Computer Modeling of Carbohydrate Molecules - American

Chapter 15

Downloaded by RUTGERS UNIV on January 1, 2018 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch015

Molecular Mechanics NMR Pseudoenergy Protocol To Determine Solution Conformation of Complex Oligosaccharides 1

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J. Neel Scarsdale , Preetha Ram , James H. Prestegard , and Robert K. Yu l

1

Department of Biochemistry and Molecular Biophysics, Medical College of Virginia, Virginia Commonwealth University, Richmond, VA 23298-0614 Department of Chemistry, Yale University, New Haven, CT 06511 2

Here we present a protocol for the determination of the solution conformation of complex oligosaccharides which relies on a systematic combination of NMR distance constraints, derived from the ratio of cross peak intensities in two dimen sional cross-relaxation correlated (NOESY) experiments, and molecular mechan ics calculations. In general, it is not possible to determine a sufficient number of distance constraints from cross-peak intensity data to permit the unambiguous determination of solution conformation from NMR distance constraint data alone. Molecular mechanics calculations, on the other hand give rise to a number of min imum energy structures which cannot be distinguished on the basis of potential energy alone. In combination, however, an accurate structural definition may arise. NMR distance constraint data, on the one hand serves to select between energetically similar conformers. Molecular mechanics calculations, on the other hand, serve to exclude energetically unreasonable NMR structural solutions. In addition, our protocol allows us to relax the assumption that the observed cross relaxation rates result from a single rigid conformer by assuming that the observed cross relaxation rates result from a weighted average over multiple conformers. As an illustration, we have applied this protocol to the problem of the determination of the solution conformation of the neutral tetrasaccharide headgroup of the glycolipid globoside. Comparison of the results from the one and two-state models suggests that only a narrow range of conformers is present in solution—a result which is consistent with the antigenic determinant and receptor functions which have been proposed for globoside.

It has long been recognized that NMR cross relaxation data can provide information on the solution conformation of biological macromolecules, mainly through the inverse sixth power dependence of the cross-relaxation rates on internuclear distance. Only recently with the advent of sophisticated two-dimensional acquisition techniques has it become possible to attempt the α-priori determination of the solution conformation 0097-6156/90AM3(>-0240$07.50/0 © 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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of a biological macromolecule. Noteworthy examples include the studies by Wüthrich and coworkers (1-4) and by Clore, Gronenborn, et al. (5-9) on a number of small proteins and polypeptides. Applications to other types of biological macromolecules are certainly feasible (10-24). Those we shall present here involve oligosaccharides occurring as the hydrophilic portion of glycolipids and of glycoproteins. The basis for the determination of solution conformationfromNMR data lies in the determination of cross relaxation rates between pairs of protons from cross peak intensities in two-dimensional nuclear Overhauser effect (NOE) experiments. In the event that pairs of protons may be assumed to be rigidly fixed in an isotopically tumbling sphere, a simple inverse sixth power relationship between interproton distances and cross relaxation rates permits the accurate determination of distances. Determination of a sufficient number of interproton distance constraints can lead to the unambiguous determination of solution conformation, as illustrated in the early work of Kuntz, et al. (25). While distance geometry algorithms remain the basis of much structural work done today (1-4), other approaches exist. For instance, those we intend to apply here represent NMR constraints as pseudoenergies for use in molecular dynamics or molecular mechanics programs (5-9). Molecular mechanics and molecular dynamics programs use empirical energy functions to represent molecular properties and provide an efficient way of representing our accumulated knowledge of preferred bond geometries. Furthermore, they allow for the placement of portions of biomolecules, such as the exocyclic C H 2 O H , OH and N-Acetyl groups of carbohydrates in reasonable orientations, even when there are insufficient NMR constraints to fix their orientations. NMR distance constraints may be incorporated into these calculations through the use of a distance dependent error function which minimizes when a preferred geometry is found, much as the energy functions representing the bonding and nonbonding interactions among atoms. Combining NMR data with theoretical molecular structure calculations through the use of such functions is particularly attractive given their complementary natures. In general it is not possible to determine a sufficient number of constraints to permit the unequivocal determination of the three-dimensional solution structure of a biological macromolecule, while potential energy calculations give rise to a number of energetically similar structures which cannot be distinguished given the limited accuracy of the empirical energy functions used in these calculations. In combination, an accurate structural definition may arise. NMR distance constraints, on the one hand, serve to exclude energetically similar conformers which are not consistent with the NMR data. Potential energy calculations, on the other hand, serve to exclude energetically unreasonable NMR structural solutions. Furthermore, the use of NMR data treated as pseudoenergies is appealing because it would seem possible to tailor the pseudoenergy function to accurately represent represent the precision of NMR distance constraint measurements. It should also be possible to allow for a realistic interplay of NMR and chemical bonding constraints by the choice of an appropriate weighting function for the pseudo potential. We present here applications using the molecular mechanics program contained in the model building package A M B E R (AMBER, copyright 1986, University of California, San Francisco, is obtained via a licensing agreement with the regents of the University of California.) Even with the proper representation of NMR data, the use of such programs suffers from at least two limitations. One is the tendency of search


