Microscopic Investigation of the Hydration Properties of Cyclodextrin

Sep 9, 2009 - Low-Frequency Vibrational Spectrum of Water around Cyclodextrin and Its Methyl-Substituted Derivatives. Madhurima Jana and Sanjoy ...
3 downloads 0 Views 892KB Size
Download PDF
pubs.acs.org/Langmuir © 2009 American Chemical Society

Microscopic Investigation of the Hydration Properties of Cyclodextrin and Its Substituted Forms Madhurima Jana and Sanjoy Bandyopadhyay* Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur - 721302, India Received June 4, 2009. Revised Manuscript Received August 13, 2009 Substitution of the hydroxyl (OH) groups of cyclodextrins (CDs) by methoxy (OCH3) groups is likely to influence the microscopic properties of water inside the cavities of these molecules and in the surrounding hydration layers. We have performed atomistic molecular dynamics (MD) simulations of aqueous solutions of β-cyclodextrin (BCD) and its two methyl-substituted forms, dimethyl β-cyclodextrin (DIMEB) and trimethyl β-cyclodextrin (TRIMEB). The calculations reveal that the translational and rotational motions of water present either in the hydration layers or in the cavities of these macrocyclic molecules are slower than that of pure bulk water. Interestingly, it is noticed that the effect of confinement inside the cavity increases with substitution of the OH groups of the BCD molecule. Most importantly, it is revealed that the time scale of relaxation of the CD-water (CW) and water-water (WW) hydrogen bonds are correlated with the microscopic dynamics of water and their degree of confinement within the cavities of these molecules.

1. Introduction Cyclodextrins (CDs) are nonreducing water-soluble cyclic oligosaccharides produced from starch by means of enzymatic conversion. They are composed of five or more D-glucopyranose units connected by R(1-4) glycosidic linkages. However, the fivemembered macrocycle does not exist naturally. Typical CDs consist of six, seven, or eight glucose monomers, and are denoted as R-, β-, and γ-CD, respectively.1-3 The CD molecules can be topologically represented as toroids with a larger and a smaller openings. The molecular structure of β-cyclodextrin (BCD) containing seven glucopyranose rings and its toroidal representation are shown in Figure 1. The wider sides of the CD molecules are formed by the secondary hydroxyl groups, while the narrower sides are formed by the primary hydroxyl groups.1 The presence of these hydroxyl groups on the outer rims makes the CD molecules water-soluble. The cavity, on the other hand, is formed by the hydrogens attached to the ring carbon atoms and the etherlike oxygen atoms. Such geometry results in a hydrophilic exterior around a hydrophobic cavity.4 Thus, the cavities of the CD molecules offer a classic example of ‘microheterogeneous environment’ with a hydrophobic matrix surrounded by a hydrophilic exterior.5 Because of the unique structure of the cavity, the CD molecules can efficiently form inclusion complexes with a wide variety of guest molecules.1,6-10 The inclusion phenomena of CDs, mostly of the β-form, generally take place in aqueous medium. As a result, these molecules have been used not only in basic research, *To whom correspondence should be addressed. E-mail: sanjoy@chem. iitkgp.ernet.in. (1) Saenger, W. In Inclusion Compounds; Atwood, J. L., Davies, J. E, MacNicol, D. D., Eds.; Academic Press: New York, 1984; Vol. 2, p 231. (2) Luzhkov, V.; Aqvist, J. Chem. Phys. Lett. 1999, 302, 267. (3) D’souza, V. T.; Lipkowitz, K. B. Chem. Rev. 1998, 98, 1741. (4) Winkler, R. G.; Fioravanti, S.; Ciccotti, G.; Margheritis, C.; Villa, M. J. Computer-Aided Mol. Des. 2000, 14, 659. (5) Cramer, F. Einschluverssbindungen; Springer: Heidelberg, 1954. (6) Connors, K. A. Chem. Rev. 1997, 97, 1325. (7) Szejtli, J. Comprehensive Supramolecular Chemistry; Szejtli, J.; Osa, T., Eds.; Pergamon: Oxford, U.K., 1996; Vol. 3, Chapter 5. (8) Szejtli, J. Chem. Rev. 1998, 98, 1743. (9) Saenger, W. Angew. Chem, Int. Ed. 1980, 19, 344. (10) Yu, Y.; Chipot, C.; Cai, W.; Shao, X. J. Phys. Chem. B 2006, 110, 6372.

13084 DOI: 10.1021/la902003y

but also in different applications in pharmaceutical and food industries. The most remarkable application of CD molecules is in drug delivery.11 The structural aspects of CDs or their complexes with guest molecules and their thermodynamic and kinetic properties have been widely studied using different experimental methods such as, NMR, UV spectroscopy, X-ray diffraction, circular dichroism, and so forth.1,7,8,12-14 Time-resolved fluorescence spectroscopic techniques have been extensively used to study the solvation dynamics of CDs and their inclusion complexes. Scypinski and Drake15 found that the fluorescence of coumarin 540A (C540A) enhances while complexing with the BCD molecule, thereby indicating the formation of a stable inclusion complex. Fluorescence anisotropy decay in an unsubstituted BCD molecule has been studied by Balabai et al.16 Fleming and co-workers17 used femtosecond-resolved fluorescence upconversion technique and compared the solvation dynamics of coumarin 480 (C480) and coumarin 460 (C460) in pure water and inside the cavity of γ-CD containing a limited number of water molecules. Long solvation time constants up to about 1.2 ns obtained from these experiments indicated the formation of an inclusion complex between γ-CD and coumarin. They concluded that such slow solvation time scale arises from the restricted environment of the γ-CD cavity. Bhattacharayya and co-workers18-20 have done significant work in this area using time-resolved fluorescence emission spectroscopy with picosecond resolution. They have studied the solvation dynamics of (11) Uekama, K.; Hirayama, F.; Irie, T. Chem. Rev. 1998, 98, 2045. (12) Schneider, H. J.; Hacket, F.; Rudiger, V. Chem. Rev. 1998, 98, 1756. (13) Rekharsky, M. V.; Inoue, Y. Chem. Rev. 1998, 98, 1875. (14) Lipkowitz, K. B. Chem. Rev. 1998, 98, 1829. (15) Scypinski, S.; Drake, J. M. J. Phys. Chem. 1985, 102, 2432. (16) Balabai, N.; Linton, B.; Napper, A.; Priyadarshy, S.; Sukharevsky, A. P.; Waldeck, D. H. J. Phys. Chem. B 1998, 102, 9617. (17) Vajda, S.; Jimenez, R.; Rosenthal, S. J.; Fidler, V.; Flemimg, G. R.; Castner, E. W., Jr. J. Chem. Soc., Faraday Trans. 1995, 91, 867. (18) Sen, S.; Sukul, D.; Dutta, P.; Bhattacharyya, K. J. Phys. Chem. A 2001, 105, 10635. (19) Mondal, S.; Roy, D.; Sahu, K.; Sen, P.; Karmakar, R.; Bhattacharyya, K. J. Photochem. Photobiol. A 2005, 173, 334. (20) Sen, P.; Roy, D.; Mondal, S.; Sahu, K.; Ghosh, S.; Bhattacharyya, K. J. Phys. Chem. A 2005, 109, 9716.

