NMR 3- Pulse sequence and NMR experiments
Instructor:
Tai-huang Huang (黃太煌)
中央研究院生物醫學科學研究所
Tel. (886)-2-2652-3036;
E. mail: bmthh@ibms.sinica.edu.tw
Web site: www.nmr.ibms.sinica.edu.tw/~thh/biophysics/NMR-2.ppt
Reference:
Cavanagh, J. et al., “Protein NMR Spectroscopy-Principles and Practice”,
Academic Press, 1996.
Term paper:
 Find a NMR paper and write a report on the
subject related to the paper.
NMR II- Pulse sequence and NMR experiments
Steps involved in determining protein structures by NMR
液態樣品
取得ＮＭＲ圖譜
圖譜分析
結構計算
( days to weeks)
( hours/days to weeks)
( weeks to months)
 Collecting NMR signals
 NMR signal is detected on the xy plane. The oscillation of Mxy generate a
current in a coil , which is the NMR signal.
Due to the “relaxation process”, signal decay with time. This time
dependent signal is called “free induction decay” (FID)
Mxy
time
(if there’s no relaxation )
(the real case with T1 &T2)
•The Bloch Equations:
dM/dt = M x B + relaxation terms
dMx(t) / dt =  [ My(t) * Bz - Mz(t) * By ] - Mx(t) / T2
--------- (1)
dMy(t) / dt =  [ Mz(t) * Bx - Mx(t) * Bz ] - My(t) / T2
--------- (2)
dMz(t) / dt =  [ Mx(t) * By - My(t) * Bx ] - ( Mz(t) - Mo ) / T1 ------ (3)
Rotating frame:
Let
[dM(t)/dt]rot = [dM(t)/dt]lab+M(t) x 
= M(t) x [γB(t) + ]
Let
Beff = B(t) + /γ ------------------- (4)
Thus, if B(t) + /γ= 0, or B(t) = - , Beff = 0
 dM(t)/dt = 0,  M(t) is time independent.
Z
Bo
Bo= Bo - o/
Y
X
In the absence of RF field and B(t) = Bo or B(t) = -Bo = - o = Larmor frequency.
In a frame rotating at Larmor frequency the magnetization is static.
 The Bloch equations become:
dMz(t) / dt = [ Mo - Mz(t)/ T1 -------------- (5)
dMx(t) / dt = - Mx(t) / T2
-------------- (6)
dMy(t) / dt = - My(t)/T2
-------------- (7)
Solutions: Mz = Mo – [Mo –Mz(0)]exp(-t/T1) -------------- (8)
Mx = Mx(0)exp(-t/T2);
-------------- (9)
My = My(0)exp(-t/T2);
-------------- (10)
 T1 relaxation in the Z-direction and T2 relaxation on the xy-plane
 If we obsere the spins in a frame which rotate at exactly the
Larmor frequency then we see the spin state stationary (Static).
 What if we observe the spin at a frequency which is  from the
Larmor frequency ?  Both Mx and My will rotate at  Hz.
Experimentally what is the rotating frame ?
Transmitter
o
106 – 109 Hz
o
Probe
Computer

Receiver
- o
Signal is in rotating frame
(kHz)
Digitizer
Effect of RF-field:
dMz(t)/dt = [Mx(t)Bry(t) – My(t)Brx(t)] – [Mz(t) – Mo]/T1
dMx(t)/dt = - My(t) – Mz(t)Bry(t) – Mx(t)/T2
dMy(t)/dt = Mx(t) – Mz(t)Brx(t) – My(t)/T2
where Brx(t) = Brocos and Bry(t) = Brosin
 = -γΔBo - rf = o - rf is the offset.
----------- (11)
Bo
In a common experimental situation in pulse NMR, B1
is applied for a time p << T1, T2 and neither B1 nor 
is time dependent. Thus, during the time when B1 is on eq. 11 becomes:
dMz(t)/dt = Mx(t)Bry(t) – My(t)Brx(t)
Br
B1
dMx(t)/dt = - My(t) – Mz(t)Bry(t)
----------- (12)
dMy(t)/dt = Mx(t) – Mz(t)Brx(t)
The solution of eq. 12 is a series of rotations about the axis perpendicular
to the applied B1 field. The signal can be described as:
Mx(t) = Mosincos(t)exp(-t/T2)
My(t) = Mosinsin(t)exp(-t/T2)
Bloch Equations (Phenomenological equations):
dMx/dt = (M x H)x – Mx/T2 -------------------- (1)
dMy/dt = (M x H)y – My/T2 -------------------- (2)
dMz/dt = (M x H)z – (Mo – Mz)/T1 ----------- (1)
and
T2 H 1 state
For H1 along the x-axis and H1 (0
in )steady
o 
1  (simultaneous
  o ) 2 T22
i.e. dM/dt = 0 we can solve the above
Equations to get:
Mx = o(oT2)
H1
1  (   o ) 2 T22
-------- (3)
(Lorenzian lineshape, absorption)
My = o(oT2)
(Dispersion)
Mx
-------- (4)
My
Fourier transformation (FT)
FT
 Function at
 = 1/T2
exponential
Lorenzian
At zero Hz
FT
FT
Lorenzian at 
Mx
Absorption: Mx = Mo/[1 + ( - )2T22]
Dispersion signal: My = Mo(-)/[1 + ( - )2T22]
M
My

