Research Seminar Long Abstract

by Eduard Chekmenev

- Department of Chemistry -
- University of Louisville, September, 2002 -

1. Introduction

It is well known that ¹³C^a isotropic chemical shifts (d_iso) correlate with protein secondary structure in solution and, therefore, they were extensively used in protein structure prediction algorithms.¹ Several years ago ab initio calculations showed that ¹³C^a shielding tensor principal components are also dependent on the backbone torsion angles (f,y)^2,3 that define local 2° structure in proteins. Moreover, chemical shielding (CS) anisotropy was used recently as constraint for 2° structure prediction.⁴ So far, there are no large CS databases that can be used in structure prediction methods even on the qualitative basis. This study targets the precise measurement of ¹³C^a and ¹⁵N glycyl chemical shielding tensor principal components in structurally significant 2° elements such as a-helix, b-strand, and 3₁-helix. The series of tripeptides with central glycyl residue serves as the simplest peptide system, where glycyl torsion angles are specified. The results are generalized for site specific 2° structure prediction and better understanding chemical shielding in proteins.

2. Background ¹³C^a and ¹⁵N Glycyl chemical shielding

NMR energy spectrum is determined by spin Hamiltonian, H, for nuclei with non-zero nuclear magnetic moment, I. The Hamiltonian ‘eigenvalue’ represents the energy of a spin state. The spin Hamiltonian is a sum of external and internal Hamiltonians in the solid state, H = H_ext + H_int. The external Hamiltonian describes the interaction of a spin with external magnetic fields, whereas the internal Hamiltonian includes the interactions within the solid, namely, CS, dipolar coupling (DC) and quadrupole (Q), H_int = H_CS + H_DC + H_Q. Measurement of CS interactions is the goal this study. Experimentally it can be accomplished only if one removes dipolar and quadrupole interactions. In polypeptide systems the following interactions cause problems for ¹³C CS measurement: ¹³C-¹H DC, ¹³C-¹⁴N DC and Q or ¹³C-¹⁵N DC in case of selectively labeled peptides with ¹⁵N. ¹⁵N-¹H DC and ¹⁵N-¹³C DC (¹³C labeled) interactions obscure ¹⁵N CS measurements. Decoupling (high power rf irradiation) ¹H and sparse nuclei (¹³C or ¹⁵N) allows to get rid off those unwanted interactions. Since natural abundance of ¹³C and ¹⁵N is low, 1.1% and 0.37% respectively, the sensitivity is relatively low. Labeling with 100% of ¹³C and ¹⁵N enhances NMR signal by 2 orders of magnitude. The cross-polarization⁵ (CP) phenomenon is also used to increase rare spin (¹³C or ¹⁵N) signal intensity. In this method ¹H spins exchange energy with rare spins under Hartman-Hahn conditions.⁶ That increases the population difference between the spin up and down states of rare spins and leads to a gain in sensitivity, h:

where N is number of spins and g is magnetogyric ratio. Since the number of protons, N_1H, is usually much larger than the number of rare spins in solid the sensitivity enhancement is determined by g_1H/g_rare and usually ~4 for ¹³C and ~10 for ¹⁵N. CP method also reduces recycling time between free induction decays by decreasing the relaxation delay, which is determined by short T₁ of ¹H nuclei rather than T₁ of rare spins when CP is not used. A triple resonance probe and 3-channel spectrometer are required to accomplish CP and decoupling.

Peptide powders used in this study consist of a multitude of randomly oriented single crystals. The NMR spectrum of a powder sample, so-called powder pattern, is a superposition of the NMR lines from all nuclei of all the grains in the sample. The three principal values, d₁₁, d₂₂, and d₃₃, of the CS tensor are usually obtained directly from the frequencies of the peak and the two shoulders (Fig. 1). The accuracy with which the components measured depends on the spectral resolution and typically ~2-3 ppm for ¹³C and ~5 ppm for ¹⁵N nuclei in peptides.

	Figure 1. Powder and MAS (nr = 1.1 kHz) 1H, 15N decoupled 13C spectra of P*GG. Spectra were obtained with 2048 and 720 transients, respectively.

