Polarization-enhanced Fast-pulsing Techniques

BERNHARD BRUTSCHER AND ZSOFIA SOLYOM

1.1 Introduction

The concept of multidimensional NMR spectroscopy 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.

1.1.1 Some Basic Considerations on NMR Sensitivity and Experimental Time

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:

[MATHEMATICAL EXPRESSION OMITTED] (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 (?exc) as well as the detected spin species (?det). Note that they may be different in heteronuclear correlation experiments. High-? 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 PSSZ 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 [square root]2 reduction in SNR for each indirect dimension owing to the requirement of phase-sensitive quadrature detection. Note that the additional [square root]2 signal loss can be avoided by so-called sensitivity-enhanced quadrature detection schemes. 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, t2 ... tn-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.

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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=SWk/?vk, with ?vk 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 [square root of Nscan. For each experimental setup (sample, NMR spectrometer, NMR experiment) there exists a minimal number of scans, NSNRscan, scan, required to achieve sufficient SNR to distinguish the NMR signals from the noise. We can thus distinguish two different scenarios: if NSNRscan >> Nsamplingscan, we call this experimental situation sensitivity-limited, while the case NSNRscan<< Nsamplingscan scan is referred to as sampling-limited. In the...