Chapter 1

INTRODUCTION TO NMR SPECTROSCOPY

1.1 Introduction

Figure 1.1. Protein struc-ture determined by NMRspectroscopy. Four struc-tures of a 130 residue pro-tein, derived from NMRconstraints, are overlaid tohighlight the accuracy ofstructure determination byNMR spectroscopy.

Nuclear magnetic resonance (NMR) is a spec-troscopic technique that detects the energy ab-sorbed by changes in the nuclear spin state. Theapplication of NMR spectroscopy to the study ofproteins and nucleic acids has provided unique in-formation on the dynamics and chemical kineticsof these systems. One important feature of NMRis that it provides information, at the atomic level,on the dynamics of proteins and nucleic acids overan exceptionally wide range of time scales, rangingfrom seconds to pico-seconds. In addition, NMRcan also provide atomic level structural informa-tion of proteins and nucleic acids in solution (seeFig. 1.1), i.e. there is no need to crystallize thesample for NMR studies. Thus NMR provides amethod of obtaining structural information if themolecule cannot be crystallized or there is somequestion regarding a structure obtained by X-raycrystallography. Lastly, it is relatively easy tostudy protein-ligand interactions under physiologi-cal conditions by simply adding ligand to the NMRsample of the unliganded protein.

Although NMR is a powerful technique, it doeshave its limitations. First, almost all experimentsrequire that the observed NMR absorption peaksare assigned to a particular atom in the protein. Although resonance assign-ment methods are well characterized, they do require considerable time for dataacquisition and analysis. Secondly, the size of the protein or nucleic acid thatcan be studied by NMR is limited. Assemblies with rotational correlation timeof greater than 25 ns (corresponding to a protein with a molecular weight of60 kDa) may be difficult to study at the detailed atomic level. However, morelimited NMR studies can be performed on much larger proteins and biologicalassemblies. Generally, it is necessary to label larger proteins with 13C, 15N,and perhaps 2H, to successfully apply NMR techniques to such large systems.

2 Introduction to NMR Spectroscopy

Labeling of this type is most easily accomplished biosynthetically in either E.coli or in tissue culture (at a much higher expense). A rough indication of theisotopic labeling requirements as a function of protein size is given in Table1.1. Lastly, due to the small energy difference between the ground and excitedstate of the nuclear spins, NMR is a particularly insensitive technique. Proteinconcentrations on the order of 0.5 to 1 mM are typical, thus a single 0.4 mlNMR sample of a 20 kDa protein would require between 4 and 8 mg of protein.Fortunately, the techniques are not destructive and the sample can be used forother purposes.

For most of this text we will employ a semi-classical model of the nuclearspins to obtain an intuitive understanding of many of the fundamental aspectsof modern NMR spectroscopy. In this chapter we will highlight a number ofimportant features of NMR spectroscopy, including:

1. How energy states are created by the magnetic field,

2. The relationship between the environment and the absorption energy,

3. Coupling between nuclear spins.

1.2 Classical Description of NMR SpectroscopyThe basic phenomenon of nuclear magnetic resonance NMR spectroscopy is

similar to other forms of spectroscopy, such as visible spectroscopy. A photonof light causes a transition from the ground state to the excited state. Forexample, in the case of visible spectroscopy the absorption of a photon by anelectron causes the electron to move from its ground state orbital to an orbitalof higher energy, the excited state. In the case of NMR, the absorption of aradio-frequency photon promotes a nuclear spin from its ground state to itsexcited state.

NMR spectroscopy differs in a number of important aspects from other formsof spectroscopy. First, the generation of the ground and excited NMR statesrequires the existence of an external magnetic field. This requirement is a veryimportant distinction of NMR spectroscopy in that it allows one to changethe characteristic frequencies of the transitions by simply changing the appliedmagnetic field strength. Second, the NMR excited state has a lifetime that is onthe order of 109 times longer than the lifetime of the excited electronic states.This difference in lifetimes follows directly from Einsteins law for spontaneousemission that relates the lifetime of the excited state, , to the frequency of the

Table 1.1. Molecular Weight Limitations for Chemical Shift Assignments

Isotopic Labeling Mol. WeightNone 10 kDa15N 10-15 kDa15N, 13C 15-30 kDa15N, 13C, 2H 30-60 kDa

3

transition, :

1

3(1.1)

The long lifetime of the excited state implies extremely narrow spectral linessince the ability to define the energy of a transition is proportional to the life-time of the excited state 1. In the case of small organic molecules, linewidthsless than 1 Hz are easily attainable. Thus it is possible to detect small changesin absorption energies that arise from subtle differences in the environmentof a nuclear spin. The persistence of the excited state also facilitates multi-dimensional spectroscopy, by allowing the resonance frequency information as-sociated with one spin to be passed to another. Finally, the long lifetime ofthe excited state permits the measurement of molecular dynamics over a widerange of time scales.

