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Solvation structure of glucosamine in aqueous solution as studied by Monte Carlo simulation using ab initio fitted potential
Chemical Physics Letters 395 (2004) 233–238 www.elsevier.com/locate/cplett
Solvation structure of glucosamine in aqueous solution as studied by Monte Carlo simulation using ab initio fitted potential Krisana Siraleartmukul a,c, Khatcharin Siriwong b, Tawun Remsungnen b,*, Nongnuj Muangsin b, Werasak Udomkichdecha a, Supot Hannongbua b,c,* a
c
Department of Materials Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand b Department of Chemistry, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand Metallurgy and Materials Sciences Research Institute, Chulalongkorn University, Bangkok 10330, Thailand Received 15 January 2004; in final form 26 July 2004 Available online 20 August 2004
Abstract The solvation structure of glucosamine in aqueous solution was investigated using Monte Carlo simulation at 298 K. The MCY ˚ from the rigid water model and ab initio glucosamine–water fitted potential were applied. The first hydration shell appears at 4.6 A center of glucosamine with a coordination number of seven water molecules where one water lies in the ligandÕs plane while two and ˚ above and below the plane, respectively. Furthermore, the mobility distribution and orientation of the four of them are about 2–4 A water molecules around the ligand have been intensively investigated and reported. 2004 Elsevier B.V. All rights reserved.
1. Introduction Chitosan is derived from the deacetylation reaction of chitin [1], natureÕs second most abundant after cellulose. Chemically, chitosan is a poly-b (1,4)-2- amino-2-deoxyD -glucose residue chain. In other words, chitosan is a 1–4 linked polymer of D -glucosamine. Chitosan is recommended as a suitable resource material due to its distinctive biomedical properties, which have been applied in many different industrial areas [2–7]. In biomedical treatments [3–12] chitosan was used to reduce cholesterol levels [8,9], as well as to control drug release and drug delivery [10–13]. The efficiency of such applications depends strongly on molecular weight, structure, crosslinking percentage, and porous size of the polymer [10–16]. These factors are known to be controlled, on the molecular level, by the *
Corresponding authors. Fax: +6622187603. E-mail addresses: [email protected] (T. Remsungnen), [email protected] (S. Hannongbua). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.07.082
interactions between chitosan, drug and solvent molecules. This relates directly to the solvation and desolvation of all species in the solution [17–20]. Understanding this behavior would facilitate directly the development and wide applications of chitosan. The above statement convinces us to investigate the solvation structure of chitosan, which is not yet available either experimentally or theoretically. Metropolis Monte Carlo procedure [21] with the developed pair potential has been applied to examine the solvation structure of its unit cell, b-D -glucosamine, in water.
2. The models and simulation details 2.1. Glucosamine–water potential function An ab initio potential function was developed to represent the glucosamine–water interaction. The X-ray crystallography of glucosamine [22] was used as a starting structure. The missing hydrogen (H) atoms were
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added and then optimized using the GAUSSIAN 98 program [23] with a DZP basis set [24]. An experimental ˚ of OH bond and geometry of water, i.e., 0.957 A 104.5 of H–O–H angle [25], was employed. To develop the pair potential, the atoms of the glucosamine molecule were classified into 12 groups by their atomic net charge obtained from the Mulliken population analysis [26] (Fig. 1a and Table 1). Total 4000 single point energies of glucosamine–water dimer were calculated at the RHF/DZP level. The data were fitted to an analytical function of the following form: ! 25 X 3 X Aij Bij qi qj DEðL; WÞ ¼ 6 þ 12 þ ; rij rij rij i¼1 j¼1 where 25 and 3 denote numbers of atoms of glucosamine (L) and water (W), respectively. Aij and Bij are fitting parameters, rij is the distance between atom i of water and atom j of glucosamine, and qi and qj are
Table 1 Atoms in glucosamine and water molecules were classified by atomic net charges (see Fig. 1a for glucosamine structure) Group
Atom
Charge (a.u.)
