Molecular interactions of a-cyclodextrin inclusion complexesusing a genetic algorithm

Wensheng Caia,*, Baoyun Xiaa, Xueguang Shaob, Qingxiang Guob, B. Maigretc,Zhongxiao Pana

aDepartment of Applied Chemistry, University of Science and Technology of China, Hefei 230026, People's Republic of ChinabDepartment of Chemistry, University of Science and Technology of China, Hefei 230026, People's Republic of China

cLaboratory of Theoretical Chemistry, Henri Poincare University Nancy I, B.P. 239 54506, France

Received 23 February 2000; accepted 28 April 2000

Abstract

Molecular interactions of inclusion complexes of mono- or 1,4-disubstituted benzenes and a-cyclodextrin have been studied

in this paper. Two types of energy terms were considered in the total interaction energies, non-bonded term and desolvation

term, and minimized by a genetic algorithm (GA). Using the consistent force ®eld (CFF91), the non-bonded energies between

all pairs of atoms in different molecules were determined by a Coulomb potential term for electrostatic interactions and a

Lennard-Jones potential for van der Waals interactions. The desolvation energy term was modeled by a simple constant term

corresponding to a penalty when polar atoms are placed in the hydrophobic cavity. The total interaction energies for 15

inclusion complexes with experimental association constants (ln K) were optimized by the GA method. Linear regression

analysis of the observed association constants against the total energies was performed. It was found that the interaction

energies of these complexes obtained by the simple interaction energy model could be correlated with their experimental

association constants, and also the desolvation term should be included. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: Molecular interaction; a-Cyclodextrin; Genetic algorithm; Molecular surface

1. Introduction

The host±guest interaction is very important to

understand the non-covalent interaction, which

controls many biological phenomena such as protein

folding, and ligand±protein interaction [1]. The a-

cyclodextrin (a-CD) is composed of six glucose

units and these cyclic oligosaccharides form a dough-

nut-shaped molecule. Because of this structure, the a-

CD exterior bristling with hydroxyl groups, is fairly

polar, whereas the interior of the cavity is non-polar

relative to the exterior, i.e. the interior is hydrophobic

property and the exterior is hydrophilic [2]. Many

computational methods have been employed to

study the cyclodextrin (CD) complexation, such as

quantum mechanics (QM), molecular mechanics

(MM), molecular dynamics (MD), and Monte Carlo

simulation (MC) [3]. The previous studies showed

that van der Waals interactions are the main driving

force for the complex formation of CD and guest

compounds. In this paper, the molecular interactions

of the host±guest systems were investigated based on

the molecular mechanics. The non-bonded interaction

energies (Einter) between guest molecules and a-CD

including van der Waals (Evdw) and electrostatic

(Eelec) interactions were calculated using the consistent

Journal of Molecular Structure (Theochem) 535 (2001) 115±119

0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.

PII: S0166-1280(00)00585-6

www.elsevier.nl/locate/theochem

* Corresponding author.

force ®eld (CFF91). Besides intermolecular interac-

tions the solvent effects also essentially determine the

structure and stability of such complexes [2,3].

However, to evaluate the contribution of solvation

effects to the entropy changes in real systems is dif®-

cult. In our study, a simple constant term (Edesol) corre-

sponding to a penalty when the polar atoms of guests

are placed inside the hydrophobic cavity of a-CD was

adopted to model the desolvation energy which is

proportional to the exposed surface area of the polar

atoms [4,5]. It is added to the total interaction energy

as a penalty term, and this modi®ed energy function

was minimized by a genetic algorithm (GA) to obtain

the positions and orientations of the guests with the

lowest energies.

