Simultaneous Measurement of ¹H^C/N-R₂’s for Rapid Acquisition of Backbone and Sidechain Paramagnetic Relaxation Enhancements (PREs) in Proteins

Abstract

Paramagnetic relaxation enhancements (PREs) are routinely used to provide long-range distance restraints for the determination of protein structures, to resolve protein dynamics, ligand-protein binding sites, and lowly populated species, using Nuclear Magnetic Resonance Spectroscopy (NMR). Here, we propose a simultaneous ¹H-¹⁵N, ¹H-¹³C SESAME based pulse scheme for the rapid acquisition of ¹H^C/N-R₂ relaxation rates for the determination of backbone and sidechain PREs of proteins. The ¹H^N-R₂ rates from the traditional and our approach on Ubiquitin (UBQ) are well correlated (R²=0.99), revealing their potential to be used quantitatively. Comparison of the S57C UBQ calculated and experimental PREs provided backbone and side chain Q factors of 0.23 and 0.24, respectively, well-fitted to the UBQ NMR structure, showing that our approach can be used to acquire accurate PRE rates from the functionally important sites of proteins but in at least half the time as traditional methods.

Introduction

Proteins adopt many conformational states and undergo a vast array of dynamics in order to perform their physiological functions^1–4. To date most experimental studies in protein Nuclear Magnetic Resonance (NMR) spectroscopy focus on the observation of isotopically labeled backbone atoms^5,6 while making assumptions and/or extrapolations about the role of the amino acid side chains when proposing functional models of proteins. This is understandable as quantitative analysis of protein side chains is often impeded by contaminating processes such as dipolar coupling and/or rapid hydrogen exchange, leading to extensive line broadening and undetectable resonances, especially at physiologically relevant pH’s^7–10. However, despite these inherent difficulties, NMR remains the most powerful methodology available to measure and isolate side chain specific phenomena.

During the past few decades, several NMR based methods have arisen and proven useful to characterize the structures, dynamics, and kinetic of side chains. Out of these, the most notable and robust are (i) methyl observe experiments which use isotopically labeled side chain methyl groups of Alanine, Isoleucine, and Valine as dynamic models of all side chains, and as indirect probes of a protein’s localized disordered states^11–15. (ii) deuterium labeling of proteins for suppressing dipolar interactions and spin diffusion between ¹H and ¹⁵N/¹³C nuclei, thereby, improving the resolution of side-chain resonances^16–18. (iii) Arginine specific ¹³C detection schemes to investigate and quantify the dynamics and interactions of charged side chains across a broad range of physiological conditions^19,20. (iv) Substitution of amino acids with structurally similar but resonantly different analogs to resolve ambiguities between side-chain nuclei in large protein complexes^21–25.

Particularly noted for the acquisition of long range distances according to the dipolar interaction between a nuclear spin and an unpaired electron, paramagnetic relaxation enhancement (PRE) measurements have become routine in protein NMR^26–29. With an electron gyromagnetic ratio which is 658 times larger than the proton nuclear gyromagnetic ratio, this means that PREs are significantly more sensitive than NOEs (which are limited to distances <5 Å). In fact, PREs can provide long range distances of up to 35 Å away from the electron, depending on the paramagnetic group²⁹. Because of this, PREs have been found to be particularly useful for helping to determining the three-dimensional structures of not only soluble proteins but, also, membrane proteins, protein-protein complexes, high molecular weight proteins³⁰, and protein-DNA complexes³¹. Moreover, PRE’s can be used to resolve large-scale dynamics and ligand binding interactions in the fast exchange regime by monitoring changes in the PRE rate as a function of spatial position and distance from the paramagnetic center³². The sensitivity of PREs is further shown by the ability to uncover lowly populated intermediates^33–35, long range contacts in intrinsically disordered proteins (IDPs)³⁶ and ¹³C detected side chain dynamics at domain interfaces³⁷.