Macroscopic sample rotation at the ‘magic angle’ of q = arccos((1/3)^1/2) = 54.74° averages out the broad powder pattern in to a narrow line.⁷ If the magic angle spinning (MAS) is smaller than the CS anisotropy (CSA), defined as (d₁₁ - d₃₃), the spinning sidebands appear displaced by ± n*n_r from the centerband, where n_r is rotation frequency and n is sideband order. The sideband intensities contain the information about principal values of CSA, which can be extracted by the Berger-Herzfeld procedure.⁸ The error limits of this approach are determined by S:N. Therefore, shielding parameters can be obtained within 1 ppm of error, if the S:N is sufficiently large (>100:1) and the spinning speed is slow enough (n_r << (d₁₁ - d₃₃)/4).⁹ Typical example of both powder pattern and corresponding MAS spectrum is shown on Fig. 1. Shielding parameters are presented in terms of (d₁₁ - d₃₃) and (d₂₂ - d₃₃) with the convention that d₁₁ is the most downfield and d₃₃ is the most upfield component. These two parameters with d_iso determine the three shielding tensor principal components. The accuracy of experimental values is tested by standard error analysis of the CS tensor parameters.

When several nuclei contribute to the spectrum, it becomes crowded even in case of MAS. The two dimensional phase-adjusted spinning sidebands (PASS) approach¹⁰ is helpful there. It places chemical shift in the first dimension and CSA information in the second, which simplifies the spectrum. The method is a constant time 2D experiment, where the only increase in total spectrum acquisition time relative to the 1D experiment is from the modest reduction in signal, ~20%. Thus the resolution advantage of the second dimension comes almost at no cost in acquisition time.

3. Solid state (SS) NMR MAS triple resonance probe design

	Figure 2.Triple resonance NMR probe circuit.

The experiments in this study require efficient triple resonance (¹H/¹³C/¹⁵N) MAS probe. The entire probe circuit (Fig. 2) is constructed on a single ground plane, which fits into the 64-mm bore of the 12-tesla magnet. In this approach,¹¹ the right side of the circuit is tuned to proton frequency, where as the left side allows tuning to ¹³C and ¹⁵N frequencies, which are separated further in the diplexer not shown here. Both channels are matched to 50 Ohm. There are three unique features that distinguish this probe from those previously described:¹¹

(i) high efficiency due to application of larger size components (Table 1),
(ii) inductively tuned ¹H channel; that eliminates arcing and keeps the channel compact,
(iii) low pass filter in ¹³C/¹⁵N channel is added; that grounds ¹H channel more efficiently. Careful layout and non-inductive leads are essential not only for tuning all three channels but also for probe efficiency.

Configuration	1H 90°, µs	13C 90°, µs	15N 90°, µs
1H/13C	2.3 (100 W)	5.0 (140 W)	N/A
1H/15N	2.3 (100 W)	N/A	6.0 (320 W)
1H/13C/15N	2.3 (100 W)	5.2 (190 W)	8.0 (280 W)

4. Sample preparation

Peptides studied at natural abundance were obtained from Bachem. The doubly labeled tripeptides with [2-¹³C, ¹⁵N]glycine (*G) were prepared by solid phase peptide synthesis. First of all, [2-¹³C, ¹⁵N]glycine was converted to t-Boc-*G. The product was acidified with HCl/acetic acid, extracted with ethylacetate and recrystallized.¹² An ~1.5-fold excess of t-Boc-*Gly was coupled to Gly-Merrifield-resin. The synthesis was finished by attachment of t-Boc amino acid, 6-fold excess, to N-terminal *G. Tripeptides were cleaved from the Merrifield resin with anhydrous HF.¹² The product was extracted and lyophilized. The purification protocol included cation exchange chromatography (Dowex 50WX8-100) and size exclusion chromatography (Sephadex LH-20). The product MW and purity were tested by MALDITOFF mass spectroscopy and silica gel thin layer chromatography. SS NMR samples of the peptides (containing 8-25 mg of labeled material) were crystallized according to the procedures described in the original X-ray literature. Cambridge Structural Database¹³ (CSD) reference codes for these structures are listed in Table 2. The unit cell parameters were determined by X-ray crystallography and conformed to the published values for all tripeptides.