Pulsed NMR spectroscopy (only signal on X-Y plan is observable)
90o-pulse:
Iz
90x
Iy
 Sees a strong signal
90x
FT
Y
X
180o-pulse:
Iz
180x
-Iz
Y
X
 Sees no signal.
180x
FT
Y
Y
X
X
Pulsed NMR spectroscopy (only signal on X-Y plan is observable)
-90o-pulse:
Iz
90x
Iy
 Sees a strong negative signal
-90x (same as 270x)
FT
Y
X
-180o-pulse:
Iz
180x
-Iz
Y
X
 Sees no signal.
-180x
FT
Y
Y
X
X
Spin-echo pulse:
90o--180o--detection
1. Refocus chemical shift.
90x

180x
2. Decouple of heteronuclear J-coupleing

Detection
FT
(Dephasing)
(Excitation)
Y
90x

Y
X
Y
X
X
180x
(Inversion)
(Refocusing)
(Detection)

Y
X

Y
X
Pulse of finite length
Sinx/x
1. Long weak pulse:
Power
B1
0

t
FT

 Square waver  SINC function (sinx/x)
1/
 If  is very short then one will excite a broad spectral region.
 Long pulse excite only finite region of the spectrum.
2. Shape pulse:

SINC function (sinx/x)  Square wave
Power
 Gaussian  Gaussian

1/
Types of NMR
Experiments
Homo Nuclear: Detect proton.
Heteronuclear – Other nuclei, 13C,
Huge Water signal
(110 M compare to 1 mM
for normal protein sample)
Water suppression is an
important issue
Dynamic range problem.
1D one pulse 1H
Aromatic & Amide
15N, 31P
Aliphatic
etc.
3. 1-1 pulse:
0t
o

=

1/to
1/to


4. 1331 pulse: Similar to 11 pulse but more complicated
5. Gradient enhanced pulse sequence (Watergate):
1H
(/2)X
(/2)-X

GZ
Gradient causes
(/2)-Y
(/2)-Y

Receiver on
Homo Nuclear 2D NMR – Need two variable times
Basic 1D Experiment
Basic 2D Experiment
Homo Nuclear 2D NMR – Need two variable times
1. Needs two time variables t1 and t2 for chemical shift to evolve.
2. Needs to decide what interaction do you wish to observe ?
J-coupling – short and long range coupling.
Take place on x-y plane only.
NOE – Take place when magnetization is in Z-direction.
3. In heterouclear NMR one needs a way to transfer magnetization
between nuclei.
J-coupling (the larger the easier to transfer magnetization).
Need to adjust the time duration of the coupling (Maximum
when coupling time  = 1/2J. If J = 100 Hz,  = 5 ms)
 J-coupling
•Nuclei which are bonded to one another could cause an influence on each
other's effective magnetic field. This is called spin-spin coupling or J
coupling.
1
H
13
1
1
H
H
three-bond
C
one-bond
•Each spin now seems to has two energy ‘sub-levels’ depending on the state
of the spin it is coupled to:
J (Hz)
ab
I
S
bb
S
I
aa
ba
I
S
The magnitude of the separation is called coupling constant (J) and has
units of Hz.
J-coupling of backbone nuclei (Hz)
= 4 – 11 Hz depends
on secondary structure.
3J(HN-CA)
Cγ
35
H
140
χ2
Cβ
35
χ1
Cα
C’
ψ
15
11
N
Ψ
< 6 Hz  -helix
> 8 Hz  -stand
H
H
2J(13C 15N)

