Computer Modeling of Carbohydrate Molecules - American Chemical

Chapter 16

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Conformational Analysis of Oligosaccharides Reconciliation of Theory with Experiment J. P. Carver , D. Mandel , S. W. Michnick , A. Imberty , and J. W. Brady 1

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Departments of Medical Genetics and Medical Biophysics, University of Toronto, Ontario, Canada M5S 1A8 Laboratoire de Physicochimie des Macromolécules, Institut National de la Recherche Agronomique, B.P. 527, 44072, Nantes, France Department of Food Science, Cornell University, Ithaca, NY 14853-7201 2

3

The primary tools for the determination of three-dimensional structure for oligosaccharides are X-ray diffraction and NMR. The latter experimental technique makes use of the nuclear Overhauser effect (NOE) which yields information on the distances between hydrogens in the molecule. When these distances span a glycosidic linkage, information regarding the torsional angles about that linkage can be deduced. However, a major problem with this otherwise ideal approach is internal flexibility. Because the NOE builds up over hundreds of milliseconds, any flexibility on this time scale will result in fluctuations in trans-glycosidic H-H distances and influence the final NOE value. To deduce three-dimensional structure from NOE measurements, one must, therefore, be able to model the internal flexibility of the oligosaccharide. It is straightforward to calculate the ensemble average steady state NOE and NOESY intensities once one has generated the ensemble. Thus by a careful comparison of quantitative NOE measurements with calculated values, i t is possible to evaluate the adequacy of the potential energy functions used to generate the ensemble. To date we have been unable to find a set of potential energy functions that allows us to predict adequately experimental NOE values. One of the more intriguing current questions in biology is the quest for the biological role of the carbohydrate components of glycoproteins and glycolipids. Cells of different lineages invest a considerable fraction of their metabolic energy into the complex biosynthetic pathways which generate these compounds with high specificity. Clearly these energetically expensive processes have been conserved and even elaborated during evolution - but why? Our laboratories have taken the approach that the information content of 4

On postdoctoral leavefromCERMAV, Grenoble, France 0097-6156/90/0430-0266$06.00/0 © 1990 American Chemical Society

French and Brady; Computer Modeling of Carbohydrate Molecules ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


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the oligosaccharide moieties l i e s in their three-dimensional structures. Thus, alterations in three-dimensional structure constitute a l t e r a t i o n s in the signals encoded by these molecules. Clues to their functions, therefore, should be available through a c o r r e l a t i o n of b i o l o g i c a l status with modifications i n primary structure that lead to alterations i n three-dimensional structure. Our focus i n this a r t i c l e i s on methods for the derivation of three-dimensional structure information from experimental NMR measurements. The "experiment-of-choice" for the exploration of the three-dimensional structures of oligosaccharides i s the one-dimensional NOE. This NMR experiment i s e a s i l y performed with modern instruments and can be readily quantified. However, the deduction of three-dimensional structure d i r e c t l y from measured NOE's i s frustrated at two l e v e l s . F i r s t , although the geometrical dependence of the NOE effect i s well understood (1), derivation of inter-hydrogen distances from measured NOE's requires that a complete set of NOE's between a l l hydrogens i n the molecule be measured. This i s r a r e l y , i f ever, possible, p a r t i c u l a r l y for^ oligosaccharides where the vast majority of resonances i n the H spectrum are crowded into 0.5 ppm. The errors associated with the use of a p a r t i a l set of NOE's vary greatly and therefore i t i s d i f f i c u l t to j u s t i f y such approximations a p r i o r i . Fortunately i t i s r e l a t i v e l y simple to calculate a l l the NOE's (observable or not) from any p a r t i c u l a r molecular geometry (2). Thus i t i s straightforward to explore torsion angle space for angles at which the predicted NOE's are in agreement with those observed (2). However, such an approach assumes that the molecule adopts only one fixed three-dimensional structure. This i s where the second complication comes i n . Considerable i n t e r n a l f l e x i b i l i t y about the g l y c o s i d i c linkage i s c l e a r l y evident from calculations of the Boltzman d i s t r i b u t i o n of molecular structures using the potential energy surfaces currently employed for oligosaccharides (2-6). S i m i l a r l y the force f i e l d s of Brady (7) and of Rasmussen (8) when used in molecular dynamics calculations (9, 10 and calculations below), reveal considerable f l e x i b i l i t y about the g l y c o s i d i c linkage. When t r a j e c t o r i e s are extended over time periods longer than 10 ps, even the force f i e l d used by Homans et a l . ( Π , 12) has been found to generate large t o r s i o n a l angle fluctuations (Dwek, R . A . , personal communication). These results suggest that we must model g l y c o s i d i c torsion angle f l e x i b i l i t y and incorporate i t into the interpretation of t r a n s - g l y c o s i d i c NOE measurements. In our e a r l i e r work (2,13,14) we were aware of this f l e x i b i l i t y but, since we were able to find s i n g l e , low-energy, conformations consistent with the NOE data, we assumed that the solvation of the oligosaccharides (neglected in the calculations referred to above) in r e a l i t y r e s t r i c t e d the f l e x i b i l i t y of the molecules. However, i n several subsequent cases these single conformations had potential energies which were quite high r e l a t i v e to the global minimum on the surface (15). We therefore became suspicious that these were what Jardetzky has termed "virtual" conformations (16) and these suspicions were confirmed when we found several examples where no single conformations compatible with the data existed (5,15; i n preparation).


