The purpose of conformational analysis is to obtain a description of the
three-dimensional structure of molecules. Such knowledge is required in
order to understand the interactions between molecules, e.g.
carbohydrates and proteins, and is also of help in the structure
determination by NMR spectroscopy. The conformation of a molecule
may be described at different levels of detail. In the simplest case a single
conformer, i.e. three-dimensional structure, may be sufficient to explain
experimental data. The assumption of a single conformer may however
result in a "virtual conformation", i.e. a physically unreasonable
structure, if the molecule is flexible. In such cases, data may be better
fitted by assuming an equilibrium between several conformers. This
approach has the advantage that the physical properties of individual
conformers may be approximated directly from suitable model
compounds. In some cases a distribution function has been fitted against a
few observables so that a continuous, e.g. a Gaussian or maximum
entropy distribution, rather than discrete distribution of conformers is
obtained.
27-29
The use of a continous distribution also requires a more
detailed understanding of the measured physical properties.
Only in a few cases has the influence of flexibility and solvation been
addressed, since this requires a large amount of experimental data and
long and complex computer simulations
3.2.1 Crystallography
30-32
From single crystal X-ray diffraction data the coordinates of all atoms
can be obtained. Crystallisation can be an obstacle as many carbohydrates
do not readily form sufficiently good crystals. If they are
microcrystalline they can still produce a powder diffraction pattern, from
which, in principle, the same information can be obtained using Monte
Carlo methods.
33-35
Starting geometries for the refinement of diffraction
data may be obtained from NMR spectroscopy
36
or molecular
modelling.37,38
Solid state structures can naturally give little information
about the flexibility of molecules, although statistical treatments of large
collections of similar structures with common fragments can give
population distributions similar to those observed in solution (table 3.1).
39
3.2.2 NMR spectroscopy
NMR data is often simpler to obtain than a crystal structure. The amount
of structural information that can be gained is however limited as data
from NMR spectroscopy is dominated by short range effects.
Conformational flexibility may complicate the picture further as
conformational changes in general are fast on the NMR time-scale so that
only time-averaged properties are observed.
Many NMR-parameters have been proposed for conformational analysis
but only couplings constants (3J)
and nuclear Overhauser effects (NOE)
have found wider use. Both homo- and heteronuclear (
3JHH,
3JCH) coupling constants
40
are dependent on the size of the torsion angle around
the connecting bond. The dependence is described by Karplus type
equations
41
which are reasonably accurate for proton-proton couplings
but much less so for carbon-proton couplings. Nuclear Overhauser effects
are inversely proportional to the sixth power of the inter-nuclear distance
making them sensitive probes for short distances. Relaxation rates, which
are dependent on molecular motion, are also often measured but the
interpretation of these is difficult since it requires a separation into global
and local contributions.
42
As experimental methods improve and more data become available it is
likely that new correlations will be discovered and the accuracy of those
in current use will improve. Even when NMR data themselves are not
sufficient to determine conformational equilibria, useful interpretations
can often be made if combined with molecular dynamics simulations,
using experimental values as restraints or by comparison with values
calculated from simulations. Unlike crystallography, NMR spectroscopy
is not an all-or-nothing method. It is always possible to get some
information, but seldom sufficient to allow an unambiguous
interpretation.
If it the energy of different conformers is known it should be possible to
calculate their relative abundance by Boltzmann weighting. Computational
chemistry provides us with such methods based on quantum mechanics
and molecular mechanics.
Quantum mechanical methods (ab initio or semi-empirical) solve
wavefunctions and have to take both electrons and nuclei into account.
This makes the calculations complex and demanding in terms of computer
time and therefore their use remains restricted to small systems, often
with fixed geometries. Despite these limitations there are calculations
which require knowledge about electron densities or excited states, e.g.
UV-spectra, that can not be performed in any other way.
