182 5.4  NMR and Other Radio Frequency and Microwave Resonance Spectroscopies

scales with its surface area, whereas the number of photoelectrons produced scales with

its volume. Thus, the relative probability of photoelectron-​related damage scales with the

effective crystal diameter. However, using small crystals reduces the x-​ray diffraction signal,

which reduces the effective spatial resolution of the biomolecular structure determination,

but also, results in inhomogeneity in the crystal (see Chapter 7) having a more pronounced

detrimental effect on the diffraction pattern relative to the signal due to homogeneous regions

of the crystal.

Another strategy to reduce x-​ray damage is the use of microbeams. Synchrotron sources

have highly collimated beams, with typical diameters of a few hundreds of microns. However,

the small beam divergence of ~μrad allows much narrower beams to be generated, to as low

as ~1 μm. That can be employed as a much finer probe for x-​ray crystallography (Schneider,

2008), reducing the effective diffraction volume in the sample exposed to the beam to just

~20 μm³. Reducing the sample volume illuminated by x-​rays substantially reduces radiation

damage. Also, it allows x-​ray crystallography to be performed on much smaller crystals,

which significantly reduces the bottleneck of requiring large and perfect crystals.

Also, the emergence of very intense, coherent x-​rays from XFEL sources has allowed

much shorter duration pulses for crystallography. This again reduces radiation damage to the

sample and similarly permits much smaller samples to be used. As opposed to a perfect 3D

crystal, 3D structural determination is now possible using x-​ray diffraction from a coherent

XFEL source using just a monolayer of protein generated on a surface.

5.4  NMR AND OTHER RADIO FREQUENCY AND

MICROWAVE RESONANCE SPECTROSCOPIES

NMR is a powerful technique utilizing the principle that magnetic atomic nuclei will undergo

resonance by absorbing and emitting electromagnetic radiation in the presence of a strong

external magnetic field. The resonance frequency is a function of the type of atom undergoing

resonance and of the strong external magnetic field but is also dependent on the smaller

local magnetic field determined by the immediate physical and chemical environment of the

atom. Each magnetic atomic nucleus in a sample potentially contributes a different relative

shift in the resonance frequency, also known as the chemical shift, hence, the term NMR

spectroscopy, in being a technique capable of acquiring the spectra of such chemical shifts.

Put in simple terms, the spatial dependence on the chemical shift can be used to reconstruct

the physical positions of atoms in a molecular structure. Other related radiowave reson­

ance techniques include electron spin resonance (ESR) and electron paramagnetic resonance

(EPR), which operate on resonance behavior in the electron cloud around atoms as opposed

to their nuclei.

5.4.1  PRINCIPLES OF NMR

To have a magnetic nucleus implies a nonzero spin angular momentum. The standard model

of particle physics proposes that atomic nuclei contain strong forces of interaction known as

the tensor interaction, which allows neutrons and protons to be paired in an atomic nucleus

in a quantum superposition of angular momentum states. These interactions can be mod­

eled by the quantum field theory of quantum chromodynamics, which bind together two

down (each of the charge –​e/​3 with paired 1/​2 spins, where e is the magnitude of the electron

charge) and one up quark (of charge +​e/​3 and 1/​2 spin) in a neutron, while a proton contains

one down and two up quarks. This implies that both the neutron and proton are spin-​1/​2

particles. Therefore, all stable isotopes whose atomic nuclei possess an odd total atomic mass

number (i.e., the number of protons plus neutrons) are magnetic (and if the atomic number

minus the neutron number is ±1 as is commonly the case for many stable isotopes the result

are spin-​1/​2 nuclei).

The most common isotopes used for biological samples are ¹H and ¹³C (see Table 5.2).

1H is the most sensitive stable isotope, whereas 13C has relatively low natural abundance

KEY BIOLOGICAL

APPLICATIONS: X-​RAYS

Determining atomic-​level pre­

cise molecular structures from

crystals; Estimating elemental

composition of biological

samples.