The Incorporation of Labile Protons into Multidimensional NMR Analyses: Glycan Structures Revisited

Glycan structures are often stabilized by a repertoire of hydrogen-bonded donor/acceptor groups, revealing longer-lived structures that could represent biologically relevant conformations. NMR provides unique data on these hydrogen-bonded networks from multidimensional experiments detecting cross-peaks resulting from through-bond (TOCSY) or through-space (NOESY) interactions. However, fast OH/H2O exchange, and the spectral proximity among these NMR resonances, hamper the use of glycans’ labile protons in such analyses; consequently, studies are often restricted to aprotic solvents or supercooled aqueous solutions. These nonphysiological conditions may lead to unrepresentative structures or to probing a small subset of accessible conformations that may miss “active” glycan conformations. Looped, projected spectroscopy (L-PROSY) has been recently shown to substantially enhance protein NOESY and TOCSY cross-peaks, for 1Hs that undergo fast exchange with water. This study shows that even larger enhancements can be obtained for rapidly exchanging OHs in saccharides, leading to the retrieval of previously undetectable 2D TOCSY/NOESY cross-peaks with nonlabile protons. After demonstrating ≥300% signal enhancements on model monosaccharides, these experiments were applied at 1 GHz to elucidate the structural network adopted by a sialic acid homotetramer, used as a model for α,2–8 linked polysaccharides. High-field L-PROSY NMR enabled these studies at higher temperatures and provided insight previously unavailable from lower-field NMR investigations on supercooled samples, involving mostly nonlabile nuclei. Using L-PROSY’s NOEs and other restraints, a revised structural model for the homotetramer was obtained combining rigid motifs and flexible segments, that is well represented by conformations derived from 40 μs molecular dynamics simulations.


1) A numerical analysis of L-PROSY TOCSY enhancements in saccharides.
To describe TOCSY experiments in exchanging systems containing several spins that interact through scalar couplings, magnetization treatments based on classical Bloch-McConnell equations are not valid. Therefore, we resort to a full density-matrix treatment that includes relaxation and chemical exchange superoperators. The Liouvillian superoperator 2,3 used in these spin simulations thus contained Zeeman (chemical shift) terms for the labile proton ( -) and the water ( . ! / ) as well as for the non-labile ( 0-), a scalar J-coupling between the latter two protons assumed to be on the saccharide, an ideal spin-lock responsible for establishing the effective isotropic Hamiltonian, relaxation within an extended T1/T2 approximation, and chemical exchanges between the labile proton and water. The ensuing master equation 1 = ;− > − @ + B C + @ where > , @ and B are Hamiltonian, relaxation and exchange superoperators respectively, was solved numerically using custom-written codes within the Spinach package. [4][5][6] Supporting Figure S1 illustrates results from these simulations for TOCSY and L-PROSY TOCSY experiments. Incoherent chemical exchanges with the solvent average out homonuclear J-couplings, dampening the coherent oscillation in Eq. 2 and reducing the efficiency of TOCSY experiments. Supporting Figure S1 illustrates this: blue dashed lines represent the fast decay of a labile diagonal peak in a conventional TOCSY experiment, while red and green dashed lines show the buildups of corresponding cross-peaks for J-couplings equal to 7 Hz (typical for three-bond coupling values) and 2 Hz (typical for longer-range couplings), respectively. Using same color code, solid lines represent the outcome of the L-PROSY TOCSY experiment. Notice the substantially higher cross-peak intensities that the latter can achieve, yielding enhancements of ≈2-3x for larger J-couplings and slower exchange rates, and ≈3-5x for long-range couplings and/or fast exchange rates.
In general, when choosing optimal L-PROSY TOCSY parameters, two generalizations can be made: the line widths of the labile protons report on the chemical exchange rates and Supporting Figure S1. Trajectories of labile and non-labile protons' spin-locked magnetization during conventional TOCSY and L-PROSY TOCSY experiments when chemical exchange with solvent is a) 50 s -1 and b) 100 s -1 . Dashed lines represent conventional TOCSY experiments while solid lines describe the evolution during L-PROSY experiments. To simulate the conventional TOCSY experiment, a CW irradiation is applied after initial excitation of labile hydroxyl proton (using perfect delta function pulse). Dashed blue curves show the fast decay of the diagonal peak due to relaxation and chemical exchange, not allowing cross-peaks (red for 7 Hz and green for 2 Hz J-coupling) to build up. The L-PROSY experiment is simulated in a similar manner, except that short CW isotropic mixing periods were interleaved with multiple selective excitation pulses on the labile proton. This in turn utilizes fast chemical exchange repolarization to provide multiple transfers of magnetization to non-labile spin yielding much stronger cross-peaks. In all simulations the aqueous pool was assumed ~150fold larger than the solute (enough to reliably simulate chemical exchange decoherent processes); both longitudinal and transverse relaxation times were chosen to be: "# $ = 0. Labile protons are allowed to undergo chemical exchange with the water, while connected to a non-labile spin pool that is receiving polarization via a generic cross-relaxation 7 process represented by a rate s. In order to include population differences between the aqueous and solute water pools exchange rates were also scaled according to: For the specific instance of a L-PROSY NOESY experiment, represents the difference between zero-and double-quantum dipole-dipole cross-relaxation rates, and can be expressed in terms of normalized spectral densities as where ( ) = Furthermore, two sets of simulations were carried out to simulate the x / -x phase-cycling  Figure   S2d, which shows that enhancements rise monotonically as the relaxation of the non-labile protons becomes slower. While this ' 0sets up an upper boundary for the , ' barely influences the looped transfer: only for very short values of ' enhancements are affected and become ~20% higher. Two effects contribute to this improvement: a less efficient transfer in the conventional experiment, and a faster effective relaxation of the labile protons that enables a faster, more complete L-PROSY looping (akin to having a faster 4( ). The effects of the nonlabile proton relaxation parameters on the cross-peak buildup, leads to a simple correlation between the number of loops ' and the mixing time !$( that can be useful when choosing optimal acquisition parameters: On the other hand, the optimal mixing time !$( will be determined by the rate of chemical exchange, which should be fast enough to provide sufficient repolarization of the labile protons over its course: !$( ≈ ( 4( ) B' . This clarifies why higher enhancements are achieved in faster exchanging systems: this exchange effectively allows for shorter mixing times until labile protons recover, and consequently more loops can be applied. Given that the NOESY experiment generally requires longer mixing times than TOCSY but that at the same time it depends on (the longer) T1 rather than on T1r, more loops will be feasible and thus larger L-PROSY enhancements will usually be achieved for this kind of correlations.

