromolecules like the CDs should be correlated with the diffusion time scales of the solvent.29 Slower diffusion of water will lead to slower hydrogen bond dynamics due to increased probability of reformation of broken bonds. To eliminate the contribution arising from water diffusion, we have calculated the time correlation function46,56
60

NðtÞ ¼

Æhð0Þð1
hðtÞÞH 0 ðtÞæ Æhð0Þhð0Þæ

ð6Þ

where, H0 (t) is unity if the two sites involved in the formation of a hydrogen bond are closer than a cutoff distance, RH (3.5 Å for both CW and WW hydrogen bonds), at time t, and zero otherwise. A nonzero value of N(t) indicates that the two sites are not hydrogen bonded, though they are in the vicinity of each other (i.e., within RH). On the other hand, N(t) = 0 suggests that the two sites are either hydrogen bonded or separated by a distance larger than RH. N(t) can therefore relax either due to reformation of broken hydrogen bonds or diffusion of the tagged molecules.46 We have calculated the function NCW(t) for the CW hydrogen bonds formed by either the hydration layer or the cavity water

kðtÞ ¼


dCðtÞ ¼ k1 CðtÞ
k2 NðtÞ dt

ð8Þ

k(t) can relax to its equilibrium value by transitions from reactants to products, i.e., from state B to state QF (eq 7). We have calculated k(t) from the derivatives of the functions CCW(t) and CWW(t) involving both hydration layer and cavity water molecules. The results are displayed in Figure 13. For comparison, the corresponding function for pure bulk water is shown in the inset of Figure 13a. Once again, consistent with earlier findings, both kCW(t) and kWW(t) involving water in and around the CDs relax much slowly than pure bulk water. Relaxations of kCW(t) and kWW(t) involving the cavity water molecules are further slower than that involving the hydration layer water due to the constrained environment inside the cavities. It can be seen that after the early transient period, both kCW(t) and kWW(t) corresponding to the hydration layer water molecules decay monotonically for all three CDs. On the other hand, the functions tend to attain plateau values for the cavity water molecules. This demonstrates that the breaking and reformation equilibria are rapidly attained within the cavities of the CD molecules due to their restricted environments. Besides, some degree of heterogeneity in the relaxation patterns of the functions can be seen within the cavities of the CDs. This correlates well with the heterogeneously restricted motions of cavity water and the relaxation time scales of the hydrogen bonds, and is consistent with the varying degree of confinement with cavity dimensions. As before,29 the least-squares fit method57,59 is employed for the data beyond the early transient period (t > 0.5 ps) to estimate the breaking (forward) and reformation (backward) rate constants (k1 and k2) for the CW and WW hydrogen bonds. The values are listed in Tables 5 and 6 for CW 6355

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Table 6. Forward (k1) and Backward (k2) Rate Constants for WW Hydrogen Bond Breaking and the Average Hydrogen Bond Lifetimes (1/k1) as Obtained from eq 8 hydration layer
1

cavity


1


1

system k1 (ps ) k1 (ps ) 1/k1 (ps) k1 (ps ) k2 (ps
1) 1/k1 (ps) ACD

0.32

0.22

3.13

0.09

0.29

11.11

BCD

0.33

0.24

3.03

0.21

0.40

4.76

GCD

0.34

0.26

2.94

0.22

0.47

4.55

of hydrogen bonds due to librational and vibrational motions, while 1/k1 additionally includes contributions from slower mobility of water molecules.

Figure 13. (a) The reactive flux, kCW(t) (semilog plot), for the breaking and reformation of CW hydrogen bonds between the glucose rings and water molecules that are present in the first hydration layers (black) and in the cavities (blue) of the three CD molecules. The inset shows the result (kWW(t)) for water in the pure bulk state for comparison. (b) The function kWW(t) for the hydrogen bonds formed among the first hydration layer or cavity water molecules of the three CDs.

Table 5. Forward (k1) and Backward (k2) Rate Constants for CW Hydrogen Bond Breaking and the Average Hydrogen Bond Lifetimes (1/k1) as Obtained from eq 8 hydration layer
1

cavity


1


1

system k1 (ps ) k2 (ps ) 1/k1 (ps) k1 (ps ) k2 (ps
1) 1/k1 (ps) ACD

0.11

0.59

9.09

0.06

0.11

16.67

BCD GCD

0.12 0.12

0.46 0.44

8.33 8.33

0.09 0.10

0.21 0.19

11.11 10.00

and WW hydrogen bonds, respectively. The 1/k1 values that correspond to average hydrogen bond lifetimes are also listed in the tables. The data indicate almost identical kinetics of hydrogen bonds involving water around the CDs in their hydration layers. However, note that, compared to BCD and GCD, the cavity water of the ACD molecule exhibit noticeably different kinetic behavior. Significantly increased degree of confinement of water inside the cavity of ACD is evident from corresponding lower k1 and k2 values. It may be noted that the estimated 1/k1 values are larger than the average hydrogen bond lifetimes (ÆτCW S æ and ÆτWW S æ), as listed earlier (Table 4). The reason for such a difference is that the data in Table 4 contain the breaking times