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algorithms to identify structures which correspond to local rather than global minima. Another is the possibility that NMR data represent an average over multiple conformers rather than the simple rigid structures identified in a conventional energy search. We shall explore the local minimum problem through the use of multiple starting structures well displaced from one another in conformational space. We shall approach the problems associated with assuming the cross relaxation data result from a single rigid conformer by comparing the results of a one-state calculation with results from a two-state model which assumes the observed cross-relaxation data pertain to an average over two discrete conformers. As an illustration of our methodology, we have chosen the determination of the solution conformation of the oligosaccharide headgroup of globoside which is the glycosphingolipid shown in Figure 1. It has a neutral tetrasaccharide headgroup and is the major glycolipid present in the erythrocytes from all but a small minority of individuals. Globoside has been implicated in a number of biological functions including serving as the P-blood group antigen (26,27) and serving as a receptor for strains of Escherichia Coli responsible for polynephritis (28). Besides being of importance with respect to antigenic and receptor functions of globoside, the conformation of the oligosaccharide headgroup of globoside provides a fair test of our methodology in that there are insufficient distance constraints to accurately determine the conformation from cross relaxation data alone, and there has been considerable speculation concerning the conformational flexibility of the oligosaccharide headgroup of cell surface glycolipids.

The Choice of a Pseudoenergy Function In order to incorporate distance constraints derived from two-dimensional crossrelaxation data in a molecular mechanics program, we have chosen to treat the constraints as a pseudoenergy function. This function should ideally reflect the distance dependence of cross relaxation rates. Previously, we had proposed a function of the form (40):

(1) In expression 1, r f> is the distance between protons a and b determined on the basis of cross relaxation rates; r & is the distance between them at a given stage of the calculation, and W is a weighting factor chosen to properly balance errors in theoretical energies and NMR pseudoenergies « 700 kcal/A which corresponds to a well depth of « 10 kcal/mol, when ro& = 3.0À. This function has the correct l / r £ distance dependence for all values of Γ &. It has a minimum at r (, = ro (» and the depth of the minimum is proportional to 1 / r ^ . These properties accurately reflect the distance dependent precision of the NMR data. This function, however, is not suitable for integration with molecular mechanics algorithms which require that the first and sometimes second derivatives be continuous for all values of r &. 0a

a

6

a

b

α

a

a

a

In order to integrate the NMR distance constraint data into a molecular mechanics minimization routine, we have chosen a smooth approximation of the above function


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with the form: NOE

E

2

17 ι =

w

ι \ i

(J

a h

lr

M

3

r

3

_ _ i

/

l (2)

6

r Oab

This function has a rninimiim at the appropriate place and a well depth proportional to l / r § . For distances r b < ro b, energies become positive with a l/r|j dependence as they should. The l / r dependence on distance for r h > ro b is not strictly correct. This long range dependence may actually assist in a rapid convergence of the calculation when trial structures have interproton distances much larger than the value observed via cross relaxation studies. This function represents a reasonable choice of a pseudoenergy term given the additional constraints imposed on the derivatives of the function. a b

a

a

b

3


6

a

a

Functions such as 1 and 2 permit the inclusion of a pseudoenergy term for all pairs of protons in a molecule, whether or not cross relaxation rates are sufficiently large to be observed. This is made possible by the fact that for sufficiently long distances, the energy contributions from these functions are negligible. For cases where no connectivity is observed between a pair of protons ro& is set equal to some distance, in our case 4.0Â, beyond which a connectivity between protons would be lost in the noise. Inclusion of a pseudoenergy term in the absence of an observed connectivity is important since it serves to exclude conformers with interproton distances short enough to produce a connectivity when none is observed. We shall make limited use of this fact in our structural determinations. a