A GA was introduced by John Holland [6] in 1975,

as probabilistic search technique. It starts from an

initial population, evolves by exploitation and

exploration acting on chromosomes, and ®nely ®nds

the best solution to a problem. The exploitation proce-

dures select parents from the population according to

their ®tness values. The exploration procedures

including recombination and mutation are operated

on the parents' chromosomes to generate a new popu-

lation with a certain probability. In a GA procedure,

the ®tness function plays an important role that is used

to evaluate the quality of the candidate solutions in

population. Due to the advantages of global and paral-

lel searching ability, GA has been applied to many

complicated optimization tasks, such as geometry

optimizations [7,8] for structures. In this paper, the

total interaction energies (Etot) between 15 mono- or

1,4-disubstituted benzenes and a-CD were evaluated

as the ®tness values and minimized by the GA proce-

dure.

In order to correlate the total energy with the stabi-

lity of these 15 complexes, linear regression analysis

of the logarithm of the experimental association

constants (ln K) [9] against the minimized energies

was performed. The correlation coef®cients are

20.868, which indicated that this simple energy

model is reasonable for these complexes. Further

analysis for each energy term showed that Evdw is

more important than the Eelec, and Edesol is a factor to

determine which substituent is located in the cavity

during the a-CD±guest complex formation. This

model will bene®t the study of other host±guest

systems.

2. Theory and method

2.1. Molecular interaction energy calculations

The most stable structure of a complex is often the

geometry with the lowest potential energy. The crys-

tallographic structure of a-CD [10] was used in all

calculations and the structures of benzene derivatives

were built by Insight II. With the assumption that the

guest molecules and a-CD are rigid structures, only

the intermolecular non-bonded interactions including

van der Waals interactions and electrostatic inter-

actions are considered. The interaction energy

between a-CD and the guest molecules is calculated

based on CFF91 force ®eld by the following potential:

Einter � Evdw 1 Eelec �Xi.j

Aij

r9ij

2Bij

r6ij

" #1Xi.j

qiqj

erij

�1�where Aij and Bij are van der Waals attractive and

disperse parameters, qi and qj are the partial charges

of the interacting atoms, rij is the distance between the

interacting atoms, and e is the dielectric constant of

the medium. e � rij is chosen for the calculation

according to Miertus et al. [11]. The CFF91 parameter

set is used in the calculation.

From the previous report [3], the solvation strongly

effects the interaction energy between the a-CD and

the guests. Therefore, the solvation effects should be

included in the total energies of the complexes of a-

CD and guests. To simplify the effects, the desolva-

tion energy term used by Hahn in his receptor surface

models [4,5] was introduced to modify the total

energy function as a penalty function. It brought

into a penalty when polar atoms were placed in the

cavity of a-CD. This is due to the hydrophobicity of

the cavity. When polar atoms are placed in this region,

the illegal contact will reduce the stability of the

complex. This energy is proportional to the exposed

surface area of the polar atom. Thus, the total inter-

action energy of the complex was modi®ed as:

Etot � Einter 1 Edesol �2�in which,

Edesol � A £ Spolar �3�in the above equation, Spolar is the exposed surface area

W. Cai et al. / Journal of Molecular Structure (Theochem) 535 (2001) 115±119116

of the polar atom calculated by Connolly's program

[12], A is an experience constant, a value of 1.0 kcal/

mol AÊ 2 is used. When polar atoms are located inside

the cavity, the corresponding desolvation energy term

is added to the total energy, which will be used as a

measure of ®tness of our GA program.

2.2. Genetic algorithms

The a-CD was ®xed in the space to de®ne the

coordinate system. Six parameters, the translation

parameters Tx, Ty, Tz and Euler angles u , f , c , were

used as genes in the GA to describe the relative posi-

tion and orientation between guests and a-CD. The

®tness function is the key factor in a GA, it determines

the performance of a GA. In the geometry optimiza-

tion problem of complexes, the interaction potential

energy of each geometry acts as a measure of ®tness.

The individual is evaluated and selected according to

this criterion. The evolution of the GA is thus straight-

forwardly directed to lower the energy till the global

minimum is located. The following main procedures

are included in the GA program:

(1) Initialization. The initial population strings

were generated randomly. Each parameter was

represented by an 8-bits `allele' of binary. The

following limits were used in this study:

Tx;Ty;Tze�23; 3� � �A�; c;f; e�0; 2p�; ue�0;p�: As

for the size of population, Np, 120 was chosen and

equally divided into four subpopulations, called

`niches' by McGarrah and Judson [13].