ω
N
55
C’
94
H
94
=9
O
15
11
Cα
Heteronuclear 2D NMR (HETCOR) –
(Need ways to couple different nuclei)
FT (t1)
Transpose (t2)
t 11
t21
t31
t41
FT (t2)
2
1
t1
2D-NMR Spectrum – stack plot
2D spectrum (Countour plot)
Determining Macromolecular Structures
(1)
Prepare
NMR samples
2H, 13C
and/or
Labeled
15N-
(2)
Obtain
NMR spectra ( 1D, 2D, 3D & 4D)
(5)
Structure
Calculation
and
refinement
(3)
Assign
NMR
resonances
(4)
Obtain
NMR restraints
distances,
dihedral angles
bond orientations
Determining Macromolecular Structures
(3)
Assign
NMR
resonances
1.
2.
3.
4.
5.
6.
Assign all resonances to a specific amino acid.
Assign to a specific nucleus.
Proton resonances are most important for structure determination.
Homonuclear 2D NMR for small proteins (< 10kDa).
Heteronuclar NMR are required for larger proteins (> 10 kDa)
Deuteration is needed for protein > 30 kDa.
Homonuclear NMR – small protein
1000 protons to assign.
1D clear is unable to do the job.
Determination of the Structure of RC-RNase
1. A pyridine-Guanine specific Ribonuclease found only in the oocyte of
bullfrog (Rana catesbeiana).
2. It is also a lectin with cytotoxic and antitumor activity.
3. A single chain poplypeptide with 111 amino acids and four disulfide
bonds.
4. The structure of RC-RNase has not been determined.
Reference:
1. Chen et al., 1996, J. Biomol. NMR 8 331-344.
2. Chang et al., 1998, J. Mol. Biol. 283 231-244.
Assignment of Protein NMR Resonances
1. Spin system (amino acid) identification:
-
-
Rely on J-coupling (2-D COSY & TOCSY)
COSY: Cross peaks observed for Nearest neighbors only (e.g. NH
to Hα only)
TOCSY: All coupled spins are potentially observable (e.g. NH to
Hα, Hβ, Hγ…etc).
Chemical shifts of the observed COSY and TOCSY cross peaks.
2. Sequential resonance assignment:
-
Assign resonances to a specific amino acid (e.g. Gly-10 etc).
NOESY (NH- Hα, Hβ etc).
Heteronuclear 3-D NMR expts. (15N-13Cα, CO).
(Nuclear Overhauser Effect SpectroscopY)
 Through space dipolar effect
 Determine NOE
 Measuring distance
 Assign resonances
(COrrelated SpectroscopY)
Through bond J-coupling
 Assign adjacent resonances
(Multiple Quantum Filtered COrrelated SpectroscopY)
Through bond J-coupling similar to COSY
 Assign adjacent resonances
 More sensitive
(Homonuclear HAtman-HAhn spectroscopY)
(TOtal Correlated SpectroscopY) (TOC SY)
Through bond relayed J-coupling
 Assign full spin system (residues type)
COSY: (MQF-COSY; DQF-COSY)
1. Off-diagonal resonances due to 1JNHC one bond J-coupling.
2. Assign adjacent resonances.
3. One can select a magnetization transfer pathway (efficiency) by
varying the evolution time.
TOCSY: ( HOHAHA)
1. Off-diagonal resonances due to relayed J-coupling.
2. Magnetization transfer thru Hartmann-Hahn cross polarization.
3. Assign long range correlated resonances (Whole a.a. system).
NOESY:
1. Off-diagonal resonances due to NOE.
2. Magnetization transfer thru energy transfer due to thru space
dipolar effect.
I  R-6  Determine distances.
3. Sequential resonance assignments.
RC-RNase
DQF-COSY (Fingerprint region)
1. NH-Hα only (Intra residue)
同一胺基酸
2. Splitting  3JHNα
TOCSY (Spin System Identification) RC-RNase
1. J-Coupling: HN→Hα→Hβ…….2. Identify Spin System(a.a. type)
δ1/ppm
1H
– 1H NOESY of RC-RNase
Nuclear Overhauser Effect (NOE)
RF
r
I
S
XNOE = 1 + (d2/4)(H/ N)[6J(H + N) – J(H - N)] T1
where
d = (ohN  H/82)(rNH-3),
XNOE  r-6
1.
Larger proteins(> 10 kDa)
1. Need to label the protein with 13C and
15N,
and may be 2H.
2. Need to do heteronuclear multidiemnsional NMR (3D or 4D)
3. Heteronculear has larger chemical shift dispersion, thus
better resolution. (13C ~ 200 ppm; 15N ~ 300 ppm)
4. Energy transfer between heteronuclei by J-coupling.
J-coupling of backbone nuclei (Hz)
= 4 – 11 Hz depends
on secondary structure.
3J(HN-CA)
Cγ
35
H
140
χ2
Cβ
35
χ1
Cα
C’
ψ
15
11
N
Ψ
< 6 Hz  -helix
> 8 Hz  -stand
H
H
2J(13C 15N)

