Reconsidering the conformational flexibility of β-cyclodextrin

Abstract

Abstract Conformational analysis of β-cyclodextrin in vacuo has been carried out using two complementary searching techniques to answer the question: what is the relationship between the conformational changes in the Φ,Ψ torsional angles around the glycosidic bonds and the fluctuations of the hydroxyl pendant groups? Because of the large number of local minima on the conformation and potential energy surface of cyclodextrin, a standard systematic search involving molecular mechanics minimization at points on a regular, fixed torsional angle space grid would generate so many points as to be impractical for conformational sampling. Instead the RAMM (RAndom Molecular Mechanics) procedure, a molecular mechanics calculation based on a random walk within torsional angle space, is used here and is compared to the results of nanosecond molecular dynamics simulation. The RAMM procedure is a semi-automatic calculation of the n-dimensional potential energy surface of a molecule which combines a grid-based conformation and search for one pair of bonds with random generation of a conformational ensemble of rotatable bonds and optimization of molecular geometry. Results are presented for six conformers of low symmetry and three conformers with higher symmetry. For all cases, random sampling of the 287-dimensional hydroxy and hydroxymethyl pendant group torsional angle conformational space improved the molecular energy. Torsional angles involving the primary hydroxyl groups exhibited larger conformational freedom than those involving secondary hydroxyls. The secondary hydroxyls of the symmetric forms are involved in a homodromic O2…O3 hydrogen bonding network. The results of the RAMM modeling agree with results from molecular dynamics simulations at 300 K (1 ns), 400 K (2 ns), and at 1000 K (1 ns) with dielectric constant 1. At the two lower temperatures, the molecule fluctuates within the Φ,Ψ space at values around 0 °,0 °. The occupancy profile, drawn in two-dimensional Φ,Ψ plots, is similar for each of the seven combinations of Φi, Ψi and has a characteristic half-moon shape. A stabilizing hydrogen bond network between O2(i)…O3(i − 1) is present during the entire simulation with a consequent decrease in the mobility of HO2 and HO3 (oscillating around χ i2 ≅ −60 °, χ i3 t-60 ° ). No conformational transitions of these groups were observed at 300 K and the first and only reorientation (χi2 ≅ 180 °, χi3 ≅ 180 °) occurred at approximately 1.7 ns at 400 K. At 1000 K, the molecule explores regions beyond Φ,Ψ equal to 0 °,0 ° and the chair conformer of the pyranose rings is not preserved. An additional 2 ns molecular dynamics simulation at 400 K with dielectric constant 4 revealed the “flip-flop” character of O2…O3 hydrogen bonding between adjacent glucose residues.