In molecular mechanics (MM) the forces between atoms are
approximated by empirical functions. These functions are simple and fast
to evaluate and allow the treatment of much larger systems containing
hundreds of molecules and thousands of atoms. The total "steric"-energy
of a conformer is given by summing the stretch, bend, torsion and non-
bonded energy terms which constitute a force field.
| Valence angle bend:
Ebend=Sum ktheta(theta-theta0)2
|
Torsion: Edihed=Sum kphi(1-cos n phi)
|
 |
 |
 |
 |
Bond stretch:
Ebond=Sum kb(r-r0)2
|
Non-bonded:
EvdW=Sum (Aij/rij12-
Bij/rij6)
|
 |
 |
 |
 |
Since the parameters, i.e. the coefficients in the equations, in
force fields
are empirical their quality relies on the availability of experimental data.
Whilst this is not generally a problem for stretch or bend interactions, the
parameters for non-bonded interactions and high energy structures are
difficult to obtain by experimental methods. Because of these difficulties
some recent force fields have been derived from quantum mechanical
calculations.
43
There has also been a certain bias towards peptides and
nucleotides in most force fields, but there are now special carbohydrate
parameters available for most force fields.
44,45
A simple force field for carbohydrates, which has been used frequently, HSEA,
46 uses fixed
geometries for the rings of the sugar residues and ignores both hydrogen
bonding and electrostatics. Despite these shortcomings it has been found
to reproduce experimental data in many cases.
To obtain the structure with lowest energy, and hence the most
populated, a geometry optimisation is performed. This is done by moving
the atoms until reaching an energy minimum. During such a minimisation
it is however not possible to cross energy barriers so that it is never
certain that the global energy minimum has been reached. The only way
to overcome this problem, referred to as the multiple-minima problem, is
to find every possible energy minimum, a task which may be
accomplished using grid search or Monte Carlo methods.
The energy of isolated molecules does not give a particularly accurate
description of the population distributions of actual molecules. A much
more realistic model is provided by Metropolis-Monte Carlo
47,48 (MMC)
or molecular dynamics (MD) simulations which, given sufficient time,
produce the proper ensembles of structures from which physical
properties may be computed. Whilst MMC is a purely statistical method,
MD is, in principle, time dependent MM. Instead of minimising the
energy of a molecule, all atoms are assigned velocities and then allowed to
move under the influence of the force field. Both statistical and dynamic
properties are readily extracted from MD.
Since many experiments are performed on molecules in solution it is
highly desirable to be able to mimic solvent effects in simulations. This is
particularly important for the study of biological interactions which take
place in the presence of water. The simplest adjustments are the increase
of the dielectric constant or the inclusion of a reaction field,
52,53 with a
dampening of the electrostatic interactions as a result. The inclusion of
stochastic forces on atoms to simulate random collisions with solvent
molecules (Langevin dynamics)
54,55 is another method to introduce
implicit solvent. When dealing with strongly hydrogen bonding solvents
such as water it may be necessary to include explicit solvent molecules
around the molecule to properly simulate solute-solvent interactions.
Using MD it is important that the simulation is allowed to run for
sufficient time so that all allowed conformations are visited several times.
If not the results of the simulation are likely to be inaccurate no matter
how accurate the model itself may be.
The conformation of carbohydrate residues can be divided into that of
the ring and that of the exocyclic torsions. In oligosaccharides the two
additional degrees of freedom across the glycosidic linkage are also of
interest.
Fig. 3.2: Degrees of conformational freedom in a saccharide
Torsions of interest are indicated in bold
The conformation of the ring is dominated by steric interactions between
axial groups. In hexopyranoses this causes a strong preference for the less
crowded 4C1 conformation
in the D-series (1C4
in the L-series) as this
places C-6 in an equatorial position. In pentoses, furanoses and
unsaturated pyranoses the differences in steric energy between
conformations are much smaller so that the conformation is often
determined by the anomeric effect. The term anomeric effect
56-61 is used
to describe the preference for placing electronegative substituents anti to
the electron pair of a heteroatom, i.e. oxygen.