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The question of how to include i n t e r n a l f l e x i b i l i t y into the i n t e r p r e t a t i o n of NOE's has been discussed by Noggle and Schirmer (1) i n their c l a s s i c book. Provided that the i n t e r n a l motions are fast compared to the l o n g i t u d i n a l relaxation rates and slow with respect to the c o r r e l a t i o n time, then the NOE effect w i l l be a function of the ensemble average values of ( 1 / r . . ) , where r . . i s the distance between the i t h and j t h hydrogens. S i n c e the l o n g i t u d i n a l relaxation times for hydrogens i n oligosaccharides are on the order of hundreds of milliseconds to seconds and the r o t a t i o n a l c o r r e l a t i o n times are usually about 100 ps, there are at least s i x orders of magnitude between these l i m i t s and i t seemed reasonable to assume i n i t i a l l y that i n t e r n a l motions l i e between these l i m i t s .


J

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Thus, i n recent studies (5,6), the ensemble average NOE's have been calculated by using an "ensemble average relaxation matrix". This matrix was generated by replacing the inverse s i x t h power of the inter-hydrogen distances, appearing i n the expressions for the bulk- and cross-relaxation terms, by t h e i r ensemble averages. The l a t t e r were calculated as the Bpltzman weighted sums over a l l the states of the values of ( 1 / r . . ) . When these ensemble average NOE's were compared to observed values, they were found to give closer agreement than single geometries corresponding to "preferred" three-dimensional structures (Table I) (5,6,15). These studies used s t a t i s t i c a l mechanics methods based on p o t e n t i a l energy surfaces derived from the rotation of fixed hexose rings about the g l y c o s i d i c torsion angles. Quite different NOE's are predicted i f different p o t e n t i a l energy surfaces are used (Table I ) . Molecular mechanics calculations for disaccharides (7,18; Imberty, Α . ; Tran, V . ; Perez S. J . Comp. Chem., i n press; also see below), not s u r p r i s i n g l y , have shown that the assumption of r i g i d geometry leads to a r t i f i c i a l l y steep potential energy surfaces. Such calculations demonstrate that permitting f l e x i b i l i t y i n bond lengths and angles further increases the magnitude of t o r s i o n a l angle fluctuations and thus has an important impact on calculated ensemble average properties. Because molecular dynamics force f i e l d s generally include this bond length and bond angle f l e x i b i l i t y and also since dynamics calculations are expected to e f f i c i e n t l y sample the s t a t i s t i c a l l y s i g n i f i c a n t regions of conformational space, we decided to examine the properties of NOE's calculated from molecular dynamics generated ensembles. This a r t i c l e represents a "progress report" describing results to date. More complete exploration of this approach w i l l be reported elsewhere. Recently, molecular dynamics calculations have been performed with e x p l i c i t i n c l u s i o n of water molecules. Although the frequencies and residence times are a l t e r e d , the amplitudes of conformational transitions about the g l y c o s i d i c bond appear not to be s i g n i f i c a n t l y changed i n these preliminary studies (Brady J . W . , unpublished r e s u l t s ; 26). Thus solvation does not appear to r e s t r i c t g l y c o s i d i c angle f l e x i b i l i t y but does have a strong damping effect and influences population d i s t r i b u t i o n s . The d i r e c t acknowledgment of f l e x i b i l i t y i n the interpretation of NOE's i s therefore absolutely e s s e n t i a l .


