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C o n f o r m a t i o n a l S t u d i e s in t h e
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E x t r a p o l a t i o n t o M o l e c u l e s in S o l u t i o n G. A. JEFFREY Department of Crystallography, University of Pittsburgh, Pittsburgh, Pa. 15213 Numerical data from crystal structure determinations give convenient starting points for calculating the geometry of conformations consistent with bond rotational barriers and non-bonding interactions. In carbohydrates this approach to conformational analysis must be applied reservedly because of the common occurrence of intra- and inter-molecular hydrogen bonding. In molecules where there are many free hydroxyls, the hydrogen bonding in the solid state is pre dominantly intermolecular, and these crystal field forces have only a secondary influence on conformation. The hydrogen bonding of such a molecule in the solid must closely resemble that in an aqueous or polar solvent, except for the difference between static and dynamic environment. Intramolecular hydrogen bonding is much more significant in determining conformation and is the most serious reser vation in computer extrapolation from the conformation in the solid to theflexiblemolecule. C r y s t a l structure determination by diffraction methods is the principal
^ and most powerful method for obtaining numerical data on bond lengths, valence angles, and the characteristic geometry of functional groups. It is the only method for the direct measurement of these quanti ties in carbohydrates, which are not suitable compounds for microwave spectroscopy or gas-phase electron diffraction. The present limits of accu racy for the most productive of the diffraction methods, single crystal x-ray diffraction, is usually 1 or 2 picometers i n bond distances and a few degrees in valence angles. (The picometer is the most convenient SI unit for reporting crystal structural data although most crystallographers continue to use the A unit; ρ = 0.01 A . ) W i t h i n these limits these data are molecular properties, which in the absence of chemical change 177 Isbell; Carbohydrates in Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1973.
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can be extrapolated from the solid-state to other phases including solutions. A recent compilation ( I ) of organic crystal structures completed between 1939-1969 lists over 4,000 entries covering representative types of the most important compounds. This number has increased from 24 in 1952 to 250 in 1964 and 800 in 1968, resulting mainly from the devel opment of computers in the Fifties and the introduction of automatic diffractometers i n the Sixties. It is estimated that there are now more than 1000 new organic crystal structures being completed every year. It is not surprising therefore that sufficient data are available to predict bond lengths and angles and much of the molecular geometry of all but the unusual organic compound. The crystallographer has therefore studied in recent years the configurational analysis for newly isolated natural products and the conformational analysis of molecules where the con figuration is known. A protein crystal structure determination is an experiment i n conformational analysis since the amino acid sequence is generally known and the precision of the observed electron density dis tribution rarely allows the identification of a pair of atoms or a bond, on the basis of the observed atomic peaks or interatomic distances. A l l the molecular data shown below are implicit in the atomic co ordinates and lattice parameters reported in a molecular crystal structure determination. Crystal Structure Data
(
Bond Distances Valence Angles Geometry of Functional Groups
Molecular or Crystal
fTorsion Angles \ Intramolecular Non-bonding and [ Η-bonding Distances
r cfal crystal
(Intermolecular Non-bonding and j Η-bonding Distances
U n t i l recently it was not customary to report measurements such as torsion angles and intramolecular non-bonding distances because they are not necessarily characteristic molecular properties. The bond torsion angles, which are of special interest in conformational analysis, are often only reported and discussed when there is a special reason for doing so which is connected with the objectives of the structure determination. Tradition dies hard, and one still finds tables of bond distances and angles in crystal structure papers which are not significantly different from the expected values, whereas torsion angles and other conformational data which are of special interest to the chemist are not reported and have
Isbell; Carbohydrates in Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1973.
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to be computed by the reader from the atomic parameters and unit cell dimensions. (The conformational chemist using such crystal structural data is cautioned because some crystal structure papers report coordinates for one molecule while others report the asymmetric contents of one particular unit cell. These two sets of coordinates are not necessarily the same, and it is seldom stated i n the paper which set is given.) Even when this structural information is a characteristic of the crystal rather than of the molecule per se, it can, if used judiciously, give valuable clues to the conformational behavior of the molecules in the liquid state. Since most of carbohydrate chemistry takes place in solution between room temperature and 100 °C, the carbohydrate crystallographer is conscious of an obligation to examine the abundance of conformational information that is implicit i n the crystal structures he is capable of producing to assist his less fortunate colleagues who are concerned with the much more complex problem of the structure of flexible molecules i n solution. One attractive and convenient approach to conformational analysis in the liquid state is to start with the numerical data given by a set of atomic coordinates from a crystal structure determination and, by com puter, calculate the geometry of all conformations which are consistent with the concepts of single-bond rotations and van der Waals radii, thereby generating the numerical conformational data for the free mole cule (this idea has been applied mainly to nucleosides (2, 3 ) ) . In the absence of any experimental means of comparing these conformational possibilities with observations, this is more an exercise i n computer pro gramming than a contribution to conformational analysis. The nuclear magnetic resonance spectra, particularly through the application of the Karplus Equation (4), do give information relating directly to torsional angles, but these usually relate to the hydrogen atoms which are the least well-defined from the x-ray structure analysis. ( Distances and angles involving hydrogens obtained from x-ray data are only reliable to about 10 ρ and 10°. T o obtain accuracy comparable with that of the carbons and oxygens, a neutron diffraction analysis is necessary (5).) Neverthe less, the concept of computing all likely conformational geometries and systematically eliminating those which are inconsistent with the N M R spectra could lead to a feasible approach in favorable cases. It has the advantage that it combines the information from two independent and distinctly different techniques. A n elegant example of the application of this type of approach to the mononucleotides using the lanthanide ion as a probe has been recently reported (5). This work shows that the average solution conformations which fitted the N M R data were generally close to the conformations observed in the crystal structures. The computer input for such a conformational calculation consists of ( 1 ) the set of atomic coordinates, (2) the bonds about which rotation
Isbell; Carbohydrates in Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1973.