Glucosamine C1 C2 N O1 O2 O3 O4 H1 H2 H3 H4 H5
C3, C4, C8, C11, C14 C15 N5 O2, O9 O12 O16 O18 H19, H20, H21, H22, H23, H24, H25 H6, H7 H1, H10 H13 H17
0.156 0.056 0.597 0.494 0.542 0.547 0.485 0.108 0.245 0.289 0.282 0.331
Water O H
O H
0.660 0.330
Table 2 Fitting parameters of the analytical function, representing interactions between atom i of the glucosamine molecule and atom j of the water molecule ˚ 6 kcal mol 1) ˚ 12 kcal mol1) ij A (A B (A C1–O C2–O N–O O1–O O2–O O3–O O4–O H1–O H2–O H3–O H4–O H5–O C1–H C2–H N–H O1–H O2–H O3–H O4–H H1–H H2–H H3–H H4–H
0.000 · 100 0.000 · 100 0.000 · 100 4.234 · 102 8.261 · 102 2.798 · 102 1.880 · 103 0.000 · 100 0.000 · 100 1.048 · 102 3.196 · 101 3.304 · 102 1.278 · 104 4.641 · 104 0.000 · 100 2.990 · 100 5.013 · 101 0.000 · 100 1.874 · 101 0.000 · 100 0.000 · 100 0.000 · 100 9.313 · 105
8.089 · 105 1.026 · 106 1.005 · 105 5.207 · 105 5.914 · 105 5.323 · 105 9.648 · 105 4.247 · 103 2.884 · 103 3.361 · 102 3.162 · 102 4.386 · 103 2.575 · 104 1.034 · 101 1.142 · 102 3.307 · 102 8.430 · 109 3.697 · 102 5.786 · 101 2.789 · 101 8.388 · 100 1.378 · 102 1.020 · 102
the Mulliken net charges of atoms i and j, respectively. The fitted parameters are given in Table 2. 2.2. Monte Carlo simulation Fig. 1. (a) Structure of glucosamine with atomic numbering. (b) Glucosamine–water stabilization energies (in the configuration shown in the inset) obtained from ab initio self-consistent field calculations (DESCF) and from the fitting function (DEFIT). The DESCF and DEFIT for all 370 dimer configurations are also compared in the inset.
Monte Carlo simulation has been carried out for a glucosamine molecule in aqueous solution at 298 K and 1 atm. The system contains one glucosamine molecule fixed at the center of the cube and 201 water molecules. The volume of a periodic box is the summation of
K. Siraleartmukul et al. / Chemical Physics Letters 395 (2004) 233–238
volume of 201 water molecules with the density of 1 g cm3 and additional space occupied by glucosamine ˚ . A spherical molecule, leading the cube length of 18.26 A cut-off for the site–site interaction potentials was applied at half of this length. The Metropolis sampling algorithm [21] was applied. The MCY [27] and the ab initio fitted potentials were employed to describe water–water and glucosamine–water interactions, respectively. Equilibrium was reached after 34 million configurations. A further 16 million configurations were generated and every 500 of them were stored for subsequent analysis.
g(r)
g(r) N5-O N5-H
(a)
0
O2-O O2-H
(b)
1
1
1
2
3
4
5
6
7
8
0
1
2
3
r/Å
4
5
6
7
8
r/Å g(r)
g(r)
O12-O O12-H
(d)
O9-O O9-H
(c)
3. Results and discussion
235
1
1
3.1. Developed glucosamine–water potential function To examine the quality of the fitted function, stabilization energies of the complex in the configurations shown in an inset of Fig. 1b were then calculated using ab initio method (DESCF) and the glucosamine–water function (DEFIT). Here, an O atom of a water molecule lay in the C3–C14–O18 plane of the ligand and this plane is perpendicular to the plane of H–O–H of the water molecule. The distance r between the O atom of water and center of glucosamine is varied from 3.2 to ˚ . The plot in Fig. 1b shows that the differences in 9.5 A the position to the minima as well as the interaction energies are almost negligible. The plot approaching ˚ justifies that correction zero at a distance of about 7.5 A of the Coulombic interactions beyond the cut-off distance in the computer simulations can be neglected. Further confirmation of the quality of the fit is the comparison plotting of all data points (Fig. 1b). The plot indicates a good agreement between both data sets, especially for the attractive regions, which is important for prediction of the simulation results.
