A molecular dynamics study of sodium chenodeoxycholate in an aqueous solution

Chemical Physics Letters 420 (2006) 489–492 www.elsevier.com/locate/cplett

A molecular dynamics study of sodium chenodeoxycholate in an aqueous solution Toshio Nakashima a

a,*

, Kensuke Iwahashi b, Susumu Okazaki

b

Department of Chemistry, Faculty of Education and Welfare Science, Oita University, Dan-noharu 700, Oita 870-1192, Japan b Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan Received 22 September 2005; in final form 28 December 2005 Available online 26 January 2006

Abstract Hydration structure and dynamics of sodium chenodeoxycholate (CDC) in water are studied by a long-time molecular dynamics calculation. Strong hydration shell around the hydrophobic region of this large solute and strong hydrogen bonds of water with both hydroxyl and carboxyl oxygen atoms have been identified. The rotation of CDC around its longitudinal axis is found to be particularly active in comparison with that around other axes of the molecule. The diffusion coefficient of CDC calculated from the slope of the meansquare displacement, 0.95 · 109 m2/s, is only 1/6 of that for water in the solution, 5.4 · 109 m2/s.  2006 Elsevier B.V. All rights reserved.

1. Introduction Amphipathic bile salts are the main product of cholesterol metabolism. Their main biological function is to solubilize dietary lipids and greatly accelerate their absorption [1]. Among many bile salts, sodium CDC is a typical substance that has carboxylic and hydroxyl groups in steroid skeleton, as shown in Fig. 1 [2]. Small et al. [2] and Mysels and Mukerjee [8] reported macroscopic experimental measurements of surface tensions, conductivities, and other physicochemical quantities [3–7]. They suggest that most bile salts aggregate step by step, e.g. from dimer to trimer, with increasing concentration but do not have a constant aggregation number, which is very different from that found for typical detergents such as SDS. As a result, the details of the microscopic structure, interaction with bulk water, and dynamic properties have never been clearly understood. Thus, it seems timely to study the formation of aggregates such as dimer and trimer in terms of hydrophilic hydration and hydrophobic interaction by a critical comparison of their hydration

*

Corresponding author. Fax: +81 97 554 7554. E-mail address: [email protected] (T. Nakashima).

0009-2614/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.12.090

structures with the hydration structure and the dynamics of monomer CDC in an aqueous solution as a reference. The present study is focused on this issue by molecular dynamics calculations. Within our knowledge, only few computational studies have yet been reported on this system. We have studied the distribution of water around the hydrophilic oxygen atoms in the COO and OH groups and the hydrophobic carbon atoms in the CH3 groups. Two-dimensional distribution functions of water around CDC and the dynamic properties such as mean-square displacements and rotational autocorrelation functions have also been calculated. 2. Calculations A molecular dynamics simulation was carried out using the CHARMm27 force field [9] for the CDC molecule and the TIP3P model for water. The potential parameters for carbon ‘CT1’ in Ref. [9] were used for those of C(10) and C(13), since the values for the latter were not given in the table. Time integration was done by the RESPA method with a time step of 0.5 fs. The temperature was controlled at 300 K by a Nose–Hoover thermostat [10,11]. One bile acid molecule and sodium ion surrounded by 1500 TIP3P ˚ 3). water molecules were set in a cubic cell (35 · 35 · 35 A

T. Nakashima et al. / Chemical Physics Letters 420 (2006) 489–492

(f)

O 25

(e) (d)

(-0.27) (-0.27)

12 (-0.27) (-0.18) 19

(a)

(-0.18)

11

( 0.14)

9

10

24

17 (-0.09) 13

(-0.09)

14

8 (-0.09)

(-0.76)

O- 26

4

(-0.18) (-0.66)

5

7

(-0.09)

6 ( 0.14) (-0.18) (-0.66)

OH 28

2.5

(-0.28)

16 (-0.18)

(-0.09)

(a)

3.0

15 (-0.18)

3

HO 27

( 0.43)

z

x

1 (0)

22

(0)

(-0.18)

2

( 0.62)

20 (-0.09) 23

18

(-0.18)

(b)

(-0.18)

21

(c)

3.5

(-0.76)

( 0.43)

y

Fig. 1. Structure of CDC molecule. The molecule is assumed to be placed parallel to the plane. Solid lines (a)–(f) correspond to the sections presented in Fig. 3. Three molecular axes, x, y, and z are also defined. The x-axis is perpendicular to the plane. Partial charges on the atoms are given in parentheses. The charges on the H atoms in the alkyl groups are only ˚ in x, y, and z directions, 0.09. The molecular sizes are 5.0, 7.0, and 17 A respectively.

