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Vibrational spectrum of water confined in and around cyclodextrins
Chemical Physics Letters 509 (2011) 181–185
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Vibrational spectrum of water confined in and around cyclodextrins Madhurima Jana, Sanjoy Bandyopadhyay ⇑ Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India
a r t i c l e
i n f o
Article history: Received 7 March 2011 In final form 30 April 2011 Available online 6 May 2011
a b s t r a c t The effects of a-, b-, and c-cyclodextrins (ACD, BCD, and GCD) on the low-frequency vibrational spectrum of water present around them and those confined inside their cavities have been investigated from molecular dynamics simulations. Attempts have been made to understand the effects of variation of the number of glucose rings and the ability of these macromolecules to form hydrogen bonds with water on the distribution of the vibrational density of states of water. It is observed that these bands for water in and around the cyclodextrins suffer blue shifts, the extent of the shifts are sensitive to the degree of confinement within the cavities and their hydrogen bonding status. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Cyclodextrins (CDs) are naturally occurring cyclic oligosaccharides containing glucose rings connected by a(1–4) glycosidic links [1]. Generally, they contain 6–8 glucose rings, and are denoted as a-, b-, and c-CD respectively. These macrocyclic molecules contain hydrophobic cavities surrounded by hydrophilic exteriors composed of hydroxyl (OH) groups [1,2]. Because of such unique features, the CDs can form inclusion complexes with suitable guest species and solubilize them in aqueous media [3–5]. As a result, CDs are widely used in pharmaceutical industries as drug delivery agents [6]. Considering the importance of the CD molecules, their characteristics in aqueous media have been the subjects of interest for many years. Different experimental, theoretical and simulation approaches have been used to explore different aspects of the problem. Time-resolved fluorescence spectroscopy has been widely used to study the dynamics of solvation and reactions occurring inside the cavities of the CDs [7–10]. Exchange of water and hydration properties of pure and substituted forms of CDs have also been studied using dielectric relaxation measurements [11]. The structural fluctuations of different CD molecules are studied recently using NMR technique [12]. From calorimetric measurements, Holm and co-workers [13] recently investigated the effect of substitution of the CDs on their ability to form inclusion complexes. In an important theoretical work, Nandi and Bagchi [14] used molecular hydrodynamics theory to study the solvation dynamics of coumarin in cyclodextrin cavities. It is shown recently from molecular dynamics (MD) simulations that the CD molecules exhibit high degree of conformational fluctuations in aqueous solutions with long residence times of water inside their cavities [15].
⇑ Corresponding author. Fax: +91 3222 255303. E-mail address: [email protected] (S. Bandyopadhyay). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.04.103
Laria and co-workers [16] from their simulation studies showed that preferential solvation of coumarin 153 by a particular glucose unit of the b-CD (BCD) molecule is responsible for its restricted orientation in the cavity. Recently, we have performed MD simulations to explore the effects of substitution of the OH groups of the BCD molecule on the properties of water in and around them [17–19]. In general, it is noticed that substitution of the OH groups increases the effect of confinement within the cavities of these molecules. In a recent work, we reported the ordering and restricted dynamics of water present in the first hydration layers and confined in the cavities of ACD, BCD, and GCD molecules [20]. In this Letter, we have studied the effect of the CD molecules on the low-frequency vibrational spectrum of water present around them in the first hydration layers and inside the cavities. As defined earlier [17], the water molecules that are present within a shell of thickness 4 Å surrounding the CDs are considered as first hydration layer water. The cavity water molecules are identified following the approach used in our earlier work [19]. According to this approach, the vectors connecting pairs of non-hydrogen atoms of the CDs are first constructed. These vectors are then divided into fine grids with 0.1 Å width. After avoiding possible over-counting the water molecules that are found within spheres of radius 0.5 Å around the grid points are considered as cavity water. The calculations are carried out by the Fourier transformation of the velocity autocorrelation function (VACF) of the water molecules. VACF is defined as
C V ðtÞ ¼
h~ v i ðtÞ ~ v i ð0Þi ~ hv i ð0Þ ~ v i ð0Þi
ð1Þ
where ~ v i ðtÞ is the velocity vector of the atom i (O or H) of a water molecule at time t. The angular brackets denote averaging overall atoms of a particular type present either in the first hydration layers or in the cavities of the CDs over different reference initial times.