0
The atom–atom radial distribution functions (RDFs) from nitrogen (N) and oxygen (O) atoms of glucosamine molecules to water molecules are displayed in Figs. 2a–f. For all plots, the RDFs to H of water are detected before those to O atom. This indicates preferential orientation of the water molecule in which one of its H atoms points towards the N or O atoms of glucosamine. The plots show well defined peaks cen˚ , except that of O16 atom (Fig. 2e). tered at about 3 A The running integration numbers up to the first minima of the N5–O, O2–O, O9–O, O12–O and O18–O RDFs are 7.4, 4.7, 11.2, 7.7 and 2.2 water molecules, respectively. Based on the criteria proposed in [28,29], a hydrogen-bond is established when the distance between the donor hydrogen and acceptor oxygen is less than 2.4 ˚ . The coordination numbers of hydrogen atoms of A
2
3
4
5
6
7
8
0
1
2
3
r/Å
5
6
7
8
g(r) O16-O O16-H
(e)
O18-O O18-H
(f) 1
1
0
4
r/Å
g(r)
1
2
3
4
r/Å
5
6
7
8
0
g(r) 50
1
3
4
5
r/Å
6
7
8
(h) 40
gE-O(r) gE-H(r)
1
2
%
(g) 30 20 10 0
3.2. Solvation structure of glucosamine
1
1
2
3
4
5
6
7
8
4
5 6 7 8 9 10 Number of water molecules
Fig. 2. (a–g) Radial distribution functions (RDFs) from O (solid line) and H (dash line) atoms of water to N5, O2, O9, O12, O16 and O18 atoms and to center of mass of glucosamine molecule where (h) the distribution of running integration number in the first solvation shell of glucosamine was also given.
˚ of the N5–H, water molecules integrated up to 2.4 A O2–H, O9–H, O12–H, O16–H and O18–H RDFs are 0.2, 0.8, 0.3, 0.6, 0.5 and 1.0, respectively. This data as well as an appearance of the first peak or the hump of the RDFs from the N or O atoms of the ligand to the H atom of water indicates clearly that water molecules lying under the first peaks of the investigated RDFs form a hydrogen bond with the glucosamine molecule. The obtained coordinate numbers, which are quite high, do not represent numbers of hydrogen bonding between
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water and the ligand because of the overlapping of the RDFs center on different atoms of glucosamine. This fact is supported by the broadening or splitting of the RDFÕs first peaks. Note that: (i) a very sharp first peak of the RDF of O18–H indicates a strong H-bond between water and O18; (ii) the difference between the distance to the first maxima of the O18–O and O18–H RDFs which are almost equivalent to the O–H bond length of water indicates a formation of a linear hydrogen-bond. In Fig. 2g, total radial distribution functions from the center of glucosamine for the entire volume (E) to oxygen and hydrogen atoms of water, gE-O(r) and gE-H(r), have been calculated. The plots display two peaks, cen˚ . Their running integration tered at about 4.3 and 5.1 A numbers, integrated up to the corresponding minima of ˚ , are seven and 26 water molecules, respec4.6 and 6.0 A
tively. An average first shell coordination number of glucosamine of seven can be analyzed more details in term of its distribution. Here, percentage of oxygen ˚ atoms of water lying within a spherical radius of 4.6 A (the first minimum of the gE-O(r) RDF) from the center of the glucosamine molecule was calculated and displayed in Fig. 2h. The plot shows a broad distribution from 5 to 9 water molecules indicating mobility and solvent exchange of water molecules between the first and the second solvation shells. This offers dynamic pictures of the ligand solvation superior the single picture provided by the average coordination number. To investigate the precise position of the seven water molecules in the first solvation shell of glucosamine, the periodic cube, which the ligand was in the middle, was sliced into eight layers by the plane parallel to the xyplane (Fig. 3a). Layers L1, L2, L3 and L4 are the vol-
Fig. 3. The periodic cube was sliced into eight layers by the xy-plane and the space around glucosamine molecule was divided by x- and y-axis into four quadrants: (a) and the contour plots of the xy-coordinate of water molecules in; (b) the upper half (b) and the lower half; (c) of each quadrant (Q) in the first coordination shell of glucosamine.
K. Siraleartmukul et al. / Chemical Physics Letters 395 (2004) 233–238
umes where 0 6 z 6 2, 2 < z 6 3, 3 < z 6 4, and ˚ , respectively. In addition, layers L1 0 , L2 0 , 4
237
tains three points, point m, part of point k in layer L3 0 , and part of point k 0 in layer L4 0 . Points k and k 0 yield from the same water molecule interacting with ˚ the ring of the glucosamine molecule at more than 3 A below the plane. At this layer, point m indicates a partial solvation of the O9 atom of the glucosamine molecule. It is interesting to note that the low density points on the contour plot, such as point f, h and j, relates to the mobility of the water molecules due to a weak glucosamine–water interaction. This event is supported by the underfine first-minimum of almost all RDFs, as well as the distribution of the coordination numbers depicted in Fig. 2h, in which the percentage of detecting 5, 6, 7, 8 and 9 water molecules around the ligand within the dis˚ from the center of the ligand are 8.6%, tance of 4.6 A 22.6%, 37.1%, 23.2% and 8.5%, respectively. The broad distribution yields the average coordination number of 7.0 water molecules around the glucosamine.