Considering the importance of capturing atomic level information about the backbone and sidechains of proteins in the development of an accurate structural and functional model of a protein in solution, we propose a simple HSQC-based 2D pulse scheme for the simultaneous measurement of transverse proton relaxation rates from both the backbone and sidechains of a protein in a single experiment. When paired with an appropriately placed spin label within a protein of interest, PREs from backbone and side chain resonances can be procured from only two experiments (with oxidized and reduced forms of the spin label attached to a protein). This method which simply requires a ¹³C,¹⁵N labeled protein with a single surface exposed CYS ligated to a suitable paramagnetic spin-label such as methanethiosulfonate (MTSL) is based on the measurement of two simultaneous HSQC’s,¹H-¹³C and ¹H-¹⁵N, each with a variable delay period, and constant time ¹³C block with gradient selection, for acquisition of concurrent side chain and backbone transverse relaxation rates. Because this is an HSQC-based method, both backbone and sidechain ¹H transverse relaxation rates can be acquired rapidly using only a single experiment and sample, therefore eliminating possible discrepancies (e.g., resulting from the experimental age of a protein) while analyzing and comparing data acquired from sidechain and backbone PREs. In other words, instead of four consecutive experiments (¹H-¹⁵N and ¹H-¹³C transverse relaxation measurements for both diamagnetic and paramagnetic samples), all backbone and sidechain ¹H transverse relaxation rates for PREs are measured within the same experiment and time window. We demonstrate this approach on¹⁵N/¹³C labeled S57C Ubiquitin.

Materials and Methods

Sample Preparation

The Ubiquitin single cysteine mutant S57C was generated using site-directed mutagenesis on the cDNA of human UBQ, inserted in a pET13b plasmid. Protein expression and purification were performed as previously described³⁸. Following purification, the S57C Ubiquitin mutant was concentrated with Amicon 3kDa cutoff filters and reduced with an ~ 20-fold molar excess of DTT for ~2 hr at room temperature. Subsequent removal of DTT was performed via a GE PD10 column which simultaneously served to buffer exchange S57C Ubiquitin into reaction buffer (100 mM sodium phosphate, pH=7.5). Next, a 10-fold molar excess of S-(1-Oxyl-2,2,5,5-tetramethylpyrroline-3- methyl) methanethiosulfonate (MTSL) was immediately added and the mixture was allowed to incubate overnight, in the dark, at room temperature. This mixture was then passed through a reverse phase HPLC column (Agilent Poroshell 300SB-C8) to remove excess spin label while using solvent A (water, 0.1% Trifluoroacetic acid, TFA) and a gradient of 0-70% solvent B (Acetonitrile, 0.1% TFA) to elute the paramagnetically tagged protein. The diamagnetic state of the protein was acquired by reducing the nitroxide spin label with a 10-fold molar excess of sodium ascorbate, prepared as a 1M stock at pH = 7.5. Liquid chromatography mass spectrometry (LC-MS) (Fig S1) and NMR (Fig S2) of the unreacted and reacted protein were used to confirm the purity, identity, and labeling efficiency of the spin labeled protein. The spin labeling reaction was continued until all S57C was conjugated to MTSL (Fig S1). All NMR experiments were performed in 50mM sodium phosphate pH = 7.5, 10% D₂O, 298K.

PRE measurements

Although both longitudinal (Γ₁) and transverse (Γ₂) PRE relaxation rates are measurable, the Γ₂ rates are, in practice, preferred for quantitative assessments of biomolecular systems in solution^28,29,39. In contrast to Γ₁ rates which are susceptible to hydrogen exchange, cross-relaxation and T₂ exchange processes⁴⁰, the Γ₂ rates are mostly affected by dipole-dipole interactions between the observed nuclei and paramagnetic tag²⁹. Using paramagnetic tags with an isotropic g tensors confers an additional advantage by suppressing Curie Spin relaxation. This effectively eliminates pseudo contact shifts (PCS) and the need to perform time-consuming experiments and analysis, to separately assign the resonances of the paramagnetic and diamagnetic states^29,39. In general, the transverse PRE rate is defined as the difference between the transverse relaxation rates of the paramagnetic and diamagnetic species of a protein and is given by the following equation (1)²⁸.

$${\mathrm{\Gamma }}_2=R_{2,para}-R_{2,dia}$$ (1)

Due to this subtraction, relaxation mechanisms which are the same in both states are effectively canceled. Thus, leaving the dipolar interaction between the electron and nuclear spins as the predominant form of relaxation. For paramagnetic systems with an isotropic g tensor, Γ₂ is defined as equation (2)

$${\Gamma }_2=\frac{1}{15}{\left(\frac{{\mu }_0}{4\pi }\right)}^2{{\gamma }_1}^2{g}^2{{\mu }_B}^{2}S(S+1)r^{-6}\left(4{\tau }_c+\frac{3{\tau }_c}{1+{w_h}^2{{\tau }_c}^2}\right)$$ (2)