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SOLUTION
is permitted, (3) the angular intervals over which this rotation w i l l be explored, and (4) a set of limiting non-bonding atomic radii. A more quantitative evaluation of the most likely conformations can be obtained if a provision is also made for calculating non-bonding atom-pair poten tial energy sums of the Lennard-Jones type (6). If the molecule can be treated as several rigid units linked by two or three rotameric bonds, then the computations can be handled on a small or moderate-sized computer. As the number of rotameric bonds increases so do the demands on computer memory and paper output. There seems to be a real advantage to the use of the graphical display equipment to give rapid pictorial computer output (7). If the rotameric bonds have atoms other than hydrogens attached to them, it becomes reasonable to assume that the staggered bond conformations w i l l have significantly lower conformational energies than the eclipsed. The rota tions can then be restricted to 2 π / 3 ± 1 0 ° ; this greatly reduces the com putation and allows consideration of more rotameric bonds. This approach, which may offer advantages particularly for inter preting C N M R spectra of carbohydrates, has the basic assumption that the crystal structure atomic coordinates are a valid starting point for calculating conformations i n solution. (The alternative method, which is commonly used for predicting polypeptide and polysaccharide con formations, is to construct an ideal model and use its atomic coordinates as the starting point (δ, 9, 10, 11). Since the dimensions of the ideal molecule are generally based on a personal selection of data from crystal structure determinations of related molecules, there is a more objective element about starting with a set of actual observed atomic parameters for the particular molecule under consideration. ) This is a premise that requires careful scrutiny for carbohydrate molecules and is the principal theme of this chapter. A t the same time we w i l l review the conforma tional data from some carbohydrate crystal structures studied recently in our department and elsewhere. 1 3
There are several reasons for reservations about applying the com puter extrapolation of crystal structure data for carbohydrates. One is that much of the crystal structure data refer to unsubstituted sugars which are only soluble i n hydroxylic or polar solvents where the confor mational analysis may be complicated by hydrolysis, isomerism (mutarotation) (12), or stereospecific solvent interactions which require a more sophisticated model. However, assuming that such chemical changes do not occur or can be suppressed, there still remain questions to be answered before the conformation observed i n the crystal can be accepted as a close enough approximation to that of one or more of the rotomers which may predominate in the solution state. (a-L-Sorbose gives an example of the coexistence of two primary alcohol rotameric
Isbell; Carbohydrates in Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1973.
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conformers i n the crystal (13), and the same phenomenon is observed i n 1-kestose (14)). Molecules with free hydroxyl groups cohere i n the solid state by systems of intermolecular Η-bonds which frequently form infinite chains (to a crystallographer an infinite chain is one w h i c h extends to the domain boundaries of a single crystal, usually about 10" mm.) which link the molecules i n a much more stereospecific and directional manner than do van der Waals forces. W e would expect that the inter molecular Η-bonds determine the torsion angles of the Ο—Η bonds and they may place significant conformational restraints on the shape of the rest of the molecule. The methylated or acetylated sugar derivatives that the N M R spectroscopist uses to simplify his problem make the crystal structure determination more difficult and less attractive to the crystal lographer since the additional atoms, n, increase the number of param eters by 9n and the computing by 81n . More importantly, it is usually the free sugar which is the molecule with biological function, and this is often the long term objective of the crystallographic research. ( A n ex ample of a crystal structure determination directed solely toward testing a N M R interpretation is that of 1,2-o-aminoisopropylidine a-D-glycopyranoside hydroiodide (15).) 4
2
The second difficulty peculiar to carbohydrates is the allowance for conformational flexibility i n the pyranose and furanose rings, which is not easily accounted for by the comparatively simple computer program described above. A third question which is important for the unsubstituted sugars is whether it is necessary to provide for additional conformational stability resulting from the formation of intramolecular Η-bonds i n solution. ( Intramolecular Η-bonds are difficult to incorporate into limiting van der Waals radii because of their vectorial character and uncertainty about their potential energy function.) These three questions w i l l be examined i n relation to the conforma tional data which have been given by recent carbohydrate crystal struc ture determinations. Because of the added reliability and accuracy arising from the use of automatic diffractometers only those numerical data w i l l be quoted where these instruments were used. How Important is the Influence of Intermolecular Molecular Conformation in the Solid State}
Η-Bonds on
The answer to this question w i l l vary from structure to structure since it depends upon the flexibility of the molecules and the degree of intermolecular H-bonding. In any one class of compounds where a number of related structures are known, it is possible to evaluate the molecular distortions arising
Isbell; Carbohydrates in Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1973.
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CARBOHYDRATES I N SOLUTION
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