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This chapter provides an overview of recently introduced fast-pulsing NMR techniques that enhance sensitivity and reduce the overall acquisition times of multidimensional experiments. We discuss the underlying theoretical concepts, different experimental implementations, and other practical aspects of proton longitudinal-relaxation-enhanced pulse sequences, such as BEST-HSQC, BEST-TROSY, and SOFAST-HMQC. Polarization-enhanced fast-pulsing techniques are complementary to sparse, non-uniform data sampling methods that can be used together for time- and sensitivity-optimized collection of multi-dimensional NMR data.

The concept of multidimensional NMR spectroscopy1,2  lies at the basis of an amazingly large number of pulse sequence experiments that have made NMR spectroscopy a versatile tool for almost all branches of analytical sciences. Increasing the dimensionality of the experiment provides the required spectral resolution to distinguish individual sites in complex molecules such as proteins and nucleic acids. It also allows encoding information about inter-nuclear spin interactions as contributions to resonance position, line width or intensity, providing valuable information on the molecular structure and dynamics. However, major drawbacks of multidimensional NMR remain its inherent low sensitivity—a direct consequence of the weak magnetic spin interactions—as well as the long experimental times associated with repeating the basic pulse scheme a large number of times. Therefore, efforts are being made by scientists and NMR spectrometer manufacturers to improve the sensitivity and speed of NMR data acquisition. In this chapter we will describe and discuss a class of recently developed NMR experiments, so-called fast-pulsing techniques, which provide increased sensitivity in shorter overall experimental times. These techniques have been developed in the context of biomolecular NMR studies of proteins and nucleic acids, but the same ideas can also be applied to other macromolecular systems.

Before discussing the particular features of fast-pulsing techniques and their experimental implementation, we will provide a brief reminder of the main factors that determine the experimental sensitivity and the required minimal data acquisition time as these are of prime importance for designing new experiments and for choosing the most appropriate pulse sequence for a given application.

The signal-to-noise ratio (SNR) obtained for a particular NMR experiment on a given NMR spectrometer depends on a number of factors that can be summarized in the following way:

Equation 1.1

Obviously, the SNR is proportional to the number of NMR-active spins that are available for excitation (Nexc). Increasing the sample concentration is therefore a valid method to improve SNR. However, for biological molecules sample concentration is often limited by molecular aggregation. SNR also depends on the gyromagnetic ratio of the excited (γexc) as well as the detected spin species (γdet). Note that they may be different in heteronuclear correlation experiments. High-γ nuclei, such as protons, are therefore preferentially used as starting spin polarization sources and for NMR signal detection. This explains why most NMR biomolecular NMR experiments rely on proton excitation and detection. The NMR instrumentation contributes to the achievable SNR via the magnetic field strength (B0) and the quality of the probe used for signal detection (fprobe). This has lead to the development of stronger magnets, currently reaching up to 23.5 T (1 GHz 1H frequency), and cryogenically cooled high-Q probes that yield a drastic reduction in the electronic noise. Finally, SNR also depends on the NMR experiment to be performed via a number of parameters: the steady state polarization PZSS of the excited spins, as will be discussed in more detail in the next section; an attenuation factor fseq taking into account signal loss during the pulse sequence owing to spin relaxation, pulse imperfections, and limited coherence and magnetization transfer efficiencies; the number of experimental repetitions Nscan; and finally the dimensionality of the experiment leading to a √2 reduction in SNR for each indirect dimension owing to the requirement of phase-sensitive quadrature detection. Note that the additional √2 signal loss can be avoided by so-called sensitivity-enhanced quadrature detection schemes.3  However, this is typically only possible in one of the indirect dimensions, and also leads to additional relaxation-induced signal loss.

The minimal experimental time for recording an n-dimensional (nD) data set, with indirect time domains t1, t2tn−1, is given by the duration of the basic pulse scheme Tscan, multiplied by the number of repetitions required for phase cycling and time domain sampling.

Equation 1.2

Here, nPC is the number of repetitions required to complete a given phase cycling scheme that is used for artifact suppression and coherence transfer pathway selection. Nowadays, with the availability of pulsed field gradients that perform a similar task to phase cycling, nPC can often be limited to a small number, typically 2 or 4. nk is the number of time points acquired in the k-th time domain. For optimal performance of the experiment (in terms of resolution and sensitivity) nk should be set to a value close to nk=SWkvk, with Δvk the natural line width of the frequency edited spin species and SWk the corresponding spectral width, resulting in typical values of nk= 100–200. The additional factor 2n−1 arises from the quadrature detection scheme in each of the n−1 indirect dimensions. Consequently, using conventional data acquisition schemes (uniform linear sampling of the grid), each additional dimension increases the experimental time by about two orders of magnitude.

Neglecting, for the sake of simplicity, relaxation-induced signal loss during the incremented time delays tk, the SNR increases with . For each experimental setup (sample, NMR spectrometer, NMR experiment) there exists a minimal number of scans, NscanSNR, required to achieve sufficient SNR to distinguish the NMR signals from the noise. We can thus distinguish two different scenarios: if NscanSNRNscansampling, we call this experimental situation sensitivity-limited, while the case NscanSNRNscansampling is referred to as sampling-limited. In the sensitivity-limited regime, the basic pulse scheme has to be repeated several times, in order to further improve SNR. Fast multidimensional NMR methods, which are the topic of this book, become of interest either for experiments in the sampling-limited regime or if the overall experimental time does become prohibitively long.

A schematic drawing of an NMR experiment is shown in Figure 1.1a. It consists of the pulse sequence (suite of pulses and delays) of duration tseq, a signal detection period (tdet), and an inter-scan delay (trec) that is also called the recycle or recovery delay. This latter delay, trec, is required to allow the spin system, which has been perturbed by the radio frequency pulses, to relax back toward thermodynamic equilibrium before repeating the pulse sequence. The effective recycle delay, during which longitudinal spin relaxation takes place, is Trec=tdet+trec, and the total scan time, as introduced in eqn (1.2), is given by Tseq=tdet+trec.

Figure 1.1

(a) Schematic representation of an NMR pulse sequence experiment, consisting of a series of pulses and delays (tseq), a data detection period (tdet), and a recycle delay (trec). This basic scheme needs to be repeated Nscan times for enhancing experimental sensitivity, phase-cycling purposes, and time incrementation in indirect dimensions for multidimensional data acquisition. (b) Sensitivity curves, calculated according to eqn (1.3), and plotted as a function of the recycle delay Trec for different longitudinal relaxation times T1. The duration of the pulse sequence was set to tseq=100 ms for the calculation. (c) Dependence of the experimental sensitivity on the duration of the pulse sequence tseq=λT1. The plotted curves have been computed for 0≤λ≤1 in steps of 0.1 (from the top to the bottom). The sensitivity maximum shifts from Trec/T1=1.25 for λ=0 to Trec/T1=1.9 for λ=1.

Figure 1.1

(a) Schematic representation of an NMR pulse sequence experiment, consisting of a series of pulses and delays (tseq), a data detection period (tdet), and a recycle delay (trec). This basic scheme needs to be repeated Nscan times for enhancing experimental sensitivity, phase-cycling purposes, and time incrementation in indirect dimensions for multidimensional data acquisition. (b) Sensitivity curves, calculated according to eqn (1.3), and plotted as a function of the recycle delay Trec for different longitudinal relaxation times T1. The duration of the pulse sequence was set to tseq=100 ms for the calculation. (c) Dependence of the experimental sensitivity on the duration of the pulse sequence tseq=λT1. The plotted curves have been computed for 0≤λ≤1 in steps of 0.1 (from the top to the bottom). The sensitivity maximum shifts from Trec/T1=1.25 for λ=0 to Trec/T1=1.9 for λ=1.

Close modal

In order to evaluate the effect of these pulse sequence parameters, and in particular the recycle delay Trec, on the performance of the experiment in terms of SNR, we can calculate the experimental sensitivity, defined as the signal-to-noise ratio obtained for a fixed amount of time Texp:

Equation 1.3

In eqn (1.3), we have assumed that spin relaxation is mono-exponential, and can thus be described by a single characteristic time constant T1. We would like to emphasize here that the parameter T1 describes the time evolution of proton polarization recovery, but can not be directly associated to a constant with a physical meaning.