M. Jana, S. Bandyopadhyay / Chemical Physics Letters 509 (2011) 181–185
a 0.9
Bulk
3. Results and discussion We have calculated the velocity autocorrelation functions (VACF) for water present in close proximity to the three CD molecules. Specifically, the calculations are carried out by separating the proximal water molecules into two types, one involving the water molecules present in the first hydration layers and the other involving only those that are present inside the cavities of the CDs. The criteria used to identify hydration layer and cavity water molecules are already mentioned before. The calculations are carried out for the oxygen ðC OV ðtÞÞ and the hydrogen ðC HV ðtÞÞ atoms of the tagged water molecules, which are displayed in Figure 1. The
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Three different simulations of ACD, BCD, and GCD molecules in aqueous solutions were carried out. The initial coordinates of the CD molecules were taken from the literature [21–23]. After adding hydrogen atoms the molecules were immersed in three separate cubic cells each with edge length of 45 Å containing well-equilibrated water. To avoid unfavorable contacts, water molecules that were found within 2 Å from the CDs were removed. Finally, the three systems contained 2969, 2903, and 2884 water molecules for the ACD, BCD, and GCD molecules respectively. The systems were first equilibrated for about 500 ps under the conditions of constant temperature (T = 300 K) and pressure ðP ext ¼ 0 atmÞ ensemble (NPT). The volumes of the cells were allowed to fluctuate isotropically during this period. At the end of the NPT runs the systems attained steady edge lengths of 44.8 Å, 44.5 Å, and 44.4 Å for the ACD, BCD and GCD molecules respectively. At this point the dimensions of the cells were fixed and the conditions were changed to that of constant temperature (300 K) and volume ensemble (NVT). The equilibration runs were continued under NVT conditions for another 1 ns duration, which were then followed by NVT production runs of 8.5 ns duration for each of the three systems. The simulations were performed using the Nosé–Hoover chain thermostat extended system method [24], as incorporated in the PINY-MD code [25]. The reversible multiple time step algorithm, RESPA [24] was used with a relatively larger MD time step of 4 fs. This was achieved using a three-stage force decomposition into intramolecular forces (torsion/bend-bond), short-range intermolecular forces, and long-range intermolecular forces. Electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method [26]. The minimum image convention [27] was employed to calculate the short-range Lennard-Jones interactions and the real-space part of the Ewald sum, with a spherical truncation of 7 Å and 10 Å for the short- and the long-range parts of the force decomposition respectively. For analysis, the trajectories were stored with a time resolution of 16 fs. As reported in our earlier studies [17,19], the potential parameters for the CD molecules were taken from the GROMOS force field [28], while the rigid three-site extended simple point charge (SPC/E) model [29] was employed for water. The parameters used for the CDs are known to reproduce fairly accurately the experimental structural properties of this class of molecules [30] and their solvation behavior [16].
GCD
0.6
C V(t)
2. System setup and simulation methods
ACD BCD
O
We have explored the effects of variation of the cavity dimension of the CDs and their ability to form hydrogen bonds with water on the vibrational density of states of water. The rest of the Letter is organized as follows. The protocol followed to set up the systems and the simulation methods employed are described in Section 2. In Section 3 we present the results obtained from our study, which is followed by the conclusions section (Section 4).
C V(t)
182
0
−0.3
−0.6 0
30
60
t (fs) Figure 1. (a) Velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding function C HV ðtÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
corresponding functions for pure bulk water as obtained from a separate MD simulation of SPC/E water under identical conditions are included in the figure for comparison. In general, the function C OV ðtÞ as evident from Figure 1a exhibits an initial small bump followed by a larger dip. Such behavior is known as the caging effect, which arises due to back-scattering of the water oxygen atoms as they collide with neighboring molecules forming cages around them. A closer examination of the results reveal that the relaxations of C OV ðtÞ for hydration layer and cavity water molecules are significantly different than that for pure bulk water. Presence of deeper minima indicate rigid nature of these water molecules due to constrained environments in and around the CDs. The effect is more prominent for water present in the cavities. This is due to increased confinement of water within the cavity volume with a consequent enhanced back-scattering. Due to identical environment the effect is almost similar for water around the CDs in the first hydration layers. However, differential degree of confinement of water within the cavities is reflected in the relaxation of the corresponding decay curves. It is found that the relaxation of the function C OV ðtÞ for cavity water is sensitive to the available volume inside the cavity. The estimated average cavity volumes for the ACD, BCD, and GCD molecules as obtained from our simulations are 163 Å3, 253 Å3, and 413 Å3 respectively. These values agree quite well with experimental data [4]. Therefore, an increase in confinement due to decrease in cavity volume is clearly evident from increasingly deeper minimum of C OV ðtÞ for the cavity water