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Methods


Calculations were performed for the disaccharide Mana(l-3)Man3 (see Figure 1 for the structure) which i s one of the key linkages i n the N-linked oligosaccharide family of structures. Relaxed Map. A relaxed or adiabatic potential energy map was calculated for the Man(al-3)Man3 linkage using the MMP2(85) version of the o r i g i n a l molecular mechanics programme MM2 (19). The procedure was as previously described for Man(al-3)Mana (Imberty, Α . ; Tran, V . ; Perez S. J . Comp. Chem., i n press) except that maps were calculated for only four combinations of the C5C6 rotamers: GT-GT, GT-GG, GG-GT and GG-GG. These four maps were merged into a single map (Figure 2) by choosing the lowest energy found for each p h i / p s i pair (phi s H1C101C and psi s C101C H' ) . On the l a t t e r map four minima were found wriich are labeled MÎ, fe, MC and MD i n Figure 2. The i n i t i a l geometry used was taken from the c r y s t a l structure of Man(al-3)Man(31-4)GlcNAc determined by Warin et a l . (20) . Molecular dynamics. Calculations were performed using the programme CHARMM (21) with a force f i e l d for saccharides based on the PEF422 force f i e l d of Rasmussen (8). Newton's equations of motion were integrated using a Verlet algorithm with time steps of 1 f s . Over a period of 5 ps, the temperature was raised to 300 Κ i n 15 degree increments with v e l o c i t y rescaling every 250 f s . This was followed by a 15 ps e q u i l i b r a t i o n period during which the v e l o c i t i e s were p e r i o d i c a l l y rescaled. A 20 ps dynamics trajectory was then generated, during which average (over 250 fs) temperature fluctuations of less than 6 degree were observed. A l l CH b o n d ^ lengths were constrained to within an error tolerance of 1x10 using the SHAKE (25) algorithm of CHARMM (21). Four t r a j e c t o r i e s of 20 ps were started from each of the four minima found i n the relaxed MMP2(85) map (MA,MB,MC and MD i n Figure 2), using a different random number seed for each run. The s t a r t i n g geometry for each c a l c u l a t i o n was derived from either the carbohydrate topology and parameter f i l e s (Brady, J . V . , unpublished results) or from the f i n a l coordinates of runs which ended up i n the appropriate minimum. These geometries were then refined by minimizing the energy using the steepest descent and conjugate gradient algorithms of CHARMM (21) . In t o t a l sixteen independent 20 ps t r a j e c t o r i e s were thus accumulated. Transitions from minima corresponding to the i n i t i a l conformation to other minima on the surface were observed during the e q u i l i b r a t i o n period i n eleven cases so that the s t a r t i n g geometries for the sixteen t r a j e c t o r i e s corresponded to minima MA,MB,MC and MD in seven, seven, zero, and two cases, respectively. NOE C a l c u l a t i o n s . Coordinates were recorded every 10 f s . From the^ time series of molecular geometries the running averages of ( 1 / r . . ) for a l l inter-hydrogen distances were calculated. These running averages were output every picosecond and used to calculate the ensemble average NOE's (5) using the programme DYNAMO, developed i n Toronto. For the relaxed maps, a 2 0 ° x 2 0 ° g r i d was used to calculate the ensemble average NOE's from the four maps corresponding to GT-GT, GT-GG, GG-GT and GG-GG. These calculations were performed i n