This form of Γ₂ is most commonly known as the Solomen-Bloembergen equation^41,42. Here r is the distance between the paramagnetic center and nuclei of interest, γ₁ is the nuclear gyromagnetic ratio, g is the electron g-factor, μ₀ is the permeability of vacuum, μ_B is the electron Bohr magneton, S is the electron spin number, τ_c is the rotational correlation time and w_h is the nuclear larmor frequency. The τ_c is the total correlation time τ_c = (τ_r⁻¹ + τ_s⁻¹), defined by the rotational correlation time of the protein, τ_r, and the effective electron relaxation time, τ_s. In order for these equations to be valid, it is assumed that (i) the time for electron relaxation is infinitesimal in comparison to the overall tumbling motion of the molecule and (ii) the dipole-dipole interaction vectors remain rigid within the molecular frame.

The pulse sequence for measuring R₂ relaxation rates arising from backbone amide and carbon side-chain protons is displayed in Fig 1. Briefly this pulse sequence utilizes a relaxation period for transverse protons between points a to b and nitrogen frequency encoding between points b to c. A constant time carbon block is used from points c to d before magnetization is transferred back to protons between points d to e. Finally, at point e, antiphase proton magnetization evolves to in-phase magnetization prior to detection. The gradient (G₃, G₄, G₅ and G₆) lengths for selecting and encoding coherences were parametrized according to the equations below:

$$G_3+G_4=-({\gamma }_{1_H}/{\gamma }_{{15}_N})\left(G_5+G_6\right)$$ (3)

$$G_3-G_4=({\gamma }_{1_H}/{\gamma }_{{13}_C})\left(G_5+G_6\right)$$ (4)

Fig 1: Pulse sequence for simultaneous measurement of Backbone and Sidechain proton PRE.

Narrow gray and wide filled black rectangular bars represent non-selective 90° and 180° pulses, respectively. The first 90° pulses on the ¹⁵N and ¹³C channels are Boltzmann purge pulses followed by a long gradient G₁. The ¹H and ¹⁵N carrier frequencies were set at 4.7 ppm (water) and 118 ppm (center of ¹⁵N spectral region), respectively. The ¹³C carrier frequencies at ¹³Cα and ¹³C’ were set at 56 ppm and 175 ppm (center of ¹³C’ spectral region), respectively. Decoupling of the¹³C-¹³C’ and ¹⁵N-¹³C’ couplings was achieved using 180° selective sinc pulses with an offset of 175 ppm. During the acquisition, Nitrogen and Carbon was decoupled from protons using the WALTZ⁵⁰ and GARP⁵¹ sequences with RF pulses of 1.25 kHz and 2.7 kHz, respectively. Pulse field gradients were used for coherence selection and residual water suppression. The delays are defined as Δ=1/(4J_NH) = 2.75 ms, τ = 1/(2J_CH)=1.8 ms, and T= 1/(4J_CC) =14ms. The variable delay (ε) periods were used to acquire the transverse relaxation rates of amide and carbon protons. Unless indicated, otherwise, pulses were x phase. Phase cycles were φ1= x, x, y, y,−x,−x, −y,−y, φ2= x, x, −y, −y, −x, −x, y, y, φ3= x,−x, φ4=25°, φ5= −x, and (φ_rec= x, x, y, y,−x,−x, −y,−y. All gradients are sine-bell shaped with 25G/cm at their center. G_1,2,3,4,5,6 = 4, 3.5, 6.7, 2.851,0.824, 0.146 ms, with respective gradient axes: xyz, −z, z, −z, z. The gradients G₃ and G₄ are used to encode nitrogen and carbon coherences, respectively. The delay δ as shown is equal to the initial value of 2kt1.