3) L-PROSY brings substantial enhancements to 3D TOCSY-fHSQC correlations.
The sequence shown in Figure 3a was used to obtain 3D HO-HC-13 C correlations for 25% labeled glucose sample utilizing NUS. Figure S3 illustrates resulting 3D cube with assignments provided in 13 C -1 H plane. Considering enhancements discussed in the main text achieved for glucose under the same conditions, acquisition of corresponding conventional 3D diagram would take >10x longer, which is a substantial difference in required instrument time. Figure S4 complements Figure 4, by experimentally examining the effects of the external field on selective NOESY and L-PROSY NOESY spectra collected on a Sia4 sample. Notice that whereas a single-loop selective NOESY experiment fails to reveal any cross-peaks at 14 °C and 600 MHz, in L-PROSY these cross-peaks start to appear. The selective NOESY spectrum at 1 GHz is slightly better than at 600 MHz, but even further advantages arise when L-PROSY is incorporated. In practice, the optimal L-PROSY conditions will be an interplay between chemical exchange rates and ensuing broadening complicating the selective pulses in this experiment. This is evidenced from the middle and bottom panels of Figure S4: higher quality spectra are obtained at 5 °C than at 14 ˚C, despite the smaller L-PROSY enhancements observed (indicated for several peaks). The absolute signal-to-noise ratio (SNR) of the crosspeaks can be appreciated from the various projections extracted for the same resonances in these spectra.

4) Magnetic field effects on L-PROSY glycan spectra. Supporting
Supporting Figure S3. 3D cube representing the correlations between hydroxyl protons (F1), aliphatic protons (F3) and their neighboring carbon (F2) atoms, acquired using 3D L-PROSY TOCSY fHSQC. Experiment is acquired using 8% NUS sampling in 15 hours using rather long relaxation delay of 2s for aliphatic protons to recover. Considering typical >3-fold gain achieved in L-PROSY (corroborated with the same sample of Glucose using 2D L-PROSY), similar conventional 3D NOESY-HSQC experiment would require at least 5 days longer acquisition time to achieve similar sensitivity. Plane F2F3 is showing 13 C-1 H projection, with included assignments. were generated from these data, from which the optimal mixing times was selected to generate distances for structure calculation.