Fig. 4. The first solvation shell of glucosamine consisting of seven water molecules labeled as W1–W7: (a) summarized distribution of water density distributing in each layer: W1(L1–L1 0 ), W2(L2 0 ), W3(L2–L3), W4(L2 0 –L3 0 ), W5(L3 0 –L4 0 ), W6(L3) and W7(L3 0 ); (b) snapshot, one out of 16 million equilibration configurations.
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Taking into account all data mentioned above, precise positions of the seven water molecules, w1–w7, in the first solvation shell of glucosamine have been drawn and displayed in Fig. 4a. The snapshot (one out of 16 million equilibrium configurations) depicted in Fig. 4b supports all detailed investigations shown in Figs. 3(b and c) and the final conclusion in Fig. 4a.
Acknowledgements Financial support from the Shell Centenary Scholarship fund and the Thailand Research Fund (RTA4680008) as well as the generous supply of computer time by the Austrian–Thai Centre for Computer Assisted Chemical Education and Research, Computer for Advanced Research Center. Faculty of Science, Chulalongkorn University, and the National Electronic and Computer Technology Center, Bangkok, are gratefully acknowledged.
References [1] R. Sheperd, S. Reader, A. Falshaw, Glycoconjugate J. 14 (1997) 535. [2] S. Hirano, Polym. Int. 48 (1999) 732. [3] R. Ravindra, K.R. Krovvidi, A.A. Khan, Carbohyd. Polym. 36 (1998) 121. [4] N. Koseva, N. Manolova, N. Markova, T. Radoucheva, I. Rashkov, Polym. bull. 43 (1999) 101. [5] B. Narasimhan, Adv. Drug Deliver. Rev. 48 (2–3) (2001) 195. [6] G. Alagona, C. Ghio, P.A. Kollman, J. Am. Chem. Soc. 107 (1985) 2229.
[7] R. Muzzarelli, Polymeric Biomaterials, Marcel Dekker, New York, 1994. [8] K. Deuchi, O. Kanauchi, Y. Imasato, E. Kobayashi, Biosci. Biotech. Bioch. 58 (1994) 1613. [9] E.A. Trautwein, U. Jurgensen, H.F. Erbersdobler, Nutr. Res. 17 (1997) 1053. [10] D. Thacharodi, K.P. Rao, J. Chem. Technol. Biot. 58 (1993) 177. [11] Y.-E. Fang, Q. Cheng, X.-B. Lu, J. Appl. Polym. Sci. 68 (1998) 1751. [12] I. Genta, P. Perugini, F. Pavanetto, Drug Dev. Ind. Pharm. 24 (1998) 779. [13] S. Nakatsuka, A.L. Andrady, J. Appl. Polym. Sci. 44 (1992) 17. [14] N. Kubota, Bull. Chem. Soc. Jpn. 66 (1993) 1807. [15] A.A. Al-Angary, A.A.M. Al-Helw, M.M. Al-Dardiri, G.M. Mahrous, Pharm. Ind. 60 (1998) 629. [16] T.Y. Hsien, G.L. Rorrer, Ind. Eng. Chem. Res. 36 (1997) 3631. [17] J. R. Cardinal, W. J. Curatolo, C. D. Ebert, US Patent 4895, (1990) 724. [18] S. Hannongbua, B.M. Rode, Chem. Phys. 162 (1992) 257. [19] S. Hannongbua, J. Phys. Chem. 100 (1996) 17655. [20] S. Udomsub, S. Hannongbua, J. Chem. Soc., Faraday Trans. 93 (1997) 3045. [21] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21 (1953) 1087. [22] Cambridge Crystallographic Data Center, Cambridge, UK. Available from: <(http://www.ccdc.cam.ac.uk)>. [23] M.J. Frisch et al., GAUSSIAN 98, Revision A, Gaussian, Inc., Pittsburgh, PA, 1998. [24] T.H. Dunning, P.J. Hay, Methods of Electronic Structure Theory, vol. 3, New York, Plenum Press, 1977. [25] W.S. Benedict, N. Gailar, E.K. Plyler, J. Phys. Chem. 24 (1956) 1139. [26] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [27] O. Matsuoka, E. Clementi, M. Yoshimeine, J. Chem. Phys. 64 (1976) 1351. [28] E.R. Caffarena, J.R. Grigera, Carbohyd. Res. 315 (1999) 63. [29] C. Molteni, M. Parrinello, J. Am. Chem. Soc. 120 (1998) 2168.