Fig 3.3: The anomeric effect
| a) Donation of electron density into the C-O bond |
b) No overlap of orbitals |
 |
 |
| Lower dipolmoment (µ)
Favoured by electrostatics |
Higher dipolmoment (µ) |
The existence of such an effect has been demonstrated in five
(furanose),
59 six (pyranose)
60 and seven-membered
54,55 rings. The existence
of a reverse anomeric effect
62
has also been suggested. The anomeric
effect has been explained using electrostatic arguments, or molecular
orbital interactions. In flexible rings it is often necessary to determine
both the structure of the preferred conformers as well as their respective
populations. Often a simplified description of the conformations, based on
pseudorotation angles and puckering amplitudes
63 is used to make the
analysis more manageable.
The first attempts to determine the ring conformation of carbohydrates
were made by Hassel and Ottar (1947) using X-ray diffraction
64 and by
Reeves (1950) from the optical rotation of cuprammonium complexes.
65
The conformation of the glycosidic linkage is described by two torsions;
ΦH (H1-C1-On-Cn, in which n is the linkage atom)
and ΨH (C1-On-Cn-Hn).
There is a general preference for a gauche arrangement of the ring
oxygen and the anomeric substituent (
ΦH≈+60° for β-D-sugars, -60°
for α-D-sugars). This is called the exo-anomeric effect
66 and is of similar origin
as the anomeric effect. The value of ΨH is mainly determined by steric
effects and is usually -50° to +50°. The conformation around the
glycosidic linkage can be determined by measuring
3JCOCH
67,68 couplings
across the linkage.
In hexopyranoses there is one more exocyclic torsion, namely that of the
C5-C6 bond. This torsion is described either by the torsion angle, Omega,
defined as O5-C5-C6-O6, or as one of three possible staggered
conformers, gt (Ω≈60°), gg (Ω≈-60°)
or tg (Ω≈180°). The conformation
distribution is determined by a combination of steric- and stereoelectronic
factors. The most important steric factor is the repulsion between the
hydroxyl groups in 4- and 6-positions (Hassel-Ottar effect).
64 There is a
preference for values of ±60° for Ω (table 3.1)
which has been explained by the gauche effect.
69
Fig. 3.4: The gauche effect (illustrated for O5-C5-C6-O6)
| C-O/C-O orbital overlap |
C-O/C-H orbital overlap |
 |
 |
| Favoured by electrostatics but has higher total energy |
Donation of electron density from the C-H bond into the C-O bond
|
The gauche effect is caused by the ability of less electronegative
substituents to donate electrons into the C-X bond when they are anti.
If the assignment of the NMR signals from the prochiral protons on C-6
is known then it is possible to determine the population in the three
rotameric states experimentally from the size of the H5-H6 couplings.
Table 3.1: Relative populations (P) of hydroxymethyl rotamers as
determined by different experimental methods (using three state
models)
| Glucose |
|
Galactose |
|
Pgt |
Pgg |
Ptg |
|
Pgt |
Pgg |
Ptg |
| 3JHH
70 |
44 | 56 | 0 | | 47 | 14 | 39 |
| Crystal structures
39 |
40 | 60 | 0 | | 58 | 8 | 34 |
| Optical rotation
71 |
75 | 25 | 0 | | 66 | 0 | 33 |
Some saccharides, such as the blood group determinants,
72 are relatively
rigid and the structures obtained by energy minimisations with simple
force fields like HSEA are in good agreement with both solution- and
solid state structures
73 despite the neglect of electrostatic interactions and
solvent. Other saccharides, like sucrose,
74,75 depend on the inclusion of
explicit water to reproduce experimental data. There are recent results
showing that both ΦH-
76 and
ΨH-trans
77 conformers can be present in some
oligosaccharides, which suggests that the conformational flexibility in
solution is greater than previously believed. The large solvent exposed
surface area of carbohydrates makes them difficult to model accurately
and the experimental data are often insufficient to solve conformational
problems. Therefore the conformational analysis of carbohydrates is
more difficult than for most other compounds and relies on the
combination of experimental and computational methods.
78