Throughout this chapter, we will refer to the dependence of the SNR on the recycle delay as a sensitivity curve. Examples of such theoretical sensitivity curves computed for different T1 time constants are plotted in Figure 1.1b. The sensitivity curves show a maximum as the result of two counteracting effects: on one hand, the steady-state spin polarization, and thus the detected NMR signal, increases for longer Trec. On the other hand, when increasing Trec, the number of repetitions that can be performed in a given experimental time decreases, thus reducing SNR. For shorter relaxation time constants T1, higher overall sensitivity is achieved with the maximum shifted toward shorter recycle delays. As long as the sequence duration tseq is negligible with respect to T1, the optimal recycle delay and the maximal sensitivity are given by:

Equation 1.4a
Equation 1.4b

Otherwise, if tseq becomes comparable to T1, a longer Trec has to be chosen in order to reach the highest SNR and the maximal sensitivity slightly decreases. Sensitivity curves computed for 0<tseq<T1 are plotted in Figure 1.1c.

Eqn (1.4) implies that under conditions of optimal sensitivity, the required overall data acquisition time is proportional to T1, while the achievable sensitivity is proportional to . Therefore, reducing T1 provides a convenient way of increasing experimental sensitivity, while at the same time reducing the minimal required experimental time. This has motivated the development of longitudinal relaxation enhanced (LRE) NMR techniques that allow speeding up NMR data acquisition, as will be presented in the following sections.

In this section, we will briefly discuss the spin interactions that govern longitudinal proton spin relaxation in slowly tumbling macromolecules, such as proteins, oligonucleotides, or polysaccharides, before discussing in more detail the experimental LRE schemes that have been developed over the last decade.

The main mechanisms responsible for proton polarization buildup are the numerous 1H–1H dipolar interactions that are present in proton-rich molecules, and that are responsible for polarization transfer from one proton to another via cross-relaxation effects. Proteins, for example, contain on average about eight protons per residue that are generally tightly packed together within a globular fold. Formally, the time evolution of the polarization of each proton spin in the molecule is given by the Solomon equations, a set of coupled first-order differential equations:

Equation 1.5

where Hiz denotes the z-component of the polarization of proton i and Hiz0 is its thermal equilibrium value that, for the sake of simplicity, will be assumed to be equal to 1 throughout this chapter. The different ρ and σ terms stand for auto- and cross-relaxation rate constants, respectively, with values depending on the distance separating the two protons involved as well as the global and local dynamics of the protein experienced at the sites of the interacting protons. The auto-relaxation rate constants that are responsible for energy exchange with the lattice (molecular motions) contain contributions from dipolar interactions with all neighboring protons, and also with neighboring hetero-atoms such as 13C and 15N in isotopic enriched molecules. If the rotational tumbling of the molecule is slow compared to the proton Larmor frequency (τc>1/ωH≈10−9 s at high magnetic field strengths), cross-relaxation rates become negative (σij<0), and as a consequence lead to spin diffusion within the dipolar-coupled spin network. It is worth mentioning here that the cross-relaxation rates (absolute value) increase with the effective rotational correlation time, making spin diffusion more efficient for larger molecules, or molecules studied at lower temperature.

For chemically labile proton sites, e.g. amide and hydroxyl protons, hydrogen exchange processes with the bulk water protons provide an additional relaxation source that under certain sample conditions (pH and temperature) may even become predominant, as we will see later on. In order to account for this exchange effect theoretically, the set of first-order differential equations (eqn (1.5)) has to be expanded to include exchange with the water 1H polarization, resulting in the so-called Bloch–McConnell equations:

Equation 1.6

with kex,i the exchange rate between proton i and water. In eqn (1.6) we have assumed that the bulk water proton polarization Wz is not changed by hydrogen exchange with the protein, which is a reasonable hypothesis in view of the ∼105 times higher concentration of water in the NMR sample tube. The chemical exchange rates kexchem depend on the local chemical environment of the labile proton, as well as the pH and temperature. Roughly, kexchem doubles when increasing the sample temperature by 7 °C or the pH by 0.3 units. The apparent exchange rates kex are further modulated by the solvent accessibility of the labile proton that formally is described by a protection factor P=kexchem/kex, varying from P=1 (no protection) to very large values, P>1000 (highly protected), in the core of stable globular proteins

Eqn (1.6) provides the theoretical basis for the development of longitudinal-relaxation enhancement schemes. A first strategy for accelerating longitudinal proton relaxation consists of the introduction of an additional auto-relaxation mechanism, for example by adding a paramagnetic relaxation agent to the sample. Dipolar interactions between the proton spins and the large dipolar moment of the unpaired electron(s) in the paramagnetic molecule enhance proton spin relaxation by adding a contribution to the rate constants ρ. A list of possible paramagnetic compounds can be found in a recent review by Hocking et al.4  We can distinguish two different types of paramagnetic relaxation agents: (i) those acting directly on the protein nuclear spins and (ii) those acting primarily on the water protons. An example of a paramagnetic chelate belonging to the first category is Ni2+-DO2A.5,6  At 10 mM concentration, Ni-DO2A has been shown to reduce T1 relaxation time constants of amide protons in proteins to about 50–200 ms.6  Of course, the LRE effect strongly depends on the solvent accessibility of the nuclear spins, which translates into a relatively large enhancement for surface residues, while the effect of the paramagnetic relaxation agent is less pronounced for residues in the interior of a protein. The use of paramagnetic relaxation agents is therefore particularly well adapted to the NMR study of highly flexible molecules where most of the residues are solvent exposed.6  Another drawback of such relaxation agents is that they may cause significant line broadening, especially in the case of specific interaction with the protein. Ni2+ has a short electronic relaxation time of T1e≈10−12 s, which limits the paramagnetic induced line broadening. Another class of paramagnetic compounds selectively enhances the 1H T1 of the bulk water. A number of such water relaxing paramagnetic chelates have been developed as contrast agents for magnetic resonance imaging (MRI). An example is gadodiamide (Figure 1.2a), Gd3+(DTPA-BMA), which has been commercialized as clinical contrast agent under the name “Omniscan”. Adding gadodiamide at 0.5 mM concentration to an aqueous solution reduces the water T1 from a few seconds to about 400 ms (Figure 1.2a). Gd3+ complexes have been successfully used for relaxation enhancement in small globular proteins and IDPs,7  as well as large perdeuterated proteins.8,9 

Figure 1.2

Options for 1H longitudinal relaxation enhancement (LRE) techniques: (a) a paramagnetic relaxation agent is added to the protein sample. As an example the chemical structure of the Gd3+ chelate gadodiamide, Gd3+(DTPA-BMA), is shown on the left. The effect of 0.5 mM gadodiamide on the water 1H longitudinal relaxation has been measured and is shown in the right panel. The apparent T1 is reduced from 3.4 to 0.44 s at 25 °C. LRE pulse schemes based on selective 1H excitation: (b) band-selective shaped pulses, and (c) scalar-coupling-based flip-back scheme.

Figure 1.2

Options for 1H longitudinal relaxation enhancement (LRE) techniques: (a) a paramagnetic relaxation agent is added to the protein sample. As an example the chemical structure of the Gd3+ chelate gadodiamide, Gd3+(DTPA-BMA), is shown on the left. The effect of 0.5 mM gadodiamide on the water 1H longitudinal relaxation has been measured and is shown in the right panel. The apparent T1 is reduced from 3.4 to 0.44 s at 25 °C. LRE pulse schemes based on selective 1H excitation: (b) band-selective shaped pulses, and (c) scalar-coupling-based flip-back scheme.

Close modal

An alternative spectroscopic method that does not require any chemical modification of the sample is to exploit the fact that the relaxation of an individual proton spin depends on the spin state of all other protons in the protein and the bulk water. In particular, solving eqn (1.6) shows that in cases where only a subset of the proton spins is of interest, a selective excitation of these spins results in a much faster recovery than a non-selective excitation.10,11  This is of significant practical interest to a large number of biomolecular NMR experiments that excite and detect only a subset of proton spins, e.g. amide, aromatic, and methyl 1H in proteins, or imino, base, and sugar 1H in nucleic acids.