Solvation structure of glucosamine in aqueous solution as studied by Monte Carlo simulation using ab initio fitted potential Krisana Siraleartmukul a,c, Khatcharin Siriwong b, Tawun Remsungnen b,*, Nongnuj Muangsin b, Werasak Udomkichdecha a, Supot Hannongbua b,c,* a
c
Department of Materials Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand b Department of Chemistry, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand Metallurgy and Materials Sciences Research Institute, Chulalongkorn University, Bangkok 10330, Thailand Received 15 January 2004; in final form 26 July 2004 Available online 20 August 2004
Abstract The solvation structure of glucosamine in aqueous solution was investigated using Monte Carlo simulation at 298 K. The MCY ˚ from the rigid water model and ab initio glucosamine–water fitted potential were applied. The first hydration shell appears at 4.6 A center of glucosamine with a coordination number of seven water molecules where one water lies in the ligandÕs plane while two and ˚ above and below the plane, respectively. Furthermore, the mobility distribution and orientation of the four of them are about 2–4 A water molecules around the ligand have been intensively investigated and reported. 2004 Elsevier B.V. All rights reserved.
1. Introduction Chitosan is derived from the deacetylation reaction of chitin [1], natureÕs second most abundant after cellulose. Chemically, chitosan is a poly-b (1,4)-2- amino-2-deoxyD -glucose residue chain. In other words, chitosan is a 1–4 linked polymer of D -glucosamine. Chitosan is recommended as a suitable resource material due to its distinctive biomedical properties, which have been applied in many different industrial areas [2–7]. In biomedical treatments [3–12] chitosan was used to reduce cholesterol levels [8,9], as well as to control drug release and drug delivery [10–13]. The efficiency of such applications depends strongly on molecular weight, structure, crosslinking percentage, and porous size of the polymer [10–16]. These factors are known to be controlled, on the molecular level, by the *
Corresponding authors. Fax: +6622187603. E-mail addresses: [email protected] (T. Remsungnen), [email protected] (S. Hannongbua). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.07.082
interactions between chitosan, drug and solvent molecules. This relates directly to the solvation and desolvation of all species in the solution [17–20]. Understanding this behavior would facilitate directly the development and wide applications of chitosan. The above statement convinces us to investigate the solvation structure of chitosan, which is not yet available either experimentally or theoretically. Metropolis Monte Carlo procedure [21] with the developed pair potential has been applied to examine the solvation structure of its unit cell, b-D -glucosamine, in water.
2. The models and simulation details 2.1. Glucosamine–water potential function An ab initio potential function was developed to represent the glucosamine–water interaction. The X-ray crystallography of glucosamine [22] was used as a starting structure. The missing hydrogen (H) atoms were
234
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added and then optimized using the GAUSSIAN 98 program [23] with a DZP basis set [24]. An experimental ˚ of OH bond and geometry of water, i.e., 0.957 A 104.5 of H–O–H angle [25], was employed. To develop the pair potential, the atoms of the glucosamine molecule were classified into 12 groups by their atomic net charge obtained from the Mulliken population analysis [26] (Fig. 1a and Table 1). Total 4000 single point energies of glucosamine–water dimer were calculated at the RHF/DZP level. The data were fitted to an analytical function of the following form: ! 25 X 3 X Aij Bij qi qj DEðL; WÞ ¼ 6 þ 12 þ ; rij rij rij i¼1 j¼1 where 25 and 3 denote numbers of atoms of glucosamine (L) and water (W), respectively. Aij and Bij are fitting parameters, rij is the distance between atom i of water and atom j of glucosamine, and qi and qj are
Table 1 Atoms in glucosamine and water molecules were classified by atomic net charges (see Fig. 1a for glucosamine structure) Group
Atom
Charge (a.u.)