For determining proton PRE rates, HSQC resonance intensities at each variable delay for the paramagnetic and diamagnetic samples were measured and used within equation (5) to calculate residue-specific PRE rates.

$${\mathrm{\Gamma }}_2=\frac{1}{T_b-T_a}\ln \frac{I_{dia(T_b)}{I}_{para(T_a)}}{I_{dia(T_a)}{I}_{para(T_b)}}$$ (5)

Errors in the PRE rates were determined and propagated using equation (6):

$$\sigma ({\mathrm{\Gamma }}_2)=\frac{1}{T_b-T_a}\sqrt{{\left\{\frac{{\sigma }_{dia}}{I_{dia(T_a)}}\right\}}^2+{\left\{\frac{{\sigma }_{dia}}{I_{dia(T_b)}}\right\}}^2+{\left\{\frac{{\sigma }_{para}}{I_{para(T_a)}}\right\}}^2+{\left\{\frac{{\sigma }_{para}}{I_{para(T_b)}}\right\}}^2}$$ (6)

where, I_dia and I_para are the peak intensities of a resonance in the diamagnetic and paramagnetic protein spectra, respectively, at time points, T_a and T_b. Here σ_dia and σ_para are the standard deviations of the noise observed in the diamagnetic and paramagnetic spectra.

The 2D pulse scheme, for the collective acquisition of backbone and sidechain ¹H transverse relaxation rates for paramagnetically tagged samples, was tested on 1mM uniformly ¹⁵N/¹³C labeled S57C human ubiquitin in 50 mM sodium phosphate, pH 7.5, at 25°C with 10% D₂O. Two-dimensional ¹H-R₂ experiments were performed using a Bruker Avance 600MHz spectrometer equipped with a room temperature ¹H/¹³C/¹⁵N triple resonance probe with an actively shielded triple axis gradient system. Spectra were processed and analyzed using NMRPipe⁴³ and sparky⁴⁴. The proposed pulse sequence was recorded with delays 2T= 28 ms, 2Δ= 5.5 ms, and 2τ= 3.6 ms. For each ¹H-R₂ experiment, the variable delay (ε) was incremented in predefined steps, to sufficiently sample the decaying ¹⁵N and ¹³C proton resonance intensities. In practice, the UBQ ¹H-R₂ HSQC spectra were acquired in an interleaved manner according to (ε) values of 0, 4, 8, 16, 20, and 40 ms. A Boltzmann purge pulse was added to the pulse sequence to completely eliminate the Boltzmann ¹⁵N/¹³C magnetizations and to reduce CSA-DD cross correlation. Interestingly, ¹H^N-R₂ rates with and without this purge pulse is highly correlated with a correlation coefficient of R²=0.99 (Figure S3) suggesting that our implementation of this pulse sequence inherently minimizes these potential artifacts. To measure the sensitivity of our method with the traditional method we evaluated the intensity ratios [I_sim/I_trad] of the paramagnetic S57C-MTSL UBQ using the simultaneous and traditional methods at ε=0 ms and ε=10 ms.The average ratio ranges from 83% to 85% as shown in Figure S4. This indicates that our method is ~15-17% less sensitive than the traditional method. The ~15-17% loss of signal occurs because our simultaneous method uses a 28 ms constant time (CT) delay. This loss would be more for larger proteins but will occur in any CT ¹H-¹³C pulse scheme⁴⁵. Furthermore, to gauge the possibility of further loss in sensitivity for residues showing large PREs, we calculated the intensity ratios [I_sim/I_trad] which revealed an average ratio of ~78% (Figure S4, highlight red). This further shows that the sensitivity for residues with large PREs does not decrease significantly in our pulse scheme. The gradients G₃-G₆ were used to selectively isolate nitrogen and carbon coherences. Although a multitude of time points were acquired, only two (εa = 0 ms and ε_b = 10ms) were used for calculating PRE rates. A total of 72 scans were collected for each experiment with 254(t1) and 2048(t2) total number of points. All spectra were zero filled by twice the number of fids in each dimension to give a 508(t1) x 4096(t2) data matrix.

Results and Discussion

The simultaneous acquisition of ¹⁵N and ¹³C HSQCs was first reported by Griesenger and coworkers⁴⁶, as well as Parella and Coworkers⁴⁷. Although, facile and time efficient, the widespread use of this methodology was hindered by poor resolution in the ¹³C^α HSQC. To overcome this issues and to increase resolution in the ¹³C dimension, Permi et al introduced a SESAME-HSQC variant for the simultaneous measurement of NH and CH correlations, primarily for one-bond RDCs⁴⁸. In contrast to the previous methods, the SESAME approach utilizes gradient selection with a sensitivity enhanced ¹⁵N and constant time ¹³C HSQC, to select the desired spin states. This not only results in increased sensitivity but also improved resolution in the indirectly detected carbon dimension⁴⁸. With this in mind, we propose a 2D pulse scheme based on a modified SESAME-HSQC for the collective acquisition of backbone and sidechain ¹H transverse paramagnetic relaxation enhancements (PREs) from ¹H-¹⁵N and ¹H-¹³C correlations in proteins.