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of the ACD molecule. Such behavior is consistent with the relative restricted motions of water in and around these macromolecules, as observed recently [20]. Interestingly, the VACFs for the water hydrogen atoms (C HV ðtÞ) as shown in Figure 1b exhibit almost similar relaxation patterns as that observed for pure bulk water. It is clear from the figure that the librational motions of water in close proximity to the CDs are either unaffected (in the hydration layers) or marginally affected (in the cavities). We will discuss this further later. We showed recently that the CDs can form strong hydrogen bonds with water [20]. It would be interesting to explore whether the formation of such cyclodextrin–water (CW) hydrogen bonds has any influence on the relaxation of the VACFs of those bound water molecules. For that we have re-calculated the functions C OV ðtÞ and C HV ðtÞ including only those water molecules that are involved in CW hydrogen bonds. We have used the same geometric conditions as described in our earlier work to define hydrogen bonds [19]. The results are displayed in Figure 2 along with that for pure bulk water. It can be seen that the function C OV ðtÞ exhibits deeper minima when only the water molecules involved in CW hydrogen bonds are considered as against that described in Figure 1a, where all the first hydration layer and cavity water molecules were included. This is particularly true for the first hydration layer, which reflects relatively stronger caging effects for the water
molecules that are bound to the glucose rings of the CDs by hydrogen bonds. Once again, while the effect of hydrogen bonds is found to be identical for the first hydration layer water, but for water in the cavities it is sensitive to the available cavity volumes. It is evident from the relaxations of C HV ðtÞ as shown in Figure 2b that formation of CW hydrogen bonds does not have any detectable influence on the librational motions of water present in the hydration layers. However, compared to Figure 1b some small but noticeable differences can be seen for the cavity water molecules that are hydrogen bonded to the CDs. Presence of deeper minima and increased oscillatory nature of the curves indicate that the water librations are affected for the cavity water molecules on formation of CW hydrogen bonds. How the experimentally observed low-frequency vibrational modes of water are affected by the CD molecules are discussed next. The low-frequency vibrational spectrum of water is characterized by two broad bands at 50 cm1 and 200 cm1 respectively [31–33]. The band around 50 cm1 is generally assigned to the O O O bending mode involving triplets of hydrogen-bonded water molecules, and the band around 200 cm1 to the longitudinal O O stretching mode between hydrogen-bonded pairs of water molecules. It is known that strong interactions between the CDs and water modify the hydrogen bonding arrangement in and around these macromolecules [19]. This in turn is likely to influence the low-frequency vibrational bands of the water molecules that are present in the first hydration layers of the CDs or
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ACD
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SO(ω) x 10 (cm)
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t (fs) Figure 2. (a) Velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are hydrogen bonded with the glucose rings and present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding function C HV ðtÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
0
0
200
400
600
800
1000
−1
ω (cm ) Figure 3. (a) Power spectra SO ðxÞ obtained by the Fourier transformation of the velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding power spectra SH ðxÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
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confined within their cavities. To explore that, we have calculated the power spectra for the oxygen ðSO ðxÞÞ and hydrogen ðSH ðxÞÞ atoms of these water molecules by the Fourier cosine transformation of the corresponding VACFs. The results are displayed and compared with bulk water data in Figure 3. It is evident from Figure 3a that the 50 cm1 band corresponding to the O O O bending mode is shifted to higher frequency (blue shifts) for water in and around the CDs. The effect is more noticeable for water in the cavities. It is found that this band is blue-shifted by 10 cm1 for the first hydration layer water, whereas for the cavity water molecules it is shifted by 20—70 cm1 . This agrees with the results shown in Figure 1a and is consistent with the degree of confinement in and around the CDs. Highly restricted transverse oscillations of cavity water molecules due to geometrical constraints result in larger blue shifts of this band. Once again, due to identical environments the position of this band is affected similarly for the first hydration layer water of the three CDs. However, systematic increase in confinement within the cavities with decrease in cavity dimensions from GCD to ACD can be easily seen from gradual increase in blue shifts of the band for the corresponding cavity water molecules. Similar effect of nanoscale confinement of water on its low-frequency band has also been demonstrated from simulations of water encapsulated in graphite pores [34]. Interestingly, compared to the bending mode, the band corresponding to the O O longitudinal oscillations or stretching of water ð 200 cm1 Þ is found to be mostly insensitive to the pres-
a
16
ACD BCD GCD Bulk
−3
SO(ω) x 10 (cm)
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b SH(ω) x 10 (cm)