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Nantes following the general methodology of Cumming and Carver (5). A l l the NOE calculations were performed for a previously described (22,23) hexa-deuterio version of Manal-3Man£ because the observed NOE's do not overlap and are much larger for this disaccharide than those for the undeuterated version. Thus the NOE's for the deuterated compound can be much more accurately measured. NOE Measurements. The one-dimensional NOE data were collected at 300 MHz on a Bruker AM-300 NMR spectrometer operating at 300 K. Because the relaxation times for the protons of the hexa-deuterated compound ranged from 0.4 s to 3-8 s, delays of 20 s. were used between scans. Values for the C T^'s were also measured and found to range from 0.32 s to 1.5 s; a l l values were consistent with a r o t a t i o n a l c o r r e l a t i o n time of 1.1x10" s. Results and Discussion Relaxed map. The relaxed map (Figure 2) for Man(al-3)Man£ shows l i t t l e difference from that calculated for Man(od-3)Mana by Imberty et a l . (Imberty, Α . ; Tran, V . ; Perez S. J . Comp. Chem., in press) but i s s t r i k i n g l y different from those previously obtained with the HSEA and HEAH potentials (6,17) in that two new low energy regions (MC and MD) have appeared. The MM2(85) potentials allow more conformational states to be reached at lower energies; thus the surface i s enlarged and low energy pathways appear between minima. The minimum at MB corresponds to that found with the HSEA potential and i s close to that found i n the c r y s t a l structure of Warin et a l . (20). The minimum at MA i s in the region of the hydrogen bonded structure o r i g i n a l l y suggested by Dwek's group (24) and i s the global minimum obtained with the HEAH potential (6,37). The p o t e n t i a l energy surface calculated using the PF0S potentials (as described i n Imberty, Α . ; Tran, V . ; Perez S. J . Comp. Chem., in press) also showed a l l four minima but the energy b a r r i e r s between minima are much higher than in the MM2(85) maps. Molecular Dynamics. As has been found by others using the Rasmussen PEF422 force f i e l d with CHARMM (9,10 and Yan, Z . _ Y . ; Bush, C A . Biopolymers, i n press), the hexose ring geometries were stable in the chair form over a l l the t r a j e c t o r i e s . Some t r a j e c t o r i e s displayed many transitions in both phi and psi (Figure 3A) while others were r e s t r i c t e d to different regions of the p h i / p s i map (Figures 3B&C). The superposition of a l l sixteen t r a j e c t o r i e s i s shown in Figure 3D. A considerable portion of the p h i / p s i map has been explored during the t o t a l of 320 ps corresponding roughly to the 8 Kcal contour on the relaxed potential energy map (Figure 2). Thus the two force f i e l d s show good agreement. Plots showing the time evolution of p h i , psi and both omega values are found in Figures 4A-D for a case with many transitions (trajectory shown in Figure 3A). Transitions are more frequently seen i n psi than in phi; however large variations i n magnitude ( + 7 0 ° in phi and +100° in psi) are found for both angles. These results appear to be in disagreement with the conclusions of Homans et a l . (11) from one 10 ps trajectory for the same linkage using a different force f i e l d [ i t should be noted that alternate d e f i n i t i o n s of phi and psi are used in ref 11]. However, the l a s t two ps of that trajectory showed a


Conformational Analysis of Oligosaccharides 271


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Φ Figure 2: The composite "relaxed" potential energy surface for Man(al-3)Mteu^ calculated by using the molecular mechanics programme MM2(85).