Description of the Pulse Sequence

Simultaneous and accurate measurements of ¹H-R₂ rates from backbone and side chain resonances in a water sample requires sufficient spectral dispersion and reliable peak picking. Additionally, water suppression should be highly effective, especially for observation of resonances close to the immense H₂O signal. In general, pulse field gradient approaches, often provide efficient and optimal water suppression.

The pulse sequence depicted in Fig. 1 can be categorized into three notable periods (i) Insensitive Nuclei Enhanced by Polarization Transfer (INEPT) with ¹H-R₂ relaxation block (ii) ¹⁵N, and constant time (CT)-¹³C chemical shift evolution, and (iii) a reverse INEPT.

The first 90° pulse of the INEPT in our scheme is non-selective and used to create transverse magnetization from protons to ¹⁵N and ¹³C via ¹J_HN and ¹J_HC coupling, simultaneously. The magnetization at point a is given by:

$$H_x$$

Echo delays of 2Δ and 2τ, where Δ=¼*J_NH and τ=½* J_CH, are then used to maximize the concomitant transfer of magnetization from the protons to the heteronuclei (¹⁵N and ¹³C). Except, here, unlike the typical INEPT, a variable delay (ε) is included to allow sampling of the heteronuclear ¹H-R₂ relaxation while maintaining the same coherence transfer, coupling, and evolution steps as without the variable delay. During the variable delay period H^N would relaxes with its own R₂, while H^C will relax with its own R₂ so the H^N relaxation during the INEPT would be R₂(H^N)*1/2*inept_Δ, while the H^C would follow its own R₂(H^C)* 1/2*inept_τ, respectively. The magnetization at the end of this INEPT at point b is:

$$2H_z{N}_z+2H_z{C}_z$$

The ¹⁵N chemical shift evolves for a time of kt₁. As the nitrogen chemical shift evolves, the ¹H-¹³C magnetization remains fixed along the z-axis with a longitudinal two-spin order of 2H_zC_z. Note, the delay δ equals the initial value of 2kt1 so that the first order phase correction is null in the nitrogen dimension. Thus, at point c, the magnetization is described as

$$2H_z{N}_x\sin [\delta w_N-2k{t}_1{w}_N]-2H_z{N}_y\cos [\delta w_N+2k{t}_1{w}_N]+2H_z{C}_z$$

where w_N is the ¹⁵N frequency shift. The scaling factor, k, here is the ratio of the sweep width of the ¹³C and ¹⁵N dimension, SW(¹³C)/SW(¹⁵N)=1.3.

Following application of the 90° φ3 pulse, the ¹³C chemical shift evolves for a constant time (CT) of 2T. For the constant time-period, the J_C-C modulation depends on the number of adjacent ¹³C atoms. Here the value of T is limited to a value of 27-29 ms in order to suppress the modulation of the antiphase 2HzCy coherence by [cos(2π J_CCT)]ⁿ, where n is the number of adjacent ¹³C atoms involved in J_C-C couplings . This CT period, resultantly, increases the resolution in the indirectly detected ¹³C dimension and removes passive interactions such as ¹J_CC, ¹J_C’Cα, ¹J_NC’, ¹J_NCα, ²J_NCα⁴⁹. This leaves the magnetization at point d as:

$${(2H_z{C}_x\sin (4w_c{t}_1)-2H_z{C}_y\cos (4w_c{t}_1))}^{\ast }{[\cos (2\pi J_{\mathit{cc}}T)]}^n+2H_z{N}_x\sin (\delta w_N-2k{t}_1{w}_N)+2H_z{N}_y\cos (\delta w_N-2k{t}_1{w}_N)$$

where w_c is the ¹³C frequency shift. To solely select ¹⁵N and ¹³C single quantum (SQ) coherences, pulse field gradients G_N and G_C, where G_N is 2.5 times that of G_C, used during the indirectly detected t₁ evolution.