4. CONCLUSIONS In this Article, we have presented results obtained from atomistic MD simulations of R-, β-, and γ-cyclodextrins (ACD, BCD, and GCD) in aqueous solutions. Our primary aim has been to compare the microscopic properties of water around the CDs and confined within their cavities. In particular, we have estimated the relative ordering of water in and around the CDs, their translational and rotational motions, and the kinetics of CW and WW hydrogen bonds. The calculations revealed that the presence of the CDs reduces the overall tetrahedral ordering of the proximal water molecules. Surprisingly, such reduction in ordering has been found to be associated with a decrease in the tagged potential energies (TPE) of those water molecules, the effect being more noticeable for water present in the cavities. This indicates that the geometrical constraints prohibit the cavity water molecules from orienting appropriately in tetrahedral arrangement. It is found that both translational and rotational motions of water present in the first hydration layers around the CDs or confined inside their cavities are significantly slower than that of water in pure bulk state. However, interestingly, it is noticed that the translational and rotational motions of water confined within the cavities of the three CDs are affected in a differential manner. We found that, although the translational mobility of the cavity water molecules is more or less independent of the cavity dimension, the rotational motion is highly sensitive to the degree of confinement. Increasingly hindered rotational motions of cavity water with decrease in cavity dimension have been found to be the origin of the drastically restricted relaxation behavior of the intermittent hydrogen bond TCFs involving both CW and WW hydrogen bonds for the ACD molecule. Further, it is noticed that the formation of stronger CW hydrogen bonds results in their longer lifetimes. Importantly, it is found that the time taken for overall structural relaxation of CW hydrogen bonds formed by the cavity water molecules is much longer. However, the inability of these water molecules to orient appropriately in the cavities results in their shorter lifetimes with respect to the CW hydrogen bonds formed by water in the hydration layers. Adopting the approach as proposed by Luzar and Chandler,46,56 we studied the kinetics of breaking and reformation of CW and WW hydrogen bonds. It is demonstrated that the confined environment inside the cavities of the CDs allows reformation of broken hydrogen bonds, thereby resulting in rapid establishment of the breaking and reformation equilibria for hydrogen bonds involving cavity water molecules. The effect is found to be maximum for the ACD 6356

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The Journal of Physical Chemistry B molecule, as it provides the most restricted cavity environment as compared to the other two CD molecules. Thus, in this work, we explored the effects of CD molecules on the microscopic properties of water in their first hydration layers and confined within their cavities. We believe that the use of other force fields will not alter the general conclusions reached from this study, as these are based on comparative analysis of results among the three CD molecules. The correlations observed in this study may have an influence in determining the ability of these macrocyclic molecules to form suitable inclusion complexes. Efforts are on in our laboratory to explore this issue further.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This study was supported in part by a grant from the Department of Science and Technology (DST) (SR/S1/PC-23/2007), Government of India. Part of the work was carried out using the computational facility created under DST-FIST programme (SR/ FST/CSII-011/2005). M.J. thanks the University Grants Commission (UGC), Government of India, for providing a scholarship. ’ REFERENCES (1) Saenger, W. In Inclusion Compounds; Atwood, J. L., Davies, J. E, MacNicol, D. D., Eds.: Academic: New York, 1984; Vol. 2, p 231. (2) Luzhkov, V.; Aqvist, J. Chem. Phys. Lett. 1999, 302, 267–272. (3) Winkler, R. G.; Fioravanti, S.; Ciccotti, G.; Margheritis, C.; Villa, M. J. Comput.-Aided Mol. Des. 2000, 14, 659–667. (4) Szejtli, J. In Comprehensive Supramolecular Chemistry; Szejtli, J., Osa, T., Eds.; Pergamon: Oxford, U.K., 1996; Vol. 3, Chapter 5. (5) Connors, K. A. Chem. Rev. 1997, 97, 1325–1357. (6) Szejtli, J. Chem. Rev. 1998, 98, 1743–1754. (7) Yu, Y.; Chipot, C.; Cai, W.; Shao, X. J. Phys. Chem. B 2006, 110, 6372–6378. (8) Uekama, K.; Hirayama, F.; Irie, T. Chem. Rev. 1998, 98, 2045–2076. (9) Douhal, A.; Fiebig, T.; Chachisvilis, M.; Zewail, A. H. J. Phys. Chem. A 1998, 102, 1657–1660. (10) Chachisvilis, M.; Garcia-Ochoa, I.; Douhal, A.; Zewail, A. H. Chem. Phys. Lett. 1998, 293, 153–159. (11) Sen, S.; Sukul, D.; Dutta, P.; Bhattacharyya, K. J. Phys. Chem. A 2001, 105, 10635–10639. (12) Mondal, S.; Roy, D.; Sahu, K.; Sen, P.; Karmakar, R.; Bhattacharyya, K. J. Photochem. Photobiol., A 2005, 173, 334–339. (13) Sen, P.; Roy, D.; Mondal, S.; Sahu, K.; Ghosh, S.; Bhattacharyya, K. J. Phys. Chem. A 2005, 109, 9716–9722. (14) Mondal, S.; Sahu, K.; Ghosh, S; Sen, P.; Bhattacharyya, K. J. Phys. Chem. A 2006, 110, 13646–13652. (15) Sasmal, D. K.; Dey, S.; Das, D. K.; Bhattacharyya, K. J. Chem. Phys. 2009, 131, 044509. (16) Shikata, T.; Takahashi, R.; Satokawa, Y. J. Phys. Chem. B 2007, 111, 12239–12247. (17) Shikata, T.; Takahashi, R.; Onji, T.; Satokawa, Y.; Harada, A. J. Phys. Chem. B 2006, 110, 18112–18114. (18) Sch€onbeck, C.; Westh, P.; Madsen, J. C.; Larsen, K. L.; St€ade, L. W.; Holm, R. Langmuir 2010, 26, 17949–17957. (19) Nandi, N.; Bagchi, B. J. Phys. Chem. 1996, 100, 13914–13919. (20) Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J. 1987, 15, 197–210.

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