The Handbook of Metabolomics pp 127-197 | Cite as

# Principles of NMR for Applications in Metabolomics

## Abstract

In this chapter, the basic principles of high-resolution NMR relevant to metabolomics are reviewed, with an emphasis on practical aspects of experimental design, execution, and interpretation of the spectral data. This includes one- and two-dimensional NMR with isotope-editing techniques for metabolite identification, quantification, and positional isotopomer analysis. The principles of isotopomer analysis by NMR for pathway determination and flux analysis are introduced. These principles are illustrated with particular examples of simplified mixtures of common metabolites. Advanced approaches for speeding data acquisition, as well as additional experiments including prospects for three-dimensional NMR for ab initio identification of unknown metabolites, especially if metabolically labeled, are introduced.

## Key words

High resolution NMR Stable isotope editing Positional isotopomer analysis Metabolic pathways## Notes

### Acknowledgments

This work was supported in part by grants from the Susan G. Komen Foundation BCTR0503648, NIH Grant Number RR018733 from the National Center for Research Resources, NSF EPSCoR EPS-0447479, and the Brown Foundation.

## Glossary

Removal of the feet. A manipulation of the free induction decay (FID) to ensure that the time domain smoothly approaches zero at the end to avoid truncation artifacts (sinc wiggles).

Classical dynamical equations that describe the time dependence of the *x*,*y*,*z* components of the magnetization, viz: \( {{d}}Mz/{{d}}t = {\omega_1} My -(Mz - {M^0})/{T_1}, \) \( {{d}}Mx/{{d}}t = - (\omega - {\omega_0})My - Mx/{T_2}, \) \( {{d}}My/{{d}}t = (\omega - {\omega_0})Mx - My/{T_2} \)

*ω* _{0} is the Larmor frequency (qv), *T* _{1} and *T* _{2} are the relaxation times (qv), and *ω* _{1} is the strength of the applied radiofrequency field.

Relative resonant frequency, defined (in ppm) as 10^{6} (*ν* _{obs} − *ν* _{ref})/*ν* _{Fref.} Depends on chemistry such as type of atom, nearest neighbors, bonding, and therefore is characteristic of local functional groups. It is also very sensitive to inductive effects from nearby ionizable groups such as carboxyls and amino functions.

NMR is a coherent form of spectroscopy because a pulse excites all spins, and the bulk magnetization (resultant) is rotated en mass to a defined axis. The magnetization vector continues to precess in phase. Dephasing will occur due to spin–spin relaxation (qv), resulting in a loss of phase coherence.

Magnetization is the observable in NMR and is a single quantum coherence. Other coherences can be created between interacting pairs (or higher order) of spins in which there is a coherence (e.g., phase) between the interacting spins. This is used extensively in multiple quantum spectroscopy where different orders of coherence can be generated through scalar coupling. For a pair of spins, both double and zero quantum coherence can be created, in which the components rotate in the same sense (2-quantum state) or in opposite direction (zero quantum state). These have distinct phase properties that can be selected by gradient or phase cycling.

Time taken for a property to decay to 1/*e* of its initial value. Usually refers to rotational correlation time, which is related to the size and shape of a molecule, and defines the timescale for reorientation of a molecule by random processes.

COrrelation SpectroscopY. Usually refers to correlation of resonances of scalar-coupled nuclei. Used for determining through-bond interactions within a covalent network. Defines molecular fragments via proton–proton connectivity.

Carr Purcell Meiboom Gill spin-echo pulse sequence consisting of a train of alternating 180° pulses orthogonal to the initial exciting pulse separated by a tunable delay. This compensates for imperfections of the 180° pulse and effectively refocuses magnetization along a defined axis. As such, it is suitable for accurate measurement of *T* _{2}. If the delay *D* is short, evolution of scalar couplings is suppressed, allowing recording of in-phase spectra of scalar-coupled spin systems. Used in metabonomics for suppressing macromolecule signals in biofluids.