ω
N
55
C’
94
H
94
=9
O
15
11
Cα
1H
Chemical Shift
13C
Chemical Shift
Advantages of heteronuclear NMR:
1.
2.
3.
4.
5.
Large chemical shift dispersion  Increased resolution.
Large coupling constant (Easy to transfer magnetization.
Thru bond connectivity  Easy assignments.
Permit easier analysis of protein dynamics.
Permit determining the structure of larger proteins (> 100 kDa).
Disadvantages of heteronuclear NMR:
1. Must label the protein with 13C and/or 15N.
a). Expensive.
b). Time consuming.
2. Technically much more complicated.
3. More demanding on spectrometers.
4. Much larger data size.
二維核磁共振基本原理(HETCOR)
Homonuclear: 同核 (1H);
Heteronuclear: 異核 (1H,
13C, 15N
etc)
2D 15N-1H Heteronuclear Single Quantum Correlation Spectroscopy)
(15N-HSQC)
90x 180
x
1H


90x
180x
180x 90x
90x

180x
t2
180x
t1
15N
Magnetization
transfer
from 1H to 15N
Decoupling
15N
chemical shift
evolution
1H
Magnetization
transfer
from 15N to 1H
Efficientcy  sin(2J)
Maximum transfer when 2J = /2.
or

= 1/4J = 1/4x94 = 2.5 ms
detection
Amide Proton Resonance Assignments of Thioesterase I
3D NOESY-HSQC
90x
1H
90x
t1
90x 180
x
NOE


90x
180x
90x

180x 90x
15N
Dec
NOESY
180x
t3
180x
t2
15N-HSQC
Decoupling
J-coupling of backbone nuclei (Hz)
= 4 – 11 Hz depends
on secondary structure.
3J(HN-CA)
Cγ
35
H
140
χ2
Cβ
35
χ1
Cα
C’
ψ
15
11
N
Ψ
< 6 Hz  -helix
> 8 Hz  -stand
H
H
2J(13C 15N)

ω
N
55
C’
94
H
94
=9
O
15
11
Cα
3D HNCA
90x 180
x
1H


90x 180
x
90x 180 90x
x
180x 90x

180x
13C

90x
13CO

t3
Decoupling
90x
t2

180x
180x
180x
t1
15N
90x
Decoupling
Decoupling
Detect: 1HN,
15N
and
13C

 = 1/4JN-CA = 1/4x10 = 25 ms for optimal detection
= 1/4JH-N = 1/4x94 = 2.5 ms
Heteronuclear multidimensional
NMR experiments for
resonance assignments
Magnetization transfer pathway:
1H