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Figure 3: Three examples out of the sixteen independent 20 ps t r a j e c t o r i e s are shown i n A-C. Part D shows the superposition of a l l sixteen t r a j e c t o r i e s . The time axis i s i n units of picoseconds.


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6 5 ° s h i f t i n phi (from - 3 3 ° to + 3 2 ° , i n our notation) accompanied by a 2 0 ° s h i f t i n psi (from + 2 1 ° to + 4 1 ° , i n our notation). These s h i f t s are consistent with a t r a n s i t i o n to MC from somewhere between MA and MB. In f a c t , recent calculations which have extended the trajectory to much longer times, result i n the observation of multiple transitions (R.A. Dwek, personal communication). Thus there i s now general agreement that multiple transitions occur for the Man(al-3)Man£ linkage over the time periods needed for NOE measurements. Nuclear Overhauser E f f e c t s . The time evolution of the NOE's calculated for hexa-deuterated Man(otl-3)Man0 from each of the sixteen t r a j e c t o r i e s are shown i n Figure 5. In each case the ensemble average NOE value derived from the complete 320 ps ensemble i s shown as a horizontal dashed l i n e . In Figure 5A are shown the calculated NOE's for [3Man H2 upon i r r a d i a t i o n of aMan HI; whereas, i n Figure 5B, the calculated NOE's for aMan H5 upon i r r a d i a t i o n of |3Man H2 are depicted. The NOE values for each of the t r a j e c t o r i e s s t a r t out at very different values because the i n i t i a l geometries differed. For those t r a j e c t o r i e s that displayed several transitions between minima, the calculated NOE's d r i f t slowly towards the 320 ps average. For those t r a j e c t o r i e s that remained l o c a l i z e d to one minimum during the 20 ps period, the NOE's are e s s e n t i a l l y constant. Since the NOE values associated with different t r a j e c t o r i e s are barely converging towards the 320 ps ensemble average, i t i s clear that 20 ps i s not nearly long enough for s t a t i s t i c a l l y s i g n i f i c a n t sampling of the conformational ensemble. It should be emphasized that although the composite 320 ps trajectory shown i n Figure 3D appears to have sampled a large region of torsion angle space, i n order for this to be a s t a t i s t i c a l l y s i g n i f i c a n t sample the trajectory must r e v i s i t the low energy regions a s u f f i c i e n t number of times to give a true Boltzman d i s t r i b u t i o n . Thus times even longer than 320 ps may be needed for proper s t a t i s t i c a l sampling of t o r s i o n a l angle space. It i s also worth pointing out that some NOE's are more s e n s i t i v e to conformational f l e x i b i l i t y than others. When linkage f l e x i b i l i t y results i n motions which cause a p a r t i c u l a r inter-hydrogen distance to fluctuate widely, then the NOE associated with that pair of hydrogens w i l l be very s e n s i t i v e to the nature of the potential energy surface used to simulate that motion. In contrast when the motions result i n very l i t t l e a l t e r a t i o n i n an inter-hydrogen distance, then the associated NOE's w i l l be i n s e n s i t i v e to the p o t e n t i a l functions used. Comparison of Molecular Dynamics with other Methods. In Table I are shown the results of the use of a variety of methods for the c a l c u l a t i o n of r e l a t i v e and absolute NOE's for the Man(ocl-3)Man0 linkage. The values of the r e l a t i v e NOE's derived from the dynamics calculations are i n better agreement with experiment than those derived from any other method (for example, the NOE to βΜ-Η4 i s 1.2 s. which i s less than two standard deviations from the observed value of 0.7+0.2 s., whereas the next closest value i s that from the HSEA surface at 2.0, more than six standard deviations from the observed value). However, the absolute NOE's are overestimated considerably. There are several possible explanations for this


16. CARVER ET AL. 40 ,

(informational Analysis of Oligosaccharides 1

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Figure 5: The time evolution for a l l sixteen t r a j e c t o r i e s (calculated as described i n "Methods") of two different calculated NOE's. A: the NOE on the resonance of the H2 of ManP when the resonance of the HI of Mancc(l-3) i s i r r a d i a t e d . B: the NOE on the resonance of the H5 of Mana(l-3) when the resonance of the H2 of Man& i s i r r a d i a t e d . French and Brady; Computer Modeling of Carbohydrate Molecules ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


