Quantitative rotational-echo double resonance for Carbon-13 spin clusters

Abstract

By using only half of the total evolution time for dephasing pulses, C{N} rotational-echo double resonance (REDOR) for clusters of ¹³C spins (RDX) results in the same universal REDOR behavior as observed for isolated ¹³C-¹⁵N pairs. RDX combines Hahn echoes with solid echoes to suppress interference from scalar J couplings.

This is crucial for long evolution times. The modified version (which we call RDX24) makes RDX quantitative for ¹³C clusters. We apply this scheme to human embryonic kidney cells labeled in culture by L-[¹³C₅ - ¹⁵N₂]-glutamine. We quantitatively characterize three separate nitrogen isotopic enrichments for: (i) the alpha nitrogens of glutamine residues in proteins (including the residues of the five amino acids synthesized from glutamine); (ii) the alpha nitrogens of the five amino-acid residues synthesized from glucose, together with those of the nine essential amino acids added to the growth medium; and (iii) the side-chain nitrogens of glutamine (and of asparagine derived from glutamine).

GRAPHICAL ABSTRACT

1. Introduction

Rotational-Echo Double Resonance (REDOR) was initially intended [1], [2] to characterize the dipolar coupling between an isolated pair of heteronuclear spins, typically ¹⁵N (dephase) and ¹³C (observe). Applications to systems in which there were clusters of ¹³Cs coupled to a single ¹⁵N were stymied by dephasing caused by ¹³C–¹³C scalar J-coupling which was often comparable to the ¹³C-¹⁵N dipolar coupling. Two general solutions to this problem have been introduced: (i) J-decoupling using a single frequency-selected ¹³C pulse [3], [4], and (ii) the interleaving of REDOR with J-based double-quantum filtering [5]. However, both methods have a sensitivity problem, the former because the ¹³C frequencies of the cluster are treated one at a time, and the latter because of the inefficiencies of the double-quantum filter.

2. Experimental methods

RDX (REDOR for ¹³C_X clusters) used a combination of Hahn echoes and solid echoes (generated by ¹³C π and π/2 pulses) to refocus both ¹³C chemical shifts and J-coupling [6]. The solid echo is effective because a ¹³C–¹³C pair acts to first order as a single spin-1. The resulting total echo formation was good, but the effect of the ¹⁵N dephasing was much less than expected and difficult to interpret.

We have now resolved these dephasing problems. The I-S (¹³C-¹⁵N) bilinear coherence generated in the first period (time to the first π/2 pulse) is shifted by 90 degrees (about the x-axis, see phase table in the caption to Fig. 1) from that generated in the second period (time after the first π/2 pulse to just before the second π/2 pulse), and the bilinear coherence in the third period is similarly shifted from that in the fourth period. That is, phase shifts interfere with direct addition of coherences in adjacent periods. In addition, the REDOR dephasing in the first and third periods (Fig. 1) generates bilinear coherence of opposite sign, resulting from the net change in sign of the dipolar coupling between the second and third periods. These two bilinear coherences self cancel (Fig. 2, top).

Fig. 1.

Pulse sequence for RDX24 C{N} rotational-echo double resonance (REDOR). The total evolution time is separated into four equal periods, each ending with a ¹³C π/2 pulse. Dipolar dephasing occurs only during the second and fourth periods. The last ¹³C π pulse generates a Hahn echo. The expanded view (bottom) shows the xy-phase alternation of the ¹⁵M π pulses while the arrows show a programmable loop for extended dephasing. The same loop but without the ¹⁵N pulses is used for periods one and three. Total evolution and dephasing times of RDX24 are 8(n + 1) and 4(n + 1), respectively, where n, the loop counter, equals 1, 2, 3, … The phases of the ¹H and ¹³C pulses are (φ₁ = (0,0,2,2)₄ ; φ₂ = (1)₁₆; φ₃ = (0,1,0,1)₄; φ₄ = (0,1,2,3)₄; φ₅ = (0,1,2,3,2,3,0,1)₂; φ₆ = (2,3,0,1,0,1,2,3)₂; φ₇ = (0,1,2,3,2,3,0,1,2,3,0,1,0,1,2,3); Φ₈ = (0,3,2,1)₄, where 0 = x; 1 = y; 2 = −x; and 3 = −y. The ¹³C phases were selected (6) for optimum So refocusing.

Fig. 2.

Signs of dipolar evolution for RDX13 (top) and RDX24 (bottom) where τ of Fig. 1 is 2Tr. The sign of the I-S dipolar coupling (D_IS) is obtained by the multiplication of two spin terms (I_z and S_z) and a space term (MAS). The cancelation of dipolar evolution for RDX13 can be avoided by insertion of an extra S-spin π pulse at the start of period 3.