1.2.1 Nuclear Spin TransitionsIn all forms of spectroscopy it is necessary to have two or more different

states of the system that differ in energy. In a system with two energy levels,the one of lower energy if often referred to as the ground state and the higherenergy state is the excited state. In the case of nuclear magnetic resonancespectroscopy, the energies of the states arise from the interaction of a nuclearmagnetic dipole moment with an intense external magnetic field. Excitationof transitions between these states is stimulated using radio-frequency (RF)electromagnetic radiation.

1.2.1.1 Magnetic Dipole

The nuclear magnetic dipole moment arises from the spin angular momentumof the nucleus. All nuclei with an odd mass number (e.g. 1H, 13C, 15N) havespin angular momentum because they have an unpaired proton. All nuclei withan even mass number and an odd charge (e.g. 2H, 14N) also have spin angularmomentum.

The spin angular momentum, S, is quantized (as is all angular momentum)and the different quantum states are indexed with the spin quantum numberI. The total angular momentum of a nuclear spin is: S = h

I(I + 1). Wewill generally be interested in the z-component of the angular moment, Sz ,which is restricted to integral steps of h ranging from I to +I. For example,a spin one-half nuclei would have two possible values of Sz: + 12 h, and

12 h,

corresponding to spin quantum numbers mz = +12 and mz =

12 , respectively.

The magnetic moment of a nuclear spin, , is proportional to its spin angularmomentum, hI by a factor, , which has units of radians sec1 gauss1.

n = nhI (1.2)

The magnitude of depends on the type of nuclei. NMR properties of various

1This is one form of Heisenbergs uncertainty principle: Et h/2.

4 Introduction to NMR Spectroscopy

Table 1.2. Properties of NMR Active Nuclei.

Nuclei1 (rad sec1 gauss1) I Natural Abundance (%)1H 26,753 1/2 99.9802H 4,106 1 0.01619F 25,179 1/2 100.000213C 6,728 1/2 1.108315N -2,712 1/2 0.37331P 10,841 1/2 100.00

1The term Protons is used interchangeably with 1H in the text.2Fluorine is not normally found in biopolymers, therefore it has to be intro-duced by chemical or biosynthetic labeling.3These isotopes of carbon and nitrogen are normally found in low levels inbiopolymers, therefore the levels of these two spins are generally enriched, of-ten to 100%, by biosynthetic labeling.CGS units.

nuclear spins, including values of , are shown in Table 1.2. NMR activeisotopes of hydrogen, carbon, nitrogen, and phosphorus exist, thus it is possibleto observe NMR signals from virtually every atom in biopolymers. Protons(1H) and phosphorus are highly abundant in natural biopolymers, while in thecase of carbon and nitrogen it is usually necessary to introduce the appropriateisotope into the sample (see footnote 4 in Table 1.2). Also note, that with theexception of deuterium (2H), all of these nuclei have a z-component of the spinangular momentum of h/2. Consequently, the material presented in this textapplies to all of the above atomic nuclei, except for deuterium. Deuterium witha spin quantum number I = 1 is a quadrapolar nuclei and in certain instancesneeds to be treated differently than spin-1/2 nuclei.

1.2.1.2 Transition Energies - Nuclear Dipole-MagneticField Interaction

B

Figure 1.2. Interaction ofmagnetic dipole with an ap-plied field.

When the orientation of a collection of nuclearspins is observed in the absence of a magnetic field,all possible orientations of the magnetic dipole arepossible (see Fig. 1.3). However, once the spins areplaced in a magnetic field, the direction of z-axisbecomes defined by the direction of the field, andthe magnetic moments of spin-1/2 nuclei assumetwo orientations, either along or opposed to themagnetic field, as illustrated in Fig. 1.3. Notethat the magnetic moments cannot orient parallelto the magnetic field because of the restrictions placed on the value of z bythe quantum mechanical properties of the system.

The energy of a state depends on the interaction of the aligned magneticdipole with an externally applied magnetic field. The size of this interaction

5

A Bz

Y

X

Z

Y

X

-1/2

+1/2