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ence of the CDs. This is an important observation, which along with our earlier studies on BCD derivatives [18] unequivocally confirm nonuniform influence of these macromolecules on the transverse and longitudinal degrees of freedom of water in and around them. To the best of our knowledge, the present work demonstrates for the first time such size-dependent nonuniform influence of CD molecules on water. The librational motions of water can be characterized from its hydrogen atom power spectrum band ðSH ðxÞÞ which for pure bulk water peaks around 500 cm1 [32]. The calculated results for water in and around the three CDs are shown in Figure 3b. Non-existence of any shift in SH ðxÞ band position for the first hydration layer water reveals that the librational motions of water in close proximity to the CDs surrounding them are unaffected. However, hindered librational motions of the cavity water molecules are reflected in increased intensities of the band and shifts in the peak position to higher frequencies by about 30—80 cm1 . The effect of confinement on hindered librational motions of water inside the cavities is found to be sensitive to the available cavity volume. Now we consider only those hydration layer and cavity water molecules that are involved in forming CW hydrogen bonds with the glucose rings of the CDs and compare their power spectra SO ðxÞ and SH ðxÞ. This will allow us to demonstrate the effect of forming CW hydrogen bonds on water power spectra. The results are shown in Figure 4 along with that for pure bulk water. It can be seen that compared to Figure 3a, the blue shifts in the peak position of the O O O bending mode are higher ð 20 cm1 Þ for those hydration layer water that are bound to the CDs by hydrogen bonds. This confirms further the relatively stronger caging effects for such bound water molecules. Due to increased geometrical constraints this band position is further shifted for the cavity water molecules involved in forming CW hydrogen bonds. Once again, variation of the size of the cavities of the CDs has a noticeable influence on this band as evident from the nonuniform shifts in the peak position. It is further found that though the O O stretching band position of water around 200 cm1 is not affected, but compared to Figure 3a a small but noticeable increase in intensity of the band can be seen for the bound water molecules. This shows increasingly restricted longitudinal oscillations of water molecules that are bound to the CDs by hydrogen bonds. Comparing Figure 4b with that described in Figure 3b, it is clear that formation of CW hydrogen bonds does not affect the librational motion of hydration layer water molecules. However, a small but noticeable increase in intensity of the peak can be seen for the cavity water molecules that are involved in CW hydrogen bonds. This is consistent with the results shown in Figure 2b and shows that geometrical constraints of the cavities lead to increased hindered librations of water on formation of CW hydrogen bonds. The effect of cavity dimension on water librations is also clear from the data. Recently, terahertz (THz) spectroscopy has been used to directly estimate the retarded dynamics of water around carbohydrates [35,36]. It may be noted that THz measurements provide the power spectra corresponding to the dipole moment autocorrelation function. However, the shifts in the spectral densities may be similar to that observed in the present study. Therefore, we believe that such experiments in combination with MD simulations can provide direct understanding of the effect of confinement on water in and around the CD molecules.
−1
ω (cm ) Figure 4. (a) Power spectra SO ðxÞ obtained by the Fourier transformation of the velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are hydrogen bonded with the glucose rings and present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding power spectra SH ðxÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
4. Conclusions Atomistic MD simulations of aqueous solutions of a-, b-, and ccyclodextrins (ACD, BCD, and GCD) were carried out to study the effect of these macrocyclic molecules on the low-frequency vibrational density of states of water molecules that are present either
M. Jana, S. Bandyopadhyay / Chemical Physics Letters 509 (2011) 181–185
in the first hydration layers or confined in the cavities. The effects of variation of the number of glucose rings of the CDs and their ability to form CW hydrogen bonds on the low-frequency modes of water have been explored. The calculations revealed that the extent of blue shifts of the O O O bending mode of water molecules depend on whether they are present in the first hydration layers or inside the cavities of the CDs. In general, this particular mode is found to suffer larger blue shifts for water in the cavities due to their restricted transverse oscillations within the confined environment. Besides, the position of the band for the cavity water is also found to depend on the dimension of the cavities. Maximum blue shift is noticed for water confined in the cavity of ACD, as among the three CDs it has the smallest cavity size. It is noticed that formation of CW hydrogen bonds further restricts the local motions of water resulting in increased blue shifts for such bound water molecules. Importantly, it is demonstrated for the first time that the position of the O O stretching mode due to longitudinal oscillations of water is insensitive to the presence of the CDs and their cavity dimensions. This clearly shows differential influence of these class of macromolecules on the transverse and longitudinal degrees of freedom of water in and around them. It is further noticed that the confined environment within the cavities hinders the librational motion of water present in them, the degree of influence being dependent on the cavity dimension. It may be noted that here we presented studies on CD molecules containing up to eight glucose rings. It will be interesting to extend the work by including CDs that contain larger number of glucose rings and are more flexible than those studied in this work. At present, we are exploring this aspect in our laboratory. Acknowledgments 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] W. Saenger, in: J.L. Atwood, J.E. Davies, D.D. MacNicol (Eds.), Inclusion Compounds, vol. 2, Academic, New York, 1984. p. 231.