Although the concentration of the present system, 37 mM, is greater than the critical micelle concentration, 5 mM [3–7], the periodic boundary condition adopted in the calculation enables approximate simulation for the solution at infinite dilution. Partial charges for the skeletal atoms are presented in Fig. 1. The Ewald method [12,13] was used for the calculation of coulombic forces. 3. Results and discussion 3.1. Calculated structural features The bond angle of C(13)–C(17)–C(20) (see Fig. 1) is found to be 120 during the 1 ns calculation, which reflects the high rigidity of cholesterol skeleton. In addition, the torsional angle of C(13)–C(17)–C(20)–C(22) is almost always in the most stable anti conformation, where the energy barrier between the gauche conformation is as high as about 20 kJ mol1. However, the torsion of C(21)–C(20)–C(22)–C(23) is slightly flexible such that frequent transitions occur between the anti and gauche conformations, since no energy barrier exists from gauche to anti and the energy difference between them is only 10 kJ mol1. 3.2. Radial distribution functions of hydrated CDC The hydration structure around CDC is studied by calculation of various radial distribution functions, gOO(r), of O(26) of the COO group and O(27) and O(28) of the OH groups of CDC with water oxygen, as shown in Fig. 2a. The function for O(26) has a very sharp peak at ˚ , due to its negatively charged group, though r = 2.65 A the second peak is weaker than the first peak, indicating that the first hydration shell is strong but the second one

Radial Distribution Functions

490

2.0 1.5 1.0 0.5 0 (b)

1.0 0.5 0 2

3

4

5

6 r/Å

7

8

9

10

Fig. 2. (a) Radial distribution functions of water from oxygens atoms of CDC molecule. Solid line: O(26), dashed line: O(27), and dotted line: O(28). (b) Radial distribution functions of water from carbon atoms of CDC molecule. Solid line: C(18), dashed line: C(19) and dotted line: C(21).

is weak. The function for O(25) has a similar feature (not shown), which implies the equivalence of these two oxygen atoms. In contrast, O(27) and O(28) in the OH groups show slightly different features from each other. The first peak for O(27), 1.91, is much higher than that for O(28), 1.44, and the second peak of O(27) is also more distinct than that of O(28). The reason is probably that O(27) is connected to the tail end of CDC, which is nearer to bulk water than O(28). No clear third peaks are found in any of these distribution functions. The hydration numbers of O(26), O(27) and O(28) are evaluated by integration of the first peak of gOO(r) to be 4.14, 3.31 and 2.65, respectively, which clearly represent strong hydration around the hydroxyl and carboxyl groups. As for the C(18), C(19) and C(21) atoms of the CH3 groups in the hydrophobic region of CDC with water oxygen, the radial distribution functions are displayed in Fig. 2b. The first peak positions assigned to these carbon ˚ , and their peak heights are atoms are all equal, r = 3.8 A ordered as C(21) > C(19) > C(18), depending on their distances from bulk water. Note that the second clear peaks ˚ represent hydrophobic hydration, being conaround 7 A trary to the weak second and third peaks observed for the hydrophilic groups stated above. The two-dimensional distribution function for water around CDC may be helpful to obtain an overview of the whole hydration structure. The distribution of all atoms of CDC and the oxygen atom of water around CDC, shown in Fig. 3, is obtained by perpendicular slices

T. Nakashima et al. / Chemical Physics Letters 420 (2006) 489–492

491

angle of the unit vector on the molecular axis, i = x, y, and z defined in Fig. 1. It is clear from the results shown in Fig. 4a that rotations around the x- and y-axes occur almost simultaneously, and that CDC rotates easily around the z-axis only. This is probably because the molecule is shaped like a rugby ball, with its z-axis aligned to the apsides. Thus the molecule can easily rotate around the line of apsides. The statistically averaged rotational autocorrelation function,  1