Published on Web 09/09/2009

Langmuir 2009, 25(22), 13084–13091

Jana and Bandyopadhyay

Figure 1. The molecular structure of BCD (a) and its schematic toroidal shape (b).

4-aminophthalimide in a BCD cavity in aqueous medium as well as in dimethylformamide (DMF).18,19 The work demonstrated that the motion of DMF inside the BCD cavity is highly constrained. Sen et al.20 studied the solvation dynamics of the dye coumarin 153 (C153) trapped inside the cavities of dimethyl β-CD (DIMEB) and trimethyl β-CD (TRIMEB) in aqueous medium. They demonstrated that the solvation dynamics of the BCD molecule slows down with substitution. Zewail and coworkers21,22 studied the femtosecond dynamics of reactions inside the nanocavity of the BCD molecule and its methyl-substituted forms. Recently, the dynamic behavior of the R-, β-, and γ-CDs and their methylated derivatives in dimethyl sulfoxide (DMSO) solution has been investigated by Shikata et al.23 They found that the hydrogen atoms of the hydroxyl groups of CDs form a hydrogen bonding network with the oxygen atoms of DMSO. Such hydrogen bonds are found to be the origin of long residence times (130-180 ps) of DMSO around the CD molecules. The dynamics of pure and chemically modified forms of CDs in aqueous solution have also been studied recently using dielectric relaxation experiments.24 The spectra obtained from these measurements indicate the presence of three relaxation modes with time scales of 8-10 ps, 20-25 ps, and 1-2.5 ns. In an important work, Li and McGown25 detected the formation of nanotube aggregates of β- and γ-CDs in solution and on solid surfaces. The formation of large one-dimensional nanotubes by γ-CDs has also been reported from solvation dynamics experiments.26 Recently, from fluorescence anisotropy decay and dynamic light scattering studies, Chattopadhyay and co-workers27 have been able to characterize the formation of an extended nanotubular suprastructure by self-aggregation of γ-CDs. Computer simulation studies in general and molecular dynamics (MD) in particular can provide valuable information on the structural and dynamical properties associated with different forms of CDs and their inclusion complexes at different levels of resolution. In an early work, Gunsteren and co-workers28 simu(21) Douhal, A.; Fiebig, T.; Chachisvilis, M.; Zewail, A. H. J. Phys. Chem. A 1998, 102, 1657. (22) Chachisvilis, M.; Garcia-Ochoa, I.; Douhal, A.; Zewail, A. H. Chem. Phys. Lett. 1998, 293, 153. (23) Shikata, T.; Takahashi, R.; Onji, T.; Satokawa, Y.; Harada, A. J. Phys. Chem. B 2006, 110, 18112. (24) Shikata, T.; Takahashi, R.; Satokawa, Y. J. Phys. Chem. B 2007, 111, 12239. (25) Li, G.; McGown, L. B. Science 1994, 264, 249. (26) Roy, D.; Mondal, S. K.; Sahu, K.; Ghosh, S.; Sen, P.; Bhattacharyya, K. J. Phys. Chem. A 2005, 109, 7359. (27) Das, P.; Mallick, A.; Sarkar, D.; Chattopadhyay, N. J. Phys. Chem. C 2008, 112, 9600. (28) Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J. 1987, 15, 197.