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Vibrational spectrum of water confined in and around cyclodextrins Madhurima Jana, Sanjoy Bandyopadhyay ⇑ Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India
a r t i c l e
i n f o
Article history: Received 7 March 2011 In final form 30 April 2011 Available online 6 May 2011
a b s t r a c t The effects of a-, b-, and c-cyclodextrins (ACD, BCD, and GCD) on the low-frequency vibrational spectrum of water present around them and those confined inside their cavities have been investigated from molecular dynamics simulations. Attempts have been made to understand the effects of variation of the number of glucose rings and the ability of these macromolecules to form hydrogen bonds with water on the distribution of the vibrational density of states of water. It is observed that these bands for water in and around the cyclodextrins suffer blue shifts, the extent of the shifts are sensitive to the degree of confinement within the cavities and their hydrogen bonding status. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Cyclodextrins (CDs) are naturally occurring cyclic oligosaccharides containing glucose rings connected by a(1–4) glycosidic links [1]. Generally, they contain 6–8 glucose rings, and are denoted as a-, b-, and c-CD respectively. These macrocyclic molecules contain hydrophobic cavities surrounded by hydrophilic exteriors composed of hydroxyl (OH) groups [1,2]. Because of such unique features, the CDs can form inclusion complexes with suitable guest species and solubilize them in aqueous media [3–5]. As a result, CDs are widely used in pharmaceutical industries as drug delivery agents [6]. Considering the importance of the CD molecules, their characteristics in aqueous media have been the subjects of interest for many years. Different experimental, theoretical and simulation approaches have been used to explore different aspects of the problem. Time-resolved fluorescence spectroscopy has been widely used to study the dynamics of solvation and reactions occurring inside the cavities of the CDs [7–10]. Exchange of water and hydration properties of pure and substituted forms of CDs have also been studied using dielectric relaxation measurements [11]. The structural fluctuations of different CD molecules are studied recently using NMR technique [12]. From calorimetric measurements, Holm and co-workers [13] recently investigated the effect of substitution of the CDs on their ability to form inclusion complexes. In an important theoretical work, Nandi and Bagchi [14] used molecular hydrodynamics theory to study the solvation dynamics of coumarin in cyclodextrin cavities. It is shown recently from molecular dynamics (MD) simulations that the CD molecules exhibit high degree of conformational fluctuations in aqueous solutions with long residence times of water inside their cavities [15].
⇑ Corresponding author. Fax: +91 3222 255303. E-mail address: [email protected] (S. Bandyopadhyay). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.04.103
Laria and co-workers [16] from their simulation studies showed that preferential solvation of coumarin 153 by a particular glucose unit of the b-CD (BCD) molecule is responsible for its restricted orientation in the cavity. Recently, we have performed MD simulations to explore the effects of substitution of the OH groups of the BCD molecule on the properties of water in and around them [17–19]. In general, it is noticed that substitution of the OH groups increases the effect of confinement within the cavities of these molecules. In a recent work, we reported the ordering and restricted dynamics of water present in the first hydration layers and confined in the cavities of ACD, BCD, and GCD molecules [20]. In this Letter, we have studied the effect of the CD molecules on the low-frequency vibrational spectrum of water present around them in the first hydration layers and inside the cavities. As defined earlier [17], the water molecules that are present within a shell of thickness 4 Å surrounding the CDs are considered as first hydration layer water. The cavity water molecules are identified following the approach used in our earlier work [19]. According to this approach, the vectors connecting pairs of non-hydrogen atoms of the CDs are first constructed. These vectors are then divided into fine grids with 0.1 Å width. After avoiding possible over-counting the water molecules that are found within spheres of radius 0.5 Å around the grid points are considered as cavity water. The calculations are carried out by the Fourier transformation of the velocity autocorrelation function (VACF) of the water molecules. VACF is defined as
C V ðtÞ ¼
h~ v i ðtÞ ~ v i ð0Þi ~ hv i ð0Þ ~ v i ð0Þi
ð1Þ
where ~ v i ðtÞ is the velocity vector of the atom i (O or H) of a water molecule at time t. The angular brackets denote averaging overall atoms of a particular type present either in the first hydration layers or in the cavities of the CDs over different reference initial times.
