Chapter 1 INTRODUCTION TO NMR SPECTROSCOPY

1 Chapter 1 INTRODUCTION TO NMR IntroductionFigure 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 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.

2 In addition, NMRcan also provide atomic level structural informa-tion of proteins and nucleic acidsin solution(seeFig. ), 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 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.

3 Although resonance assign-ment methods are well characterized, they do require considerable time for dataacquisition and analysis. Secondly, the size of the proteinor nucleic acid thatcan be studied by NMR is limited. Assemblies with rotationalcorrelation 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 proteinsand biologicalassemblies. Generally, it is necessary to label larger proteins with13C,15N,and perhaps2H, to successfully apply NMR techniques to such large to NMR SpectroscopyLabeling of this type is most easily accomplished biosynthetically in in tissue culture (at a much higher expense).

4 A rough indication of theisotopic labeling requirements as a function of protein Lastly, due to the small energy difference between the ground and excitedstate of the nuclear spins, NMR is a particularly on the order of to 1 mM are typical, thus a single mlNMR sample of a 20 kDa protein would require between 4 and 8 mg , the techniques are not destructive and the sample can be used forother most of this text we will employ a semi-classical model ofthe nuclearspins to obtain an intuitive understanding of many of the fundamental aspectsof modern NMR SPECTROSCOPY . In this Chapter we will highlightanumberofimportant features of NMR SPECTROSCOPY , including:1.

5 How energy states are created by the magnetic field,2. The relationship between the environment and the absorption energy,3. Coupling between nuclear Classical Description of NMR SpectroscopyThe basic phenomenon of nuclear magnetic resonance NMR SPECTROSCOPY issimilar 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 absorptionof 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 SPECTROSCOPY differs in a number of important aspects fromotherformsof SPECTROSCOPY .

6 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 allowsone to changethe characteristic frequencies of the transitions by simplychangingtheappliedmagnetic field strength. Second, the NMR excited state has a lifetime that is onthe order of 109times longer than the lifetime of the excited electronic difference in lifetimes follows directly from Einstein s law for spontaneousemission that relates the lifetime of the excited state, ,tothefrequencyoftheTable Weight Limitations for Chemical Shift AssignmentsIsotopic LabelingMol.

7 WeightNone 10 kDa15N10-15 kDa15N,13C15-30 kDa15N,13C,2H30-60 kDa3transition, : 1 3( )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 ,linewidthsless than 1 Hz are easily attainable. Thus it is possible to detect small changesin absorption energies that arise from subtle differences inthe 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 Nuclear Spin TransitionsIn all forms of SPECTROSCOPY it is necessary to have two or moredifferentstates of the system that differ in energy.

8 In a system with twoenergy levels,the one of lower energy if often referred to as the ground stateandthehigherenergy state is the excited state. In the case of nuclear magnetic resonancespectroscopy, the energies of the states arise from the interaction of anuclearmagnetic dipole momentwith an intense external magnetic field. Excitationof transitions between these states is stimulated using radio-frequency (RF)electromagnetic Magnetic DipoleThe nuclear magnetic dipole moment arises from thespin angular momentumof the nucleus. All nuclei with an odd mass number ( ,13C,15N) havespin angular momentum because they have an unpaired nuclei withan even mass number and an odd charge ( ,14N) also have spin spin angular momentum, S,isquantized(asisallangularmomentum)and the different quantum states are indexed with the spin quantum : S= h!

9 I(I+1). Wewill generally be interested in thez-component of the angular moment,Sz,which is restricted to integral steps of hranging from Ito + ,aspinone-halfnucleiwouldhavetwopossible valuesofSz:+12 h,and 12 h,corresponding to spin quantum numbersmz=+12andmz= 12, magnetic moment of a nuclear spin, ,isproportionaltoitsspinangularmomentum, h Iby a factor, ,whichhasunitsofradians sec 1gauss 1. n= n h I( )The magnitude of depends on the type of nuclei. NMR properties of various1 This is one form of Heisenberg s uncertainty principle: E t to NMR SpectroscopyTable of NMR Active (rad sec 1 gauss 1) INaturalAbundance(%)1H26,7531 , ,1791/2 ,7281 ,7121 ,8411 term Protons is used interchangeably is not normally found in biopolymers, therefore ithas to be intro-duced by chemical or biosynthetic 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.

10 CGS spins, including values of , NMRactiveisotopes of hydrogen, carbon, nitrogen, and phosphorus exist, thus it is possibleto observe NMR signals from virtuallyeveryatom 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 ). Also note, that with theexception of deuterium (2H), all of these nuclei have az-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 withaspinquantumnumberI=1isaquadrapolarn ucleiandincertaininstancesneeds to be treated differently than spin-1/2 Transition Energies - Nuclear Dipole-MagneticField Interaction BFigure ofmagnetic dipole with an ap-plied 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.)