Langmuir 2009, 25(22), 13084–13091

Article

lated the crystal structure of R-CD hexahydrate and compared with the experimental data. In an important work, Nandi and Bagchi29 used multishell continuum model (MSCM) and molecular hydrodynamics theory (MHT) to study the solvation dynamics of charged coumarin in γ-CD in aqueous medium. It was shown that only the long-time decay of the solvation time correlation function (TCF) is affected by the constrained environment of the cavity of the CD molecule. The short-time dynamics was found to be still controlled by the libration/ vibration of bulk water. Winkler et al.4 studied the hydration properties of BCD from MD simulations. In agreement with experimental information, they showed that, while the outer rims of BCD interact hydrophilically, the region inside the cavity is predominantly hydrophobic in nature. The solubility of BCD and DIMEB in aqueous medium and the structure of water around them have been investigated from simulations by Saenger and co-workers.30 It is shown that the negative solubility coefficient of DIMEB is correlated with breaking of hydration shells around its methyl groups. Lawtrakul et al.31 also studied the properties of the BCD molecule in aqueous medium from MD simulations. The origin of the differential solubility of R-, β-, and γ-CDs in water was investigated by Naidoo et al.32 from MD simulations. The diffusion coefficients calculated from these studies were found to be in agreement with that obtained from NMR. Duarte and co-workers33 recently carried out density-functional-based MD simulations to study the structure and dynamics of β-CD in aqueous solution. They showed that the presence of solvent reduces the flexibility of the structural framework of the molecule. Interestingly, a major fraction of the water molecules were found to enter the cavity through the wider opening of BCD. The conformational flexibility and hydration properties of CDs containing different number of glucose rings have been investigated recently.34 Binding of different guest molecules to CDs have also been explored through MD simulations. Wang and co-workers35 reported the binding of benzyl alcohol to β-CD in aqueous solution. They observed reversible binding between the guest and the host molecules with the structure of the complex being similar to that determined from X-ray diffraction studies. Yu et al.10 recently studied the interaction between CDs and cholesterol from MD simulations. The calculations revealed two preferred binding modes of the complex. They further showed that the entry of cholesterol into the cavity of the CDs is guided by electrostatic interaction. Only recently, the complexes formed between β-CD and aziadamantane have been studied from MD simulations with explicit water by Zifferer and co-workers.36 The preferential orientation and energetics of the aziadamantane molecules inside CD have been explored in detail. In another important recent work, Laria and co-workers37 studied the solvation dynamics of an external probe (Coumarin 153 or C153) confined within the cavities of BCD and its derivatives from MD simulations. They found that the probe molecule is preferentially solvated by a particular glucose unit, resulting in its (29) Nandi, N.; Bagchi, B. J. Phys. Chem. 1996, 100, 13914. (30) Starikov, E. B.; Br€asicke, K.; Knapp, E. W.; Saenger, W. Chem. Phys. Lett. 2001, 336, 504. (31) Lawtrakul, L.; Viernstein, H.; Wolschann, P. Int. J. Pharm. 2003, 256, 33. (32) Naidoo, K. J.; Chen, J. Y.; Jansson, J. L. M.; Widmalm, G.; Maliniak J. Phys. Chem. B 2004, 108, 4236. (33) Heine, T.; Santos, H. F. D.; Patchkovskii, S.; Duarte, H. A. J. Phys. Chem. A 2007, 111, 5648. (34) Raffaini, G.; Ganazzoli, F. Chem. Phys. 2007, 333, 128. (35) Varady, J.; Wu, X.; Wang, S. J. Phys. Chem. B 2002, 106, 4863. (36) Sellner, B.; Zifferer, G.; Kornherr, A.; Krois, D.; Brinker, U. H. J. Phys. Chem. B 2008, 112, 710. (37) Rodriguez, J.; Martı´ , J.; Guardia, E.; Laria, D. J. Phys. Chem. B 2008, 112, 8990.

DOI: 10.1021/la902003y

13085

Article

Jana and Bandyopadhyay

tightly confined orientation inside the cavity. The dynamical response of water, however, has been found to be independent of encapsulation of the probe molecules. In related works, Debenedetti and co-workers38,39studied in detail the hydration properties of simple carbohydrates at different concentrations and temperatures. Using a combination of terahertz spectroscopy and molecular simulations, Havenith and co-workers40,41 recently studied the dynamics of water around different carbohydrates. It is clear that water plays an important role in guiding the properties of different forms of CDs and their derivatives. In this work, we have investigated the microscopic properties of water present inside the cavity and in the hydration layer surrounding BCD and its two methyl substituted forms, dimethyl BCD (DIMEB) and trimethyl BCD (TRIMEB) in aqueous medium using atomistic MD simulations. Efforts have been made to explore the effects of substitution of the hydroxyl (OH) groups on the dynamic properties of water molecules. The rest of the article is organized as follows: In Section 2, we give a brief description of the system setup and the simulation methods employed. The results obtained from our investigations are presented and discussed in Section 3. In the last section (Section 4), we summarize the important findings and the conclusions reached from our study.

2. System Setup and Simulation Details Three simulations, one with the BCD molecule, and other two with the DIMEB and the TRIMEB molecules in aqueous medium were carried out. The potential parameters for these molecules were taken from the GROMOS force field,28 while the rigid threesite SPC/E model42 was employed for water. The initial coordinates of the BCD molecule were first taken from the literature.43 The hydrogen atoms were then added, and the whole molecule was immersed in a large cubic cell of wellequilibrated water. The initial edge length of the cubic cell was 45 A˚. To avoid any unfavorable contact, the BCD molecule was immersed carefully by removing those water moelcules that were found within 2 A˚ from any of its atoms and also from the cavity. The final system contained the BCD molecule in a cubic cell containing 2903 water molecules. At first, a short MD run of 50 ps was carried out by keeping the BCD molecule flexible and the water molecules frozen at their starting positions. Initially, the temperature of the system was kept low, which then gradually increased to the room temperature of 300 K. Next, the water molecules were allowed to move, and the system was equilibrated at constant temperature (T = 300 K) and pressure (Pext = 0) (NPT) for about 400 ps. During this run, the volume of the simulation cell was allowed to fluctuate isotropically. At the end of this equilibration run, the volume of the system attained a steady value with a box edge length of 44.5 A˚. At this point, we fixed the cell dimensions, and the simulation conditions were changed to constant temperature (300 K) and volume (NVT). The NVT equilibration run was continued further for another 1 ns duration. This was followed by a NVT production run of approximately 3.5 ns duration. The MD trajectory was stored during the NVT run with a time resolution of 400 fs for subsequent (38) Roberts, C. J.; Debenedetti, P. G. J. Phys. Chem. B 1999, 103, 7308. (39) Lee, S. L.; Debenedetti, P. G.; Errington, J. R. J. Chem. Phys. 2005, 122, 204511. (40) Heugen, U.; Schwaab, G.; Br€undermann, E.; Heyden, M.; Yu, X.; Leitner, D. M.; Havenith, M. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 12301. (41) Heyden, M.; Br€undermann, E.; Heugen, U.; Niehues, G.; Leitner, D. M.; Havenith, M. J. Am. Chem. Soc. 2008, 130, 5773. (42) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Chem. Phys. 1987, 91, 6269. (43) Sharff, A. J.; Rodseth, L. E.; Quiocho, F. A. Biochemistry 1993, 32, 10553.

