Ring dihedral Principal Component Analysis of furanose conformation - Carbohydrate Chemistry: Chemical and Biological Approaches - page 395

- the RdPCA representation proved to be an effective method to de-
scribe collective, global motions of the ring carbohydrate, with the two or
three principal components containing the largest mean-square

fluctuation.
- a three-dimensional RdPCA approach incorporating one additional
principal component is needed to obtain an adequate energy profile for
the understanding of the dynamics of ring motion, both from the ther-
modynamic and kinetic point of view. In particular it suggests possible
pathways through the transition state that are not apparent on the 2D
landscapes. The fact of projecting the conformational behaviour,
particularly in the range near the energy maximum, onto a given two-
dimensional coordinate system can result in significant distortions, in
either direction, of the energy landscape.
- the use of a two-dimensional Altona energy map as a function of P
and y m is appropriate for a qualitative understanding of the equilibrium
conformational space. However, for quantitative purposes, a three-di-
mensional RdPCA representation provides a less distorted representation
of the conformational space based on the major fluctuations PC1, PC2
and PC3.

Additional studies are underway to assess the ability of the
RdPCA model to represent conformational space among different
species. The perspectives opened by this preliminary research are to
incorporate exocyclic dihedral angles into the RdPCA analysis, in order
to probe the effects of exocyclic substituents on ring dynamics
and eventually to analyse correlated motions within oligosaccharide
structures, as well as to generalize this RdPCA analysis to other cyclic
structures, such as not only furanosides, but also pyranose rings and
even cyclodextrins.

Computational details
''Static'' quantum calculations
Density functional theory (HF-DFT with the B3LYP hybrid functional and
the triple-zeta augmented with diffuse and polarization function
6-311 þþ G** basis set) was employed to obtain all the results of section 3.
Calculations were performed using the Gaussian 09 package. 35 In order to
explore the complete potential energy profile E = f(P), a set of 180 initial
geometries was generated with puckering values equally distributed in the
range 0-360. For this, a value of y m = 401 was considered. These geometries
were then relaxed, fixing the puckering to its initial value by freezing one or
two dihedral angles during the relaxation. In a next stage, these 180
geometries were then fully optimized (without any constraint). Most of
them converged towards the same minimum on the potential energy
surface, and only a few solutions were obtained, characterized by a final
puckering value P (angle) and amplitude y m (radius). The zero point cor-
rected energy of these minima was highlighted on the pseudo-rotational
cycle using a grey scale. Solvent effect was addressed within the polarized
continuum model (PCM 36 )inthefieldofwater.