In order to achieve selective excitation of only a subset of the proton spins in a molecule, two different experimental approaches have been proposed. A first method (Figure 1.2b), that we will refer to as “frequency-selective”, uses band-selective shaped pulses to manipulate only the spins of interest, while leaving all others unperturbed, or at least little affected by the pulse sequence. The obvious disadvantage of this approach is that it is limited to proton species that are sufficiently different chemically to resonate in distinct spectral regions. Furthermore, in highly structured molecules, such as proteins, ring-current effects may shift a particular resonance far away from the typical chemical shift region, and as a consequence such protons may not become excited by the selective pulses. A second “coupling-selective” method (Figure 1.2c) exploits the presence or absence of a scalar coupled heteronuclear spin X (typically 15N or 13C) to achieve selective proton excitation. For this purpose, broadband 1H pulses are used to excite (and refocus) all proton spins together. Scalar-coupling evolution during a time interval equal to 1/JHX then creates a 180° phase shift of protons coupled to X, with respect to all others. A final 90° (flip-back) pulse restores the 1H polarization for the uncoupled spins. In addition, the use of a band-selective 180° X pulse allows even more selectivity by restricting the excitation, for example, to 13Cα-bound protons, while protons bound to other aliphatic or aromatic 13C are flipped back at the end of the sequence. This scheme is especially attractive for heteronuclear correlation experiments performed on protein samples with partial or no isotope enrichment. It is also a good choice for performing 1Hα excitation while leaving the water protons that resonate in the same spectral window, close to equilibrium. A major drawback of such coupling-based flip-back techniques is that the efficiency of restoring the 1H polarization depends on the quality of the applied pulses, and even more importantly on the transverse-relaxation induced coherence loss during the spin evolution delay 1/JHX. This explains why, in practice, the frequency-selective pulse excitation scheme outperforms the coupling-based flip-back scheme whenever both approaches are feasible.

In the following, we will focus on amide 1H selective experiments of proteins. The large majority of amide protons resonate in a narrow spectral window (∼6 to 10 ppm) that is well separated from most other (aliphatic) protein protons and the bulk water (Figure 1.3a). Amide protons can thus be selectively manipulated by means of appropriate shaped pulses, as discussed in more detail later on. The effect of selective versus non-selective proton spin inversion on the longitudinal relaxation behavior of amide protons is illustrated in Figure 1.3b for two amide proton sites in the small protein ubiquitin, located in a well-structured β-sheet (F4), and a highly dynamic loop region (G10). For both amide protons, selective spin inversion leads to significant longitudinal relaxation enhancement, while of course the exact relaxation properties also depend on the local structure (average distance to other protons, solvent accessibility) and dynamics (local effective tumbling correlation time), resulting in significant differences in the apparent relaxation curves. Another observation is that the polarization recovery after non-selective spin inversion is well described by a mono-exponential curve requiring a single relaxation time constant (T1non-sel). This is generally not the case after selective spin inversion that is best described by a bi-exponential behavior with a fast relaxation component (T1fast) and a slow relaxation contribution (T1slow). The magnitude of the latter is to a good approximation equal to the relaxation time constant in the non-selective case (T1slowT1non-sel). Although this is not a rigorous treatment, in the remainder of this chapter we will characterize the polarization recovery under selective conditions by a single time constant T1=T1fast that is obtained either by fitting the first part of the inversion-recovery curve to a mono-exponential function, or from the zero-crossing time t0 as T1=t0/ln 2=1.44t0.

Figure 1.3

(a) 1H spectrum of ubiquitin. The spectral regions for amide, aliphatic, and water protons are highlighted. (b) Experimental 1H polarization recovery curves for selected amide sites in ubiquitin,11  highlighted by spheres on the ubiquitin structure (right panel). The solid lines are bi-exponential fits to the data measured for selective (filled squares) and non-selective spin inversion (filled circles).

Figure 1.3

(a) 1H spectrum of ubiquitin. The spectral regions for amide, aliphatic, and water protons are highlighted. (b) Experimental 1H polarization recovery curves for selected amide sites in ubiquitin,11  highlighted by spheres on the ubiquitin structure (right panel). The solid lines are bi-exponential fits to the data measured for selective (filled squares) and non-selective spin inversion (filled circles).

Close modal

In order to quantify the achievable LRE effects for amide protons, and the relative contributions from dipolar interactions and water exchange processes, we have measured apparent T1 relaxation time constants for different proteins and experimental conditions (pH and temperature). We distinguish three different experimental scenarios depicted in Figure 1.4a: (i) amide-proton selective spin inversion; (ii) water-flip back (wfb) spin inversion, and (iii) non-selective spin inversion. In the first case, only amide proton spins are inverted, while in the second case all protein protons are inverted leaving only the water protons at equilibrium, and finally in the third case the water protons are also inverted. The measured inversion-recovery curves of amide 1H polarization have been fitted to a mono-exponential function, as explained in the last section, and the apparent T1 values are plotted in Figure 1.4b–d as a function of the peptide sequence. Figure 1.4b shows the LRE effects obtained for the small globular protein ubiquitin (τc≈3 ns). Except for a loop region (residues 9–13) and the last four C-terminal residues, the measured relaxation time constants are quite uniform with a non-selective T1non-sel≅900 ms that is reduced to T1sel≅200 in the selective case. The main mechanisms for this 4.5-times acceleration of longitudinal relaxation are the dipolar interactions with neighboring non-amide protons, while water exchange processes only marginally contribute to the LRE effect. The observed situation is completely different for amides located in the highly flexible protein regions, where a non-selective T1 of up to T1non-sel≅2.5 s is observed, a value that approaches the T1 of water (3.4 s at 25 °C, see Figure 1.2a). Under these conditions, the selective and wfb inversion schemes perform the same, leading to relaxation times T1sel=T1wfb=40−70 ms, clearly demonstrating that water exchange is the main mechanism for the observed LRE effect.

Figure 1.4

Residue-specific amide proton T1 time constants measured for several proteins under different initial conditions. (a) Pulse schemes used for spin inversion of different sets of 1H spins in inversion-recovery experiments: amide 1H (HN), aliphatic 1H (HC), and water 1H (HW). The displayed inversion-recovery block is followed by a 2D 1H–15N readout sequence and a recycle delay of 6 s. For amide proton-selective inversion (left panel, red bars) a REBURP pulse shape was applied with a bandwidth of 4.0 ppm centered at 9.0 ppm; for water-flip-back inversion (central panel, green bars) a 179° inversion pulse is followed by a short delay of 10 ms during which radiation damping brings the water back to equilibrium; for non-selective 1H inversion (right panel, black bars) a broad-band inversion pulse is followed by a strong pulsed field gradient to spatially defocus residual water transverse magnetization. A low-power magnetic field gradient is applied during the entire relaxation delay Trelax to avoid radiation-damping effects. Apparent amide 1H T1 relaxation time constants measured for (b) the small globular protein ubiquitin (pH 7.5, 25 °C), and two intrinsically disordered proteins (IDPs),26  (c) NS5A (pH 6.5, 5 °C) and (d) α-synuclein (pH 7.4, 15 °C).

Figure 1.4

Residue-specific amide proton T1 time constants measured for several proteins under different initial conditions. (a) Pulse schemes used for spin inversion of different sets of 1H spins in inversion-recovery experiments: amide 1H (HN), aliphatic 1H (HC), and water 1H (HW). The displayed inversion-recovery block is followed by a 2D 1H–15N readout sequence and a recycle delay of 6 s. For amide proton-selective inversion (left panel, red bars) a REBURP pulse shape was applied with a bandwidth of 4.0 ppm centered at 9.0 ppm; for water-flip-back inversion (central panel, green bars) a 179° inversion pulse is followed by a short delay of 10 ms during which radiation damping brings the water back to equilibrium; for non-selective 1H inversion (right panel, black bars) a broad-band inversion pulse is followed by a strong pulsed field gradient to spatially defocus residual water transverse magnetization. A low-power magnetic field gradient is applied during the entire relaxation delay Trelax to avoid radiation-damping effects. Apparent amide 1H T1 relaxation time constants measured for (b) the small globular protein ubiquitin (pH 7.5, 25 °C), and two intrinsically disordered proteins (IDPs),26  (c) NS5A (pH 6.5, 5 °C) and (d) α-synuclein (pH 7.4, 15 °C).

Close modal

Figure 1.4 also shows the measured LRE effects for two so-called intrinsically disordered proteins (IDPs) that have been studied under different sample conditions: low pH (6.4) and low temperature (5 °C) for the first one—NS5A (Figure 1.4c)—and physiological pH (7.5) and higher temperature (15 °C) for the second one—α-synuclein (Figure 1.4d). IDPs have found widespread interest in recent years in structural biology in general, and in biomolecular NMR spectroscopy in particular.12,13  These highly dynamic proteins or protein fragments, which are particularly abundant in eukaryotes and viruses, have been ignored since the early days of structural investigation of proteins. Although they have no stable structure, IDPs are involved in many cellular signaling and regulatory processes, where structural flexibility presents a functional advantage in terms of binding plasticity and promiscuity.14  During recent years, NMR spectroscopy has become the technique of choice to characterize residual structure in IDPs and their interaction with binding partners. Owing to the low chemical shift dispersion in the NMR spectra of IDPs, and the often-encountered low solubility and limited lifetime of NMR samples, fast multidimensional data acquisition techniques are of primary importance for NMR studies of IDPs.

