Application of restrained minimization, simulated annealing and molecular dynamics simulations for the conformational analysis of oligosaccharides
S.W.Homans and M.Forster1 Department of Biochemistry, University of Dundee, Dundee DD1 4HN and 'Department of Informatics, National Institute of Biological Standards and Control, Blanche Lane, South Mimms, Potters Bar EN6 3QG, UK
Key words: conformational analysis/NMR/NOE/oligosaccharides
Introduction A fundamental difficulty which is often encountered in the solution conformational analysis of oligosaccharides by NMR is the number and quality of experimental distance constraints. Often, only one or two nuclear Overhauser effects (NOEs) are measurable across the glycosidic linkages, and since these linkages are the primary source of conformational variance, the overall three-dimensional structure of the oligosaccharide may be seriously under-defined by NOEs alone. Additional constraints can be obtained from long-range heteronuclear (13C-'H) coupling constants across the glycosidic linkages (Hamer et al., 1978; Tvaroska et al., 1989; Poppe and van Halbeek, 1991b,c), but this may require an order of magnitude more material than is available from the biological source. In view of the lack of distance constraints, early studies on oligosaccharide conformations relied heavily on molecular mechanical or quantum mechanical energy calculations to restrict the number of possible conformations which were consistent with the NMR data (Bock, 1983; Brisson and Carver, 1983a,b; Sabesan et al., 1984; Homans et al., 1986, 1987a,b; © Oxford University Press
An alternative strategy for conformational analysis which is routinely used for the determination of the solution structures of proteins and nucleic acids (Wuthrich, 1986), but which has found only limited applicability to oligosaccharides (Scarsdale et al., 1988; Homans et al., 1989), is to include NOE distance constraints in molecular mechanical energy calculations and dynamics simulations as pseudoenergy terms, by which minimization and searching of conformational space is dependent on theoretical and experimental constraints simultaneously. The very large number of available constraints from proteins is such that the overall folding pathway of at least the Co backbone can be obtained widi a minimal regard for the precise nature of the molecular mechanical 'Hamiltonian', as exemplified by the success of the distance geometry approach (Braun and Go, 1985; Havel and Wuthrich, 1985). However, the conformational analysis of oligosaccharides is loosely equivalent to the determination of side-chain orientation in proteins and here the use of a full molecular mechanical force field, and in particular the explicit inclusion of solvent water, would appear to be essential (Homans, 1990). Prompted by the availability of a full molecular mechanical force field for oligosaccharides (Homans, 1990) derived from the original work of Ha et al. (1988), and in the light of recent 143
Downloaded from http://glycob.oxfordjournals.org/ at University of Birmingham on November 20, 2014
The purpose of the present study was to determine the confidence with which the small number of 'H NMR nuclear Overhauser effect (NOE) distance constraints measurable across glycosidic linkages in oligosaccharides could be used for solution conformational analysis. This was assessed by use of these constraints in restrained molecular mechanical minimization of the tetrasaccharide Gal/31-4(Fucal-3)GlcNAqSl-3Gal, a model compound of the Lewis-X antigenic determinant. This presents a particularly severe test case in view of extreme resonance overlap and a dearth of interresidue distance constraints. It is concluded that these constraints, when used in conventional restrained minimization, result in the generation of 'virtual conformations' and local minima about glycosidic linkages. However, these restraints are nevertheless found to be useful in the initial stages of a conformational analysis strategy involving restrained minimization combined with dynamical simulated annealing to define more accurately the global minimum energy configuration, together with molecular dynamics simulation to explore conformational mobility about this minimum. Theoretical ROE values calculated over the time course of the MD simulation, using a formalism appropriate for the time scale of the internal motion, are compared with those obtained experimentally in the oligosaccharide.
Paulsen et al., 1986). These studies were based on the assumption that the majority of glycosidic linkages were essentially rigid on the NMR time scale. However, later work based primarily on in vacuo grid search calculations about the glycosidic linkages of model disaccharides (Cumming et al., 1987) and molecular dynamics simulations (Homans et al., 1987c) suggested that significant torsional oscillations exist about glycosidic linkages, and this led to the conclusion that NOE distance restraints could not be used with confidence for the conformational analysis of oligosaccharides due to the definition of 'virtual conformations' (Cumming and Carver, 1987). Experimental NOE data were thus included in the analysis only in terms of comparison with theoretical NOEs generated by a sampling of Boltzmann-weighted discrete microstates over the potential surface, on the assumption that the rate of internal motion was slow with respect to molecular tumbling (Cumming and Carver, 1987; Imberty etal., 1989; Peters etal., 1990). Recently, however, it has become clear that in vacuo simulations of oligosaccharides give an erroneously large estimate for the extent of torsional oscillation about glycosidic linkages. These recent conclusions are based on molecular dynamics simulations (Brady, 1986, 1987) of di- and tri-saccharides, some with explicit inclusion of solvent water (Edge et al., 1990; Homans, 1990; Madsen et al., 1990; Tran and Brady, 1990), from which it is clear that the torsional oscillations are highly damped due to the combined effects of solvent viscosity and stabilization by hydrogen bonding. An important additional result of these simulations is that torsional oscillations about glycosidic linkages are not slow with respect to molecular tumbling, under which conditions the abovementioned formalism for the computation of theoretical NOEs is inappropriate.