There are two possible modifications to the RDX pulse sequence which will eliminate these bilinear coherence cancelations. The first we call RDX13 which consists of the original RDX pulse sequence but with an S-spin π pulse inserted at the beginning of the third period (coincident with the I-spin π/2 pulse), and omission of the S-spin dephasing pulses in periods two and four. The second modification we call RDX24 is even simpler and consists of just omitting the S-spin dephasing pulses in periods one and three (Figs. 1 and 2, bottom). Both sequences give rise to quantitative REDOR dephasing for ¹³C spin clusters (as well as single ¹³Cs) coupled to a single ¹⁵N dephasing spin which is indistinguishable [7] from that of an isolated ¹³C-¹⁵N pair (Figs. 3 and 4, left panel). This is true for values of ΔS/So between 0 and the approach to 1 (where ΔS = So – S, So is the full echo, and S is the dephased echo). Minor deviations appear in the REDOR “wiggles” for long evolution times, possibly due to contributions from J-based coherence transfers. Imperfect ¹³C π/2 pulses present in RDX24 but not in standard REDOR will result in reductions in S and So but not in ΔS/So, assuming no distributions of couplings.

Fig. 3.

Dipolar phase evolution during RDX24 (Fig. 1) for an ¹⁵N-¹³C₁-¹³C₂ triad (black and colored lines) compared to standard REDOR dipolar phase evolution (dotted lines) for isolated ¹⁵N-¹³C₁ (top) and ¹⁵N-¹³C₂ (bottom) pairs with D_CN/2. RDX24 and standard REDOR dipolar phase evolutions are indistinguishable for up to 13 ms evolution time (6.5 ms dephasing time).

Fig. 4.

RDX24 C{N} REDOR for the three carbons of 10% L-[¹³C₃-¹⁵N₂]-alanine re crystallized with 90% unlabeled L-alanine. Values of ΔS/So (where ΔS = So – S, So is the full echo, and S is the dephased echo) calculated (symbols) using SIMPSON are shown on the left with experimental values (symbols) shown on the right. The solid lines are conventional REDOR calculations for isolated ¹³C-¹⁵N pairs in alanine with half values of DCN’s. (Only half of the total evolution time is involved in dephasing.) Magic-angle spinning was 6250 Hz.

3. Theory for RDX24

For a single ¹³C (I₁) coupled to a single ¹⁵N (S), the pulse sequence of Fig. 1 yields [2], [5]

$$\mathrm{S}∕\text{So}=\cos (\Delta {\Phi }_{(1)}[4\tau ])$$ (1)

where ΔΦ₍₁₎ is the average IS dipolar coupling over a rotor period multiplied by the dipolar evolution time. For an I-spin pair coupled to S, we find for I₁

$$\begin{gathered} \mathrm{S}∕\text{So}={\cos }^2({\mathrm{J}}_{12}\tau )\cos (\Delta {\Phi }_{(1)}[4\tau ])+{\sin }^2\left({\mathrm{J}}_{12}\tau \right)\cos (\Delta {\Phi }_{(1)}[2\tau ])\cos (\Delta {\Phi }_{(2)}[2\tau ])+\{{\cos }^2\left({\mathrm{J}}_{12}\tau \right)- \\ \cos \left({\mathrm{J}}_{12}\tau \right)\cos \left(2{\mathrm{J}}_{12}\tau \right)\}{\sin }^2(\Delta {\Phi }_{(1)}[2\tau ]) \end{gathered}$$ (2)

A similar expression holds for I₂. Closed-form expressions for spin-clusters of I spins larger than two coupled to a single S spin are too complicated to be insightful. However, we can always expand a large spin cluster into a sum of two-spin pairs. For example, the three-spin cluster of alanine is well represented by I₁-I₂ coupled to S plus I₂-I₃ coupled to S. Because two-bond ¹³C–¹³C scalar couplings are small and can be ignored, there is no I₁-I₃ term. Applying this analysis to the RDX24 experiments on alanine, all the cross terms of Eq. (2) disappear because sin²(J₁₂τ) is close to zero while cos²(J₁₂τ) is close to one. In addition, the factor inside the curly bracket is close to zero so the sin²(J₁₂τ) ΔΦ₍₁₎[4τ] term disappears (Fig. 3). That is, the expected RDX24 S/So (and equivalently ΔS/So) for I₁ of the I₁-I₂ pair in alanine is the same as the expected (and observed) S/So for an isolated I spin (Fig. 4). Similar direct agreements for calculated values of S/So (isolated spins compared to clusters) are found for the six-spin ¹³C cluster of histidine coupled to a single ¹⁵N (Fig. 5, left). The experimental values of S/So for histidine are also in reasonable agreement with the calculated values, particularly for shorter evolution times (Fig. 5, right).