It is common practice to assume that observed cross relaxation rates result from a single rigid conformer. In these cases the pseudoenergy function described above is adequate. Violation of this assumption would not, however, be at all unusual. Violation would give rise to the possibility that the observed cross relaxation rates represent an average over multiple conformers, each significantly different than the single state structural solution which best fits the observed cross relaxation data. In certain cases, it is possible to relax this assumption. If two or more conformers were to exist and interconvert on a time scale which was short compared to the cross relaxation time, but long compared to the correlation times which were important for spin relaxation (10"~ 0.5À) for these structures. With the exception of the 111(1 )—11(5) constraint, which may be an artifact due to strong coupling between the 11(5) and 11(6) protons (41), all of the constraints corresponding to experimental constraints are satisfied within experimental error. It is also worth noting that the structures obtained via a combination of distance constraint pseudoenergies and molecular mechanics calculations show significant improvements in fitting distance constraints involving exocyclic methylene groups over structures obtained using the distance constraint pseudoenergies with Bock and Lemieux's HSEA program (40). This improvement also arises from relaxing the assumptions of rigid crystal structure geometries for the individual residues.

N M R Refined Two-State Conformational Solutions Although distance constraints are reasonably well satisfied in the one-state calculation, it is only done at a sacrifice of molecular mechanics bonding energies. All of the one state NMR refined structural solutions are higher in energy than the energy rninimized structures A ' and B'. It is therefore desirable to explore other means of fitting the NMR data. Another possible explanation for the lack of agreement between



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the proton distances in structures determined in the absence of distance constraints and experimental distances is that multiple conformers exist in solution. The observed cross relaxation data would then be an average of the cross relaxation rates for the individual conformers. In order to test this hypothesis, we have tried fitting the ex perimental distance constraint data using the two-state model described previously and a set of starting points which corresponds to combinations of the various mini mum energy structures in the absence of distance constraint pseudoenergies. None of the individual structures satisfies the observed data within experimental error. The two-state model allows for the possibility that combinations of structures near these minima represent an adequate fit of the experimental data. A summary of φ, φ values and fractional populations for the individual conformers from the various two-state structural solutions is presented in Table VI. A ball and stick drawing of the lowest two-state structural solution is presented in Figure 6. In examining the data in Table VI for the various structural solutions, several facts are worth noting. The lowest energy two-state structural solutions both involve significant occupation of only one conformational state. In each of these structural solutions, the dominant conformer is similar to structures A" and C" which were obtained as one-state structural solutions in the presence of distance constraint pseudopotentials. The third two-state structural solution involves significant occupation of two rather different conformational states similar to structures A' and B . This structural solution suggests conformational flexibility at the terminal IV,III linkage, which is consistent with our earlier work (40). Some additional flexibility is predicted at the Ι Ι Ι , Ι Ι linkage. This additionalflexibilitywas not predicted in our previous work, probably because the assumption of rigid residue geometry excluded some conformers which should have been allowed. ;

In Table V we present rms deviations for the distance constraints for each of the various two-state NMR structural solutions. In Table V, we also present a list of signif icant violations (deviations > 0.5À) for these structural solutions. With the exception of the ΠΙ(1)-ΙΙ(5) constraint, all distance constraints corresponding to observed con nectivities were satisfied within experimental error.

Discussion Since both the one and two-state structural solutions provide an adequate fit of the experimental data, we must rely on an additional criterion to favor one approach over the other. Such a criterion is provided by the molecular mechanics energy. The lowest energy one-state structural solution has a molecular mechanics energy of 6.4 kcal/mol, while the lowest energy two-state structural solution had a molecular mechanics energy of —1.4 kcal/mol—significantly lower than lowest energy one-state structural solution. Fractional occupation of the second conformational state is small (.01) increasing to « 0 . 1 when a constant dielectric of 10 is used instead of a distance dependent dielectric. In Figure 7, we present a stereoview of the superposition of the dominant con formers from the lowest energy two-state structural solutions, D'A' and D'B' and the one-state structural solutions A", B" and C" when all atoms in the oligosaccharide moiety of globoside were included in the comparison. In Figure 7, we also present



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Figure 5. Stereoview of the superposition of the NMR refined one-state structural solution, A " (-), B" ( - · ) , and C " (—) (a) with unconstrained exocyclic groups included in the comparison and (b) excluded from the comparison.