Glucosamine C1 C2 N O1 O2 O3 O4 H1 H2 H3 H4 H5
C3, C4, C8, C11, C14 C15 N5 O2, O9 O12 O16 O18 H19, H20, H21, H22, H23, H24, H25 H6, H7 H1, H10 H13 H17
0.156 0.056 0.597 0.494 0.542 0.547 0.485 0.108 0.245 0.289 0.282 0.331
Water O H
O H
0.660 0.330
Table 2 Fitting parameters of the analytical function, representing interactions between atom i of the glucosamine molecule and atom j of the water molecule ˚ 6 kcal mol 1) ˚ 12 kcal mol1) ij A (A B (A C1–O C2–O N–O O1–O O2–O O3–O O4–O H1–O H2–O H3–O H4–O H5–O C1–H C2–H N–H O1–H O2–H O3–H O4–H H1–H H2–H H3–H H4–H
0.000 · 100 0.000 · 100 0.000 · 100 4.234 · 102 8.261 · 102 2.798 · 102 1.880 · 103 0.000 · 100 0.000 · 100 1.048 · 102 3.196 · 101 3.304 · 102 1.278 · 104 4.641 · 104 0.000 · 100 2.990 · 100 5.013 · 101 0.000 · 100 1.874 · 101 0.000 · 100 0.000 · 100 0.000 · 100 9.313 · 105
8.089 · 105 1.026 · 106 1.005 · 105 5.207 · 105 5.914 · 105 5.323 · 105 9.648 · 105 4.247 · 103 2.884 · 103 3.361 · 102 3.162 · 102 4.386 · 103 2.575 · 104 1.034 · 101 1.142 · 102 3.307 · 102 8.430 · 109 3.697 · 102 5.786 · 101 2.789 · 101 8.388 · 100 1.378 · 102 1.020 · 102
the Mulliken net charges of atoms i and j, respectively. The fitted parameters are given in Table 2. 2.2. Monte Carlo simulation Fig. 1. (a) Structure of glucosamine with atomic numbering. (b) Glucosamine–water stabilization energies (in the configuration shown in the inset) obtained from ab initio self-consistent field calculations (DESCF) and from the fitting function (DEFIT). The DESCF and DEFIT for all 370 dimer configurations are also compared in the inset.
Monte Carlo simulation has been carried out for a glucosamine molecule in aqueous solution at 298 K and 1 atm. The system contains one glucosamine molecule fixed at the center of the cube and 201 water molecules. The volume of a periodic box is the summation of
K. Siraleartmukul et al. / Chemical Physics Letters 395 (2004) 233–238
volume of 201 water molecules with the density of 1 g cm3 and additional space occupied by glucosamine ˚ . A spherical molecule, leading the cube length of 18.26 A cut-off for the site–site interaction potentials was applied at half of this length. The Metropolis sampling algorithm [21] was applied. The MCY [27] and the ab initio fitted potentials were employed to describe water–water and glucosamine–water interactions, respectively. Equilibrium was reached after 34 million configurations. A further 16 million configurations were generated and every 500 of them were stored for subsequent analysis.
g(r)
g(r) N5-O N5-H
(a)
0
O2-O O2-H
(b)
1
1
1
2
3
4
5
6
7
8
0
1
2
3
r/Å
4
5
6
7
8
r/Å g(r)
g(r)
O12-O O12-H
(d)
O9-O O9-H
(c)
3. Results and discussion
235
1
1
3.1. Developed glucosamine–water potential function To examine the quality of the fitted function, stabilization energies of the complex in the configurations shown in an inset of Fig. 1b were then calculated using ab initio method (DESCF) and the glucosamine–water function (DEFIT). Here, an O atom of a water molecule lay in the C3–C14–O18 plane of the ligand and this plane is perpendicular to the plane of H–O–H of the water molecule. The distance r between the O atom of water and center of glucosamine is varied from 3.2 to ˚ . The plot in Fig. 1b shows that the differences in 9.5 A the position to the minima as well as the interaction energies are almost negligible. The plot approaching ˚ justifies that correction zero at a distance of about 7.5 A of the Coulombic interactions beyond the cut-off distance in the computer simulations can be neglected. Further confirmation of the quality of the fit is the comparison plotting of all data points (Fig. 1b). The plot indicates a good agreement between both data sets, especially for the attractive regions, which is important for prediction of the simulation results.