M. Jana, S. Bandyopadhyay / Chemical Physics Letters 509 (2011) 181–185
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3. Results and discussion We have calculated the velocity autocorrelation functions (VACF) for water present in close proximity to the three CD molecules. Specifically, the calculations are carried out by separating the proximal water molecules into two types, one involving the water molecules present in the first hydration layers and the other involving only those that are present inside the cavities of the CDs. The criteria used to identify hydration layer and cavity water molecules are already mentioned before. The calculations are carried out for the oxygen ðC OV ðtÞÞ and the hydrogen ðC HV ðtÞÞ atoms of the tagged water molecules, which are displayed in Figure 1. The
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Three different simulations of ACD, BCD, and GCD molecules in aqueous solutions were carried out. The initial coordinates of the CD molecules were taken from the literature [21–23]. After adding hydrogen atoms the molecules were immersed in three separate cubic cells each with edge length of 45 Å containing well-equilibrated water. To avoid unfavorable contacts, water molecules that were found within 2 Å from the CDs were removed. Finally, the three systems contained 2969, 2903, and 2884 water molecules for the ACD, BCD, and GCD molecules respectively. The systems were first equilibrated for about 500 ps under the conditions of constant temperature (T = 300 K) and pressure ðP ext ¼ 0 atmÞ ensemble (NPT). The volumes of the cells were allowed to fluctuate isotropically during this period. At the end of the NPT runs the systems attained steady edge lengths of 44.8 Å, 44.5 Å, and 44.4 Å for the ACD, BCD and GCD molecules respectively. At this point the dimensions of the cells were fixed and the conditions were changed to that of constant temperature (300 K) and volume ensemble (NVT). The equilibration runs were continued under NVT conditions for another 1 ns duration, which were then followed by NVT production runs of 8.5 ns duration for each of the three systems. The simulations were performed using the Nosé–Hoover chain thermostat extended system method [24], as incorporated in the PINY-MD code [25]. The reversible multiple time step algorithm, RESPA [24] was used with a relatively larger MD time step of 4 fs. This was achieved using a three-stage force decomposition into intramolecular forces (torsion/bend-bond), short-range intermolecular forces, and long-range intermolecular forces. Electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method [26]. The minimum image convention [27] was employed to calculate the short-range Lennard-Jones interactions and the real-space part of the Ewald sum, with a spherical truncation of 7 Å and 10 Å for the short- and the long-range parts of the force decomposition respectively. For analysis, the trajectories were stored with a time resolution of 16 fs. As reported in our earlier studies [17,19], the potential parameters for the CD molecules were taken from the GROMOS force field [28], while the rigid three-site extended simple point charge (SPC/E) model [29] was employed for water. The parameters used for the CDs are known to reproduce fairly accurately the experimental structural properties of this class of molecules [30] and their solvation behavior [16].
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2. System setup and simulation methods
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We have explored the effects of variation of the cavity dimension of the CDs and their ability to form hydrogen bonds with water on the vibrational density of states of water. The rest of the Letter is organized as follows. The protocol followed to set up the systems and the simulation methods employed are described in Section 2. In Section 3 we present the results obtained from our study, which is followed by the conclusions section (Section 4).
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t (fs) Figure 1. (a) Velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding function C HV ðtÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
corresponding functions for pure bulk water as obtained from a separate MD simulation of SPC/E water under identical conditions are included in the figure for comparison. In general, the function C OV ðtÞ as evident from Figure 1a exhibits an initial small bump followed by a larger dip. Such behavior is known as the caging effect, which arises due to back-scattering of the water oxygen atoms as they collide with neighboring molecules forming cages around them. A closer examination of the results reveal that the relaxations of C OV ðtÞ for hydration layer and cavity water molecules are significantly different than that for pure bulk water. Presence of deeper minima indicate rigid nature of these water molecules due to constrained environments in and around the CDs. The effect is more prominent for water present in the cavities. This is due to increased confinement of water within the cavity volume with a consequent enhanced back-scattering. Due to identical environment the effect is almost similar for water around the CDs in the first hydration layers. However, differential degree of confinement of water within the cavities is reflected in the relaxation of the corresponding decay curves. It is found that the relaxation of the function C OV ðtÞ for cavity water is sensitive to the available volume inside the cavity. The estimated average cavity volumes for the ACD, BCD, and GCD molecules as obtained from our simulations are 163 Å3, 253 Å3, and 413 Å3 respectively. These values agree quite well with experimental data [4]. Therefore, an increase in confinement due to decrease in cavity volume is clearly evident from increasingly deeper minimum of C OV ðtÞ for the cavity water
