Free-energy landscapes of the coupled conformational transition and inclusion processes of <i>altro</i>-cyclodextrins

<p>Mono-<i>altro</i>-cyclodextrin (<i>altro</i>-CD) may undergo a conformational change of its altropyranose unit when encapsulating guest molecules of different sizes. This conformational transition is found to be coupled to the inclusion processes. In the present contribution, the possible conformational transition pathways in the four (self-)inclusion processes of <i>altro</i>-α and -β-CDs with moieties of variant shapes are explored from the insights of free-energy calculations. The two-dimensional free-energy landscapes characterising the coupled (self-)inclusion and isomerisation processes are determined, and the lowest free-energy pathways (LFEP) connecting the minima of the landscapes are located. The conformational statistics of the altropyranose units along the LFEPs reveal different transition pathways in the four (self-)inclusion processes. It can be concluded that when accommodating a free bulky guest molecule, the altropyranose unit will adjust its conformation to match the guest. However, such induced fit effect in the self-complexation of <i>altro</i>-CD derivatives will be weakened. The conformation of the altropyranose unit changes accompanying the self-complexation, but always adopts the ⁴C₁ one in the self-inclusion complex, irrespective of the shape of the guest moieties. The present results help determine the transition states of the (self-)inclusion processes of CDs and further improve the understanding of the mechanical properties of CD-based molecular shuttles.</p

Three benzenoids composed of 8 benzene rings possessing the same F indexes vector.

<p>Three benzenoids composed of 8 benzene rings possessing the same F indexes vector.</p

An illustration of two benzenoids possessing the same F indexes vector.

<p>An illustration of two benzenoids possessing the same F indexes vector.</p

Atomic asymmetry of an achiral benzenoid.

<p>The reflection line of molecule was represented by double headed arrow. a) atom numbers; b) binary codes; c) atomic sums; d) weighted atomic sums.</p

The binary codes and partial sums of atom 1 of benzenoid M in Figure 1.

<p>The binary codes and partial sums of atom 1 of benzenoid M in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0102043#pone-0102043-g001" target="_blank">Figure 1</a>.</p

An asymmetric atom possessing weighted atomic sum of zero.

<p>An asymmetric atom possessing weighted atomic sum of zero.</p

The numbers of the achiral benzenoids and all the benzenoids in 2D space, and the number of benzenoids in 3D space.

<p>The numbers of the achiral benzenoids and all the benzenoids in 2D space, and the number of benzenoids in 3D space.</p

Graph Theoretical Representation of Atomic Asymmetry and Molecular Chirality of Benzenoids in Two-Dimensional Space

<div><p>In order to explore atomic asymmetry and molecular chirality in 2D space, benzenoids composed of 3 to 11 hexagons in 2D space were enumerated in our laboratory. These benzenoids are regarded as planar connected polyhexes and have no internal holes; that is, their internal regions are filled with hexagons. The produced dataset was composed of 357,968 benzenoids, including more than 14 million atoms. Rather than simply labeling the huge number of atoms as being either symmetric or asymmetric, this investigation aims at exploring a quantitative graph theoretical descriptor of atomic asymmetry. Based on the particular characteristics in the 2D plane, we suggested the weighted atomic sum as the descriptor of atomic asymmetry. This descriptor is measured by circulating around the molecule going in opposite directions. The investigation demonstrates that the weighted atomic sums are superior to the previously reported quantitative descriptor, atomic sums. The investigation of quantitative descriptors also reveals that the most asymmetric atom is in a structure with a spiral ring with the convex shape going in clockwise direction and concave shape going in anticlockwise direction from the atom. Based on weighted atomic sums, a weighted F index is introduced to quantitatively represent molecular chirality in the plane, rather than merely regarding benzenoids as being either chiral or achiral. By validating with enumerated benzenoids, the results indicate that the weighted F indexes were in accordance with their chiral classification (achiral or chiral) over the whole benzenoids dataset. Furthermore, weighted F indexes were superior to previously available descriptors. Benzenoids possess a variety of shapes and can be extended to practically represent any shape in 2D space—our proposed descriptor has thus the potential to be a general method to represent 2D molecular chirality based on the difference between clockwise and anticlockwise sums around a molecule.</p></div

The examples of benzenoids composed of 1–6 benzene rings on a hexagonal lattice.

<p>The examples of benzenoids composed of 1–6 benzene rings on a hexagonal lattice.</p

Atomic asymmetry of a pair of enantiomers M and OM.

<p>a) atom numbers; b) binary codes; c) atomic sums; d) weighted atomic sums.</p