Fig. 5.

RDX24 C{N} REDOR for the six carbons of 10% L-[¹³C₆ - α-¹⁵N]-histidine recrystallized with 90% unlabeled L-histidine. Values of ΔS/So (where ΔS = So – S, So is the full echo, and S is the dephased echo) calculated (symbols) using SIMPSON are shown on the left with experimental values (symbols) shown on the right. The solid lines are conventional REDOR calculations for isolated ¹³C-¹⁵N pairs in alanine with half values of DCN’s. The numbers in the histidine structure (inset) are the dipolar couplings (in Hz) to the ¹⁵Nα. Scalar ¹³C–¹³C couplings are in reference 6. Magic-angle spinning was 6410 Hz.

4. Application results and discussion

We decided to apply RDX24 to characterize the ¹⁵N distribution in intact human embryonic kidney cells (HEK-293 T) labeled in vitro by L-[¹³C₅-¹⁵N₂]-glutamine. Cells were cultured in high-glucose Dulbecco’s Modified Eagle’s Medium (DMEM) containing 10% fetal bovine serum. The growth medium also contained the nine essential amino acids. (For details, see reference [8]) Glutamine is directly responsible for the synthesis of five amino acids (glutamate, asparagine, aspartate, arginine, and proline). These six amino acids are expected to be heavily ¹³C-labeled and therefore account for the full-echo ¹³C spectrum (Fig. 6, bottom). The intensity of the corresponding natural-abundance ¹³C spectrum (no labeling) was negligible. We used Dante (delays and nutations for tailored excitation) frequency-selective inversion pulses [9], [10], [11] to interrogate the left, center, and right parts of the broad peptide carbonyl-carbon peak (Fig. 6: a, b, and c). These selections cover all of the peptide carbonyl-carbon shifts for the six ¹³C-labeled amino-acid protein residues. After a 50-ms mixing time (with no proton irradiation), we observe those alpha-carbons (55 ppm) and side-chain carbons (30 ppm) which are directly coupled to the selected ¹³C peptide carbonyl carbons. The similarities of the Dante difference spectra (Fig. 6, middle three ΔS spectra) show that the three glutamine carbons, -Cα(C)-C(=O)-, remain together in glutamate, asparagine, aspartate, arginine, and proline residues in proteins.

Fig. 6.

Dante-selected 125.7-MHz ¹³C ΔS differences (where ΔS = So – S, So is the full echo, and S is the echo with a frequency-selected inversion) after a 50-ms mixing time (with no proton irradiation) for three inversion frequencies between 166 and 182 ppm (red a, b, and c) for lyophilized whole cells of HEK-293 T labeled in culture by L-[¹³C₅-¹⁵N₂]- glutamine. (The Dante pulse train had 64 1-μs pulses with a 40-μs pulse spacing asynchronous with the rotor.) The peaks near 55 and 30 ppm in the three middle ΔS spectra arise from ¹³C spin diffusion from the inversion site. The glutamine carbons (top inset) remain intact for a variety of protein residues derived from glutamine. The ΔΔS at the top of the figure is the 8-Tr C{N} REDOR difference spectrum for the peaks selected by Dante inversion at 166 ppm (red c, second from top). The minor peak labeled by “gly” (top spectrum) suggests minor leakage of label from glutamine into protein residues normally labeled by glucose. Magic-angle spinning was 8 kHz.

There are two major sources of nitrogen for the growth in culture of the HEK-293 T cells: the two ¹⁵Ns of glutamine (6 mM in the growth media) and the ¹⁴Ns of the nine essential (mostly) branched chain and aromatic amino acids (approximately 1 mM for each in the growth media). De-amidation of glutamine results in glutamate and ¹⁵NH₃ [12], the two of which can supply the nitrogen for the five amino acids synthesized from glucose (alanine, glycine, serine, threonine, and cysteine), as well as exchange with all other alpha nitrogens, both ¹⁴N and ¹⁵N. We separate the resulting ¹⁵N distribution into three groups: (i) alpha-¹⁵N of the six amino-acid residues connected to glutamine; (ii) alpha-¹⁵N of the remaining fourteen amino-acid residues; and (iii) the amide-¹⁵Ns of glutamine and asparagine. We take the isotopic enrichment of the two amide nitrogens in proteins (f₀) as equal to 1. This decision is based on the notion that when a glutamine or asparagine is needed for protein synthesis, molecules that have not undergone first a deamidation and then a re-amidation are readily available.

