Journal of Chemistry

Volume 2017 (2017), Article ID 6907421, 9 pages

https://doi.org/10.1155/2017/6907421

## Molecular Dynamics Study of the Factors Influencing the *β*-Cyclodextrin Inclusion Complex Formation of the Isomers of Linear Molecules

Departamento de Física, Universidad de La Laguna, La Laguna, 38206 Tenerife, Spain

Correspondence should be addressed to E. Alvira

Received 19 February 2017; Accepted 2 May 2017; Published 22 May 2017

Academic Editor: Jaime Villaverde

Copyright © 2017 E. Alvira. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The influence of the size, composition, and atomic distribution of linear guests on -cyclodextrin inclusion complex formation is clarified by means of a molecular dynamics simulation at constant temperature. The intermolecular energy is modelled by a Lennard-Jones potential, where the molecular composition is represented by various parameters and by a continuum description of the guest and cavity walls. It is concluded that the parameters related to the atomic size require minimum values for the confinement of linear molecules inside the cavity. The isomer with optimal affinity for -cyclodextrin as predicted by the free energy presents an asymmetrical molecular structure, and the position probability density shows that the isomer tends to insert the portion with largest atoms into the cavity, although the preferential binding site of the guest is not always located in regions of the host with maximum discriminatory power.

#### 1. Introduction

Cyclodextrins (CDs) are macrocyclic molecules composed of glucose units (6 for -CD, 7 for *β*-CD, 8 for *γ*-CD, etc.) forming truncated cone-shaped compounds, giving rise to cavities of different internal diameters capable of including molecules of different structure, size, and composition. The capacity of CDs for catalysis and chiral recognition is due mainly to the formation of inclusion complexes, when some lipophilic part of a molecule enters the hydrophobic cyclodextrin cavity [1–3]. A well-known experimental finding is the existence of an appropriate size of the guest to reach maximum binding affinity in each CD [4–7], but there is no theoretical justification for this result and the factors influencing this affinity are not known. CDs and their inclusion complexes have been theoretically studied using different computational methods: molecular mechanics (MM) [8, 9], molecular dynamics (MD) [6, 10], and Monte Carlo simulations (MC) [11, 12], where all the atoms of both CDs and guest molecules have been described.

The present study is part of a broader work devoted to *β*-cyclodextrin inclusion complex formation, based on a continuum description of the guest and cavity walls. In this work, different types of guests have been considered: atoms and cyclic, spherical, and linear molecules. Moreover, two simulation methods (MM and MD) have been applied to analyse the potential energy surfaces and mobility of the guest inside and around the CD. We started by studying the interaction energy between *β*-CD and atoms and cyclic or spherical guest molecules, proposing an analytical model for this energy when the guest’s centre of mass is located along the cavity axis [13]. This model was extended for points away from the axis and used to examine the mobility of these types of guests by means of a molecular dynamics simulation [14]. The interaction between *β*-cyclodextrin and symmetrical linear molecules with different lengths was carried out by MM and MD [15, 16], where the composition of the guest was characterized by the parameters , . To study the interaction between *β*-cyclodextrin and asymmetrical linear molecules, new parameters were introduced to represent the molecular composition . These parameters allow different atomic distributions to be represented in the linear molecule which result in positional isomers. The potential surfaces, energy and configuration of inclusion complexes, and their dependence on molecular length, composition, and atomic distribution have already been analysed [17–19]. The curve joining the minimum potential energy for every plane = constant defines the penetration potential, which describes the variation in interaction energy when its path through the cavity is nonaxial. The penetration potential resembles a well potential or two minima separated by a potential barrier, because the interaction energy is deeper inside than outside the cavity, which represents an attractive force to include the guest into a complex. However the shape of this curve is a consequence of the atomic distribution, particularly the position of the larger atoms in the linear guest. The molecular composition is related to the magnitude of the interaction energy, and there are no molecular parameters for which the penetration potential presents special characteristics that can justify the affinity of some types of molecules for *β*-CD.

Theoretically, there are several necessary conditions for the isomers to be separated by CD: they must be able to enter the cavity (where the complexes formed are more stable), and the differences in retention time of these complexes have to be enough to allow experimental detection. In the mentioned simulation methods, the elution order in an isomeric separation is usually determined from the differences in free energy, where lower interaction energy means a more tightly bound analyte and this is linked with longer retention time. However, MD also allows us to determine the time spent by the guest inside the cavity (residence time) and provides a huge amount of statistical information to also calculate where and how selective binding takes place [20, 21]. The aim of this study was to determine the differences in residence time and free energy for the isomers of a linear molecule, so as to predict the preferential molecular parameters of this type of guests and thus facilitate separation by CD.

#### 2. Simulation Method

The interaction energy between *β*-CD and a linear molecule is represented by the van der Waals contribution, modelled by a Lennard-Jones (6, 12) potential. It depends on two parameters , where is the depth of the well and is the position where the repulsive branch crosses zero [22–24].

In previous work, we analysed the dependence of the interaction energy between *β*-CD and linear guest molecules on the length, composition, and atomic distribution of the latter [19]. A minimum value of the molecular length was obtained for the differences in the interaction energy between isomers to be appreciable and thus their capacity to be separated. Therefore the present article deals with linear molecules with length Å. The interaction energy between the atoms of the system is represented by the parameters . With the ensemble , we try to generalize atoms of different size or type without the obscuring complications of too many material parameters, and represents the ratio of each pair , . The positions of different atoms on the linear molecule are represented by the parameters [19]. The same atomic distributions (7 cases) are used as previously to assess the influence of molecular stereochemistry on the interaction energy ( being ):(A)The atoms whose interaction with *β*-CD is characterized by being distributed together, from the top to the centre of the linear molecule(B)Distributions , , , with at (C), , , with around the centre of the guest(D), , , , (E)As in (B) but with the composition , , (F)As in (C) but with , , (G), , , , [19]The linear molecule can be symmetrical or asymmetrical depending on the atomic distribution and therefore on parameters . For instance, to represent a symmetrical molecule type (C), two parameters and are used, being that and (Figure 1). In contrast, to represent the asymmetrical atomic distribution of linear molecules type (A), only one parameter is needed whose value is .