Interaction strength between two scalar- (through-bond) coupled magnetic nuclei. The scalar coupling constant (denoted *J*) is a measure of nuclear interactions transmitted through the bonding network. Three-bond *J* values provide information on the torsion angle.

Interaction between magnetic nuclei via dipole–dipole interactions. This depends on the inverse sixth power of the internuclear separation, and the intrinsic magnetic strength of the two nuclei.

Rotating magnetization induces a voltage in the receiver coil (magnetic induction) which decays exponentially by *relaxation processes*. The time-dependent voltage is digitized and converted into a frequency response by *Fourier transformation* (qv). The two signals in quadrature are: \( S({{real}}) = {a_0}\exp ( - t/{R_2})\cos (\omega t), \) \( S({{imaginary}}) = {a_0}\exp ( - t/{R_2})\sin (\omega t). \)

Mathematical trick for converting one periodic function into another function. In NMR, the raw data comprise an exponentially decaying sum of cosinusoidal functions. The FT converts time into frequency. The decaying part of the signal becomes manifest as a broadening of the resonance. The FT of a single resonance is: \( {\rm Re} \left[ {{a_0}\int {{{d}}t \exp ( - i\Omega t) \exp (i\omega - 1/T)t} } \right] \) \(= (2{a_0}/T)/({(\Omega - \omega )^2} + 1/{T^2}) \)

width at half height *L* = 1/*πT*

*T* is the decay time constant (also called “*T* _{2}”)

γ is a property of nuclei that determines the strength of the nuclear magnetic moment and is characteristic for each isotope. The fundamental frequency is proportional to the product of γ and the applied magnetic field strength.

G-matrix Fourier transform NMR. A projection method that reduces dimensionality by incrementing indirect time dimension in lock step (cf Accordion spectroscopy) allowing a large saving in NMR time for higher dimensional experiments. Functionally equivalent projection-reconstruction methods.

Heteronuclear Multiple Quantum Coherence. Formation of multiple quantum coherence via scalar coupling between nuclei, e.g., C–H or N–H, occurs in any multipulse experiment. The coherence common evolution of the coupled spins is not directly observable, but its effects are detectable on reconversion to SQC. Such experiments are commonly used in inverse detection of low γ nuclei. MQC also has different relaxation properties (involves terms at higher frequencies) than SQC.

Heteronuclear Single Quantum Coherence. Homologue of HMQC, but only single quantum coherences are selected. This experiment requires more pulses than HMQC, but has more favorable relaxation properties and is the experiment of choice for ^{15}N–H systems.

Combination of two experiments that can be used in 3D mode or as 2D. The former correlates a heteronucleus (e.g., ^{13}C with the directly attached proton, and other protons that are in the same molecular fragment). This is useful for assignments of compounds in complex mixtures when some atoms are enriched or otherwise rare (e.g., ^{15}N in amino or amido compounds or ^{31}P in phosphorylated compounds). HCCH-TOCSY specifically selects for two or more directly bonded heteroatoms such as ^{13}C in molecular fragments of the type HC–CH, and the protons are correlated with one another. This experiment edits complex spectra and shows where multiply labeled compounds retain their bonds, or if new bonds are formed between labeled compounds.

Incredible Natural Abundance Double Quantum Transfer Experiment. This experiment, developed for tracing carbon networks in small molecules at natural abundance with ^{13}C detect, has been improved to proton detection, and as the two-quantum COSY, for proton correlations over three bonds.

Insensitive Nuclei Enhanced by Polarization Transfer. Magnetization from an abundant high γ spin is transferred to one of low *γ* by transfer through scalar coupling. The enhancement is equal to *γ* _{A}/*γ* _{B} and is governed by a rate sin *πJ*Δ where Δ is the delay time. Typically achieved using a pulse sandwich comprising a 90° pulse on the high *γ* nucleus, followed by a delay Δ = 1/2*J* and then simultaneous 90° pulses on the two coupled nuclei. Refocusing of chemical shift evolution is often included using a 180° pulse on both nuclei at Δ/2.