(2) Evaluation. Each parameter in an individual

string was decoded to a real value and used to

calculate the interaction energy by Eq. (2), and

the minus of the energy was adopted as the raw

®tness.

(3) Selection. The principle of roulette selection

criterion [14] was employed in the GA program,

and the raw ®tness was rescaled in order to control

the level of competition among members in the

population.

(4) Recombination and mutation. Random pairing

recombination, the simplest one-point cut crossover

and the bit-level jump mutation were employed in

the GA program.

3. Results and discussion

The program of the GA was written in Fortran 77

language and run on SGI R5000 workstation.

To test the energy model, 15 mono- or 1,4-disub-

stituted benzenes with or without polar atoms were

docked into a-CD. The lowest energies obtained by

GA optimization and the corresponding observed ln K

values for the inclusion complexes between a-CD and

X±C6H4±Y are listed in Table 1. Linear regression

analysis for observed ln K values with each energy

term was performed, respectively. The respective

linear relationships are obtained as follows:

ln K � 214:87 2 1:14E tot

�r � 20:868; sd � 0:505; n � 15��4�

ln K � 20:351 2 0:330Evdw

�r � 20:561; sd � 0:843; n � 15��5�

ln K � 5:24 1 0:220Eelec

�r � 0:273; sd � 0:979; n � 15��6�

W. Cai et al. / Journal of Molecular Structure (Theochem) 535 (2001) 115±119 117

Table 1

The experimental associate constants (ln K) and the lowest energies

obtained by GA optimization for the inclusion complexes between

a-CD and X±C6H4±Y (ln K, logarithm value of the experimental

associate constants [9]; Evdw, van der Waals energy; Eelec, electro-

static energy; Etot, total energy; the energy unit is kcal/mol)

No. X Y ln K Evdw Eelec Etot

1 CH3 CH3 4.28 215.84 20.26 216.42

2 F H 3.68 215.64 20.51 216.15

3 Cl H 4.72 216.11 21.03 217.14

4 Cl Cl 5.42 217.13 21.04 218.17

5 Br Br 6.93 217.35 20.93 218.29

6 Cl F 4.17 216.39 21.02 217.42

7 Br F 5.52 216.81 21.05 217.87

8 Et H 4.60 216.29 21.35 217.65

9 CH3 OH 3.92 215.08 21.36 216.44

10a CHO H 4.62 217.96 21.63 216.77

11 Cl NH2 5.53 216.05 21.72 217.77

12 CH3 NH2 4.05 213.25 23.24 216.49

13 Cl OH 5.61 216.72 21.34 218.06

14 Br OH 6.56 216.98 21.03 218.00

15 H NH2 4.03 211.41 25.20 216.61

a The desolvation energy is 2.81 kcal/mol.

The correlation coef®cient of Etot �r � 20:868�indicated that the interaction energy can be correlated

with the stability of the complexation. The plot of ln K

against the total energy is given in Fig. 1. Further-

more, from Table 1 and the correlation coef®cients

of Evdw and Eelec in Eqs. (5) and (6), it can be

concluded that the van der Waals interaction should

be the main driving force for the inclusion complexes

between a-CD with mono- or 1,4-disubstituted

benzenes, rather than the electrostatic force [9].

In the minimum energy structures obtained by the

GA optimization for the inclusion complexes in Table

1, the same orientations of the guest molecules

(substitutent X is located in the cavity) were also

reported in Ref. [9]. As two examples, the structures

of a-CD´p-bromo¯uorobenzene complex and a-

CD´p-chloro¯uorobenzene complex are shown in

Fig. 2, in which, the bromine and chlorine are well

inserted and near the primary hydroxyl rim, and the

¯uorine is towards the secondary hydroxyl rim of a-

CD. All these results showed that the total energy

model proposed in this paper is reasonable and can

be corrected with the stability constants.