In our pulse sequence gradient coherence selection was used rather than sensitivity enhancement. However, our choice was driven by the need to observe as many resonances as possible, especially when considering the effects of the paramagnetic label on resonances of the protein sample. Residues in close proximity to the paramagnetic moiety show very high proton R₂’s and broad resonances. In other words, sensitivity enhancement would lengthen the duration of complete magnetization transfer back to the proton for detection and, hence, lower the number of observed resonances.

Prior to the final 90° heteronuclear pulse, the active SQ coherences are H_yC_z, H_yN_z, or MQ coherences are 2HyNx (2HyCx). These coherences are then transferred back to protons via ¹⁵N, ¹³C and ¹H 90° pulses. This leaves the magnetization at pointe as:

$$-2H_y{C}_x\sin (4w_c{t}_1)+2H_y{C}_z\cos (4w_c{t}_1)-2H_y{N}_x\sin (\delta w_N-2k{t}_1{w}_N)+2H_y{N}_z\cos (\delta w_N-2k{t}_1{w}_N)$$

Subsequently, the antiphase magnetization evolves to in-phase proton magnetization Heteronuclear coupling is eliminated using WALTZ⁵⁰ and GARP⁵¹ decoupling sequences on the nitrogen and carbon channel during acquisition. Thus, the magnetization detected at point f is:

$$H_x\cos (\delta w_N-2k{t}_1{w}_N)-H_x\cos (4w_c{t}_1)$$

All density operator calculations have been performed with POMA⁵² using the first phase of the phase cycle.

Validation of Methodology

To demonstrate the applicability of our method for measuring simultaneous backbone and sidechain ¹H-R₂ rates, we tested our approach on Ubiquitin (UBQ) (MW 8.6 kDa, 76 amino acid residues) where the ε modulated intensity decays of UBQ were measured and fit to single exponential decays to extract the transverse ¹H^N-R₂ rates. For cross validation of our method, we also measured a set of amide ¹H^N-R₂ rates using the traditional approach, originally, developed by Clore and coworkers³⁹. Importantly, the ¹H^N-R₂ rates of the traditional and our SESAME based approach are well-correlated with a correlation coefficient of 0.99 and an average error of 3%, as shown in Fig 2. This means that our pulse sequence can be used to effectively and accurately measure the backbone amide transverse relaxation rates of protons. As aforementioned, however, our method has a distinct advantage in that we can also acquire ¹H^C-R₂ rates of the side chain protons with minimal loss of sensitivity. While not specifically performed for the experiments in this proof-of-principle study, our proposed pulse sequence could additionally be used with different delays of ε to capture either fast H^α-C^α and/or slow ¹H-¹⁵N, ¹H-¹³C ¹H-R₂ rates. Furthermore, because the value of ³J_HN-Hα coupling is quite low (~5.5-8 Hz) compared to ¹J_H-N (~90 Hz), the R₂ rates are much less effected by homonuclear ³J_HN-Hα modulation which can be completely eliminated by using the intensity ratio of the paramagnetic and diamagnetic state when calculating the PRE.

Fig 2: Correlation plot of the backbone amide.

¹H^N-R₂ transverse relaxation time constants acquired for Ubiquitin using our method, in comparison to the common approach. The correlation coefficient is 0.99. Measurements were acquired at 600 MHz and 298 K. The buffer for Ubiquitin was 50 mM sodium phosphate, 10% D₂O, pH 7.5.

While using the SESAME based pulse sequence for our experiments, there were some notable observations, confirmed in our work, that were previously highlighted by Permi, et. al⁴⁸. The addition of a 2T period in the SESAME scheme, results in a roughly ~15-17% decrease in sensitivity when compared with the traditional sequence^29,39. Furthermore, the CH correlations are affected by the decay of the longitudinal two spin coherence order 2H_ZC_Z during kt1. However, incorporation of the R₂ relaxation block did not introduce further sensitivity loss in either the NH or CH correlations when compared with the original SESAME-HSQC. It should be further noted that these numbers are for the fairly small protein UBQ. For larger proteins (> 30 kDa), sensitivity loss will be higher due to the rapid decay of the 2H_zC_z coherence. Although, these additional losses due to the protein size can be mitigated by optimizing the nitrogen dimension shift scaling factor (k) for the aliphatic, methyl regions, and faster relaxing H^α-C^α correlations for each protein.

