Principles and Applications of NMR Spectroscopy

Instructor: Tai-huang Huang (bmthh@ibms.sinica.edu.tw), (02) 2652-3036

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/)

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.

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.

Course Outline

Lect # Date Topics 1 9/21 NMR and Energy level 2 10/5 Vector Model 3 10/8 Fourier Transform and Data processing 4 10/12 How 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

NMR Historic Review

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.

Felix Bloch 1952, Physics

Edward M. Purcell 1952, Physics

Kurt Wuthrich 2002, Chemistry

Richard R. Ernst 1992, Chemistry

Isador I. Rabi1944, Physics

Paul Lauterbur 2003, Medicine

Peter Mansfield 2003, Medicine

CW NMR 40MHz(1960)

Basic Nuclear Spin Interactions

Nuclear Spin i Nuclear Spin j

Electrons

Phonons

3

1

Dominant interactions: H = HZ + HD + HS + HQ.

HZ = Zeeman Interaction HD = Dipolar Interactions HS = Chemical Shielding Interaction. HQ = Quadrupolar Interaction

6

HoHo

4

5

4

3

1 2

4

Lecture 2: Vector Model

Bulk Magnetization: The sum of all magnetic moments (1020 spins)

Larmor frequency:

o = Bo (rad·S-1);

or = Bo /2 (Hz)

Detection:

Mo

z

xB1

yo

x

Mxyy

90 deg pulse

a deg pulse

Signal:

Pulse

ot

Mo

MosinX

Y

Z

b. Effect of external RF field B1: 0BM

dt

dM

Effect of external magnetic field:

1

BMdt

dM

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)

Mxy

time

(if there’s no relaxation ) (the real case with T1 &T2)

Rotating frame: A reference frame which rotate with respect to the Z-axis of the laboratory frame at frequency rot

ot

Mo

MosinX

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 + B1Rotating frame: Beff = B + B1

Tilt angle:

M will rotate about Beff at a rate of eef = Beff

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 (90o, 180o pulse)180o pulse is also called the “inversion pulse”

ot

Mo

MosinX

Y

Z

Bo

Rot/

B1

For arbitrary angle :

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 ?

= 90o = /2 = B1 x12X10-6 1 = B1 = /24x106

1 = /2 = 20.8 kHzB = 10 ppm/2 = 5x500 = 2.5 kHz << 1 Ans: Yes, it is a hard pulse.

Detection in the rotating frame :

ProbeTransmitter

ReceiverDigitizer

Computer

rot

roto

rot - rotkHzmHz

mHz

mHz

Basic pulse acquiring scheme :

More than one resonance:

Pulse calibration:Spin Echo :

Pulses of different phases:

X Y

Z

Y-pulse (90y) X-pulse (90X or 90)

1

BMdt

dM

Relaxation (Inversion recovery expt):

NMR RelaxationNMR Relaxation

= o - rot = the offset frequency

90%

1.6

To record a 200 ppm 13C 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 13C ?

Selective excitation of a range of resonances:

Selective inversion (Soft pulse):

Shaped pulses are designed to affect only the resonances of interest