1

2

Figure 6. Ball and stick drawing of the dominant (1) and minor (2) conformers from the lowest energy two-state structural solution D'A'. (Reproduced from ref. 40. Copyright 1986 American Chemical Society.)


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a stereoview of the superposition of these structures obtained when unconstrained exocyclic groups were excluded from the comparison.


From the data in Table VI and Figure 7, it is clear that the dominant conformer from the lowest energy two-state structural solution is quite similar to the lowest energy one-state structural solution, the chief difference being in the orientation of the terminal /3-D-GalNAc residue. We conclude, therefore, that structures which are similar to the lowest energy one-state structural solution A", represent the predominant conformer present in solution. The one-state procedure thus provides a reasonable and time efficient approach to structural analysis for this molecule. This does not mean that iriinor conformers and/or motional averaging are unimportant. The presence of even small amounts of minor conformers or limited conformational averaging as is suggested by the lowest energy two state structural solution could significantly affect the observed cross relaxation rate. The inverse sixth power dependence of the cross relaxation rate on interproton distance serves to strongly weight contributions from conformers with short interproton distances. Therefore the presence of even small amounts of conformers with short interproton distances can exert a disproportionate amount of influence on the observed cross relaxation rate. The heavy weighting of conformers with short interproton distances could explain the significant decrease in the molecular mechanics energies obtained for the predominant conformer when we relax the assumption that NMR cross relaxation data are satisfied by a single rigid conformer. By allowing the presence of an additional conformational state, we no longer require that a single conformer satisfy all of the constraints imposed by NMR cross-relaxation data. Those constraints which were satisfied via structural distortions which exacted a considerable penalty in terms of the molecular mechanics energy in the single state structural solution could now be satisfied via a combination of conformational states, a predominant conformer with a geometry which is closer to the minimum energy geometry and the presence of minor conformers with appropriately short interproton distances. This is shown graphically in Figure 8 where we present a stereoview of the superposition of the dominant conformer from the lowest energy two-state structural solution, D'A', the lowest energy one-state structural solution, A " and the apparent global rninimum energy structure D'. From these data, it is apparent that the predominant conformer from the lowest energy two-state structural solution exhibits smaller deviations from the apparent global minimum energy structure than the lowest energy one-state structural solution.

Conclusion We have developed a protocol which relies on a combination of molecular mechanics calculations and distance constraint pseudoenergies to predict the solution conformation of biomolecules. When a simplified potential surface is used during the initial stages of the calculation, the final structures obtained upon convergence of the calculation are remarkably similar, even though the starting structures were grossly different. In other words, our protocol seems rather immune to some of the local minimum problems which plague molecular mechanics calculations. This protocol has enabled us to



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Figure 7. Stereoview of the superposition of the N M R refined structural solutions A " (—), B" (—), and C " (—) and dominant conformer from the lowest energy two-state structural solution D'A' (-) (a) with unconstrained exocyclic groups included in the comparison and (b) excludedfromthe comparison.

Figure 8. Stereoview of the superposition of apparent global minimum for globoside, structure D' (-), the dominant conformer from the lowest energy two-state structural solution, D'A' ( - · ) and the lowest energy one-state structural solution A " (—) (a) with unconstrained exocyclic groups included in the comparison and (b) excluded from the comparison. French and Brady; Computer Modeling of Carbohydrate Molecules ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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generate viable one state descriptions of the globoside oligosaccharide headgroup that agree with the general L " shape postulated to be important in receptor function.


M

We have explored the possibility that NMR data might be better represented through use of a model which permits interpretation of NMR data in terms of an average over discrete conformational states. Although this model led to structural solutions with very small occupation of minor conformational states and dominant conformers that were visually very similar to the lowest energy one-state structural solution, the molecular mechanics energies for these dominant conformers were sig nificantly lower. These dominant conformers were also similar to the lowest energy structural solutions obtained in the absence of NMR distance constraints. These data indicate that only a narrow range of structures are likely to be present in solution and are consistent with the receptor and antigenic determinant functions proposed for globoside in that a certain amount of structural rigidity is likely to be necessary for these proposed biological functions.

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Computer Modeling of Carbohydrate Molecules - American

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