Interestingly, despite their high degree of internal flexibility, the LRE effects observed in IDPs are similar to those discussed above for a globular protein. Under conditions that do not favor solvent exchange (Figure 1.4c), but where the local tumbling correlation times are in the slow tumbling regime, the dipolar relaxation mechanism dominates (similar to the structured parts of ubiquitin), resulting in a significant reduction in the apparent average T1 time constants from T1non-sel≅1 s to T1sel≅200 ms. This observation also indicates that a few protons at close proximity are sufficient for efficient spin diffusion, and thus LRE effects. At higher pH and temperature the solvent exchange rates increase and become the main source of amide proton relaxation. Consequently, the relaxation behavior of amide protons in α-synuclein (Figure 1.4d) is very similar to that observed for the flexible loop and C-terminus in ubiquitin with T1non-sel≅2.3 s and T1sel =T1wfb≅60 ms. Note that this impressive LRE translates into a sensitivity gain of up to a factor of 6 if optimal short recycle delays are chosen, and if the pulse sequence performs perfectly in terms of selective spin manipulation.

To conclude this section, significant LRE effects are observed for amide protons in proteins of different size and structure, and under a variety of experimental conditions, as a result of two complementary relaxation mechanisms, which are dipolar interactions and solvent exchange processes. Therefore LRE pulse schemes are expected to be of great value for all types of amide proton-based NMR experiments.

The concepts introduced for LRE, and exemplified above for amide protons in proteins, can also be exploited for NMR experiments involving other proton spins in slowly tumbling molecules. The requirements to obtain significant LRE effects are the following: (i) the protons of interest can be excited (manipulated) by either shaped pulses or via a coupling-based flip-back scheme, and (ii) the selective excitation leaves neighboring protons as well as water protons, in the case of exchangeable sites, close to their thermodynamic equilibrium. These requirements are fulfilled for amide, aromatic, and aliphatic Hα and methyl protons in proteins, and for imino, base and sugar protons in nucleic acids (DNA, RNA). Especially for imino 1H the relaxation behavior is very similar to the one discussed above for amide protons, with dipolar interactions as well as solvent exchange contributing to the observed LRE effects.15  Imino protons can be easily manipulated by shaped pulses as they resonate in a well-separated frequency range (∼10–15 ppm). Examples of LRE-optimized NMR experiments for different types of protons will be given later.

In this section we will describe the basic features and experimental performance of longitudinal relaxation enhanced pulse schemes that use band-selective shaped 1H pulses for selective manipulation of a subset of protons in the molecule. Such experiments have been termed BEST, an acronym for Band-selective Excitation Short-Transient.16  As explained in more detail in the previous section, such BEST experiments yield enhanced steady-state 1H polarization of the excited spins at short recycle delays, allowing for faster repetition of the pulse sequence, and thus reducing the overall experimental time requirements.

The performance of BEST-type experiments in terms of LRE efficiency and overall sensitivity critically depends on the choice and appropriate use of shaped pulses. Therefore, we will briefly discuss the basic properties of some of the most prominent pulse shapes. Major efforts were made in the early 1990s in developing band-selective pulses using numerical optimization methods. These band-selective pulse shapes are characterized by a top-hat response in frequency (chemical shift offset) space that is uniform (constant rotation angle) over the chosen bandwidth (excitation/inversion band), and close to zero (no effect) for spins resonating outside this spectral window. A narrow transition region exists in between where spin evolution is undefined. Examples of such numerically optimized “top-hat” pulse shapes are the BURP pulse family,17  the Gaussian pulse cascades,18,19  the SNOB pulses,20  and polychromatic (PC) pulses.21  An additional feature of shaped pulses is that they have been optimized for a particular rotation angle, typically 90° or 180°, and some of them, so-called excitation (90°) or inversion (180°) pulse shapes, only perform such a rotation when starting from pure spin polarization (Hz), while their action on spin coherence is a priori undefined.

The shapes and excitation (or inversion) profiles of the band-selective pulses used in BEST-type experiments (PC9, EBURP-2, REBURP and Q3) are shown in Figure 1.5a. We have recently demonstrated by numerical simulations of the spin evolution during such pulse shapes that their effect on the spin density operator can be described reasonably well (first order approximation) by a sequence of free evolution delays and an additional time period accounting for the effective pulse rotation of β=90° or 180° over the chosen frequency band: τ1R(β)−τ2. These binary (delay/pulse rotation) replacement schemes,22  as we like to call them, are also shown in Figure 1.5a, with empty boxes representing the free evolution delays and filled boxes corresponding to the pulse rotation. Clearly, the resulting schemes are very different for pulse shapes optimized to perform the same type of action, a selective 90° or 180° rotation. While, for example, for the symmetric PC9 and REBURP pulses, chemical shift and coupling evolution is active during the entire pulse length, no spin evolution at all is observed for Q3. Similar results have recently been obtained by a factorization into individual Euler-angle rotation operators of the propagator describing the action of the shaped pulse on the spin system.23  With these binary pulse schemes in hand, it becomes straightforward to replace standard hard pulses in complex pulse sequences by appropriate shaped pulses, and to properly adjust coherence transfer and chemical shift editing delays taking into account spin evolution during the shaped pulses as described by the binary schemes. In particular, this allows application of such pulse shapes even in cases where several coherence transfer pathways need to be realized at the same time. BEST-implementations for the most common building blocks (INEPT, sensitivity-enhanced reverse INEPT, and single-transition-to-single-transition transfer) used for 1H–X heteronuclear coherence transfer are shown in Figure 1.5b–d.

Figure 1.5

Properties of band-selective pulse shapes used in BEST and SOFAST experiments. (a) The amplitude-modulated time-domain profiles of PC9,21  EBURP-2,17  REBURP,17  and Q319  are plotted together with the corresponding binary replacement schemes obtained from numerical simulations.22  Chemical shift and heteronuclear coupling evolution during the pulse shape is represented by open squares, while the time during which the actual spin rotation is occurring is represented by a black square. In addition the corresponding frequency-response of the spins is shown for each pulse shape. The binary replacement schemes make it straightforward to account for spin evolution in the basic BEST-type pulse sequence elements: (b) INEPT, (c) sensitivity-enhanced reverse INEPT (SE REVINEPT), and (d) single-transition-to-single-transition polarization transfer (ST2-PT).

Figure 1.5

Properties of band-selective pulse shapes used in BEST and SOFAST experiments. (a) The amplitude-modulated time-domain profiles of PC9,21  EBURP-2,17  REBURP,17  and Q319  are plotted together with the corresponding binary replacement schemes obtained from numerical simulations.22  Chemical shift and heteronuclear coupling evolution during the pulse shape is represented by open squares, while the time during which the actual spin rotation is occurring is represented by a black square. In addition the corresponding frequency-response of the spins is shown for each pulse shape. The binary replacement schemes make it straightforward to account for spin evolution in the basic BEST-type pulse sequence elements: (b) INEPT, (c) sensitivity-enhanced reverse INEPT (SE REVINEPT), and (d) single-transition-to-single-transition polarization transfer (ST2-PT).

Close modal

A second important property of the shaped pulse in the context of BEST-type experiments is its off-resonance behavior, as even a slight perturbation of the spin magnetization in a fast-pulsing experiment, typically employing several such pulse shapes, can have a severe effect on the resulting steady-state spin polarization. If the fraction of spin polarization of a set of protons after a single repetition (scan) of the pulse sequence is given by f, then the steady-state polarization Hzss of these protons at the beginning of each scan can be expressed in an analytical form as:

Equation 1.7

with Trecand T1 the recycle delay and longitudinal relaxation time constants, respectively. The proton polarization relevant for longitudinal spin relaxation at the beginning of the recycle delay Trec is then given by fHzss. The computed 1H polarization is plotted in Figure 1.6a as a function of Trec for different T1 values assuming a 5% perturbation of the equilibrium proton polarization after a single scan (f=0.95). If we focus on a recycle delay of Trec=200 ms, a typical value for BEST-type experiments, we see that even such a slight perturbation results in a dramatic reduction in the steady-state polarization for protons characterized by long T1 values of a few seconds. This is notably the case for the bulk water, while it is less of an issue for others, e.g. aliphatic protein protons. In order to check experimentally the effect of different pulse shapes on the water protons, we have measured the water polarization under steady-state conditions after applying a series of identical shaped pulses with a nominal excitation bandwidth of 4 ppm every 100 ms at varying offsets from the water frequency. Our experimental data indicate that off-resonance effects (non-zero excitation) are more pronounced for 180° pulse shapes than for pulse shapes optimized for 90° rotations. Off-resonance profiles measured on a last generation triple-resonance cryoprobe for the two 180° pulse shapes REBURP and Q3 are shown in Figure 1.6b (straight lines). Under the given experimental conditions (25 °C), the water proton T1 equals 3.4 s (see Figure 1.2a), and thus even slight perturbations are expected (Figure 1.6a) to have a measurable effect on the steady-state water polarization. For both pulse shapes the off-resonance behavior is close to optimal (Wzss>0.9) at frequency offsets ΔΩ>3.8 ppm. Consequently, for optimal sensitivity in situations where solvent exchange processes contribute significantly to the LRE effect, as discussed in the previous section, the frequency offset of the shaped pulses should be set at least 3.8 ppm×BW (ppm)/4 away from the water resonance, with BW being the excitation bandwidth chosen for the shaped pulses.