0
The atom–atom radial distribution functions (RDFs) from nitrogen (N) and oxygen (O) atoms of glucosamine molecules to water molecules are displayed in Figs. 2a–f. For all plots, the RDFs to H of water are detected before those to O atom. This indicates preferential orientation of the water molecule in which one of its H atoms points towards the N or O atoms of glucosamine. The plots show well defined peaks cen˚ , except that of O16 atom (Fig. 2e). tered at about 3 A The running integration numbers up to the first minima of the N5–O, O2–O, O9–O, O12–O and O18–O RDFs are 7.4, 4.7, 11.2, 7.7 and 2.2 water molecules, respectively. Based on the criteria proposed in [28,29], a hydrogen-bond is established when the distance between the donor hydrogen and acceptor oxygen is less than 2.4 ˚ . The coordination numbers of hydrogen atoms of A
2
3
4
5
6
7
8
0
1
2
3
r/Å
5
6
7
8
g(r) O16-O O16-H
(e)
O18-O O18-H
(f) 1
1
0
4
r/Å
g(r)
1
2
3
4
r/Å
5
6
7
8
0
g(r) 50
1
3
4
5
r/Å
6
7
8
(h) 40
gE-O(r) gE-H(r)
1
2
%
(g) 30 20 10 0
3.2. Solvation structure of glucosamine
1
1
2
3
4
5
6
7
8
4
5 6 7 8 9 10 Number of water molecules
Fig. 2. (a–g) Radial distribution functions (RDFs) from O (solid line) and H (dash line) atoms of water to N5, O2, O9, O12, O16 and O18 atoms and to center of mass of glucosamine molecule where (h) the distribution of running integration number in the first solvation shell of glucosamine was also given.
˚ of the N5–H, water molecules integrated up to 2.4 A O2–H, O9–H, O12–H, O16–H and O18–H RDFs are 0.2, 0.8, 0.3, 0.6, 0.5 and 1.0, respectively. This data as well as an appearance of the first peak or the hump of the RDFs from the N or O atoms of the ligand to the H atom of water indicates clearly that water molecules lying under the first peaks of the investigated RDFs form a hydrogen bond with the glucosamine molecule. The obtained coordinate numbers, which are quite high, do not represent numbers of hydrogen bonding between
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water and the ligand because of the overlapping of the RDFs center on different atoms of glucosamine. This fact is supported by the broadening or splitting of the RDFÕs first peaks. Note that: (i) a very sharp first peak of the RDF of O18–H indicates a strong H-bond between water and O18; (ii) the difference between the distance to the first maxima of the O18–O and O18–H RDFs which are almost equivalent to the O–H bond length of water indicates a formation of a linear hydrogen-bond. In Fig. 2g, total radial distribution functions from the center of glucosamine for the entire volume (E) to oxygen and hydrogen atoms of water, gE-O(r) and gE-H(r), have been calculated. The plots display two peaks, cen˚ . Their running integration tered at about 4.3 and 5.1 A numbers, integrated up to the corresponding minima of ˚ , are seven and 26 water molecules, respec4.6 and 6.0 A
tively. An average first shell coordination number of glucosamine of seven can be analyzed more details in term of its distribution. Here, percentage of oxygen ˚ atoms of water lying within a spherical radius of 4.6 A (the first minimum of the gE-O(r) RDF) from the center of the glucosamine molecule was calculated and displayed in Fig. 2h. The plot shows a broad distribution from 5 to 9 water molecules indicating mobility and solvent exchange of water molecules between the first and the second solvation shells. This offers dynamic pictures of the ligand solvation superior the single picture provided by the average coordination number. To investigate the precise position of the seven water molecules in the first solvation shell of glucosamine, the periodic cube, which the ligand was in the middle, was sliced into eight layers by the plane parallel to the xyplane (Fig. 3a). Layers L1, L2, L3 and L4 are the vol-
Fig. 3. The periodic cube was sliced into eight layers by the xy-plane and the space around glucosamine molecule was divided by x- and y-axis into four quadrants: (a) and the contour plots of the xy-coordinate of water molecules in; (b) the upper half (b) and the lower half; (c) of each quadrant (Q) in the first coordination shell of glucosamine.
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umes where 0 6 z 6 2, 2 < z 6 3, 3 < z 6 4, and ˚ , respectively. In addition, layers L1 0 , L2 0 , 4
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tains three points, point m, part of point k in layer L3 0 , and part of point k 0 in layer L4 0 . Points k and k 0 yield from the same water molecule interacting with ˚ the ring of the glucosamine molecule at more than 3 A below the plane. At this layer, point m indicates a partial solvation of the O9 atom of the glucosamine molecule. It is interesting to note that the low density points on the contour plot, such as point f, h and j, relates to the mobility of the water molecules due to a weak glucosamine–water interaction. This event is supported by the underfine first-minimum of almost all RDFs, as well as the distribution of the coordination numbers depicted in Fig. 2h, in which the percentage of detecting 5, 6, 7, 8 and 9 water molecules around the ligand within the dis˚ from the center of the ligand are 8.6%, tance of 4.6 A 22.6%, 37.1%, 23.2% and 8.5%, respectively. The broad distribution yields the average coordination number of 7.0 water molecules around the glucosamine.