The 2D ¹H-¹⁵N and ¹H-¹³C spectrum of ubiquitin using the ¹H^N/C-R₂ SESAME pulse sequence, at 600MHz is displayed in Fig 3. Implementation of the constant time ¹³C period provided excellent resolution and sensitivity for the NH and CH correlations of ubiquitin. In addition, with the phase of the ¹H-¹³C HSQC inverted, the proton bonded ¹³C resonances are easily identifiable from those bonded to ¹⁵N. The opposite signs of some cross peaks in ¹H-¹³C are due to [cos(2π J_CCT)]ⁿ and a negative value of cos(2π J_CCT). Here the delay T was set to achieve cos(2π J_CCT)= −1 so that the sign of the ¹H-¹³C cross peaks depends on the number of adjacent ¹³C atoms (n)⁴⁵.The chemical shift assignments of the backbone and side chain resonances were extracted from the BMRB code 15410. Stereospecific assignments were not used during analysis of the side chain. The H_α resonances which can be hidden under the broad water resonance are clearly resolvable as a result of excellent water suppression.

Fig 3: Simultaneous ¹⁵N, ¹³C HSQC.

2D Simultaneous ¹⁵N, ¹³C HSQC of 400 μM Ubiquitin in 50 mM sodium phosphate, 10% D2O, pH 7.5 acquired at 600 MHz and 298K using our pulse sequence, as shown in Fig 1.

Representative ε-dependent ¹H-R₂ relaxation curves of the side chain and backbone protons (¹H^N, ¹H^δ and ¹H^γ) are shown in Fig 4A, 4B and 4C. Each ¹H^C/N-R₂ relaxation curve was well-fit to a single exponential decay to acquire the transverse relaxation constants of ¹H^N, ¹H^α, ¹H^γ and ¹H^δ respectively.

Fig 4:

Representative ¹H-R₂; decay curves of select residues from the ¹H-¹⁵N and ¹H-¹³C regions of the 2D spectrum. Each decay was well-fit to a single exponential. Residues and their associated relaxation rate constants are shown in supplementary Table S1.

The side chain ¹H-R₂’s are notably longer than those of the backbone amides, particularly as the proton distance from the backbone increases, as seen in the relaxation curves of ¹H^γ and ¹H^δ’s. This proton positional effect on the rate of ¹H-R₂ is indicative of the flexible side chain motions and means that the transverse relaxation constants of the protons along the side chains, such those of the methylene and methyl protons, can be quite informative about the surrounding environment. For example, a surface exposed proton would be expected to show a much different ¹H-R₂ than a proton that is buried and/or engaged in a binding event.

In general, side chain ¹H-R₂’s can provide information about various protein modes such as dynamics, conformational entropy, allostery and substrate binding. For soluble folded proteins, side-chain ¹H-R₂’s are heterogeneously dispersed over the protein structure, with higher ¹H-R₂’s observed in areas known to be involved in protein folding and intermolecular interactions⁵³. Furthermore, according to Law et al., side chain dynamics of a protein are conserved throughout evolution⁵⁴. In other words, side chain dynamics are intimately connected to the physio-chemical properties and functionality of proteins. As such, extraction of sidechain ¹H-PREs alongside those of the backbone, can provide a deeper understanding of protein structure and, even more so, dynamics. Accordingly, our method provides a means to acquire both backbone and sidechain ¹H-R₂’s within a single experiment with reasonably good sensitivity and resolution, thereby, alleviating sample-to-sample R₂ variations as a result of using two different samples. We envision that this type of approach can be extended to other experiments, such as CPMG, CEST, and J-modulation.

Backbone and Sidechain PRE measurements on ubiquitin S57C mutant

The S57C substitution is known to introduce minimal perturbations to the ubiquitin structure. This was confirmed in our study by noting that the chemical shift perturbations are localized to the mutation sites, as seen in supplementary Fig S5. Tagging S57C MTSL also induces minor resonance shifts near S57C-MTSL most likely due to the change in environment experienced by amides close to the tag such as L56, 60N, 61T, 62Q. Chemical shift table of WT Ubiquitin, S57C mutant and S57C- MTSL are shown in supplementary table S2. With the UBQ structure confirmed as intact, we proceeded to determine the side chain and backbone PREs of S57C-MTSL.