Figure 1.6

(a) Effect of a slight perturbation (5%) by a single scan on the steady-state 1H polarization as a function of the recycle time Trec, calculated from eqn (1.7) for T1 time constants varying from 400 ms to 3.4 s. (b) Off-resonance performance of two commonly used refocusing (180°) pulse shapes, REBURP (black curves) and Q3 (red curve). The steady-state water 1H polarization has been measured after applying the shaped pulse (nominal band width of 4 ppm) 32-times with an inter-pulse delay of 100 ms. The off-resonance profile is obtained by repeating the measurement for different shaped pulse offsets with respect to the water frequency. Straight lines correspond to measurements on a last generation cryoprobe, while the black dashed line shows the result obtained on an old cryoprobe. (c) Intensity ratios measured for individual amide 1H sites in ubiquitin (pH 7.4, 20 °C) in 1H–15N BEST-TROSY spectra measured on samples with and without a paramagnetic water relaxation compound (0.5 mM gadodiamide).

Figure 1.6

(a) Effect of a slight perturbation (5%) by a single scan on the steady-state 1H polarization as a function of the recycle time Trec, calculated from eqn (1.7) for T1 time constants varying from 400 ms to 3.4 s. (b) Off-resonance performance of two commonly used refocusing (180°) pulse shapes, REBURP (black curves) and Q3 (red curve). The steady-state water 1H polarization has been measured after applying the shaped pulse (nominal band width of 4 ppm) 32-times with an inter-pulse delay of 100 ms. The off-resonance profile is obtained by repeating the measurement for different shaped pulse offsets with respect to the water frequency. Straight lines correspond to measurements on a last generation cryoprobe, while the black dashed line shows the result obtained on an old cryoprobe. (c) Intensity ratios measured for individual amide 1H sites in ubiquitin (pH 7.4, 20 °C) in 1H–15N BEST-TROSY spectra measured on samples with and without a paramagnetic water relaxation compound (0.5 mM gadodiamide).

Close modal

Finally, it is worth mentioning that the situation may be less optimal for older (cryo)probes or other hardware imperfections. The dashed black curve in Figure 1.6b displays the results obtained for REBURP on an older NMR spectrometer equipped with a cryogenic probe. This time, significant perturbations of the water 1H polarization are observed, notably at certain frequency offsets. A closer inspection reveals that the measured curve is similar to the result of numerical simulations obtained for B1 fields that are about 15% below their nominal value, explaining that the observed effect is owing to a slight detuning of the probe under fast-pulsing conditions. Recording such an off-resonance profile thus provides an easy and convenient way to check the hardware performance for BEST-type fast-pulsing experiments. If a problem of probe detuning under fast-pulsing conditions has been identified several solutions are possible: (i) the frequency offset of the shaped pulses can be shifted further away from the water resonance; (ii) the power level of the shaped pulses can be adjusted to account for the detuning, or (iii) a small amount of a water relaxation agent can be added to the sample to reduce the water 1H T1 (Figure 1.2a). The effect of adding 0.5 mM gadodiamide on the cross peak intensities in a BEST 1H–15N spectrum of ubiquitin measured on such a slightly detuned NMR probe is shown in Figure 1.6c. As expected from the curves in Figure 1.6a, for solvent-accessible regions, an up to 60% sensitivity increase is observed for the Gd3+-containing sample, which is explained by the significantly larger steady-state water polarization achieved under these experimental conditions. However, for certain amide protons a slight signal decrease is observed, most likely owing to a paramagnetic relaxation-induced line broadening. Note that no significant signal enhancement could be observed for the Gd3+-containing sample if the same BEST experiments were performed on a well-tuned probe.

The basic BEST pulse sequence blocks, introduced in Figure 1.5b–d can be combined to set up a variety of pulse sequences that correlate amide protons with other backbone and side-chain 13C and 15N nuclei in 2D, 3D, or even higher dimensional NMR experiments. We distinguish two types of BEST experiments: BEST-HSQC16,24  and BEST-TROSY.15,25,26  They differ in the way amide 15N and 1H coherence is evolving and frequency labeled. In a scalar-coupled heteronuclear two-spin system, such as 1H–15N, each spin has two allowed single-quantum (SQ) transitions, as explained in more detail in any standard NMR textbook. This results in peak doublets in the NMR spectrum under conditions of free spin evolution (Figure 1.7a). A first option to avoid scalar-coupling-induced line splitting consists of heteronuclear decoupling that averages the two single-transition frequencies, and results in a single resonance line. In this HSQC method, used since the early days of 2D spectroscopy,27  both SQ transitions contribute to the detected NMR signal. A second, alternative approach selects only one out of the two transitions by so-called spin-state selection techniques.28,29  This is realized in TROSY-type experiments,30  introduced in the late 1990s, where the 1H and 15N transitions with the most favorable relaxation properties (narrow lines) are selected (Figure 1.7a). This line narrowing effect results in improved spectral resolution in TROSY compared to HSQC spectra, and may under certain experimental conditions also compensate for the reduced intrinsic sensitivity of TROSY experiments owing to the spin-state selection. Note that, although only one out of four peaks in the multiplet is selected in TROSY, the signal loss associated with this selection process is a factor of 2 (and not 4). TROSY-type experiments are preferably performed at high magnetic field strength B0 where line narrowing resulting from CSA-dipolar cross-correlation31–33  is most effective.

Figure 1.7

(a) Different ways of reducing the multiplet pattern observed in a scalar coupled two-spin systems to a single cross peak, either using heteronuclear decoupling (HSQC) or single-transition spin state selection (TROSY). Pulse sequences for (b) BEST-HSQC and (c) BEST-TROSY experiments. The numbers under the 1H pulse symbols indicate the shaped pulse type used: (1) REBURP, (2) PC9, and (3) EBURP-2. An asterisk indicates time and phase reversal of the corresponding pulse shape. They typically cover a bandwidth of 4 ppm (centered at 8.5 ppm). To account for spin evolution during the shaped pulses, the transfer delays are set to τ1=1/(4JNH)−0.5δ1−0.5δ2, τ2=1/(4JNH)−0.5δ1, and τ3=1/(4JNH)−0.5δ1−0.6δ3, with δ1, δ2, δ3 the pulse lengths of PC9, EPURP-2, and REBURP, respectively. A generic relaxation delay Δ accounts for the 1H, 15N relaxation behavior in different experiments, where this delay is replaced by additional transfer and chemical shift editing periods. (d) Sensitivity curves measured for ubiquitin (800 MHz, 20 °C) using BEST-HSQC (blue); BEST-TROSY (red), or a conventional HSQC sequence with a relaxation delay Δ=100 ms. The intensity points have been obtained from integration of the recorded 1D amide 1H spectra. (e) Signal intensity ratios for individual cross peaks measured in BEST-HSQC (BH) and BEST-TROSY (BT) 2D iHN(CA) spectra of a 138-residue protein, and plotted as a function of the BH peak intensity.25  The observed correlation indicates a tendency toward a stronger enhancement effect (S/N gain) for weaker correlation peaks.