Fig. 4. The first solvation shell of glucosamine consisting of seven water molecules labeled as W1–W7: (a) summarized distribution of water density distributing in each layer: W1(L1–L1 0 ), W2(L2 0 ), W3(L2–L3), W4(L2 0 –L3 0 ), W5(L3 0 –L4 0 ), W6(L3) and W7(L3 0 ); (b) snapshot, one out of 16 million equilibration configurations.
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Taking into account all data mentioned above, precise positions of the seven water molecules, w1–w7, in the first solvation shell of glucosamine have been drawn and displayed in Fig. 4a. The snapshot (one out of 16 million equilibrium configurations) depicted in Fig. 4b supports all detailed investigations shown in Figs. 3(b and c) and the final conclusion in Fig. 4a.
Acknowledgements Financial support from the Shell Centenary Scholarship fund and the Thailand Research Fund (RTA4680008) as well as the generous supply of computer time by the Austrian–Thai Centre for Computer Assisted Chemical Education and Research, Computer for Advanced Research Center. Faculty of Science, Chulalongkorn University, and the National Electronic and Computer Technology Center, Bangkok, are gratefully acknowledged.
References [1] R. Sheperd, S. Reader, A. Falshaw, Glycoconjugate J. 14 (1997) 535. [2] S. Hirano, Polym. Int. 48 (1999) 732. [3] R. Ravindra, K.R. Krovvidi, A.A. Khan, Carbohyd. Polym. 36 (1998) 121. [4] N. Koseva, N. Manolova, N. Markova, T. Radoucheva, I. Rashkov, Polym. bull. 43 (1999) 101. [5] B. Narasimhan, Adv. Drug Deliver. Rev. 48 (2–3) (2001) 195. [6] G. Alagona, C. Ghio, P.A. Kollman, J. Am. Chem. Soc. 107 (1985) 2229.
[7] R. Muzzarelli, Polymeric Biomaterials, Marcel Dekker, New York, 1994. [8] K. Deuchi, O. Kanauchi, Y. Imasato, E. Kobayashi, Biosci. Biotech. Bioch. 58 (1994) 1613. [9] E.A. Trautwein, U. Jurgensen, H.F. Erbersdobler, Nutr. Res. 17 (1997) 1053. [10] D. Thacharodi, K.P. Rao, J. Chem. Technol. Biot. 58 (1993) 177. [11] Y.-E. Fang, Q. Cheng, X.-B. Lu, J. Appl. Polym. Sci. 68 (1998) 1751. [12] I. Genta, P. Perugini, F. Pavanetto, Drug Dev. Ind. Pharm. 24 (1998) 779. [13] S. Nakatsuka, A.L. Andrady, J. Appl. Polym. Sci. 44 (1992) 17. [14] N. Kubota, Bull. Chem. Soc. Jpn. 66 (1993) 1807. [15] A.A. Al-Angary, A.A.M. Al-Helw, M.M. Al-Dardiri, G.M. Mahrous, Pharm. Ind. 60 (1998) 629. [16] T.Y. Hsien, G.L. Rorrer, Ind. Eng. Chem. Res. 36 (1997) 3631. [17] J. R. Cardinal, W. J. Curatolo, C. D. Ebert, US Patent 4895, (1990) 724. [18] S. Hannongbua, B.M. Rode, Chem. Phys. 162 (1992) 257. [19] S. Hannongbua, J. Phys. Chem. 100 (1996) 17655. [20] S. Udomsub, S. Hannongbua, J. Chem. Soc., Faraday Trans. 93 (1997) 3045. [21] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21 (1953) 1087. [22] Cambridge Crystallographic Data Center, Cambridge, UK. Available from: <(http://www.ccdc.cam.ac.uk)>. [23] M.J. Frisch et al., GAUSSIAN 98, Revision A, Gaussian, Inc., Pittsburgh, PA, 1998. [24] T.H. Dunning, P.J. Hay, Methods of Electronic Structure Theory, vol. 3, New York, Plenum Press, 1977. [25] W.S. Benedict, N. Gailar, E.K. Plyler, J. Phys. Chem. 24 (1956) 1139. [26] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [27] O. Matsuoka, E. Clementi, M. Yoshimeine, J. Chem. Phys. 64 (1976) 1351. [28] E.R. Caffarena, J.R. Grigera, Carbohyd. Res. 315 (1999) 63. [29] C. Molteni, M. Parrinello, J. Am. Chem. Soc. 120 (1998) 2168.