ð2Þ ð1Þ C R ðtÞ ¼ 3 cos2 hi ðtÞ  1 2 is displayed in Fig. 4b. Despite an appreciable statistical error, the decay in the autocorrelation of the longitudinal zaxis of CDC is significantly slower than the x- and y-axes. Finally, the self-diffusion coefficient of CDC, DC and that of water, DW, were evaluated from the slope of the calculated mean-square displacement plotted in Fig. 5. The resultant DC value, 0.95 · 109 m2 s1 is only 1/6 of DW, 5.4 · 109 m2 s1; this manifests the difficulty of translation of this large CDC molecule. The DW value obtained for

(a)

x 1 0

3.3. Intra-system motions of CDC molecule

cos θi(t)

y

1 0 -1

z

1 0 -1

0

0.2

0.4

0.6

0.8

1

t / ns (b) 1

x y z

(2)

along the longitudinal axis of CDC, as shown in Fig. 1; the molecular coordinates are defined by C(10), C(12), and C(15). The distribution is normalized to the average density of bulk water, taken as unity. Relatively high water density is found around the oxygen atoms of OH, as shown in Fig. 3a. This feature is consistent with the findings in the radial distribution function for O(27) shown in Fig. 2a. A part of the CDC skeleton appears in this sliced section in Fig. 3b; the influence of O(27) is clearly found as a strong hydration shell in the lower left part of this figure. Figs. 3b–d represent a huge rugby-balllike cavity formed by the CDC molecule. A slightly broad distribution of CDC carbon atoms found in Fig. 3e demonstrates that the tail chain of CDC has flexibility in its torsion. Other CH3 groups of C(19) and C(18) are almost rigidly fixed to the CDC skeleton. High water density is observed around the oxygen atoms of COO, as shown in Fig. 3f. A survey of these distribution functions 3(a)– (f) clearly demonstrates a strong hydration shell which covers the large solute.

-1

C R (t)

Fig. 3. Two-dimensional distribution of atoms on the planes (a)–(f) parallel to the x, y axes, defined in Fig. 1. Molecular coordinates are defined by three atoms, C(10), C(12), and C(15), see Fig. 1.

0 0

0.02

0.04

0.06

0.08

t / ns

For an analysis of the rotation of the CDC molecule, we have examined cos hi(t), where hi(t) denotes the rotational

Fig. 4. (a) Calculated cos hi(t) for i = x, y and z and (b) statistically averaged autocorrelation function, Eq. (1).

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T. Nakashima et al. / Chemical Physics Letters 420 (2006) 489–492

strates the difficulty of translation of the large CDC molecule.

180

Mean-square Displacement / Å

2

160 140

Acknowledgements

120 100 80

Water

60 40 CDC

20 0 0

10

20

30

40

50

This work was supported by NAREGI Nanoscience Project, Ministry of Education, Culture, Sports, Science and Technology, Japan and the Joint Studies Program (2002–2005) of the Institute for Molecular Science. The work was also supported in part by a Grant-in-Aid for Scientific Research(S) (17105001) from Japan Society for the Promotion of Science (JSPS). The calculations were carried out on the computers at Okazaki Research Center for Computational Science, National Institutes of Natural Sciences.

t / ps Fig. 5. Mean-square displacements of CDC and water in aqueous solution.

water corresponds well to that reported by Mark et al. [14], 5.6 · 109 m2 s1, for pure TIP3P water. 4. Conclusions A molecular dynamics calculation is carried out for a sodium CDC molecule in water. The radial distribution function of water from the carboxyl oxygen atoms in the hydrophilic region shows an intense peak, but the peaks for the hydroxyl oxygen atoms are much weaker. Three CH3 groups on the hydrophobic plane of cholesterol skeleton show strong correlation with water even at large r such that the second peak is still clearly found. From the two-dimensional distribution function, the molecule looks like a large rugby ball surrounded by a strong hydration shell except in the region of the tail chain. The molecule rotates easily around the line of apsides, but not around the other axes. The self-diffusion coefficient of CDC calculated from the slope of the mean-square displacement, 0.95 · 109 m2 s1, only 1/6 of that for water, 5.4 · 109 m2 s1, demon-

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