13086 DOI: 10.1021/la902003y

analysis. A part of the equilibrium trajectory (∼500 ps) was also stored at a higher time resolution of 16 fs to calculate ultrafast properties. The initial coordinates of the two substituted forms (DIMEB and TRIMEB) were obtained by replacing the hydroxyl (OH) groups of BCD by methoxy (OCH3) groups. The two molecules were then immersed separately in two cubic cells of water with same edge length as that used for the BCD molecule. Finally, the DIMEB-water system contained one DIMEB molecule immersed in 2846 water molecules, while the TRIMEB-water system contained one TRIMEB molecule immersed in 2843 water molecules. These two simulations were also carried out for about a 5 ns duration following the same procedure as that employed for the BCD simulation. The final edge lengths of the simulation cells for the DIMEB and TRIMEB systems were 44.2 and 44.3 A˚, respectively. All the simulations utilized the Nose-Hoover chain thermostat extended system method,44 as implemented in the PINY-MD code.45 The use of a reversible multiple time step algorithm, RESPA,44 allowed us to employ 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 (a 7.0 A˚ RESPA cutoff distance), and longrange intermolecular forces. Electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method.46 The PME and RESPA were combined following the method suggested by Procacci et al.47,48 The minimum image convention49 was employed to calculate the Lennard-Jones interactions and the real-space part of the Ewald sum, using a spherical truncation of 7 and 10 A˚, respectively, for the short- and long-range parts of the force decomposition.

3. Results and Discussion 3.1. Water Structure Around CDs. The replacement of the OH groups by OCH3 groups in DIMEB and TRIMEB is likely to influence the properties of water around these molecules as compared to that around the BCD molecule. To investigate such influence on water structure, we have calculated the pairwise correlation function, commonly known as the radial distribution function, g(r), of the water molecules with the oxygen atoms of the BCD molecule and its substituted forms. The calculations are carried out by averaging over all the different types of oxygen atoms of the CD molecules, as shown in Figure 2. The distribution curves are characterized by sharp first peak at around 3 A˚, which corresponds to the first hydration shells of the molecules. This along with the presence of a second peak of sufficient intensity around 5 A˚ indicate strong influence of the molecules on the structuring of water around them. However, interesting differences can be noticed between the distribution function for the BCD molecule and that of its substituted forms. A sharp decrease in the intensity of the first peak has been observed when the OH groups are substituted by OCH3 groups. We have calculated the number of water molecules that are within the first nearest neighbor distance or the first coordination shell of the oxygen atoms of the three molecules. This is done by (44) Martyna, G. J.; Tuckerman, M. E.; Tobias, D. J.; Klein, M. L. Mol. Phys. 1996, 87, 1117. (45) Tuckerman, M. E.; Yarne, D. A.; Samuelson, S. O.; Hughs, A. L.; Martyna, G. J. Comput. Phys. Commun. 2000, 128, 333. (46) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089. (47) Procacci, P.; Darden, T.; Marchi, M. J. Phys. Chem. 1996, 100, 10464. (48) Procacci, P.; Marchi, M.; Martyna, G. J. J. Chem. Phys. 1998, 108, 8799. (49) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, 1987.

Langmuir 2009, 25(22), 13084–13091

Jana and Bandyopadhyay

Article

Figure 2. Radial distribution functions, g(r), of the oxygen atoms of the BCD molecule and its substituted forms (DIMEB and TRIMEB) with water oxygen atoms.

integrating the g(r) curves up to about 3.8 A˚. It is found that, on average, there are approximately 4.1, 3.2, and 2.6 water molecules per oxygen atom of the BCD, DIMEB, and TRIMEB molecules, respectively. Such differences are likely to arise due to enhanced hydrophobicity of substituted BCD molecules, thereby resulting in relative lowering of water structure around them as compared to that around the pure BCD molecule. Reduced water structure around the substituted forms as observed here is consistent with earlier simulation studies.30 3.2. Water Dynamics Around CDs. The differential water structure around the BCD molecule and its two methyl substituted forms (DIMEB and TRIMEB) should also affect the translational and rotational motions of water in and around them. This in turn may influence the inclusion properties of these macrocycles. The dynamics of water molecules are discussed in this section. In particular, the calculations are carried out for the water molecules that are present within a shell of thickness 4 A˚ surrounding the CD molecules. These water molecules essentially constitute the first hydration layer around the CDs. The calculations are also carried out separately for the cavity water, i.e., the water molecules that are confined within the cavities of the CD molecules. We have used a simplistic approach to select the cavity water molecules. In this approach, the vectors connecting pairs of non-hydrogen atoms of the CD molecules are first identified. All these vectors are then divided into fine grids with a spacing of 0.1 A˚. Water molecules whose oxygen atoms are found within spheres of radius 0.5 A˚ around the grid points are identified as cavity water after carefully avoiding overcounting. It may be noted that, on average, eight, seven, and five water molecules are found within the cavities of BCD, DIMEB, and TRIMEB molecules, respectively. 3.2.1. Translational Motion. We have calculated the translational motion of the water molecules by measuring their mean square displacements (MSD) ÆΔr2æ from the simulated MD trajectories. The MSD is defined as ÆΔr2 æ ¼ Æjri ðtÞ - ri ð0Þj2 æ

ð1Þ

where the 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 the tagged water molecules at different time origins. The results are displayed in Figure 3 for the BCD molecule and its substituted forms. The calculations are carried out for the hydration layer water molecules as well as for the cavity water, as defined above. For comparison, the corresponding result for pure bulk water as obtained from a separate Langmuir 2009, 25(22), 13084–13091

