1. Principles and Applications of NMR Spectroscopy Instructor: Tai-huang Huang (bmthh@ibms.sinica.edu.tw), (02) 2652-3036bmthh@ibms.sinica.edu.tw http://www.nmr.sinica.edu.tw/~thh/lecture.html Time: Tuesday and/or Friday 2-5 PM (9/21, 10/5, 10/8, 10/12, 10/15, 10/22, 10/26, 10/29, 11/2, 11/9, 11/12, 11/16, 11/19, 11/30, 12/7) Place: Rm. N617, IBMS, Academia Sinica Textbooks: 1. Lecture by James Keeler on “Understanding NMR spectroscopy” (http://www-keeler.ch.cam.ac.uk/lectures/)http://www-keeler.ch.cam.ac.uk/lectures/ 2. Rules, G.S. and Hitchens, T.K. “Fundamentals of Protein NMR spectroscopy” 3. Cavanagh, Fairbrother, Palmer, and Skelton: “Protein NMR spectroscopy – Principles and practice” Academic press, 1996. 4. Selected review articles.

2. Curse Content This will be a comprehensive lecture course, focusing on modern high field NMR spectroscopy in solution, with applications to protein structure, dynamics and functional studies. Topics to be covered include: 1. Basic NMR theory, including quantum mechanical and vectorial descriptions of NMR spectroscopy. 2. Basic experimental aspects of NMR: NMR data acquisition and processing. 3. Product operator formalism analysis of pulse programs. 3. Spin dynamics: Coherent selection, phase cycling, gradient enhanced spectroscopy. 4. Heteronuclear multidimensional NMR spectroscopy. 5. Relaxation and protein dynamics. 6. Special topics: TROSY, RDC, PRE and reduced dimensionality etc. 7. Applications to protein NMR in solution.

3. Course Outline Lect # DateTopics 1 9/21 NMR and Energy level 2 10/5 Vector Model 3 10/8 Fourier Transform and Data processing 4 10/12How the spectrometer works 5 10/15 Product Operator 6 10/22 7 10/26 Two dimensional NMR 8 10/29 9 11/2 Coherence selection and phase cycling 10 11/5 11 11/9 Relaxation 12 11/12 Selective topics 13 11/16 Selective topics 14 11/19 Selective topics 15 11/30 Selective topics 16 12/7 Selective topics

4. NMR Historic Review

5. 2002 Nobel prize in Chemistry was awarded to Kurt Wuthrich NMR is a versatile tool and it has applications in wide varieties of subjects in addition to its chemical and biomedical applications, including material and quantum computing.

6. Felix Bloch 1952, Physics Edward M. Purcell 1952, Physics Kurt Wuthrich 2002, Chemistry Richard R. Ernst 1992, Chemistry Isador I. Rabi 1944, Physics Paul Lauterbur 2003, Medicine Peter Mansfield 2003, Medicine

7. CW NMR 40MHz (1960)

9. Basic Nuclear Spin Interactions Nuclear Spin i Nuclear Spin j Electrons Phonons 3 1 Dominant interactions: H = H Z + H D + H S + H Q. H Z = Zeeman Interaction H D = Dipolar Interactions H S = Chemical Shielding Interaction. H Q = Quadrupolar Interaction 6 HoHo HoHo 4 5 4 3 12 4

10. Lecture 2: Vector Model Bulk Magnetization: The sum of all magnetic moments (10 20 spins) Larmor frequency:  o =  Bo (rad·S -1 ); or =  Bo /2  (Hz) Detection:  Mo z x B1 y oo x Mxy y 90 deg pulsea deg pulse Signal: Pulse   ot Mo Mosin  X Y Z

11. Effect of external magnetic field:

12.  Collecting NMR signals The detection of NMR signal is on the xy plane. The oscillation of Mxy generate a current in a coil, which is the NMR signal. Due to the “relaxation process”, the time dependent spectrum of nuclei can be obtained. This time dependent spectrum is called “free induction decay” (FID) time Mxy time (if there’s no relaxation )(the real case with T1 &T2)

13. Rotating frame: A reference frame which rotate with respect to the Z-axis of the laboratory frame at frequency  rot   ot Mo Mosin  X Y Z Lamor frequency in the rotating frame:  =  o -  Rot  =  B then  B =  /  = Bo -  Rot/  For  Rot =  o  B = 0 Bo  Rot/  In the rotating frame with  rot =  o the signal one observe is Mosin  (No oscilation) and  B = 0 Effective field: In the presence of RF-field (Radio frequency) B1 the total field: Static frame: B = Bo + B1 Rotating frame: Beff =  B + B1 Tilt angle: M will rotate about Beff at a rate of  eef =  Beff

14. Effective field in frequency unit: On resonance pulse:  rot =  o and  = 0   eff =  1 (The magnetization will rotate w.r.t. the B1 axis by an angle, (the flipping angle)  =  1   =  o   o pulse (90 o, 180 o pulse) 180o pulse is also called the “inversion pulse”   ot Mo Mosin  X Y Z Bo  Rot/  B1 For arbitrary angle  :

15. Hard pulse: If B1 >>  B the effectiv field lies along B1 and all resonances appeared to be on resonance. Example: Is P(90o) = 12 us pulse a hard pulse for  B = 10 ppm in 500 MHz spectrometer ?  = 90 o =  /2 =  B1 x12X10 -6   1 =  B1 =  /24x10 6  1 =  /2  = 20.8 kHz  B = 10 ppm/2 = 5x500 = 2.5 kHz <<  1 Ans: Yes, it is a hard pulse. Detection in the rotating frame : Probe Transmitter Receiver Digitizer Computer  rot oo  rot -  rot kHz mHz Basic pulse acquiring scheme : More than one resonance:

16. Pulse calibration: Spin Echo :

17. Pulses of different phases: X Y Z Y-pulse (90 y )X-pulse (90 X or 90) Relaxation (Inversion recovery expt):

18. NMR Relaxation

20.  =  o -  rot = the offset frequency 90% 1.6 To record a 200 ppm 13 C spectrum at 600 MHz spectrometer:  = 200 ppm x 150 = 3o kHz;  1 =  /1.6 = 30000/1.6 =18,750 Hz = ? Gauss ?  P(90) = ? Us for 13 C ?

21. Selective excitation of a range of resonances:

22. Selective inversion (Soft pulse): Shaped pulses are designed to affect only the resonances of interest