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Table I Comparison of Observed and Calculated NOE's f o r Man(al-3)Man3 I r r a d i a t i o n of HI of Man(al-3) a

Relative NOE [ (3M-H2 ] [βΜ-Η4]

Absolute NOE [ (3M-H2] [ (3M-H4]

Method HSEA HEAH PFOS PFOS-H MMP2(85) MD(320ps) Obs'd

a

1.2 11 13 18 8.2 1.1 1.8+0.4

2.0 3.2 1.7 0.36 1.1 1.2 0.7+0.2

1.2 5.7 7.8 20.3 7.4 5.9 1.8+0.4

2.0 1.6 1.0 0.4 1.0 6.5 0.7+0.2

R e l a t i v e to the NOE on oM-H5.



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discrepancy which w i l l be the subject of a future communication. B r i e f l y , however, one possible source for this discrepancy i s that we have not s u f f i c i e n t l y sampled torsion angle space; we are currently exploring this p o s s i b i l i t y by extending the t r a j e c t o r i e s to longer times. Possible problems with the calculated NOE's could a r i s e from the neglect of the presence of the isopropyl group and of a small residual of hydrogens at positions 6 and 6' of the aMan residue. However, i f these were important effects then one would not expect both NOE's to be equally affected. The agreement between the observed and calculated r e l a t i v e NOE's suggested that the discrepancy arises from a constant factor affecting a l l NOE's equally. A possible cause for a systematic error i n the calculated absolute NOE's would be an incorrect choice for the spectral density function used to calculate the relaxation matrix. C l a s s i c a l spectral density functions (1) were used i n these calculations ^ together with the r o t a t i o n a l c o r r e l a t i o n time derived from the C T^'s. These are reasonable choices i f the assumption that i n t e r n a l motions are slow with respect to the r o t a t i o n a l c o r r e l a t i o n time i s valid. However, the dynamics t r a j e c t o r i e s suggest that this i s not so. Transitions between l o c a l minima on the potential energy surface appear to occur with a frequency of about one every 10 ps. If this observation corresponds to the true s i t u a t i o n i n solution then the i n t e r n a l motions are an order of magnitude faster than the r o t a t i o n a l c o r r e l a t i o n time. Under such circumstances, the spectral density function used in these calculations i s i n c o r r e c t . This aspect requires further investigation, p a r t i c u l a r l y once the data from dynamics calculations s p e c i f i c a l l y including water become available. Conclusion Molecular dynamics using the Rasmussen force f i e l d PEF422 in vacuo predicts that the Mana(l-3)Man£ linkage i s highly f l e x i b l e , e x h i b i t i n g excursions of +70° in phi and +100° i n p s i . The ensemble average r e l a t i v e NOE values calculated from the 320 ps of combined t r a j e c t o r i e s are i n close agreement with those observed and are in better agreement than those obtained from a previous s t a t i s t i c a l mechanics approach (15,16). C l e a r l y , an i n s u f f i c i e n t length of time was examined i n previous dynamics studies (11,12) which concluded that the linkage i s fixed. Furthermore, t r a j e c t o r i e s of several hundred picoseconds w i l l be needed before a s t a t i s t i c a l l y s i g n i f i c a n t exploration of conformational space has occurred for this force f i e l d and this linkage. Thus extensive dynamics calculations w i l l be required to predict adequately the ensemble NOE's by this approach. Acknowledgmen t s This work was supported by Grants MT-3732 and MA-6499 from the Medical Research Council of Canada. We g r a t e f u l l y acknowledge valuable discussions and the sharing of unpublished results with Drs. Serge Perez (Nantes), Igor Tvaroška (Bratislava) and members of the Oxford Glycobiology Unit.


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