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 3- Pulse sequence and NMR experiments

液態樣品 取得ＮＭＲ圖譜 圖譜分析結構計算

( hours/days to weeks) ( weeks to months)( days to weeks)

Steps involved in determining protein structures by NMR

NMR II- Pulse sequence and NMR experiments

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.

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)

Bo= Bo - o/

X

Y

Z

Bo

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 Probe

Receiver Digitizer

Computero

o - o

Signal is in rotating frame (kHz)

106 – 109 Hz

Effect of RF-field:dMz(t)/dt = [Mx(t)Br

y(t) – My(t)Brx(t)] – [Mz(t) – Mo]/T1

dMx(t)/dt = - My(t) – Mz(t)Bry(t) – Mx(t)/T2 ----------- (11)

dMy(t)/dt = Mx(t) – Mz(t)Brx(t) – My(t)/T2

where Brx(t) = Br

ocos and Bry(t) = Br

osin

= -γΔBo - rf = o - rf is the offset.

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)Br

y(t) – My(t)Brx(t)

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) = Mosincos(t)exp(-t/T2) My(t) = Mosinsin(t)exp(-t/T2)

B1

Bo

Br

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)

For H1 along the x-axis and H1 0 and in steady statei.e. dM/dt = 0 we can solve the above simultaneous Equations to get:

Mx = o(oT2) -------- (3)

(Lorenzian lineshape, absorption)

My = o(oT2) -------- (4)

(Dispersion)

22

212

)(1

)(

T

HT

o

o

22

21

)(1 T

H

o

My

Mx

Fourier transformation (FT)

FT

FT

FT

Function at

exponential LorenzianAt zero Hz

Absorption: Mx = Mo/[1 + ( - )2T22]

Dispersion signal: My = Mo(-)/[1 + ( - )2T22]

Lorenzian at

MMx My

= 1/T2

Pulsed NMR spectroscopy (only signal on X-Y plan is observable)

90o-pulse: Iz Iy Sees a strong signal

180o-pulse: Iz -Iz Sees no signal.

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

90x

180x

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

180x

90x

FT

FT234 233 232 231 230 229 228 227 226 225 224 223

f1 ppm

X X

X X

Y Y

Y Y

Pulsed NMR spectroscopy (only signal on X-Y plan is observable)

-90o-pulse: Iz Iy Sees a strong negative signal

-180o-pulse: Iz -Iz Sees no signal.

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

90x

180x

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

-180x

-90x (same as 270x)

FT

FT234 233 232 231 230 229 228 227 226 225 224 223

f1 ppm

Y Y

Y Y

X X

X X

Spin-echo pulse: 90o--180o--detection1. Refocus chemical shift. 2. Decouple of heteronuclear J-coupleing

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

90x

FT234 233 232 231 230 229 228 227 226 225 224 223

f1 ppm

Y

X

180x

00.100.200.300.400.500.600.700.800.901.00t1sec

Detection

90x

180x

(Inversion)

XX

Y Y

Y

X

Y

X

(Dephasing)

(Refocusing)

(Excitation)

00.100.200.300.400.500.600.700.800.901.00t1sec

(Detection)

Pulse of finite length

1. Long weak pulse:

Square waver SINC function (sinx/x) 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

Gaussian Gaussian

tB1

0

1/

FT

Power

Sinx/x

1/

Power

1D one pulse 1H

Aliphatic Aromatic & Amide

Types of NMR

Experiments

Homo Nuclear: Detect proton.

Heteronuclear – Other nuclei, 13C, 15N, 31P etc.

Huge Water signal(110 M compare to 1 mM for normal protein sample)

Water suppression is an important issueDynamic range problem.

3. 1-1 pulse: = 0

to

1/to

1/to

4. 1331 pulse: Similar to 11 pulse but more complicated

5. Gradient enhanced pulse sequence (Watergate):

Receiver on(/2)-X

(/2)X

(/2)-Y (/2)-Y

GZ

1H

Gradient causes

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.

13C

1H 1H 1H

one-bondthree-bond

•Each spin now seems to has two energy ‘sub-levels’ depending on the state of the spin it is coupled to:

The magnitude of the separation is called coupling constant (J) and has units of Hz.

aa

ab ba

bb

I SS

S

I

IJ (Hz)

ψ Ψ

Cα

Cβ

Cγ

ωN

χ1

χ2

C’

N

H

H

H H

O

C’

Cα

94

1115

2J(13C15N) = 9

35

55

140

35

15

94

11

J-coupling of backbone nuclei (Hz)3J(HN-CA) = 4 – 11 Hz depends on secondary structure.