Figure 3. MSD of water molecules present in the hydration layers (without symbols) and in the cavities (with symbols) of the BCD molecule and its substituted forms (DIMEB and TRIMEB). MSD of water in pure bulk state is also shown for comparison. Table 1. The Exponent r for the Water Molecules in the Hydration Layers and in the Cavities of the BCD Molecule and Its Substituted Forms (DIMEB and TRIMEB) r system

hydration layer

cavity

BCD DIMEB TRIMEB

0.87 0.86 0.88

0.74 0.72 0.71

MD simulation of SPC/E water under identical conditions is also displayed in the figure. It can be seen that the translational motion of water inside the cavity or around the CD rings are significantly restricted. The effect is more pronounced for the water molecules confined within the cavities. Interestingly, differential dynamics of the water molecules have been noticed among the pure and the di- and tri- substituted BCD molecules. This is particularly true for the cavity water molecules. It is found that the mobility of the cavity water molecules further diminishes with substitution. This indicates that the effect of confinement increases with substitution of OH groups of the BCD molecule. The restricted mobility of water within the cavities of these macrocyclic molecules or around them is an example of anomalous sublinear diffusion in a confined environment.50 To explore the extent of such an anomaly, the MSD curves are fitted to a law:50-52 ÆΔr2 æ ∼ tR

ð2Þ

For an isotropic liquid, a linear increase of particle MSD occurs with time with the exponent R value unity. However, for water within the confined environment in and around a macromolecule, the value of R becomes less than unity. Such sublinear trend in MSDs indicate the degree of confinement of water and its consequent anomalous behavior. We have calculated the R values for the three systems, which are listed in Table 1. Significant deviation of the R values from unity clearly shows the anomalous diffusion behavior of water confined within the cavities of these molecules. 3.2.2. Rotational Motion. The rotational motion of water molecules present in the cavities and in the hydration layers of the (50) Rocchi, C.; Bizzarri, A. R.; Cannistratro, S. Phys. Rev. E 1998, 57, 3315. (51) Chanda, J.; Bandyopadhyay, S. J. Phys. Chem. B 2006, 110, 23482. (52) Sinha, S. K.; Chakraborty, S.; Bandyopadhyay, S. J. Phys. Chem. B 2008, 112, 8203.

DOI: 10.1021/la902003y

13087

Article

Jana and Bandyopadhyay Table 2. Average Reorientational Time Constants, Æτμæ, of Water Present in the Hydration Layers and in the Cavities of the BCD Molecule and Its Substituted Forms (DIMEB and TRIMEB)a Æτμæ (ps) system

hydration layer

cavity

BCD DIMEB TRIMEB bulk water

16.44 19.08 20.55

51.70 108.33 281.76

a

Figure 4. Reorientational TCF of the water dipoles, Cμ(t), for water molecules present in the hydration layers (without symbols) and in the cavities (with symbols) of the BCD molecule and its substituted forms (DIMEB and TRIMEB). The corresponding function for water in pure bulk state is also shown for comparison.

molecules is also expected to be influenced in a differential manner. The rotational motion of a water molecule can be investigated by measuring the reorientational dynamics of its electrical dipole μB, 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 correlation function (TCF), defined as Cμ ðtÞ ¼

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

ð3Þ

where μˆ 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. As before, the calculations are carried out with the water molecules that are present in the hydration layers and in the cavities of the pure and substituted forms of BCD. The results are displayed in Figure 4. For comparison, we have also included the result for pure bulk water in the figure. It is evident that water molecules present in the cavities or in the hydration layers reorient much slowly compared to bulk water. The effect is more severe for water molecules that are confined inside the cavities. Further, it can be noticed that the effect of substitution of the BCD molecule does not seem to have much influence on the rotational motion of the corresponding hydration layer water molecules. This is consistent with the trend observed for the translational mobility of those water molecules (see Figure 3). However, significant differences in the rotational motion of the cavity water molecules have been noticed between the BCD molecule and its two substituted forms. It is found that the reorientation of the cavity water molecules slows down further with substitution. This agrees with the trend observed for the translational motion of the corresponding water molecules and further confirms the enhanced confinement of the cavity in the substituted forms of BCD. It is found that the function Cμ(t) relaxes in a nonexponential manner in all cases. To obtain an average estimate of the reorientational time constant, Æτμæ, we have fitted all the decay curves to multiexponentials of the form Cμ ðtÞ ¼

N X

Ai expð -t=τi Þ

ð4Þ

i ¼1

where τi and Ai values correspond to different time constants and their amplitudes. Here, we have used a sum of three exponentials 13088 DOI: 10.1021/la902003y

4.57

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

(N = 3) to fit the data for each case. The amplitude-weighted Æτμæ values as obtained from the fitted parameters are listed in Table 2. It can be seen that, compared to pure bulk water, the Æτμæ values are about 3-5 times longer for water in the hydration layers of the molecules. On the other hand, the time scale of reorientation of the cavity water molecules has been found to be more than an order of magnitude longer than bulk water. Interestingly, the Æτμæ value has been found to be more than 5 times longer for the cavity water molecules in TRIMEB relative to those in the pure BCD molecule. The enhanced degree of confinement within the cavities of the substituted BCD molecules is also reflected from the average residence times of water inside those cavities. From a preliminary calculation using a suitable TCF, the average residence time of a water molecule present inside the cavity of the BCD molecule has been found to be approximately 100 ps, while that for the DIMEB and TRIMEB were found to be around 220 and 300 ps respectively. Further detailed work is however necessary to understand the correlation between the water residence time and their motions inside the cavities. The substitution of the OH groups of the BCD molecule may modify the properties of hydrogen bonds formed by these macrocycles with water. It would be interesting to investigate whether the dynamics of hydrogen bonds between these molecules and water are correlated with the modified translational and rotational motions of water in and around them. This is discussed in the next section. 3.3. Hydrogen Bond Dynamics. The presence of a macromolecule such as CD in an aqueous solution is likely to modify the regular water-water (WW) hydrogen bond network at the interface due to the formation of CD-water (CW) hydrogen bonds. The time scale of formation and breaking of the CW hydrogen bonds can affect the dynamics of water around these molecules. Generally, either a geometric53-55 or an energetic56-59 criterion is employed to define a hydrogen bond. In this work, we have employed purely geometric criteria to define CW and WW hydrogen bonds. According to the definitions, two water molecules are considered to be hydrogen bonded if their interoxygen distance is within 3.5 A˚, and, simultaneously, the hydrogen-oxygen distance is within 2.45 A˚ and the oxygen-oxygen-hydrogen angle is less than 30.55 The first condition for the formation of a hydrogen bond between the CD molecules and water is that the distance between the oxygen atoms of the two molecules be within 3.5 A˚. It may be noted that the oxygen atoms of the CDs can either donate or accept hydrogen bonds. When it acts as an acceptor, (53) Luzar, A.; Chandler, D. Nature 1996, 397, 55. Luzar, A.; Chandler, D. Phys. Rev. Lett. 1996, 76, 928. (54) Mezei, M.; Beveridge, D. L. J. Chem. Phys. 1981, 74, 622. (55) Luzar, A; Chandler, D. J. Chem. Phys. 1993, 98, 8160. (56) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (57) Rahman, A.; Stillinger, F. H. J. Chem. Phys. 1971, 55, 3336. (58) Stillinger, F. H.; Rahman, A. J. Chem. Phys. 1974, 60, 1545. (59) Rapaport, D. C. Mol. Phys. 1983, 50, 1151.

