Ring dihedral Principal Component Analysis of furanose conformation - Carbohydrate Chemistry: Chemical and Biological Approaches - page 390

unstructured along a full revolution pathway, indicating a single state
and a random ensemble of conformational states. It is clear that no
special well-delimited spot appears, indicating that all conformations are
rather frequently visited along the ring torus in the range 0 o P o 200 and
25 o y m o 45, and that no significant barrier exists within this domain. It
is necessary to consider flexibility not only along the pseudo-rotational
pathway, but also with respect to the degree of puckering amplitude.
Evidence of this is given Fig. 8 (right side) when the free energy obtained
along the minimum energy pathway of the 2D-representation is com-
pared to the 1D-plot G = f(P). The failure to explicitly consider puckering
amplitude significantly overestimated the magnitude of the barrier
around P = 260. Averaging G over all y m in the one-dimensional plot
G = f(P) thus distorted an important aspect of the ring conformational
dynamics.
But the question arises of whether this set of two variables P and y m
describes the greatest part of the ring motions. Reducing a five-dimen-
sional space to two dimensions necessarily loses information. However,
while taking nothing away from the tremendous value of Altona's model
for the qualitative description of ring conformation, one can ask whether
these two axes are the most appropriate for the projection of an energy
profile.
In our new approach, which we term Ring dihedral Principal
Component Analysis (RdPCA), the collective motions of the ring are
characterized by the most significant contributors to ring movement
rather than by conceptually reasonable, but energetically arbitrary
descriptors such as P and y m . We took advantage of the relatively recently
described dPCA (dihedral principal component analysis) method 31 to
represent the multidimensional free-energy landscape of a chemical
system and to describe the ring flexibility of furanoses. This methodology
(dPCA) has been recently applied to studies of proteins. 32
This new representation model does not postulate any particular as-
sumption and thus affords several advantages:
- the definition of P and y m (being previously a source of ambiguity) is
no longer present: it is thus not necessary to consider the same y m for
each dihedral angle.
- it treats all endocyclic torsions equally, so that results are in-
dependent of atom numbering
- it is not limited to endocyclic dihedral angles, since exocyclic di-
hedral angles also may be included in the RdPCA analysis.
- the model is able to express all the non-equilibrium and non-
symmetrical situations explored by molecular dynamics.
The original idea of dPCA is that a covariance matrix, which provides
information on the correlations of the system, quantifies correlated
internal motions of a protein. Here, the dynamic behaviour of the small
network of the five dihedral angles has been investigated by applying a
dPCA on the sine and cosine transformed endocyclic dihedral angles (y 1 ,
y 2 , y 3 , y 4 , y 5 ) of the carbohydrate. The consideration of dihedral angles
rather than cartesian coordinates is appealing since we try to describe