Modelling

4.3.5.1 Structural implications of ROE data for exchangeable protons

Only two tians-glycosidic NOEs are observed in A^-acetyllactosamine that do not involve exchangeable protons. In order to assess the impact of the additional restraints obtained, it is necessary to take into account the veiy rapid (picosecond) motional averaging of the hydroxyl groups about their respective C-O bond, which gives rise to fluctuating internuclear distances. A convenient method for achieving this is by simulation of the molecular dynamics trajectory of the glycan in vacuo for a period of time that is longer than the timescale of the internal motions. In this present study a 500ps restrained MD simulation was computed, with restraints derived from the inter-glycosidic NOEs involving non­ exchangeable protons. These restraints were applied as ‘fixed’ distances, corresponding with the ‘single conformation’ model involving limited torsional fluctuations about the glycosidic linkage. The time averaged inter-glycosidic NOEs involving exchangeable protons were then calculated over the timecourse of the simulation, using a full relaxation matrix analysis using a formalism appropriate for fluctuating inter-nucleai' distances due to internal motions which are rapid with respect to overall isotropic tumbling (Tropp, 1980; Homans and Forster, 1992). One of these NOEs involves GlcNAc-OH6, which forms pait of the pendent hydroxymethyl group whose internal rotation about the C5-C6 bond is slow with respect to overall tumbling. It is therefore necessary to compute two MD simulations with the dihedral angle (O about the C5-C6 bond weakly constrained to two conformations (gg and gt) observed to exist in the disacchaiide on the basis of homonuclear spin-coupling constant measurements. A weighted average [gg (6 6%) and gt (34%)] was then taken over the two simulations. Results for the relevant trans-glycosidic ROEs involving exchangeable protons are given in Table 4.4, where it can be seen in particular the ROE between Gal-Hl and GlcNAc-0H3 is severely underestimated in these simulations. This immediately suggests that substantial torsional fluctuations exist in the disaccharide in free solution, and indeed the experimental ROEs compare more favourably with predicted values when the restraint bounds corresponding to the two original NOEs are relaxed (Table 4.4). The resulting torsional fluctuations about 9 and \\f lie within the global minimum energy region of

Chapter 4: Application - N-Acetyilactosamine 130

the glycan, and offer a plausible model for the dynamic behaviour of the glycan in solution

(figure 4.11).

(B)

(C)

(A)

s

Figure 4.11 - (A) Instantaneous values of the glycosidic torsion angles (j) and v|/ over the 500ps restrained MD simulation in vacuo for Gal|5l-4GlcNAc. (B) Instantaneous values of the glycosidic torsion angles (|) vs. time over the 500ps restrained MD simulation. (C) Instantaneous values of the glycosidic torsion angles y vs. time over the 500ps restrained MD simulation.

Chapter 4: Application - N-Acetyllactosamine 131

43.5.2 Assessment o f model

Long range spin-coupling constants are important NOE-independent data which can be used to assess the models proposed by restrained molecular dynamics simulations. Theoretical coupling constants were computed from a two 500ps dynamics simulation, one with the two inter-glycosidic non-exchangeable restraints as fixed distances and the other with all the non­ exchangeable and exchangeable NOE restraints, with in-house written software ‘MDPROCESS’ with a trans-glycosidic ^Jch Karplus relationship derived by Tvaroska et al.

(1989) and the tians-glycosidic ^Jcc Karplus relationship derived in this present study (see chapter 3). Table 4.5 lists these theoretical data, with the back-calculated values from the model with ‘fixed’ restraints showing poor agreement with the experimental values, especially the ^Jcai-ci, gicnac-cs, and gicnac-c4 values. This is in agreement with the

NOEs to the hydroxyl protons where they could not be accurately simulated using a model with limited torsional fluctuations. In comparison, the model where these restraints are relaxed, and the hydroxyl proton restiaints included, are in good agreement with those measured experimentally, and this suggests that this model of increased torsional fluctuation is a reasonable representation of the dynamics of iV-acetyllactosamine in solution.

Chapter 4\ Application - N-Acetyllactosamine 132

Table 4.4 - Experimental ROEs involving exchangeable protons compared with theoretical values derived from two 500ps restrained MD simulations in vacuo for Gaipi-4GlcNAc.

ROE Connectivity ROE Intensities (%)

Experimental*^ Theoretical

‘Fixed’ restraints** ‘Relaxed’ restraints'^

Gal HI - GlcNAc 0H3 0.7 0 . 1 1 . 2

Gal HI - GlcNAc OH6* 0.5“ 1 . 0 0 . 2

Gal OH2 - GlcNAc H6*" 2 . 0 1.0 2.3

(a) Restraints; Gal HI -GlcNAc H4; 2.34Â<r<2.54Â; Gal HI - GlcNAc H6; 2.92Â<r<3.12Â; force constant = 10 kcal/Â^,

(b) Restraints: Gal HI - GlcNAc H4: 1.8Â<r<2.7Â; Gal HI - GlcNAc H6: 1.8Â<r<5.0Â; force constant = 10 kcal/Â^.

(c) Experimental values (±10%) expressed as the sum of intensities of a and p anomers. (d) Estimated error ±25% due to low cross-peak intensity.

(e) Theoretical value computed as the sum of the ROEs to each hydroxymethyl proton. treated as a pseudoatom.

Table 4.5 - Comparison of experimental trans-glycosidic coupling constants vs. theoretically computed values derived from a 510ps in vacuo molecular' dynamics simulation.

Trans-glycosidic Coupling

Experimental** (Hz)

Theoretical Value(Hz)

‘Fixed’ Restraints ‘Relaxed’ Restraints ^Jcc Gal C2 - GlcNAc C4 2.9 3.3 2.3 Gal Cl - GlcNAc C3 < 1 . 0 1 . 0 0 . 6 Gal Cl - GlcNAc C5 1 . 6 0 . 8 1 . 6 ^JcH Gal HI - GlcNAc C4 4.4 3.1 4.0 Gal C l - GlcNAc H4 n.d" 5.2 4.7

(a) Errors in these measurements estimated as ±0.5 Hz.

Chapter 4\ Application - N~Acetyllactosamine 133

4.4 Conclusions

The accurate quantitation of an inter-glycosidic NOE coincident with an intia-residue NOE was obtained by the application of heteronuclear NMR experiments on a carbon-13 enriched oligosacchaiide. To supplement the two inter-glycosidic NOEs to C-linked protons, low temperature studies allowing observation of the exchangeable protons, have provided an additional three ROEs. Unlilce NOEs involving non-exchangeable protons, which tend by nature to involve protons close to the glycosidic linkage, and therefore aie not very sensitive to torsional fluctuations about the glycosidic linkage, NOEs involving OH and NH protons in oligosaccharides aie not necessarily proximal to the glycosidic linkage, and hence aie much more sensitive to conformation. In this example, sufficient ROEs to exchangeable protons have been observed to confirm that substantial torsional fluctuations exist about the glycosidic linkage, a result that in the past has not been obvious without recourse to detailed relaxation-time measurements.

Using aU of the distance restiaints in a restrained molecular dynamics simulations, the resulting torsional fluctuations predicted lie within the global minimum energy region of the glycan, and the back-calculated NOE and spin coupling constants (carbon-carbon and carbon-proton) are within reasonable agreement suggesting that this flexible model is consistent with the experimental data.

Chapter 5

Heteronuclear NMR Investigation of the Solution

Structure and Dynamics of the carbohydrate moiety