S.W.Horaans and M.Forster
(iii) Simulated annealing. Energy minimization by dynamical simulated annealing was achieved under otherwise identical conditions to molecular dynamics simulations, except that the system was equilibrated for 10 ps with a thermal bath at 300 K and thereafter successively for 1 ps with a thermal bath 10 K lower in temperature until a final temperature of 10 K was obtained, giving a total simulation time of 39 ps. Following simulation for a further 1 ps at 5 K, the resulting geometry was minimized by use of a steepest descents algorithm until the maximum derivative was r \
ciinj-r0,/,
if rtJ < r%
where rtj and r0,, are the calculated and target interproton distances, respectively, and C\ and c2 are force constants given by: c, = k75/(2(A/) 2 )
Theoretical Conventions The glycosidic torsion angles
> T;) and under these motional conditions the Overhauser effect is given by: 2
NOE'AX a
TC
£
n=-2
4.2
•4.4
(2) G-1M ' 1 N-4+N-6 N-6
where Y^ (6, ) are the normalized second-rank spherical harmonics: y M = (5/4T) 1 / 2 [ ^ C O S ^
90» ' 0 )
-
1/2]
•i 11
Y2l = -(15/8ir) 1/2 sinO costf exp(/0) Y-n = (15/32ir)1/2 sirrtf exp(2*)
88O> GO O I
• IP
Y,_m = ( - i r n,*
j j ) 3Gr3
"I*
1
•4.8
N-5 jQ|
I'
l
l
F-3
FA
G-2
5.0
£90 U
i
, 1
ppm
3.8
ppm
5.2
F-2
N-2+N-4 N-3 •
3.6
3.4
Fig. 1. Reporter region of the 'H homonuclear ROESY spectrum of Gal/31^(Fucal-3)GlcNAc/31-3Galj91-4Glc. Relevant cross-peak correlations between through-space coupled protons are shown in obvious notation, where N = GlcNAc/Sl-3, F = Fucal-3, G = Gal£l-4, 3G = -|31-3Gal.
Results and discussion The conformational properties of the Gal/3 l-4(Fucal-3)GlcNAc/Sl-3Gal moiety were examined experimentally from Overhauser effect measurements in the model compound Gal£l-4(Fucal-3)GlcNAc|31-3Gal£l^Glc. The presence of the additional glucose residue avoids complications during the analysis within the Le* determinant from 'anomerization effects', i.e. the doubling of certain resonances due to the presence of two anomers in solution. Since the rotational correlation time of this pentasaccharide is such that only small negative NOEs were observable at a proton spectrometer frequency of 500 MHz, Overhauser effect data were obtained by use of rotating frame Overhauser effect (ROESY) measurements. The 'reporter' region of the ROESY spectrum of Gal/31^(Fucal-3)GlcNAq31-3GaljSl^Glc is shown in Figure 1. All cross-peak intensities are negative with respect to the diagonal, indicating that HOHAHA-type cross-peaks are essentially purged under these experimental conditions. Each cross-peak was assigned to a proton pair by use of the complete proton resonance assignments for Gal/31-4(Fucal-3)GlcNAc/31-3Gal/31-4Glc (Homans, 1992). The volume of each cross-peak was integrated, from which a series of internuclear distances was obtained (Table I) by comparison of inter-residue cross-peak intensities with intra-residue cross-peak intensities corresponding to known, 'fixed' internuclear distances. These distances were then used as constraints in theoretical simulations as described in Experimental procedures. Only seven inter-residue ROEs were measurable and, as discussed below, the fidelity of the distance constraints corresponding to four of these was low due to cross-peak overlap and the absence of stereospecific assignments. The strategy which we have utilized to analyse the conformation and dynamics of the oligosaccharide is illustrated in Table n. This is closely related to published strategies for the conformational analysis of proteins (Clore et al., 1986; Wuthrich, 1986), but differs significantly in the choice of starting structures. In contrast to proteins, contiguous residues in oligosaccharides exist in a rather limited subset of available
Table I. Intemuclear distances derived from ROESY measurements on Gal/31 -4
