Experimental Molecular Biophysics TIGP CBMB Lou-sing Kan, Ph. D. Institute of Chemistry, Academia Sinica March 16, 2006 NMR(I)- NMR theory and experiments

The original of nuclear magnetic resonance Nuclear spin The Resonance Phenomenon

Magnetization

 E =  hBo/2  where h is Planck's constant (6.63 x erg sec)  E = h o =  Bo/2  Larmor equation  o = 2  o is the angular Larmor resonance frequency The gyromagnetic ratio  is a constant for any particular type of nucleus and is directly proportional to the strength of the tiny nuclear magnet. Natural Gyromagnetic Sensitivity†Electric Nucleus Spin Quantum AbundanceRatio  (% vs. 1H) Quadrupole Number (I) (%) (10 -7 rad/Tsec) Moment (Q) (e·1024cm2) 1 H 1/ H C 1/ N 1/ F 1/ P 1/

N upper /N lower  e  E/ kT  e  h / kT k is the Boltzmann constant, and T is the absolute temperature (°K). Boltzmann constant = × m 2 kg s -2 K -1

Chemical Shift 5mg Adenosine in DMSO, M = C 10 H 13 N 4 O 4

 = (  /2  )B local = (   /2  )(1-  )  = ( - REF ) x10 6 / REF

Protons Chemical shift (ppm) H H NH H 1’ ’-OH5.42 5’-OH5.40 3’-OH5.16 H2’4.60 H3’4.13 H4’3.95 H5’3.66 H5”3.54 HDO3.25 DMSO2.49 Impurities1.23

Spin-Spin Coupling (Splitting) Observation: A nucleus with a magnetic moment may interact with other nuclear spins resulting in mutual splitting of the NMR signal from each nucleus into multiplets.

The number of components into which a signal is split is 2nI+1, where I is the spin quantum number and n is the number of other nuclei interacting with the nucleus. For proton, I = 1/2 Neighbor group has one proton Neighbor group has two protons Neighbor group has three protons Two neighbor groups have one proton each

Assignment 10Hz Karplus equation for determining dihedral angle Coupling consts.J, Hz H 1’ -H 2’ 5.9 H 2’ -H 3’ 5.5 H 3’ -H 4’ 3.0 H 4’ -H 5’ 4.1 H 4’ -H 5” 3.5 H 5’ -H 5” 12.3 H 2’ -C 2’ -OH6.6 H 3’ -C 3’ -OH4.7 H 5’ -C 5’ -OH7.2 H 5” -C 5’ -OH4.4 decoupled

Proton couples with other nuclei

Peak intensity

Summary

Relaxation Relaxation processes, which neither emit nor absorb radiation, permit the nuclear spin system to redistribute the population of nuclear spins. Some of these processes lead to the nonequilibrium spin distribution (N lower – N upper ) exponentially approaching the equilibrium distribution. (N lower – N upper ) = (N lower – N upper ) equil (1 – e -  /T1 ) Where the time constant for the exponential relaxation is T1, the spin-lattice relaxation time.  =3s  =2s  =0.5s  =0.25s  =0.005s Inverse-recovery

dM z /dt = -(M o -M z )  /T 1 M o -M z t = Aexp(-  /T 1 )  M z = -M o  M o (M o -M t )/2M o = exp(-  /T 1 ) ln[(M o -M t )/2M o ] = -  /T 1 Plot ln[(M o -M t )/2M o ] against , T 1 equals to the minus reciprocal of slope.

There are additional relaxation processes that adiabatically redistribute any absorbed energy among the many nuclei in a particular spin system without the spin system as a whole losing energy. Therefore, the lifetime for any particular nucleus in the higher energy state may be decreased, but the total number of nuclei in that state will be unchanged. This also occurs exponentially and has a time constant T2, the spin-spin relaxation time. Under some circumstances,the linewidth of an NMR signal at half-height, W1/2, can be related to T2 by W1/2 = 1/(  T2) Rate of proton exchange M xy = M xy o exp(-  /T2) Spin-echo

Nuclear Overhauser enhancement (NOE) When two nuclei are in sufficiently close spatial proximity, there may be an interaction between the two dipole moments. The interaction between a nuclear dipole moment and the magnetic field generated by another was already noted to provide a mechanism for relaxation. The nuclear dipole-dipole coupling thus leads to the NOE as well as T1 relaxation. If there is any mechanism other than from nuclear dipole-dipole interactions leading to relaxation, e.g., from an unpaired electron, the NOE will be diminished – perhaps annihilated. Summary: Parameters generated by NMR Chemical shift Coupling constant Peak area Spin-lattice relaxation Spin-spin relaxation Nuclear Overhauser enhancement

Experimental Methods Pulse NMR Fourier transform Faster Measure dilute solution or less materials Measure relaxation times Do 2D and multidimensional NMR FID

The meanings of pulse angle

Right intensity Wrong intensity

2D NMR Experiments that irradiate the sample with two rediofrequency fields. For examples: chemical shifts and coupling constants.

1’ 2’ 2’-OH5’-OH 3’-OH 3’ 4’ 5’ 5’’ By 2D J-res

2D COSY (correlation spectroscopy)

The frequent used 2D pulse programs.

Carbon-13 NMR

C2C2 C8C8 C 1’ C 4’ C 2’ C 3’ C 5’ C4C4 C5C5 C6C6

DEPT (distortionless enhancement by polarization transfer)

2D HSQC (Heteronuclear single quantum coherence)

 ppm 1 J CH, Hz C C C C C C1’ C2’ C3’ C4’ C5’ The chemical shifts and one bond C-H coupling constant of adenosine. The chemical shift range of selected function groups.

Conclusion: (Homework: Please write a conclusion of this course.)

References Edwin D. Becker High Resolution NMR, Theory and Chemical Applications, 3rd Edition Academic Press, Ray Freeman Magnetic Resonance in Chemistry And Medicine Oxford, 2003 Joseph P. Hornak The Basic of NMR General T.C. Farrar An Introduction To Pulse NMR Spectroscopy Farragut Press, Chicago, H. Gunther "Modern pulse methods in high-resolution NMR spectroscopy." Angew. Chem.. Int. Ed. Engl.22: (1983) Basic Pulse NMR Ad Bax Two-Dimensional Nuclear Magnetic Resonance in Liquid Delft University Press, 1982 Richard R. Ernst, Geoffrey Bodenhausen, Alexander Wokaun Priciples of NMR in One and Two Dimensions Oxford, D NMR Peter Bigler NMR Spectroscopy Processing Strategies VCH, 1997 Data Process H. Duddeck, W. Dietrich Structure Elucidation by Modern NMR, A Workbook Springer-Verlag, 1989 Application: small molecules Kurt Wuthrich NMR of Proteins and Nucleic Acids John Wiley & Sons, 1986 C. A. G. Haasnoot NMR in Conformation Analysis of Bio-organic Molecules Application: Peptides and Proteins Application: Nucleic Acids G. C. K. Roberts NMR of Macromolecules, A Practical Approach IRL Press, Application: Others S. Braun, H.-O. Kalinowske, S. Berger 100 and More Basic NMR Experiments VCH, 1996 S. W. Homans A Dictionary of Concepts in NMR Oxford, 1992 Handbook of High Resolution Multinuclear NMR John Wiley & Sons, 1981 Dictionary