5. ¹³C^a and ¹⁵N Glycyl chemical shielding

The important practical considerations in the study are the reliability and sensitivity of the shielding values. That was investigated by summarizing results obtained with several peptides using stationary and spinning samples and different decoupling schemes with labeled and unlabeled samples. Experiments, for example, with and without ¹³C^a, ¹⁵N labeling of the central gly residue allow direct assessment of the effects of dipolar coupling between C^a and bonded ¹⁴N or ¹⁵N. For the standard peptidic N-C^a bond length of 1.47A, the dipolar coupling, n_r, is 690 Hz or 5.5 ppm for ¹⁴N and 960 Hz or 7.7 ppm for ¹⁵N nuclei. However, ¹⁴N is spin = 1 nucleus and due to additional quadrupolar interactions its effect on ¹³C spectra, therefore, is larger. Although these DCs are ~10-15% of (d₁₁- d₃₃), ¹³C^a powder patterns look very distorted in these coupled spin systems with directly bonded ¹⁴N or ¹⁵N.¹³ The effect on MAS spectra is different due to sample rotation.¹⁵ This study showed that at 12T and n_r ~ 1.2 kHz ¹⁴N and ¹⁵N dipolar couplings alter sideband intensities by a few percents and shielding parameters by 1-2 ppm.⁹ The application of higher magnetic field, > 18 Tesla, would allow to reduce these effects to less than 1 ppm. Shielding parameters were obtained by 1D or 2D with ¹⁵N decoupled (¹³C^a) or ¹³C decoupled (¹⁵N) MAS spectra of samples with *G in the central residue with one exception, WGG.

The data presented here (Table 2) sample glycyl residues in a variety of backbone conformations close to a-helix, b-strand, 3₁-helix/polygly II and fully extended 2° structures. For a-helices, examples of both left and right-handed helices were studied.

Table 2. Shielding tensor data for central gly residues. Numbers in parentheses are 95% joint confidence intervals. a_R-helix and a_L-helix are right and left-handed a-helices. Shielding parameters are in ppm relative to TMS. The (f,y) angles for the central residues are based on the X-ray coordinates. The 2° conformation is labeled according to the standard structure with which it most closely corresponds. The empty cells in the table correspond to unpublished data.

Remarkably, the range of ¹³C^a anisotropies, (d₁₁- d₃₃), varies from 34.7 ppm (V*GG, b-strand) to 53.0 ppm (PGG, 3₁-helix); an order of magnitude larger than the range of isotropic shifts. Table 2 also provides four trends relating glycyl shielding parameters to 2° structure. (i) ¹³C^a d_iso for a-helix residues are downfield from b-strand residues with an average shift of 1.5 ppm. This is in agreement with the protein chemical shift index.¹ (ii) In terms of 2° conformations, 3₁ helices have largest (50.7 and 53.0 ppm), a-helices have intermediate (41.3 to 50.3 ppm) and b-strands have the smallest (34.7 and 35.2 ppm) ¹³C^a (d₁₁-d₃₃). (iii) The ratio ¹³C^a (d₂₂-d₃₃)/(d₁₁-d₃₃) is less than 1/2 for both a-helix and 3₁-helix/polygly II but greater than 1/2 for b-strands. (iv) ¹⁵N (d₁₁-d₃₃) of b-strands are ~15 ppm larger than the ones for helices and have the largest deviation from axial symmetry, (d₂₂-d₃₃) ~ 35 ppm, compared to all helices, which have small (d₂₂-d₃₃) values.

¹³C^a ab initio calculations¹⁶ (Oldfield and coworkers) allow direct comparison of theoretical and experimental data. Six glycyl conformations with (f,y) angles close to a-helix, b-strand, 3₁ helix were chosen from Table 2. Their experimental values of (d₁₁-d₃₃) and (d₂₂-d₃₃) were compared with the calculations of for a tripeptide-like fragment, N-formyl glycyl amide.¹⁷ The correlation plot⁹ brings rmsd error of 3.0 ppm and indicates a good agreement between theory and experiment (r² = 0.97). Therefore, in most cases calculated values of (d₁₁-d₃₃) and (d₂₂-d₃₃) are reliable within several ppm.