9) 3 JCH measurements on Sia4
Heteronuclear coupling constants were measured using the PIP-HSQMBC experiment. The PIP-HSQMBC was used as published 9 but with minor modifications for water signal removal through coherence selection. A final spectral resolution of 0.5 and 30 Hz/point were used for the 1 H and 13 C dimensions, respectively. Briefly, in-phase and anti-phase PIP-HSQCMBC experiments, optimized to observe 6 Hz 3 JCH, were collected Supporting Figure S8. Fully assigned OH region of a 150 ms HSQC-NOESY collected at -10 °C on a 78.7 mM sample, in 90:10 H2O:D2O, pH 7.5 at 700 MHz. DSS was used as internal reference. Longrange correlations are labeled in red. The observed correlations are fully consistent with those detected by L-PROSY-NOESY experiments at 5 ˚C (see Table 1 and main text for further discussion). on a ca. 160 mM Sia4 sample containing 10% 2 H2O and 0.1% DSS. The resulting experiments were added and subtracted to yield in-phase spectra with cross peaks with chemical shifts offset by the n JCH. Coupling constants were determined by frequency difference between the offset cross peaks. Representative PIP-HSQCMBC spectra are shown in Supporting Figure S9.
Only the two set of six 3 J coupling constant values that were consistent with a defined torsion angle value were used for NMR structure calculation at -10 °C and at 5 °C. Based on the measured 3 J, the following torsion angle values were used: w6 (H6-C6-C7-H7)= ± 90 ± 30° for residues I, II, III and IV and w8(H7-C7-C8-H8)= 180 ± 30° for residues I and IV. We have also measured 3 JH8C2, which can be correlated to the y (H8-C8-O2'-C2'), yielding 2.9±0.5 Hz, 4.2±0.5 Hz and 5.0±0.5 Hz for residue I, II and III, respectively. These values remained fairly constant, withing the experimental error, for the temperature range tested (-10 °C, 5 °C and 37 °C), suggesting a similar conformational preference for these torsions over -10 °C to 37 °C temperature range. However, the y torsions were not restrained for structure calculation because the data cannot be unambiguously interpreted from a a2,8 Sia-specific Karplus-like parameterization (not available).
Supporting Figure S9. Set of PIP-HSQMBC spectra collected on a ca. 160 mM Sia4 sample on a 700 MHz instrument at -10 °C (a).
The overlaid spectra with blue/teal and red/pink cross peaks were obtained by either subtracting or adding the anti-phase /in-phase PIP-HSQMBC spectra, respectively. Panel b shows resulting 1D projections from the IIIH8-IVC2 cross peaks shown in Panel a, with the corresponding measured 3 JHC. Supporting Figure S10. Values for the torsion angles adopted by the linkers between Sia residues for the structures shown in Figure 6a (Sia4 NMR ensemble -10 °C, blue squares) and 6b (Sia4 NMR ensemble 5 °C, red squares), overlayed over contour plots from the MD simulation at 5 °C. In some cases, such as f for Residue I and f and y for Residues II and III, the torsions change with temperature. The values for w8 are temperature dependent mainly for Residue II, while in Residues I, III and IV w8 is less affected. Note that most of the resulting torsion values while represented on the MD simulation do not coincide with MD energy minima, which might be due to experimental sampling limitations, simulated annealing bias or force-field imperfections. Most likely it is a combination of those factors, which our studies attempt to disentangle.

11) Sia4 OH's chemical shift temperature dependence.
The OH chemical shifts as a function of temperature were acquired with the hsqcdietgpsi Bruker sequence with minor modifications. A 10 ms of DIPSI2 isotropic mixing was used. The same acquisition parameters as for the HSQC-NOESY experiment were employed except that 512 complex points (32 scans/t1) and uniform sampling were used instead. Data were acquired at -10, -5, 0, and 5 °C.
Measured OH chemical shifts were plotted as a function of temperature and fitted to a linear function to yield the temperature coefficients with error representing fitting error.

12) Hydrogen bond detection experiment.
A long-range HSQMBC sequence 10 was used for H-bond detection, albeit with minor modifications to remove water interference. The carrier frequency, spectral window, number of points for the direct and indirect dimensions were set to: 4.7 ppm, 100 ppm; 10 ppm, 180 ppm; 4096, 1024, respectively. The spectra shown in Figure S11b was  Supporting Figure S12. a) Previously proposed Sia4 structure, involving an extended helical model inconsistent with the L-PROSY correlations shown with the dashed lines. b) NMR ensembles composed of 100 structures generated via simulated annealing, recalculated using data reported for the helical model 11 (Only the ring and linker chain heavy atoms are shown, with carbon and oxygen atoms shown in white and red, respectively; close to mean structures are shown in blue. Residue numbering is indicated by Roman numerals, where "I" indicates the "reducing" and "IV" the "non-reducing end", respectively.  Table S1. NMR ensemble statistics from the models shown in Figure 6. Non-sequential inter-residue NOEs