3.1 IntroductionThe 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 Experimental methods
3.2.1 Crystallography 30-32From 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 spectroscopyNMR 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.
3.3 Computational methodsIf 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.
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.
3.4 Solvent models 49-51Since 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.
3.5 Application to carbohydratesThe 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.
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, ω, 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