The next obvious question arises, is whether or not these observations extend beyond this data set? For this reason ~500 examples of gly residues found in a-helices, b-strands, and 3₁-helix/polyglycine II, were selected from randomly chosen set of proteins in the Protein Data Bank. The chemical shift calculator¹⁸ was used for theoretical prediction of C^a shielding parameters. The histogram, figure 4, displays their distribution for each 2° structure. In most cases, (d₁₁-d₃₃) and (d₂₂-d₃₃)/(d₁₁-d₃₃) values distinguish between a-helix (red) and 3₁-helix/polygly II (blue) but neither is well separated from b-strands (green), which has a very distributed range of values due to the wide range of torsion angles in selected conformations. Only a fraction of b-strands, that has (d₂₂-d₃₃)/(d₁₁-d₃₃) > 0.5 may be distinguished from the other 2° elements at this stage. Fortunately, ¹⁵N (d₂₂-d₃₃) and (d₁₁-d₃₃) allows distinguishing between b-strands and a-helix (red) with 3₁-helix/polygly II as it was mentioned earlier.

	Figure 3. Histograms of (d22-d33) and (d22-d33)/(d11-d33) constructed from the protein torsion angles (PDB) and the theoretical CS parameters.17 The color coding: a-helix (red), 31-helix (blue) and b-strand (green).

In summary, measurement of gly shielding parameters by MAS spectroscopy is a helpful experimental technique for qualitative investigations of 2° structure in proteins. The attractive area of application includes proteins not amenable to crystallization or solubilization in their native state, where determination of 2° structure is important and currently difficult.

6. Theoretical aspects of ¹⁷O electric field gradient in the solid state.

Ab initio calculations allow assessing various effects that alter ¹⁷O electric field gradient (EFG). Those include hydrogen bonding, van der Waals interactions, etc. The effect of the mentioned interactions is hard to measure or establish by any experimental approach.

A large non-uniform EFG is produced by the charge of surrounding electrons and other nuclei,

with     ,

where f is the potential due to external sources.

Nuclei with spin >1/2 posses a quadrupole moment and, thus, interact with EFG. These interactions are measured by NMR and three principal axes system (PAS) components, V_xx^PAS, V_yy^PAS, and V_zz^PAS, can be obtained as well as their orientation within molecular frame.¹⁹ In this study Gaussian’98²⁰ program is used to calculate ¹⁷O EFG tensors of oxalic acid and compare them with experimental values.¹⁹

The simplest model for ¹⁷O EFG calculation is ice, where the effects of H-bonding, cluster size, level of theory and basis set can be addressed.²¹ The method of choice was DFT aug-cc-pVDZ with b3LYP functional. It was found that H-bonding reduces the values of all three PAS EFG components on additive basis as compared to single H₂O molecule. Each H-donor (H₂O in ice lattice) has the effect of ~0.5 MHz and each H-acceptor has the effect of ~1.25 MHz on the largest component. The similar trend is also observed in oxalic acid calculations. It was also found that the minimum cluster size must have at least 17 H₂O molecules (2 layers of hydration) for an adequate calculation. Finally, the 42-molecule cluster provided the values within 5% compared to the experimental ones.

The oxalic acid (OA) crystal lattice²² has three magnetically not equivalent oxygens, carboxyl, hydroxyl, and oxygen of water molecule (W). The simplest adequate clusters were (OA molecule + 6 Ws) for hydroxyl and carboxyl oxygens and (1 W + 3 OAs) for water oxygen. These clusters account for H-bonding of the target oxygen. The addition of other layers of atoms led to improvement in ab initio EFG values as it was seen in the ice calculations. The best/largest clusters calculations yielded the following errors: carboxyl ¹⁷O ~3%, hydroxyl ¹⁷O ~8%, and H₂O ¹⁷O ~17%.