Although most of the desolvation terms of the polar

atoms are zero (the polar atom is outside the cavity) in

W. Cai et al. / Journal of Molecular Structure (Theochem) 535 (2001) 115±119118

Fig. 1. Plot of ln K observed vs the total energy Etot.

Fig. 2. The minimum energy structures obtained by GA: (a) the

inclusion complex of a-CD and p-bromo¯uorobenzene; and (b)

the inclusion complex of a-CD and p-chloro¯uorobenzene.

Fig. 3. The minimum energy structures obtained by GA for the

inclusion complex of a-CD and p-bromophenol: (a) using energy

function with the penalty of desolvation; and (b) using energy func-

tion without the penalty of desolvation.

the ®nal energies for the complexes in Table 1, it is

important in the optimization procedure for it deter-

mines which substituent is located in the cavity during

the host±guest complex formation for the guests with

polar atoms. For example, in a-CD´p-bromophenol

complex, according to the previous studies [9], the

hydroxyl is highly electron-releasing while the

bromine is large and hydrophobic, in consequence

the bromine is proposed to stay in b -CD cavity. The

structure of a-CD´p-bromophenol complex optimized

by our method is shown in Fig. 3(a), in which the

bromine is located near the narrower rim of the cavity.

But lower energy structure of it with opposite orienta-

tion could be obtained when the interaction energy

function without the penalty of desolvation was used

in the GA optimization procedure, as in Fig. 3(b), the

hydroxyl is located near the narrower rim. Therefore,

the desolvation term is useful to con®ne polar atoms

to enter the cavity.

All these results showed that the total energy model

proposed in this paper is reasonable and can be

corrected with the stability constants. The limitation

of this method is that the desolvation term is too

simple, the hydrophobic interactions between apolar

atoms are not considered, i.e. the effect of hydro-

phobic surface area to the structure of the complex

has not been taken into account.

4. Conclusion

The energy model described in this paper is reliable

and a combination of the GA program it is convenient

to predict the inclusion stability for complex between

mono- or 1,4-disubstituted benzenes and a-CD. It

may provide us an alternate tool to study the inter-

actions of the host±guest systems. The calculation

results give a good relationship between observed

ln K values vs the total energies minimized. The linear

regression results also suggest that the van der Waals

interactions are more important than the electrostatic

interactions, which is in agreement with our precious

studies [9]. The desolvation effects determine the

orientation of the guest molecule with polar atoms

in the hydrophobic cavity of a-CD.

References

[1] J. Szejtli, Chem. Rev. 98 (1998) 1743.

[2] K.A. Connors, Chem. Rev. 97 (1997) 1325.

[3] K.B. Lipkowitz, Chem. Rev. 98 (1998) 1829.

[4] M. Hahn, J. Med. Chem. 38 (1995) 2080.

[5] M. Hahn, D. Rogers, J. Med. Chem. 38 (1995) 2091.

[6] J.H. Holland, Adaptation in Natural and Arti®cial Systems,

University of Michigan Press, Ann Arbor, MI, 1975.

[7] J. Mestres, G.E. Scuseria, J. Comput. Chem. 16 (1995) 729.

[8] W.-S. Cai, F. Yu, X.-G. Shao, Z.-X. Pan, Chin. J. Chem., 18

(2000) 475.

[9] L. Liu, Q.X. Guo, J. Phys. Chem. B 103 (1999) 3461.

[10] K. Harata, Bull. Chem. Soc. Jpn 49 (1975) 2409.

[11] S. Miertus, V. Frecer, E. Chiellini, F. Chiellini, R. Solaro, J.

Tomasi, J. Incl. Phenom. Mol. Recogn. 32 (1998) 23.

[12] M.L. Connolly, J. Appl. Cryst. 16 (1983) 548.

[13] B.D. McGarrah, R.S. Judson, J. Comp. Chem. 14 (1993) 1385.

[14] C.B. Lucasius, G. Kateman, Comput. Chem. 18 (1994) 137.

W. Cai et al. / Journal of Molecular Structure (Theochem) 535 (2001) 115±119 119