Figure 1.7

(a) Different ways of reducing the multiplet pattern observed in a scalar coupled two-spin systems to a single cross peak, either using heteronuclear decoupling (HSQC) or single-transition spin state selection (TROSY). Pulse sequences for (b) BEST-HSQC and (c) BEST-TROSY experiments. The numbers under the 1H pulse symbols indicate the shaped pulse type used: (1) REBURP, (2) PC9, and (3) EBURP-2. An asterisk indicates time and phase reversal of the corresponding pulse shape. They typically cover a bandwidth of 4 ppm (centered at 8.5 ppm). To account for spin evolution during the shaped pulses, the transfer delays are set to τ1=1/(4JNH)−0.5δ1−0.5δ2, τ2=1/(4JNH)−0.5δ1, and τ3=1/(4JNH)−0.5δ1−0.6δ3, with δ1, δ2, δ3 the pulse lengths of PC9, EPURP-2, and REBURP, respectively. A generic relaxation delay Δ accounts for the 1H, 15N relaxation behavior in different experiments, where this delay is replaced by additional transfer and chemical shift editing periods. (d) Sensitivity curves measured for ubiquitin (800 MHz, 20 °C) using BEST-HSQC (blue); BEST-TROSY (red), or a conventional HSQC sequence with a relaxation delay Δ=100 ms. The intensity points have been obtained from integration of the recorded 1D amide 1H spectra. (e) Signal intensity ratios for individual cross peaks measured in BEST-HSQC (BH) and BEST-TROSY (BT) 2D iHN(CA) spectra of a 138-residue protein, and plotted as a function of the BH peak intensity.25  The observed correlation indicates a tendency toward a stronger enhancement effect (S/N gain) for weaker correlation peaks.

Close modal

BEST implementations of basic HSQC and TROSY experiments are displayed in Figure 1.7b and 1.7c, respectively. They both start with an initial INEPT-type 1H–15N transfer. The relaxation delay Δ stands for additional chemical shift editing and coherence transfer steps. The two sequences differ mainly in the 1H–15N back transfer step, which is performed by a sensitivity-enhanced INEPT (SE-REVINEPT) sequence in HSQC, and a single-transition to single-transition coherence transfer sequence (ST2-PT) in TROSY. Another difference is the absence of composite 15N decoupling during 1H detection in BEST-TROSY, a feature that becomes of practical interest if long signal acquisition times are required where composite decoupling under fast-pulsing conditions may lead to significant probe heating.

An additional specific feature of TROSY, that becomes particularly interesting for BEST-TROSY experiments, is the simultaneous detection of coherence transfer pathways originating from both 1H and 15N polarization:

Equation 1.8a
Equation 1.8b

with the single-transition spin states selected by the ST2-PT sequence given in bold letters. The phase ϕ0 of the last 1H pulse in the INEPT sequence needs to be adjusted in order to add the contributions from the two pathways. Most interestingly, the TROSY sequence has a built-in compensation mechanism for relaxation-induced signal loss during the relaxation delay Δ (Figure 1.7c).25  In fact, 1H polarization that builds up during Δ is transferred by the ST2-PT sequence into enhanced off-equilibrium 15N polarization, which will be available for the next scan as long as it survives relaxation during the recycle delay (Trec). Note that an additional 15N 180° pulse has been added to the TROSY sequence after the signal detection period in order to create 15N polarization that is of the same sign as equilibrium polarization.

Equation 1.8c

As a consequence of this third coherence transfer pathway, the steady-state 15N polarization in TROSY depends on the longitudinal relaxation rate constants T1H and T1N, as well as the pulse sequence delays Δ and Trec. The expected 15N polarization enhancement can be calculated by the following expression:

Equation 1.9

15N polarization enhancement becomes particularly pronounced for short T1H and long T1N, as well as short recycle delays Trec. This is exactly the situation encountered in BEST-TROSY experiments at high magnetic field strengths. For a protein with an 8 ns correlation time at 800 MHz, typical relaxation time constants are T1H=50–300 ms (Figure 1.4) and T1N≈1 s. For a typical recycle delay Trec=200 ms and assuming an overall relaxation delay Δ=100 ms, this results in enhancement factors varying form λN=2.5 to λN=7.3. The steady-state 15N polarization enhancement is expected to further increase with the magnetic field strength and the size of the protein (rotational correlation time).25 

Experimental sensitivity curves measured on a sample of ubiquitin (5 °C, 800 MHz, τc≅8 ns) with the 1D pulse sequences of Figure 1.7b and 1.7c (with Δ=100 ms), as well as a conventional HSQC sequence are shown in Figure 1.7d. These curves, obtained by integrating the intensities measured in the 1D spectra, reflect intrinsic sensitivity differences of the pulse schemes without taking into account the additional line narrowing in TROSY experiments. It is interesting to note that the sensitivity optimum shifts to slightly shorter Trec values for BEST-TROSY with respect to BEST-HSQC. The sensitivity advantage of BEST-TROSY (BT) with respect to BEST-HSQC (BH) becomes even further pronounced when comparing individual peak intensities in 2D 1H–15N correlation spectra, as illustrated in Figure 1.7e for a 16 kDa protein (20 °C, 800 MHz, τc≅10 ns). The intensity ratios (BT/BH) vary from about 1.5 in the most flexible protein regions to more than 4. An interesting observation is the correlation between the peak intensity measured in the BH spectrum and the intensity gain from BT, indicating that weak peaks are enhanced more than already stronger peaks. As a result, the peak intensity distribution for proteins displaying heterogeneous conformational flexibility becomes more uniform in BEST-TROSY spectra compared to the BEST (or conventional) HSQC counterparts.

In summary of this section, the appropriate use of band-selective pulse shapes on the 1H channel, the basis of BEST experiments, allows us to set up a variety of NMR experiments for the study of proteins and nucleic acids. A non-exhaustive list of BEST-type experiments, proposed to date for the study of proteins or nucleic acids is provided in Table 1.1. These pulse schemes provide an advantage in terms of experimental sensitivity and data acquisition speed. Under fast pulsing conditions, the sensitivity improvement achieved by BEST pulse schemes compared to conventional hard-pulse-based analogues may reach up to one order of magnitude in the most favorable cases. As a rule of thumb, at moderate field strength (<700 MHz) and tumbling correlation times τc<10 ns, BEST-HSQC implementations are typically advantageous in terms of experimental sensitivity. At higher magnetic field strengths and/or for larger molecules, BEST-TROSY outperforms BEST-HSQC both in terms of spectral resolution and experimental sensitivity, with the additional advantage that no 15N decoupling is applied during signal detection allowing for long acquisition times without the need to care about duty cycle requirements of the NMR hardware.

Table 1.1

Non-exhaustive list of LRE-optimized 1H-detected experiments that have been proposed in the literature for NMR investigations of proteins or nucleic acids.