The other isotopic enrichments (f_α and f_ex) are determined by RDX24 C{N} spectra (Fig. 7). Based on the results of Fig. 3, Fig. 4, Fig. 5, we expect close to full dephasing for a 1-bond ¹⁵N-¹³C coupling after a dephasing time of 12 Tr (1.5 ms). The ΔS/So for a 2-bond coupling and a dephasing time of 12 Tr is less than 5%. However, full dephasing of a 2-bond ¹⁵N-¹³C coupling is expected for a dephasing time of 52 Tr (6.5 ms). The placement of proximate labels for adjacent residues in proteins is: – N-C(C)-C(=O) – N-X-Y–. All the ¹³C labels are counted in the first residue. Thus, f_α is determined by the intra-residue 1-bond ¹⁵N-¹³C coupling of the six amino-acid residues derived from labeled glutamine (Fig. 6, ΔS/So = 0.50, Table 1). The f_ex isotopic enrichment is determined by the inter-residue 1-bond ¹⁵N-¹³C coupling (Fig. 7, ΔS/So = 0.37, Table 1). However, an accounting of the the contribution of the glutamine and asparagine amide nitrogens to the observed ΔS/So must first be made. Since f₀ = 1, and there are two amide nitrogens responsible for ΔS and ten carbonyl carbons responsible for So (six main-chain carbonyl carbons, two side-chain carboxyl carbons, and two side-chain amide carbonyl carbons), the 1-bond side-chain ΔS/So in proteins is 2/10 = 0.2. The algebra for extracting f_ex is detailed in the footnotes to Table 1.

Fig. 7.

RDX24 C{N} REDOR for whole cells of HBK-293T labeled in culture by L-[¹³C₅-¹⁵N₂]- glutamine for two values of the dephasing time.

Table 1.

C{N} RDX24 of HEK Cells Labeled by L-[¹³C₅-¹⁵N₂]-glutamine.

	Ria	xα	fα	xex	fex	favg	(ΔS/So}fit/calc	(ΔS/So}obs
1-bond alpha	6/6	6/6	0.50	–	–	–	0.50	0.50
1-bond crbnyl b	6/10	6/20	0.50	14/20	0.19	0.28c	0.37	0.37
2-bond alpha d	6/6	–	0.50	–	–	0.43	0.64	0.63
2-bond crbnyl e	6/10	–	0.50	–	–	0.43	0.58	0.51

^aRatio of the number of labeled carbons contribution to ΔS relative to the number of labeled carbons contributing to So.

^b(ΔS/So}_{1-bond carbonyl} = (ΔS/So)_{1-bond side-chain carbonyl} + R_{carbonyl main-chain}(x_α(f_α + x_exf_ex).

^cf_avg = x_αf_α + x_exf_ex.

^d(ΔS/So}_{2-bond alpha} = (ΔS/So}^{1-bond alpha} + R_α(1 – f_α)(f_avg).

^e(ΔS/So)_{2-tond carbonyl} = (ΔS/So}_{1-bond carbonyl} + R_{carbonyl main-chain}(1 – f_avg)(f_α).

Two-bond ¹⁵N-¹³C ΔS/So values (Fig. 7, right) afford an opportunity to check the self-consistency of our nitrogen-distribution modeling. The ΔS/So for the alpha-carbon will have an inter-residue contribution only if the intra-residue nitrogen is ¹⁴N. The ΔS/So of the carbonyl- carbon will have an intra-residue contribution only if the inter-residue nitrogen is ¹⁴N (Table 1, footnotes). Observed and expected ΔS/So are in reasonable agreement (Table 1) even with our imposition of several simplifying assumptions. We conclude that based on the RDX24 results, the nitrogen distribution in HEK-293 T proteins is heterogeneous (f₀ > f_α > f_ex).

We anticipate that RDX24 will have a broad applicability in using solid-state NMR to characterize quantitatively ¹³C and ¹⁵N labeling in metabolomics.

Highlights.

• ¹³C-¹³C J-couplings cause unwanted dephasing in C{N} REDOR experiments on ¹³C-spin clusters.

• We show that a simple modification of an existing REDOR pulse sequence for clusters solves the problem.

• Each ¹³C of the cluster has the same C{N} REDOR behavior as an isolated C-N pair.

• We apply this new sequence to examine labeling of lyophilized whole kidney cells by L-[¹³C₅-¹⁵N₂]-glutamine.