15N

13C

15N
 1H  1H Detection
 Detect 1H, 13C, 15N resonances
Permit sequential correlation of
backbone 1H-13C-15N resonances !!!
9Hz
11Hz
N
C
CO
N
C
CO
1. In HNCA experiment the stronger cross peak belongs to its own CA
and the weaker one belongs to precedent amino acid.
2. Combine HNCA with HN(CO)CA one can assign the CA resonances
unambiguously.
3. Use several sets of thru-bond 3D experiment one can assign all
Backbone resonances.
4. Side chain resonances: HCCH-TOCSY, TOCSY-HSQC or NOESY-HSQC.
Side-Chain assignments
Resonance Assignments
I. Homonuclear:
1. Use 2D NMR (COSY, TOCSY, NOESY) to assign spin system (a.a. type).
2. Use NOESY to do sequential assignments.
II. Heteronuclear:
1. Use backbone correlated heteronuclear 3D NMR to do sequential
resonance assignments of all heteronuclei. (Need seveal sets)
2. Use HCCH-TOCSY, TOCSY-HSQC or NOESY-HSQC to assign side
chain resonances.
III. New developments:
Chemical shift information may be crucial for easy resonance assignents.
Chemical shift table
Possible term paper topics –I
Instruction:
1. Paper submission and topic selection approval all by e. mail to bmthh@ibms.sinica.edu.tw
2. Send me a title of the term paper from the list below or your choice for approval by April 15.
3. Team paper due date: May 15, 2003.
4. Format: Use Microsoft word file format (or other text format).
5. Content:
I. Introduction: Describe the biological background and the problems to be solved.
II. NMR techniques employed: Describe succinctly what type of NMR techniques are applied
and give some description of the NMR techniques.
III. Results.
IV. Discussion.
Some possible topics:
1. Strategies in assigning protein NMR resonances with examples.
Ref. Lin, T. H., C. P. Chen, et al. (1998). " Multinuclear NMR resonance assignments and the secondary structure of
Escherichia coli thioesterase/protease I: A member of a new subclass of lipolytic enzymes. J. Biomol. NMR, 11,
363-380." J. Biomol. NMR 11: 363-380.
2. Strategies in protein structure determination by NMR with examples.
Ref. Chang, C.-F., H.-T. Chou, et al. (2002). "Solution Structure and Dynamics of the
Lipoic Acid-bearing Domain of Human Mitochondrial Branched-chain alpha -Keto Acid
Dehydrogenase Complex." J. Biol. Chem. 277(18): 15865-15873.
3. NMR and protein dynamics.
Ref. Huang, Y. T., Y. C. Liaw, et al. (2001). "Backbone dynamics of Escherichia coli thioesterase/protease I:
Evidence of a flexible active-site environment for a serine protease." J. Mol. Biol. 307: 1075-1090.
4. Applications of NMR in studying protein folding.
Ref. Fersht, A. R. and V. Daggett (2002). "Protein folding and unfolding at atomic resolution." Cell 108(4): 573582.
Possible term paper topics - continue
5. Applications of NMR in drug discovery.
Ref. Peng, J. W., C. A. Lepre, et al. (2001). "Nuclear Magnetic Resonance-based Approaches for lead generation in
drug discovery." Method. Enzymology 338: 202-230.
6. Applications of NMR in enzyme catalysis.
Ref. Xiao, B., C. Jing, et al. (2003). "Structure and catalytic mechanism of the human histone methyltransferase
SET7/9." Nature 421(6923): 652-656.
7. Strategies in determining the structures of DNA and RNA by NMR.
Ref. Allen, M., L. Varani, et al. (2001). " Nuclear magnetic resonance methods to study structure and dynamics of
RNA-protein complexes." Method. Enzymology 339: 357-376.
8. Strategies in determining the structure of large proteins by NMR.
Ref. Fiaux, J., E. B. Bertelsen, et al. (2002). "NMR snalysis of a 900 kDa GroEl-GroES complex." Nature 418(11):
207-211.
Riek, R., J. Fiaux, et al. (2002). "Solution NMR Techniques for Large Molecular and Supramolecular Structures."
J. Am. Chem. Soc. 124(41): 12144-12153.
9. Use of residual dipolar coupling in NMR structure determination and refinement.
Ref. Prestegard, J. H. (2000). "NMR structure of biomolecules using field oriented media and residual dipolar
couplings." Q. Rev. Biophys. 33(4): 371-424.
10. NMR in structural genomics.
Ref. Yee, A., X. Chang, et al. (2002). "An NMR approach to structural proteomics." PNAS 99(4): 1825-1830.
11. NMR in determining membrane protein structure.
Ref. Fernandez, C., C. Hilty, et al. (2002). " Lipid-protein interactions in DHPC micelles containing the integral
membrane protein OmpX investigated by NMR spectroscopy." Proc. Natl . Acad. Sci. 99(21): 13533-13537.
Fernandez, C., C. Hilty, et al. (2001). "Solution NMR studies of the integral membrane proteins OmpX and
OmpA from Escherichia coli." FEBS Lett. 504(3): 173-178.
12. Functional MRI:
Ref. Ugurbil K, Toth L, Kim DS.Related Articles, Links How accurate is magnetic resonance imaging of brain
function? Trends Neurosci. 2003 Feb;26(2):108-14.