LRE techniqueApplicationPurposeRefs.
SOFAST Proteins 2D 1H–15N or 1H–13Schanda 200538,39  
Amero 200942  
ST-SOFAST Proteins 2D 1H–15N or 1H–13Kern 200848  
J-SOFAST Proteins 2D 1H–15N or 1H–13Kupce 200749  
Mueller 200850  
ultraSOFAST Proteins 2D 1H–15N or 1H–13Gal 200754  
Kern 200848  
SOFAST RNA (iminos) 2D 1H–15Farjon 200915  
SOFAST RNA (bases) 2D 1H–13Sathyamoorthy 201458  
BEST-HSQC Proteins 2D 1H–15Pervushin 200210  
BEST-HSQC Proteins 3D Backbone assignment expts: Schanda 200616  
Lescop 200724  
HNCO, HNCA, HNCACB, HN(CO)CA, HN(CO)CACB, iHNCA, iHNCACB, HNN 
Kumar 201059  
BEST-HSQC Proteins Backbone J coupling and RDC measurements: N–HN, Cα–Hα, CO–H HN, N–CO… Rasia 201160  
BEST-HSQC Proteins Measurement of RDCs between amide 1Schanda 200761  
BEST-TROSY Proteins 2D 1H–15Pervushin 200210  
Favier 201125  
BEST-TROSY RNA (iminos) 2D 1H–15Farjon 200915  
BEST-TROSY Proteins Backbone assignment: Pervushin 200210  
Favier 201125  
3D HNCO, HNCA, HNCACB, HN(CO)CA, HN(CO)CACB, iHNCA, iHNCACB, (H)N(COCA)NH, (HN)CO(CA)NH Solyom 201326  
BEST-TROSY Proteins Bidirectional HNC experiments with enhanced sequential correlation pathway: HNCA+, HNCO+, HNCACB+ Gil-Caballero 201462  
BEST-TROSY IDPs Proline-selective 1H–15N correlation experiments Solyom 201326  
BEST-TROSY RNA (iminos) Trans-hydrogen-bond correlation experiment: HNN-COSY Farjon 200915  
HET-SOFAST/BEST Proteins Quantification of LRE effect from water exchange or 1H–1H cross-relaxation Schanda 200657  
Rennella 201456  
Flip-back Proteins 2D 1H–15Deschamp 200663  
Flip-back Proteins Backbone assignment: Diercks 200564  
3D HNCO, HNCA 
Flip-back Proteins Aromatic side chain assignment Eletsky 200565  
LRE techniqueApplicationPurposeRefs.
SOFAST Proteins 2D 1H–15N or 1H–13Schanda 200538,39  
Amero 200942  
ST-SOFAST Proteins 2D 1H–15N or 1H–13Kern 200848  
J-SOFAST Proteins 2D 1H–15N or 1H–13Kupce 200749  
Mueller 200850  
ultraSOFAST Proteins 2D 1H–15N or 1H–13Gal 200754  
Kern 200848  
SOFAST RNA (iminos) 2D 1H–15Farjon 200915  
SOFAST RNA (bases) 2D 1H–13Sathyamoorthy 201458  
BEST-HSQC Proteins 2D 1H–15Pervushin 200210  
BEST-HSQC Proteins 3D Backbone assignment expts: Schanda 200616  
Lescop 200724  
HNCO, HNCA, HNCACB, HN(CO)CA, HN(CO)CACB, iHNCA, iHNCACB, HNN 
Kumar 201059  
BEST-HSQC Proteins Backbone J coupling and RDC measurements: N–HN, Cα–Hα, CO–H HN, N–CO… Rasia 201160  
BEST-HSQC Proteins Measurement of RDCs between amide 1Schanda 200761  
BEST-TROSY Proteins 2D 1H–15Pervushin 200210  
Favier 201125  
BEST-TROSY RNA (iminos) 2D 1H–15Farjon 200915  
BEST-TROSY Proteins Backbone assignment: Pervushin 200210  
Favier 201125  
3D HNCO, HNCA, HNCACB, HN(CO)CA, HN(CO)CACB, iHNCA, iHNCACB, (H)N(COCA)NH, (HN)CO(CA)NH Solyom 201326  
BEST-TROSY Proteins Bidirectional HNC experiments with enhanced sequential correlation pathway: HNCA+, HNCO+, HNCACB+ Gil-Caballero 201462  
BEST-TROSY IDPs Proline-selective 1H–15N correlation experiments Solyom 201326  
BEST-TROSY RNA (iminos) Trans-hydrogen-bond correlation experiment: HNN-COSY Farjon 200915  
HET-SOFAST/BEST Proteins Quantification of LRE effect from water exchange or 1H–1H cross-relaxation Schanda 200657  
Rennella 201456  
Flip-back Proteins 2D 1H–15Deschamp 200663  
Flip-back Proteins Backbone assignment: Diercks 200564  
3D HNCO, HNCA 
Flip-back Proteins Aromatic side chain assignment Eletsky 200565  

13C direct detection is a routine tool for NMR studies of small molecules, mainly because of the higher spectral resolution achieved in the 13C spectrum with respect to the corresponding 1H spectrum. Recently, a series of 13CO-detected experiments has been proposed and shown to provide useful additional NMR tools for protein studies,34  especially in the context of molecules with a high degree of intrinsic disorder (IDPs) or proteins containing paramagnetic centers where 13CO detection offers some advantages: (i) the 13CO line width is not affected by solvent exchange; (ii) signals from proline residues can be observed; (iii) 13CO detection is less affected by paramagnetic line broadening. The major inconvenience of 13C-detection is the lower intrinsic sensitivity due to the ∼four-fold smaller gyromagnetic ratio of 13C with respect to 1H (see eqn (1.1)). This situation has been significantly improved over recent years by the development of 13C-optimized cryogenic triple-resonance probes and pulse sequence improvements. Among those tools, the use of 1H as a starting polarization source for the coherence transfer pathway has been proposed in order to increase experimental sensitivity.35,36  Such 1H-start and 13C-detect experiments are amenable to BEST-type LRE optimization, as recently demonstrated for the 2D HN-BEST CON experiment,37  which starts from amide 1H polarization, but only detects 15N and 13CO chemical shifts in a 2D correlation spectrum. This CO–N spectrum is of particular interest for the study of IDPs at close to physiological temperature and pH where solvent-exchange line broadening of amide 1H may prevent their detection in a 1H-detected experiment. Other 13C-detected experiments starting from aliphatic 1H polarization have been optimized in terms of LRE by using a coupling-based flip back scheme, as depicted in Figure 1.2c.

So far, we have described LRE optimization in heteronuclear single-quantum correlation experiments, HSQC and TROSY. In this section, we will focus on heteronuclear multiple-quantum correlation (HMQC) experiments, and in particular on 2D 1H–15N and 1H–13C HMQC, where BEST-optimization can be combined with Ernst-angle excitation to further enhance the steady-state 1H polarization for very short recycle delays (TrecT1H). This type of experiments is called band-Selective Optimized Flip Angle Short Transient (SOFAST) HMQC.38,39 

Let us consider a simple one-pulse experiment with a nominal pulse flip-angle β. As a consequence of such a simple pulse scheme, part of the spin polarization (cos β) is preserved, and can thus be directly used for the subsequent transient without the need for any relaxation period, while a fraction sin β gives rise to the detected NMR signal. In practice, the steady-state polarization will depend on the recycle delay Trec and the effective longitudinal relaxation time T1, as described by eqn (1.7) with the factor f=cos β. The resulting SNR is then given by:

Equation 1.10

Sensitivity curves SNR(Trec) according to eqn (1.10) for T1=200 ms and different flip angles β are plotted in Figure 1.8a. Choosing smaller flip angles (β<90°) shifts the sensitivity maximum to shorter recycle delays, with the highest overall sensitivity obtained for β≈60°.

Figure 1.8

SOFAST-HMQC experiments. (a) Sensitivity curves computed according to eqn (1.10) for flip angles of β=90° (straight line), β=60° (dashed line), and β=30° (dotted-dashed line). A relaxation time T1= 200 ms and a pulse sequence duration of tseq=20 ms have been assumed for the calculation. (b) Excitation profile of PC9 pulse of 3 ms duration measured for different flip angles in the range 20°–150°. Different implementations of SOFAST-HMQC: (c) standard SOFAST,38,39  (d) single-transition (ST) SOFAST,48  (e) J-SOFAST,49,50  and (f) single-scan ultra-SOFAST.48,54 

Figure 1.8

SOFAST-HMQC experiments. (a) Sensitivity curves computed according to eqn (1.10) for flip angles of β=90° (straight line), β=60° (dashed line), and β=30° (dotted-dashed line). A relaxation time T1= 200 ms and a pulse sequence duration of tseq=20 ms have been assumed for the calculation. (b) Excitation profile of PC9 pulse of 3 ms duration measured for different flip angles in the range 20°–150°. Different implementations of SOFAST-HMQC: (c) standard SOFAST,38,39  (d) single-transition (ST) SOFAST,48  (e) J-SOFAST,49,50  and (f) single-scan ultra-SOFAST.48,54 

Close modal

The flip angle providing the highest sensitivity for a given recovery time Trec is called the Ernst angle.1  Closer inspection of eqn (1.10) shows that highest sensitivity is achieved if the following relation is satisfied:

Equation 1.11

with the assumption that tseqTrec. In a single-pulse experiment, Ernst-angle excitation is realized by adjusting the nutation angle of the excitation pulse. It becomes, however, a non-trivial task when dealing with multi-pulse sequences employing a series of 90° and 180° pulses. Although even complex pulse sequences may still be designed in a way that some of the 1H spin polarization is restored at the end, their practical utility is very limited. Because the magnetization component that is finally restored follows a complex trajectory during the pulse sequence, longitudinal and transverse spin relaxation effects, as well as pulse imperfections, reduce its magnitude, and thus severely compromise the overall sensitivity of the experiment. Exceptions to this rule are HMQC-type experiments that require only a single proton excitation pulse followed by one (or several) 180° pulses. In this case, Ernst angle excitation can still be realized by taking into account that the effective flip angle is now given by βopt=αopt+n(180°) with αopt being the flip angle of the excitation pulse and n the number of additional 180° pulses present in the sequence.40 

In order to combine BEST-type LRE with Ernst angle excitation, a pulse shape is required that performs band selective excitation for a wide range of flip angles (power levels). This is not the case for the majority of pulse shapes (BURP, SNOB, Gaussian pulse cascades, etc.) reported in the literature that show strong distortions of the excitation profile if the power level is moved away form its nominal value. An exception is the polychromatic PC9 pulse,21  which preserves a “top-hat” excitation profile for a range of power levels corresponding to on-resonance flip angles between 0° and 150° (Figure 1.8b).

