1. Nuclear Magnetic Resonance (NMR) Spectroscopy Kurt Wuthrich Chemistry-2002 Richard Ernst Chemistry -1991 Felix Bloch & Edward Purcell Physics-1952 Paul Lauterbur & Peter Mansfield Medicine-2003 Brian Sykes Lewis Kay

2. Principles of NMR Protein Spectroscopy What does NMR tell us ? 1) Primary structure characterization 2) Dynamics - psec-sec timescales 3) Equilibrium binding 4) Folding/Unfolding 5) Three dimensional structure Some Advantages 1) Solution based 2) Non-destructive 3) Residue specific information

3. Principles of NMR Protein Spectroscopy Wavelength (nm) 10 100 1000 10 4 10 5 10 6 10 7 10 8 10 9 UV/Vis IR NMR Nuclear spin transitions Electron transitions Crystallography X-rays Radio waves

4. Principles of NMR Protein Spectroscopy Absorption of energy by nucleus - depends on nuclear spin (I) = sum of unpaired protons + neutrons (spin 1/2) 1 H 1/2 1 0 12 C 0 6 6 13 C 1/2 6 7 14 N 1 7 7 15 N 1/2 7 8 NucleusI# Protons# Neutrons I≠0 - NMR observed - spin will have magnetic moment  =  I For proteins 1 H, 13 C, 15 N ( 31 P)

5. Principles of NMR Protein Spectroscopy I = 1/2  =  I z =  m I h m I = -1/2  Under normal conditions the difference between these is negligible N S S N Now lets put these in a static magnetic field N S m=(-I, -I+1 ….I-1, I) m I = +1/2  BoBo

6. Principles of NMR Protein Spectroscopy x y z BoBo In a magnetic field E = -  B o = -  I z B o = -  hm I B o m=(-I, -I+1 ….I-1, I)  =-  I z Normal Magnetic Field (B o )

7. Principles of Protein NMR Spectroscopy m I = -1/2  N S S N N S m I = +1/2  So how does this give us an “NMR signal” ? E = 1  hB 0 2 -  hm I B 0 - 1  hB 0 2    E =  hB 0

8. Principles of Protein NMR Spectroscopy    E =  hB 0 This occurs for all 1 H, 13 C, 15 N in magnetic field B 0 = 11.75 T (500 MHz) 14.09 T (600 MHz) 18.79 T (800 MHz) B0B0 1 H 26.75 13 C 6.73 15 N -2.72    rad / T sec) As B 0 so does  E !

9. Principles of Protein NMR Spectroscopy    E =  hB 0 = h We can use this to select for the nucleus of interest =  B 0 22 (Hz)  =  B 0 (rad) Larmor Precession Use frequency to stimulate transitions ! 1 H 26.75600.00 13 C 6.73150.87 15 N -2.71 60.82    rad / T sec) Nucleus at 14.09 T

10. Principles of Protein NMR Spectroscopy    E =  hB 0 = h NMR is an insensitive method Populations of  determined by  E - Boltzman distribution n  -n  =  n = N  hB 0 2kT 1 H N=10 6 11.75T 18.79T 499,980 500,020 499,968 500,032  n = 40  n = 64 Only measure net difference (  n) Insensitivity Larger magnet = sensitivity

11. Principles of Protein NMR Spectroscopy Sensitivity n  -n  =  n = N  hB o 2kT M o =n   z  + n   z  =  n  z  = 1  h  n = 1 N (  h) 2 B o 2 4kT - it turns out the observed signal (S) - varies with B o 2 x y z BoBo x y z BoBo

12. Principles of Protein NMR Spectroscopy Net Magnetization x y z x y z MoMo BoBo BoBo oo Rotating Frame

13. Principles of Protein NMR Spectroscopy How is the NMR Signal Obtained ? x y z MoMo BoBo -employ a rf pulse at of desired nucleus x y z 2  *pw*  B 1 =  “rf pulse”  B1B1 B1B1

14. Principles of Protein NMR Spectroscopy x y z MoMo BoBo x y z 2  *pw*  B 1 =   =  /2  rf on off pw= 1 4*  B 1 B1B1 B1B1 pw = 6  sec  B 1 = 41 kHz

15. Principles of Protein NMR Spectroscopy x y z  rf on off B1B1 x y z MoMo BoBo B1B1 x y z B1B1 receiver FT time

16. Principles of Protein NMR Spectroscopy x y z off B1B1 x y z B1B1 receiver time T1T1 x y z B1B1 T2T2 M z (t) = M o (1-e -t/T 1 ) M y (t) = M y (0)*e -t/T 2

17. Principles of Protein NMR Spectroscopy 100 10 1 0.1 0.01 0.001 Correlation Time,  c (nsec) Molecular Weight T 1, T 2 (sec) 100 10 1 0.1 0.01 0.001 T1T1 T2T2 1/2 = 1  T 2 * Linewidths MW 100 0.5 Hz MW 20,000 10 Hz

18. Principles of Protein NMR Spectroscopy NMR Instrumentation Magnet - B o 18.79 T vacuum N 2(l) He (l) magnet 22.31 T (2006) probe

19. Principles of Protein NMR Spectroscopy Magnet Technology Ribonuclease (1957) - 40 MHz Lysozyme (1995) - 750 MHz 0.94 T 1 17.62 T 351 22.31 T 563 Field S/N

20. Principles of Protein NMR Spectroscopy Probe Technology BoBo B1B1

21. Principles of Protein NMR Spectroscopy Cold “Cryogenic” Probe S/N ~ 1/{R s *(T s +T pa )+(R c *(T c +T pa )} 1/2 T pa, T c - lowered 298˚K 20˚K R s, T s - near 298˚K 3-4 time more sensitive 500 MHz + cold probe = 1.6x S/N 800 MHz

22. Principles of Protein NMR Spectroscopy Block Diagram of NMR Spectrometer Probe Transmitter Preamplifier Duplexer CPU Receiver Computer obs, lk obs, dec, lk