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of the ACD molecule. Such behavior is consistent with the relative restricted motions of water in and around these macromolecules, as observed recently [20]. Interestingly, the VACFs for the water hydrogen atoms (C HV ðtÞ) as shown in Figure 1b exhibit almost similar relaxation patterns as that observed for pure bulk water. It is clear from the figure that the librational motions of water in close proximity to the CDs are either unaffected (in the hydration layers) or marginally affected (in the cavities). We will discuss this further later. We showed recently that the CDs can form strong hydrogen bonds with water [20]. It would be interesting to explore whether the formation of such cyclodextrin–water (CW) hydrogen bonds has any influence on the relaxation of the VACFs of those bound water molecules. For that we have re-calculated the functions C OV ðtÞ and C HV ðtÞ including only those water molecules that are involved in CW hydrogen bonds. We have used the same geometric conditions as described in our earlier work to define hydrogen bonds [19]. The results are displayed in Figure 2 along with that for pure bulk water. It can be seen that the function C OV ðtÞ exhibits deeper minima when only the water molecules involved in CW hydrogen bonds are considered as against that described in Figure 1a, where all the first hydration layer and cavity water molecules were included. This is particularly true for the first hydration layer, which reflects relatively stronger caging effects for the water
molecules that are bound to the glucose rings of the CDs by hydrogen bonds. Once again, while the effect of hydrogen bonds is found to be identical for the first hydration layer water, but for water in the cavities it is sensitive to the available cavity volumes. It is evident from the relaxations of C HV ðtÞ as shown in Figure 2b that formation of CW hydrogen bonds does not have any detectable influence on the librational motions of water present in the hydration layers. However, compared to Figure 1b some small but noticeable differences can be seen for the cavity water molecules that are hydrogen bonded to the CDs. Presence of deeper minima and increased oscillatory nature of the curves indicate that the water librations are affected for the cavity water molecules on formation of CW hydrogen bonds. How the experimentally observed low-frequency vibrational modes of water are affected by the CD molecules are discussed next. The low-frequency vibrational spectrum of water is characterized by two broad bands at 50 cm1 and 200 cm1 respectively [31–33]. The band around 50 cm1 is generally assigned to the O O O bending mode involving triplets of hydrogen-bonded water molecules, and the band around 200 cm1 to the longitudinal O O stretching mode between hydrogen-bonded pairs of water molecules. It is known that strong interactions between the CDs and water modify the hydrogen bonding arrangement in and around these macromolecules [19]. This in turn is likely to influence the low-frequency vibrational bands of the water molecules that are present in the first hydration layers of the CDs or
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t (fs) Figure 2. (a) Velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are hydrogen bonded with the glucose rings and present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding function C HV ðtÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
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ω (cm ) Figure 3. (a) Power spectra SO ðxÞ obtained by the Fourier transformation of the velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding power spectra SH ðxÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
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confined within their cavities. To explore that, we have calculated the power spectra for the oxygen ðSO ðxÞÞ and hydrogen ðSH ðxÞÞ atoms of these water molecules by the Fourier cosine transformation of the corresponding VACFs. The results are displayed and compared with bulk water data in Figure 3. It is evident from Figure 3a that the 50 cm1 band corresponding to the O O O bending mode is shifted to higher frequency (blue shifts) for water in and around the CDs. The effect is more noticeable for water in the cavities. It is found that this band is blue-shifted by 10 cm1 for the first hydration layer water, whereas for the cavity water molecules it is shifted by 20—70 cm1 . This agrees with the results shown in Figure 1a and is consistent with the degree of confinement in and around the CDs. Highly restricted transverse oscillations of cavity water molecules due to geometrical constraints result in larger blue shifts of this band. Once again, due to identical environments the position of this band is affected similarly for the first hydration layer water of the three CDs. However, systematic increase in confinement within the cavities with decrease in cavity dimensions from GCD to ACD can be easily seen from gradual increase in blue shifts of the band for the corresponding cavity water molecules. Similar effect of nanoscale confinement of water on its low-frequency band has also been demonstrated from simulations of water encapsulated in graphite pores [34]. Interestingly, compared to the bending mode, the band corresponding to the O O longitudinal oscillations or stretching of water ð 200 cm1 Þ is found to be mostly insensitive to the pres-