Langmuir 2009, 25(22), 13084–13091

Jana and Bandyopadhyay

Article

then the second condition is that the angle between one of the O-H bond vectors of the tagged water molecule and the vector connecting the oxygen atoms be within 35. On the other hand, an OH group is considered to act as a hydrogen bond donor if the angle between the tagged O-H bond vector of the molecule and the vector connecting its oxygen atom with that of the water molecule is within 35. It is important to note that the ability to donate a hydrogen bond to water diminishes in DIMEB, and it disappears completely in TRIMEB as a result of full substitution of the OH groups. A water molecule on the other hand, can form a maximum of two CW hydrogen bonds. Applying the hydrogen bonding criteria as described above, we find that most of the water molecules present in the hydration layers and close to the hydrogen bonding sites of the CD molecules form single CW hydrogen bonds. Similar behavior is also noticed for the cavity water molecules except for the pure BCD molecule, for which the average number of CW hydrogen bonds formed by each of its cavity water molecules has been found to be ∼1.5. The dynamics of CW and WW hydrogen bonds have been studied by calculating two TCFs, namely, the intermittent hydrogen bond TCF, C(t), and the continuous hydrogen bond TCF, S(t). These are defined as59,60 CðtÞ ¼

Æhð0ÞhðtÞæ Æhð0Þhð0Þæ

ð5Þ

Æhð0ÞHðtÞæ Æhð0Þhð0Þæ

ð6Þ

The definitions are based on two hydrogen bond population variables h(t) and H(t). The variable h(t) is unity when a particular pair of sites (CW or WW) are hydrogen bonded at time t according to the definition used and zero otherwise. The variable H(t), on the other hand, is defined as unity when the tagged pair of sites remain continuously hydrogen bonded from time t = 0 to time t, and zero otherwise. The function C(t) describes the probability that a particular tagged hydrogen bond is intact at time t, given that it was intact at time zero. Thus C(t) is independent of possible breaking of hydrogen bonds at intermediate times and allows reformation of broken bonds. In other words, it takes into account recrossing of the barrier separating the bonded and the free states, as well as the long-time diffusive behavior. Therefore, the function of C(t) provides information about the structural relaxation of a particular type of hydrogen bonds. The function S(t), on the other hand, describes the probability that a hydrogen bond formed between two sites at time zero remains bonded at all time up to t. In other words, S(t) provides a strict definition of the lifetime of a tagged hydrogen bond. We have calculated the function CCW(t) for the hydrogen bonds formed between the CD molecules and water. The calculations are carried out for both the hydration layer water and the cavity water molecules for the BCD molecule and its substituted forms, DIMEB and TRIMEB. The results are displayed in Figure 5. The decay of the corresponding function CWW(t) for pure bulk water is also shown in the figure for comparison. It is evident that the structural relaxation of the CW hydrogen bonds formed by all the three molecules with water are much slower than that for WW hydrogen bonds in pure bulk water. Further, for (60) Stillinger, F. H. Science 1980, 209, 451. Stillinger, F. H. Adv. Chem. Phys. 1975, 31, 1.

Langmuir 2009, 25(22), 13084–13091

formed between the glucose rings and water molecules present in the hydration layers (without symbols) and in the cavities (with symbols) of the BCD molecule and its substituted forms (DIMEB and TRIMEB). The function for water in pure bulk state, CWW(t), is also shown for comparison. Table 3. Average Relaxation Times of Intermittent CW, ÆτCW C æ, and WW, ÆτWW C æ, Hydrogen Bond TCFs for Water Present in the Hydration Layers and in the Cavities of the BCD Molecule and Its Substituted Forms (DIMEB and TRIMEB)a ÆτCW C æ (ps)

and SðtÞ ¼

Figure 5. Intermittent TCF, CCW(t), for the hydrogen bonds

ÆτWW C æ (ps)

system

hydration layer

cavity

hydration layer

cavity

BCD DIMEB TRIMEB bulk water

45.21 49.68 42.21

77.67 74.02 238.50

5.82 7.33 7.70

44.11 89.62 195.36

a

The

ÆτWW C æ

6.52 value for pure bulk water is also listed for comparison.