< 6 Hz -helix > 8 Hz -stand

Heteronuclear 2D NMR (HETCOR) – (Need ways to couple different

nuclei)

t1

t11

t21

t31

t41

FT (t2)

FT (t1) Transpose (t2)

2

1

2D-NMR Spectrum – stack plot

2D spectrum (Countour plot)

Determining Macromolecular Structures

(1)Prepare

NMR samples2H, 13C and/or 15N-

Labeled

(3)Assign NMR

resonances

(2)Obtain

NMR spectra -( 1D, 2D, 3D & 4D)

(4)Obtain

NMR restraintsdistances,

dihedral angles bond orientations

(5)Structure

Calculation and

refinement

Determining Macromolecular Structures

(3)Assign NMR

resonances

1. Assign all resonances to a specific amino acid.2. Assign to a specific nucleus.3. Proton resonances are most important for structure determination.4. Homonuclear 2D NMR for small proteins (< 10kDa).5. Heteronuclar NMR are required for larger proteins (> 10 kDa)6. 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).

(COrrelated SpectroscopY)Through bond J-coupling Assign adjacent resonances

(Nuclear Overhauser Effect SpectroscopY) Through space dipolar effect Determine NOE Measuring distance Assign resonances

(TOtal Correlated SpectroscopY) (TOC SY)

Through bond relayed J-coupling Assign full spin system (residues type)

(Homonuclear HAtman-HAhn spectroscopY)

(Multiple Quantum Filtered COrrelated SpectroscopY)Through bond J-coupling similar to COSY Assign adjacent resonances More sensitive

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-RNaseDQF-COSY (Fingerprint region)

1. NH-Hα only (Intra residue)

同一胺基酸

2. Splitting 3JHNα

δ1/ppm

TOCSY (Spin System Identification) RC-RNase

1. J-Coupling: HN→Hα→Hβ…….2. Identify Spin System(a.a. type)

1H – 1H NOESY of RC-RNase

r

RF

Nuclear Overhauser Effect (NOE)

XNOE = 1 + (d2/4)(H/ N)[6J(H + N) – J(H - N)] T1

where d = (ohN H/82)(rNH-3),

XNOE r-6

I S

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.

ψ Ψ

Cα

Cβ

Cγ

ωN

χ1

χ2

C’

N

H

H

H H

O

C’

Cα

94

1115

2J(13C15N) = 9

35

55

140

35

15

94

11

J-coupling of backbone nuclei (Hz)3J(HN-CA) = 4 – 11 Hz depends on secondary structure.

< 6 Hz -helix > 8 Hz -stand

1H Chemical Shift

13C

Chem

ical Sh

ift

15 N Shi

ft

Advantages of heteronuclear NMR:

1. Large chemical shift dispersion Increased resolution.2. Large coupling constant (Easy to transfer magnetization.3. Thru bond connectivity Easy assignments.4. Permit easier analysis of protein dynamics.5. 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)

Decoupling

1H

15N t1

t2

2D 15N-1H Heteronuclear Single Quantum Correlation Spectroscopy) (15N-HSQC)

Efficientcy sin(2J)Maximum transfer when 2J = /2. or = 1/4J = 1/4x94 = 2.5 ms

Magnetization transfer from 1H to 15N

15N chemical shift evolution

Magnetization transfer from 15N to 1H

1H detection

90x 90x 90x180x 180x 180x

180x180x 90x

Amide Proton Resonance Assignments of Thioesterase I

Decoupling

1H

15N t2

t3

3D NOESY-HSQC

NOESY 15N-HSQC

90x 90x 90x180x 180x 180x

180x180x 90x

NOE

90x90x

Dec

t1

ψ Ψ

Cα

Cβ

Cγ

ωN

χ1

χ2

C’

N

H

H

H H

O

C’

Cα

94

1115

2J(13C15N) = 9

35

55

140

35

15

94

11

J-coupling of backbone nuclei (Hz)3J(HN-CA) = 4 – 11 Hz depends on secondary structure.

< 6 Hz -helix > 8 Hz -stand

Decoupling

1H

15N t1

t3

3D HNCA

90x 90x 90x180x 180x 180x

180x180x 90x

Decoupling13Ct2

180x 90x

90x 180x

180x

13CO Decoupling

90x

90x

= 1/4JN-CA = 1/4x10 = 25 ms for optimal detection= 1/4JH-N = 1/4x94 = 2.5 ms

Detect: 1HN, 15N and 13C

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 !!!

N NC CCO CO11Hz

9Hz

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 –IInstruction: 1. Paper submission and topic selection approval all by e. mail to bmthh@ibms.sinica.edu.tw2. 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 Esc

herichia 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 o

f 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): 573- 582.

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): 207-21

1. Riek, R., J. Fiaux, et al. (2002). "Solution NMR Techniques for Large Molecular and Supramolecular Structures." J. A

m. 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 couplin

gs." 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.