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ence of the CDs. This is an important observation, which along with our earlier studies on BCD derivatives [18] unequivocally confirm nonuniform influence of these macromolecules on the transverse and longitudinal degrees of freedom of water in and around them. To the best of our knowledge, the present work demonstrates for the first time such size-dependent nonuniform influence of CD molecules on water. The librational motions of water can be characterized from its hydrogen atom power spectrum band ðSH ðxÞÞ which for pure bulk water peaks around 500 cm1 [32]. The calculated results for water in and around the three CDs are shown in Figure 3b. Non-existence of any shift in SH ðxÞ band position for the first hydration layer water reveals that the librational motions of water in close proximity to the CDs surrounding them are unaffected. However, hindered librational motions of the cavity water molecules are reflected in increased intensities of the band and shifts in the peak position to higher frequencies by about 30—80 cm1 . The effect of confinement on hindered librational motions of water inside the cavities is found to be sensitive to the available cavity volume. Now we consider only those hydration layer and cavity water molecules that are involved in forming CW hydrogen bonds with the glucose rings of the CDs and compare their power spectra SO ðxÞ and SH ðxÞ. This will allow us to demonstrate the effect of forming CW hydrogen bonds on water power spectra. The results are shown in Figure 4 along with that for pure bulk water. It can be seen that compared to Figure 3a, the blue shifts in the peak position of the O O O bending mode are higher ð 20 cm1 Þ for those hydration layer water that are bound to the CDs by hydrogen bonds. This confirms further the relatively stronger caging effects for such bound water molecules. Due to increased geometrical constraints this band position is further shifted for the cavity water molecules involved in forming CW hydrogen bonds. Once again, variation of the size of the cavities of the CDs has a noticeable influence on this band as evident from the nonuniform shifts in the peak position. It is further found that though the O O stretching band position of water around 200 cm1 is not affected, but compared to Figure 3a a small but noticeable increase in intensity of the band can be seen for the bound water molecules. This shows increasingly restricted longitudinal oscillations of water molecules that are bound to the CDs by hydrogen bonds. Comparing Figure 4b with that described in Figure 3b, it is clear that formation of CW hydrogen bonds does not affect the librational motion of hydration layer water molecules. However, a small but noticeable increase in intensity of the peak can be seen for the cavity water molecules that are involved in CW hydrogen bonds. This is consistent with the results shown in Figure 2b and shows that geometrical constraints of the cavities lead to increased hindered librations of water on formation of CW hydrogen bonds. The effect of cavity dimension on water librations is also clear from the data. Recently, terahertz (THz) spectroscopy has been used to directly estimate the retarded dynamics of water around carbohydrates [35,36]. It may be noted that THz measurements provide the power spectra corresponding to the dipole moment autocorrelation function. However, the shifts in the spectral densities may be similar to that observed in the present study. Therefore, we believe that such experiments in combination with MD simulations can provide direct understanding of the effect of confinement on water in and around the CD molecules.
−1
ω (cm ) Figure 4. (a) Power spectra SO ðxÞ obtained by the Fourier transformation of the velocity autocorrelation function C OV ðtÞ for the oxygen atoms of the water molecules that are hydrogen bonded with the glucose rings and present either in the first hydration layers (solid lines) or in the cavities (dashed lines) of the CD molecules. The corresponding power spectra SH ðxÞ for the hydrogen atoms of these water molecules are shown in b. The results for pure bulk water are included for comparison.
4. Conclusions Atomistic MD simulations of aqueous solutions of a-, b-, and ccyclodextrins (ACD, BCD, and GCD) were carried out to study the effect of these macrocyclic molecules on the low-frequency vibrational density of states of water molecules that are present either
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in the first hydration layers or confined in the cavities. The effects of variation of the number of glucose rings of the CDs and their ability to form CW hydrogen bonds on the low-frequency modes of water have been explored. The calculations revealed that the extent of blue shifts of the O O O bending mode of water molecules depend on whether they are present in the first hydration layers or inside the cavities of the CDs. In general, this particular mode is found to suffer larger blue shifts for water in the cavities due to their restricted transverse oscillations within the confined environment. Besides, the position of the band for the cavity water is also found to depend on the dimension of the cavities. Maximum blue shift is noticed for water confined in the cavity of ACD, as among the three CDs it has the smallest cavity size. It is noticed that formation of CW hydrogen bonds further restricts the local motions of water resulting in increased blue shifts for such bound water molecules. Importantly, it is demonstrated for the first time that the position of the O O stretching mode due to longitudinal oscillations of water is insensitive to the presence of the CDs and their cavity dimensions. This clearly shows differential influence of these class of macromolecules on the transverse and longitudinal degrees of freedom of water in and around them. It is further noticed that the confined environment within the cavities hinders the librational motion of water present in them, the degree of influence being dependent on the cavity dimension. It may be noted that here we presented studies on CD molecules containing up to eight glucose rings. It will be interesting to extend the work by including CDs that contain larger number of glucose rings and are more flexible than those studied in this work. At present, we are exploring this aspect in our laboratory. Acknowledgments 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] W. Saenger, in: J.L. Atwood, J.E. Davies, D.D. MacNicol (Eds.), Inclusion Compounds, vol. 2, Academic, New York, 1984. p. 231.
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