each of the three forms, the function CCW(t) relaxes more slowly for the hydrogen bonds formed by the cavity water molecules. This is consistent with slower translational and rotational motions of these water molecules as discussed earlier (see Figures 3 and 4). It can be seen that the relaxation patterns of CCW(t) for the CW hydrogen bonds formed by the hydration layer water are quite similar for the three forms of BCD. However, note the effect of substitution of the OH groups of the BCD molecule on the dynamics of the CW hydrogen bonds formed by the cavity water molecules. Significant heterogeneous relaxation of the CW hydrogen bonds formed by the cavity water molecules has been noticed. In particular, it is found that, for TRIMEB. the relaxation of the CW hydrogen bonds formed by its cavity water is significantly restricted. This agrees with severely restricted translational and rotational motions of the water molecules present inside the cavity of the TRIMEB molecule, and confirms the highly restricted environment inside its cavity. The average relaxation time constants, ÆτCW C æ, as obtained from triexponential fittings of the CCW(t) decay curves (see eq 4) are listed in Table 3. The corresponding value for the WW hydrogen bonds in bulk water is also listed for comparison. It can be seen that the average relaxation times for the CW hydrogen bonds formed by hydration layer water are 6 to 7 times longer than that for bulk water for the three molecules. However, for the hydrogen bonds formed by the cavity water, the corresponding values are more than an order of magnitude longer than bulk water. Additionally, the ÆτCW C æ value for the hydrogen bonds formed by cavity water of TRIMEB is about 3 times longer than that formed by the cavity water of BCD and DIMEB molecules. Thus these calculations provide an estimate of the drastic modification of the confined environment DOI: 10.1021/la902003y

13089

Article

Figure 6. Intermittent TCF, CWW(t), for the hydrogen bonds formed between the water molecules present in the hydration layers (without symbols) and in the cavities (with symbols) of the BCD molecule and its substituted forms (DIMEB and TRIMEB). The function for water in pure bulk state is also shown for comparison.

inside the cavity of the BCD molecule due to substitution. Note that the frequency or rates of CW hydrogen bond breaking and reformation are expected to be correlated with the microscopic motions of the confined water molecules.53 However, further studies are necessary to establish such correlations. In Figure 6, we show the relaxation of the intermittent TCF, CWW(t), for the hydrogen bonds formed among the water molecules present either in the hydration layers or within the cavities of the BCD molecule and its two substituted forms. For comparison, the corresponding function for bulk water is again included in the figure. It can be seen that the relaxation of the function for the hydration layer water molecules are quite similar to that of bulk water with slightly slower time scales for water around DIMEB and TRIMEB. However, note the restricted relaxation behavior of the function for the cavity water molecules. The cavity water molecules are trapped within the confinement and thus form hydrogen bonds, which relax over a much longer time scale. Interestingly, significant heterogeneity has been noticed among the water molecules present within the cavities of the three molecules. The relaxation of the function becomes slower with substitution of the OH groups of the BCD molecule. This is consistent with the restricted dynamics of these water molecules as discussed earlier (see Figures 3 and 4). The average relaxation time constants, ÆτWW C æ, as obtained by fitting each of the decay curves with a sum of three exponentials (see eq 4) are listed in Table 3. It can be seen that, although the ÆτWW C æ values are quite close to that of bulk water for the hydration layers, the corresponding values are longer by an order of magnitude for the cavity water molecules, particularly for DIMEB and TRIMEB molecules. It is found that, while the ÆτWW C æ value for the disubstituted form (DIMEB) is twice as long as that for the BCD molecule, it is more than four times longer for the trisubstituted form (TRIMEB). Thus, the enhanced degree of confinement of the cavity water molecules due to substitution of the OH groups of the BCD molecule has strong influence on the dynamics of these water molecules and the relaxation time scales of the hydrogen bonds formed by them. In Figure 7, we display the relaxation of the continuous TCF, SCW(t), for the hydrogen bonds formed by the BCD molecule and its substituted forms with water molecules present either in their hydration layers or in the cavities. The decay of the corresponding function SWW(t) for pure bulk water is also shown in the figure for comparison. The calculations are carried out by averaging over the hydrogen bonds that are formed at different time origins. In 13090 DOI: 10.1021/la902003y

Jana and Bandyopadhyay

Figure 7. Continuous TCF, SCW(t), for the hydrogen bonds formed between the glucose rings and water molecules present in the hydration layers (without symbols) and in the cavities (with symbols) of the BCD molecule and its substituted forms (DIMEB and TRIMEB). The function for water in pure bulk state, SWW(t), is also shown for comparison. Table 4. Average Relaxation Times of Continuous CW, ÆτCW S æ, and WW, ÆτWW æ, Hydrogen Bond TCFs for Water Present in the S Hydration Layers and in the Cavities of the BCD Molecule and its Substituted Forms (DIMEB and TRIMEB)a ÆτCW S æ (ps)

ÆτWW æ (ps) S

systems

hydration layer

cavity

hydration layer

cavity

BCD DIMEB TRIMEB bulk water

5.32 2.04 1.06

2.68 1.18 1.50

0.48 0.57 0.54

0.64 2.71 3.73

a

The

ÆτWW æ S

0.63 value for pure bulk water is also listed for comparison.

all cases, a rapid initial decay of the correlation function arising primarily as a result of the fast librational and vibrational motions of the hydrogen bonded sites has been observed. It can be seen that, in all cases, the relaxation of the function for the CW hydrogen bonds (SCW(t)) is slower than that for the WW hydrogen bonds in bulk water (SWW(t)). We have again fitted the decay curves with triexponentials (see eq 4) and obtained the amplitudeweighted average CW hydrogen bond lifetimes (ÆτCW S æ), which are listed in Table 4. The average lifetime of WW hydrogen bonds in bulk water (ÆτWW S æ) is also listed for comparison. We notice that the ÆτCW S æ values for the CW hydrogen bonds formed by either the hydration layer or the cavity water molecules are approximately 2-8 times longer than that for pure bulk water. It may be noted that, as the function S(t) provides information about the breaking of hydrogen bonds, the strength of the CW hydrogen bonds may be responsible for their longer lifetimes. The average interaction energy between a water molecule and the glucose unit with which it is hydrogen bonded has been found to be in the range of -6.5 to -7.5 kcal/mol, for the BCD molecule and its two substituted forms. This is lower than the average WW hydrogen bond energy of -4.6 kcal/mol in pure bulk water. Thus the water molecules present in the hydration layers or in the cavities in general form stronger hydrogen bonds with the glucose rings, and hence have longer lifetimes. Interestingly, a heterogeneous relaxation behavior of the function SCW(t) is noticed among the BCD molecules. Unlike the function CCW(t), the heterogeneous behavior of SCW(t) is also significantly noticeable for the CW hydrogen bonds formed by the hydration layer water molecules. Surprisingly, the effect of substitution of the OH groups of the BCD molecule on the Langmuir 2009, 25(22), 13084–13091

Jana and Bandyopadhyay

Article

SWW(t) at long times. It can be seen from Table 4 that, while the average lifetime of WW hydrogen bonds formed by the cavity water is close to that of bulk water for the BCD molecule, they are about 4-6 times slower for DIMEB and TRIMEB. Further studies are necessary to correlate such differential WW hydrogen bond behavior with the confined environment of the cavities.