Detection of a “weak” X nucleus (low *γ*) via a strong nucleus (usually ^{1}H) usually via INEPT. Usually applies to proton detection of ^{13}C, ^{15}N. Requires scalar coupling between the X nucleus and the ^{1}H atom, generally (but not exclusively) by one bond. The sensitivity enhancement (SNR) possible is given by the ratio (*γ* _{H}/*γ* _{X})^{5/2}. This is >300 fold for ^{15}N.

Are versions of the same compound in which differ by the distribution of isotopes of each element. In a 3-carbon compounds such as lactate, there are eight possible stable isotopomers (^{12}C and ^{13}C) corresponding to ^{12}C-3, ^{13}C-3, and three each of ^{12}C-1^{13}C-2, and ^{13}C-1^{12}C-2. In NMR, these correspond to eight distinguishable compounds. In mass spectrometry, there are only four mass isotopomers *m*0, *m* + 1 *m* + 2 and *m* + 3 because the three isotopomers of *m* + 1 and *m* + 2 have identical mass.

Fundamental rotation frequency of the spins produced by the torque produced by the external magnetic field acting on the spin magnetic moments (qv). The Larmor frequency depends on the magnetic field strength and the intrinsic magnetic moment (qv) of the spin.

Protons and neutrons have the property of spin. As these are particles having charged components, they must have a magnetic moment (i.e., behave as magnets). Some nuclei have an imbalance of protons and neutrons, such that the nuclear spins are not all paired, leaving a net magnetic moment. The strength of the magnetic moment is a fundamental nuclear property, that is described by the gyromagnetic ratio, which is related to the effective distribution of spinning charge in the nucleus (in the classical picture).

Nuclear Overhauser Enhancement. Increase in magnetization of a spin when the magnetization of a neighboring spin is perturbed from equilibrium. The NOE depends on *r* ^{−6} and is therefore the primary source of distance information within a molecule.

Nuclear Overhauser Enhancement SpectroscopY- 2D experiment to measure NOE effects.

Characteristic time for the return of bulk magnetization to the equilibrium value. Comes in two main flavors, *T* _{1}-spin–lattice relaxation and *T* _{2}, spin–spin relaxation. *T* _{1} is the relaxation time that described return of *z*-magnetization and is a process that is associated with changes in enthalpy. *T* _{2} is a loss of phase coherence among spins in the *x*–*y* plane and is an entropic process.

Larmor frequencies are in the 100s of MHz and vary by a few tens of kHz for similar spins. It is convenient to remove this high frequency rotation from consideration by working in a frame rotating at the Larmor frequency. In this frame, the spins appear stationary.

Rotating frame Overhauser Enhancement SpectroscopY. ROEs are positive for all molecular correlation times. Exchange has opposite sign, and so this experiment is useful for distinguishing exchange reactions from dipolar interactions.

Through-bond interactions, nuclei interact via bonding electrons, which transmit the information about nuclear spin state through the covalent network. This gives rise to the coupling constant (qv) which is a measure of the interaction strength.

Property of particles that has a classical analog (a spinning top has spin angular momentum, etc.). In the original Schrödinger wave mechanics, there were only three quantum numbers and no spin. Spin arises naturally as a consequence of a relativistic treatment of wave mechanics (cf. P.A.M. Dirac). Spin is also quantized; only discrete values are possible. For the common case, the spin quantum number is 1/2, i.e., there are but two spin states (up and down, α and β). Magnetic nuclei are also referred to as spins.

Total Correlation Spectroscopy. Also known as HOHAHA. Provides (scalar) correlations within an entire spin system. Especially useful for identification of compounds in mixtures, and also for quantitative analysis of isotopomer distributions.

Is the energy of the interaction of a magnetic moment due to a spin with the external magnetic field.

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