The standard SOFAST-HMQC experiment (Figure 1.8c)39  is a simple modification of the basic HMQC sequence where band-selective PC9 and REBURP pulse shapes replace the 90° and 180° hard pulses, respectively, to enhance the 1H steady-state polarization and the overall experimental sensitivity under fast-pulsing conditions. This sequence also achieves good water suppression by a built-in “Watergate” sequence (PFG-180 sel-PFG),41  as long as the water resonates outside the chosen excitation band, and homonuclear 1H decoupling during the 1H–X transfer delays and the t1 chemical shift labeling period. In general, SOFAST-HMQC requires some phase cycling (nPC≥2) in order to remove artefacts e.g. residual solvent signals from the spectra. For the highest sensitivity of the experiment, the flip angle should be adjusted to α≈120° with a recycle delay TrecT1. Alternatively, if data acquisition speed is the major objective (Trec=Tdet), a larger flip angle (α≈150°) typically further increases experimental sensitivity. Under favourable experimental conditions (high magnetic field strength, cryogenic probe, protein concentration of a few hundred μM), 2D SOFAST-HMQC fingerprint spectra can be recorded in less than 5 s for molecular systems ranging from small globular proteins (Figure 1.9a), large molecular assemblies (Figure 1.9c), to nucleic acids (Figure 1.9d). This has opened new perspectives for site-resolved real-time NMR investigations of molecular kinetics, such as protein folding, oligomerization and assembly.42–45  It also allows the study of proteins and cell metabolites in living cells under sample conditions characterized by short lifetimes.46,47 

Figure 1.9

2D SOFAST-HMQC spectra of different biomolecular systems. (a) amide 1H–15N correlation spectrum of the small protein ubiquitin (8.5 kDa, 0.2 mM, 25 °C, 18.8 T); (b) ultraSOFAST-HMQC spectrum of a 2 mM ubiquitin sample recorded in a single scan; (c) methyl 1H–13C correlation spectrum of a large molecular assembly, the TET2 protease (468 kDa, 80 μM, 0.9 mM, 37 °C, 18.8 T); (d) imino 1H–15N correlation spectrum of tRNAVal (26 kDa, 25 °C, 18.8 T). Figure reproduced with permission from E. Rennella and B. Brutscher, ChemPhysChem 2013, 14, 3059 (ref. 43).

Figure 1.9

2D SOFAST-HMQC spectra of different biomolecular systems. (a) amide 1H–15N correlation spectrum of the small protein ubiquitin (8.5 kDa, 0.2 mM, 25 °C, 18.8 T); (b) ultraSOFAST-HMQC spectrum of a 2 mM ubiquitin sample recorded in a single scan; (c) methyl 1H–13C correlation spectrum of a large molecular assembly, the TET2 protease (468 kDa, 80 μM, 0.9 mM, 37 °C, 18.8 T); (d) imino 1H–15N correlation spectrum of tRNAVal (26 kDa, 25 °C, 18.8 T). Figure reproduced with permission from E. Rennella and B. Brutscher, ChemPhysChem 2013, 14, 3059 (ref. 43).

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An alternative SOFAST-HMQC pulse sequence is shown in Figure 1.8d. The single-transition (ST) version48  selects one of the 1H doublet components (TROSY line) in the direct detection dimension, while heteronuclear decoupling is still applied in the indirect (t1) dimension. The basic idea behind this scheme is that both quadrature components present after the t1 free evolution delay are converted into detectable in-phase and anti-phase 1H coherence. As a consequence of the single-transition spin state selection, the sensitivity of ST-SOFAST is a factor √2 lower as compared to the standard SOFAST version. Despite this reduced sensitivity, ST-SOFAST-HMQC presents some interesting features that make it a valuable alternative to be considered for practical applications: (i) reduced RF load owing to the absence of composite X-spin decoupling during signal detection; (ii) suppression of strong signals from the solvent or sample impurities in a single scan by the use of pulsed-field-gradient-based coherence-transfer-pathway selection; (iii) as the pulse sequence employs an even number of 180° 1H pulses, Ernst-angle excitation is achieved by setting the PC9 pulse to a nominal flip angle α <90°, for which a cleaner off-resonance performance is observed.

Finally, the J-SOFAST-HMQC49,50  (Figure 1.8e) uses a coupling-based flip-back scheme, instead of band-selective pulses, for 1H excitation. In order to achieve Ernst-angle excitation, the transfer delay of the first INEPT block is adjusted to λ/2JHX with λ = cos α. J-SOFAST-HMQC presents an attractive alternative for 1H–13C experiments of samples at natural-abundance or with a low level of isotope enrichment. This sequence becomes also of interest if the selection of observed and unperturbed protons is preferably done by exploiting the characteristic 13C or 15N chemical shift ranges by means of band-selective inversion pulses, as already discussed above (Figure 1.2c).

The speed of 2D data acquisition can be even further enhanced by combining SOFAST-HMQC with gradient-encoded single-scan multidimensional NMR.51–53  In the so-called ultraSOFAST-HMQC experiment48,54  (Figure 1.8f), the incremented time delay t1 is replaced by a spatial chemical shift encoding, where nuclear spins in the sample are progressively excited according to their position along a spatial coordinate, typically the z-axis, by the use of a magnetic field gradient acting in combination with a frequency-swept radiofrequency (CHIRP) pulse. This results in a spatial winding of the spin magnetization with a position-dependent phase CΩ1z, where Ω1 is the resonance frequency of the nuclear spin, and C is a spatio-temporal constant depending on the sample length and some user-defined acquisition parameters. A spatial frequency decoding or unwinding of the resulting helix is achieved during the signal detection period by the use of a second magnetic field gradient. As a result of this acquisition gradient Ga, a spin echo is created whose position in time depends on the resonance frequency Ω1 as well as on the strength of Ga. This reading process can be repeated numerous (N2) times by oscillating the sign of the readout gradients, yielding a set of indirect time-domain spectra as a function of the t2 time evolution. Fourier transformation along the t2 dimension only results in the desired 2D NMR spectrum. For a more thorough discussion of single-scan NMR, we refer the reader to Chapter 2 by Gal.

The pulse sequence in Figure 1.8f is based on ST-SOFAST-HMQC,48  thus avoiding the need for heteronuclear decoupling during the readout process. This allows the use of weaker acquisition gradients, resulting in reduced filter bandwidth, and therefore increases the overall sensitivity of the experiment. Interestingly, in contrast to the conventional ST-SOFAST-HMQC experiment, in the case of spatial frequency encoding the spin-state selection process does not lead to any additional sensitivity loss, making this sequence the optimal choice under all circumstances. An amide 1H–15N spectrum of the small protein ubiquitin, recorded in a single scan, is shown in Figure 1.9b.

As a major application, ultraSOFAST-HMQC allows the recording of 1H–15N (and 1H–13C) correlation spectra with repetition rates of up to a few s−1, thus enabling real-time studies of molecular kinetics occurring on time scales down to a few seconds.54,55 

Fast-pulsing techniques provide a convenient way to reduce the acquisition time of multidimensional NMR spectra without compromising, often even significantly improving, experimental sensitivity, and without the need for non-conventional data processing tools. Therefore, there is no good reason for not using fast-pulsing techniques whenever possible, and in situations where LRE effects are expected to be sizeable. The only drawback may be the loss of some 1H signals with unusual resonance frequencies, owing for example to an important ring current shift contribution. The use of typical recycle delays of 200 to 300 ms in BEST experiments reduces the data acquisition time required for a high-resolution 3D data set to a few hours, which often corresponds to or is less than the time needed to obtain sufficient SNR in the final spectrum (sensitivity limited regime). The situation is of course different for higher dimensional (>3D) experiments that are of particular interest for the study of larger proteins, as well as IDPs. Here, the time requirements, even for BEST-type experiments, are dictated by sampling requirements, especially if high spectral resolution in all dimensions is desired. In order to shift these high dimensional experiments again from the sampling-limited to a sensitivity-limited regime, we need to combine the fast-pulsing techniques described here with one of the non-uniform sparse data sampling methods that will be described in subsequent chapters.

LRE effects can also be quantified by measuring effective amide 1H T1 relaxation time constants under various experimental conditions as shown in Figure 1.4, or by comparing peak intensities in a reference SOFAST/BEST spectrum with those measured after perturbation of either the bulk water or aliphatic protons, as implemented in the HET-SOFAST/BEST experiments.56,57  This experiment provides valuable information on solvent exchange rates, and the efficiency of dipolar-driven spin diffusion that can be related to the local compactness at the site of a given amide proton.

Finally, fast-pulsing multidimensional SOFAST- and BEST-type experiments offer new opportunities for site-resolved real-time NMR studies of protein folding and other kinetic processes that occur on a seconds to minutes time scale, and that are difficult or even impossible to investigate by other high-resolution methods.43 

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