Using our SESAME-based pulse sequence, ¹H-R₂’s from the backbone and side-chain ¹H nuclei were acquired on the diamagnetic and paramagnetic forms of UBQ S57C-MTSL while using the two-time point approach suggested by Clore and Iwahara, to determine the PREs^28,29. We then determined and compared the experimentally observed PREs to those back calculated from the NMR structure, PDB: 1D3Z, of ubiquitin (Fig 5B)⁵⁵. Residue-specific ¹H-R₂’s measured for the paramagnetic and diamagnetic states along with the calculated PREs are shown in supplementary Table S3. For the calculated PREs, we needed to consider that the paramagnetic probe MTSL is attached to S57C of UBQ via a flexible linker and, as such, a single conformation of this tag would not be adequate to define the orientational space occupied by this tag with respect to the position of the protein. In order to do this, we used the XPLOR-NIH package⁵⁶ to covalently bond the MTSL moiety to S57C of the UBQ NMR structure followed by simulated annealing to define the position and flexibility of the paramagnetic tag. During the minimization procedure, the number of MTSL conformers relative to the protein structure was varied from n=1 to n =8 wherein the protein was treated as a rigid body while the flexible MTSL group was given freedom to fully sample torsional angle space. We then compared the agreement between the experimental and calculated PREs, as the number of conformers increases, using a parameter called the Q factor defined as⁵⁷

$$Q=\sqrt{\frac{\sum {\{{{\Gamma }_2}^{\mathit{obs}}(i)-{{\Gamma }_2}^{\mathit{cal}}(i)\}}^2}{\sum {{\Gamma }_2}^{\mathit{obs}}{(i)}^2}}$$ (7)

Where the Q factor value ranges from 0 to 1 with a smaller value representing stronger agreement between experimentally observed and calculated PRE values in reference to the protein structure.

Fig 5: PREs for the single cysteine mutant S57C of Ubiquitin, measured at 600 MHz and 298K.

(A) Correlation plot of the backbone amide ¹H^N PREs observed using our pulse sequence with those predicted from the NMR structure. The correlation coefficient is 0.95 with a Q factor of 0.23 (B) Experimental and calculated transverse amide ¹H^N PREs are shown as red and black, respectively. The measured PREs were fit using an ensemble of three conformationally distinct MTSL conformers attached to Ubiquitin S57C. A total of 100 structures were calculated. Then the calculated PRE dataset was obtained by averaging the calculated PREs from the 10 lowest energy structures. (C) Correlation plot of sidechain PREs acquired using our pulse sequence with those predicted from the structure. The correlation coefficient is 0.97.

As shown in Fig S6 for the backbone ¹H^N-R₂ and side chain ¹H^C-R² PREs, the Q factor decreases as the number of conformers increase, with n=3 showing the best agreement between the calculated and experimental results. Fig 5A and 5C show the correlation plot between the calculated and experimental PREs of UBQ. Note, the calculated PRE was determined from the average PRE value observed in the 10 lowest energy, out of 100, structures of UBQ. The correlation coefficient is R=0.95 for the backbone amides (HN) and R=0.97 for the side chain suggesting a high degree of correlation between the experimental and calculated PREs.

The backbone and sidechain observed PREs, exhibit Q factors of 0.23 and 0.24, respectively, which corresponds to an excellent fit to the UBQ NMR structure. This suggests that our ¹H^C/N-R₂ SESAME based approach did not introduce anomalous results. The backbone and side-chain PREs results can be acquired with only two experiments (one with the paramagnetic and the other with the diamagnetic form of the protein).

Conclusion

In summary, we have developed and demonstrated the viability of a fast SESAME-based 2D HSQC experiment which can be used to acquire all proton backbone and side-chain transverse relaxation rates in a single experiment. The method was demonstrated on Ubiquitin and compared with the conventional approach for acquiring backbone PREs. Importantly, good agreement was shown between the traditional and our approach as well as between the back-calculated and experimental PRE values of UBQ. Our method would additionally be of excellent use for time sensitive protein samples where acquisition of side-chain PREs are sought but challenging to acquire on the same “state” of a protein, precluding consecutive and separate side-chain experiments and, thereby, preventing the ability to coalesce backbone and side-chain PRE data into a workable model for describing the structure and dynamics of a protein in solution. In short, the acquisition of side chain PREs along with those of the backbone are important for understanding protein folding, allostery, binding and molecular recognition. Our approach provides an avenue to acquire these PREs using subtle but unique modifications to routine HSQC experiments.