4. Conclusions

Figure 8. Continuous TCF, SWW(t), for the hydrogen bonds formed between the water molecules present in the hydration layers (without symbols) and in the cavities (with symbols) of the BCD molecule and its substituted forms (DIMEB and TRIMEB). The function for water in pure bulk state is also shown for comparison.

relaxation pattern of SCW(t) has been found to be opposite to that noticed for the function CCW(t). It is observed that SCW(t) for the CW hydrogen bonds formed by the hydration layer water molecules relaxes faster with increase in substitution of the OH groups. This is reflected in the calculated average lifetimes (ÆτCW S æ) of these hydrogen bonds that are listed in Table 4. The average CW hydrogen bond lifetime for the hydration water is about 5 times reduced for the TRIMEB molecule as compared to the BCD molecule. The function corresponding to the CW hydrogen bonds formed by the cavity water molecules relaxes faster than that formed by the hydration layer water for BCD and DIMEB molecules. However, a reverse trend is noticed for the TRIMEB molecule. It is found that, while the ÆτCW S æ values for the CW hydrogen bonds formed by the cavity water are about 2 times shorter than that formed by the hydration layer water for BCD and DIMEB molecules, the corresponding value for the TRIMEB molecule is slightly higher for the hydrogen bonds formed by the cavity water molecules. To understand such surprising behavior, we have separately calculated the CW hydrogen bond interaction energies for the three forms. The calculated values are -7.5, -7.0, and -6.5 kcal/mol for the BCD, DIMEB, and TRIMEB molecules, respectively. Thus, it is clear that, compared to DIMEB and TRIMEB molecules, BCD in general forms stronger CW hydrogen bonds with longer lifetimes. The shorter lifetimes of the CW hydrogen bonds formed by the cavity water molecules of BCD and DIMEB as compared to that for the bonds formed by the hydration layer water molecules may arise due to differential confined environment inside the cavities of these molecules. However, this needs to be investigated further. We have also calculated the continuous hydrogen bond TCF, SWW(t), for the hydrogen bonds formed among the water molecules present either in the hydration layers or within the cavities of the BCD, DIMEB, and TRIMEB molecules. The results are shown in Figure 8 along with that for pure bulk water. In most of the cases, we observe a rapid initial decay of the function arising from fast librational and vibrational motions of the tagged water molecules. This is particularly true for the hydration layer water molecules, for which the hydrogen bond lifetimes are close to that of bulk water as listed in Table 4. Interestingly, substitution of the OH groups of the BCD molecule seems to have an opposite effect on the relaxation pattern of the function SWW(t) as compared to that for SCW(t). The increased confinement of water molecules within the cavities of the substituted forms leads to slowing down of the decay of the function Langmuir 2009, 25(22), 13084–13091

Let us first summarize the main results of this article. In this work we have presented results obtained from atomistic MD simulations of aqueous solutions of the BCD molecule and its diand tri- methyl substituted forms (DIMEB and TRIMEB). It is observed that the overall translational and rotational motions of the water molecules present either in the hydration layers of these molecules or inside their cavities are slower than that of bulk water. Interestingly, the effect of substitution of the OH groups of the BCD molecule has been found to have a strong influence on the relative dynamics of the cavity water molecules. Both translational and rotational motions of cavity water molecules are further restricted with substitution. However, no such noticeable differences have been observed among the hydration layer water molecules of the three forms of the BCD molecule. Our calculations reveal that the structural relaxation of the CW hydrogen bonds formed by the three macrocyclic molecules with water are much slower than that of WW hydrogen bonds in bulk water. The effect of substitution on the heterogeneous time scale of relaxation of the intermittent TCF for the CW hydrogen bonds formed by the cavity water molecules have been found to be in agreement with the relative translational and rotational motions of those water molecules. It is further noticed that the structural relaxation times (ÆτWW C æ) of the hydrogen bonds formed by water present within the hydration layers of the three molecules are not much different from each other and that of bulk water. However, the ÆτWW C æ values for the cavity water molecules are an order of magnitude longer than that for the hydration layer water. It is further found that water molecules form stronger CW hydrogen bonds with the glucose rings of the molecules, and hence they have longer lifetimes. The lifetimes of WW hydrogen bonds formed by the water molecules present either in the hydration layers or inside the cavities have been found to be similar to that of bulk water except for those formed among the cavity water molecules of DIMEB and TRIMEB. Thus, in this work we have attempted to explore the effect of substitution of the OH groups of the BCD molecule by OCH3 groups on the dynamical properties of water around the molecule as well as those present inside the cavity. Our calculations revealed that the substitution of the OH groups has a strong influence on the microscopic dynamics of water, particularly those present inside the cavities. It would be interesting to explore whether the heterogeneous properties of water around the BCD molecule and its substituted forms and the relative occupancy of water inside the cavities are correlated with the ability of these macromolecules to form inclusion complexes. Some of these aspects are under investigation in our laboratory. 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 the DST-FIST programme (SR/FST/CSII-011/2005). We thank Professor Kankan Bhattacharyya for many insightful discussions during the course of the work. M.J. thanks the University Grants Commission (UGC), Government of India, for providing a scholarship. DOI: 10.1021/la902003y

13091