1. NMR II- 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) ;
E. mail:
Web site:
Reference:
Cavanagh, J. et al., “Protein NMR Spectroscopy-Principles and Practice”,
Academic Press, 1996.

2. NMR II- Pulse sequence and NMR experiments
Steps involved in determining protein structures by NMR
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3. NMR Spectroscopy Bo Radio Wave hn Larmor Equation:
Biol. important nuclei: 1H, 2D, 13C, 15N, 19F, 31P
Radio Wave hn
Classical view Bo
Quantum mechanical view
Energy
Larmor Equation:
n =  Bo/ 2 n = Larmor frequency;
= nuclear gyric ratio
Bo = magnetic field strength (Telsla)
E = hn
Bo= 0 Bo

4. Ho Ho Basic Nuclear Spin Interactions Electrons Phonons Nuclear Spin j6
Electrons 3 3
Nuclear Spin j Ho Ho
Nuclear Spin i 1 2 1 5 4 4
Phonons 4
Dominant interactions: H = HZ + HD + HS + HQ . HZ = Zeeman Interaction HD = Dipolar Interactions HS = Chemical Shielding Interaction HQ = Quadrupolar Interaction

5. Dominant interactions: HZ = Zeeman Interaction : I with magnetic field. Path 1 ( BO ~ 109) HD = Dipolar Interactions: I with adjacent spins Path 2,3. ( ISR-3 ~103-5) HS = Chemical Shielding Interaction.: Nuclear spin with magnetic field but shielded by electrons. Path 6and (Dep. Nature of the bond ~ 1-105) HQ = Quadrupolar Interaction: Nuclear spins with surrounding electric field gradient. Path 3. (For I > ½ nuclei; ) Total Interactions: H = HZ + HD + HS + HQ (All second order tensors)
In solid the resonance frequency is orientation dependent and the spectrum will be very complex. There is often too much information to digest.
In solution, many of the interactions average out to zero or scalar quantities (non-orientational independent). These remaining interactions contain rich structure-dynamic information. The trick is how to separate them and how to detect them.

6. In solid the resonance frequency is
orientation dependent and the
spectrum will be very complex
In solution, many of the interaction vanish
But many more become orientational independent.

7. NMR Parameters employed for determining protein structure
1. Chemical Shift Indices: Determining secondary structure J-coupling: Determine dihedral angles (Karplus equation) Nuclear Overhauser Effect (NOE): Determine inter-atomic distances (NOE  R-6) Residual dipolar coupling: Determine bond orientations Relaxation rates (T1, T2 etc): Determine macromolecular dynamics. 1H R 1H BO 1H 
15N I t

8.  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)
time

9. Fourier transformation (FT)

10. In addition, most molecules examined by NMR have several sets of nuclei, each with a different precession frequency.
Time (sec)
The FID (free induction decay) is then Fourier transform to frequency domain to obtain each vpression ( chemical shift) for different nuclei.
frequency (Hz)

12. 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.
90x
90x FT Y Y X X
180x
180x FT Y Y X X

13. 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.
90x
-90x (same as 270x) FT Y Y X X
180x
-180x FT Y Y X X

14. Water suppression is an important issue Dynamic range problem.
Types of NMR
Experiments
Homo Nuclear: Detect proton.
Heteronuclear – Other nuclei, 13C, 15N, 31P etc.
Water suppression is an important issue
Dynamic range problem.
Huge Water signal
(110 M compare to 1 mM for normal protein sample)
1D one pulse 1H
Aromatic & Amide
Aliphatic

15. How to suppress water signal ?
Sinx/x
Presaturation:
1. Long weak pulse:
Square waver  SINC function (sinx/x)
If  is very short then one will excite a broad spectral region.
SINC function (sinx/x)  Square wave
2. Shape pulse:
Gaussian  Gaussian
Power B1 FT  t 
1/
Power 
1/

16. 4. 1331 pulse: Similar to 11 pulse but more complicated=   to
1/to
1/to  
pulse: Similar to 11 pulse but more complicated
5. Gradient enhanced pulse sequence:
(/2)X
(/2)-X
(/2)-Y
(/2)-Y 1H  
Receiver on GZ
Gradient causes

17. Homo/Hetero Nuclear 2D NMR
Basic 1D Experiment
Basic 2D Experiment

18. 二維核磁共振基本原理(HETCOR)

19. (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)

20. 2D-NMR Spectrum

21. aa ab ba bb I S S I  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 3 C H
one-bond
three-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 S S I
J (Hz)

22. Cγ χ2 H Cβ H H χ1 Cα C’ N ω Ψ ψ C’ Cα N O H
J-coupling of backbone nuclei (Hz)
3J(HN-CA) = 4 – 11 Hz depends
on secondary structure.
< 6 Hz  -helix
> 8 Hz  -stand Cγ 35 χ2 H
140 Cβ H H χ1 35 94
2J(13C15N) = 9 Cα C’ N 55 11 15 11 ω Ψ 15 ψ C’ Cα N 94 O H

23. COSY: (MQF-COSY; DQF-COSY)
Off-diagonal resonances due to 1JNHC one bond J-coupling.
Assign adjacent resonances.
One can select a magnetization transfer pathway (efficiency) by
varying the evolution time.
TOCSY: ( HOHAHA)
Off-diagonal resonances due to relayed J-coupling.
Magnetization transfer thru Hartmann-Hahn cross polarization.
Assign long range correlated resonances (Whole a.a. system).
NOESY:
Off-diagonal resonances due to NOE.
Magnetization transfer thru energy transfer due to thru space
dipolar effect.
I  R  Determine distances.
3. Sequential resonance assignments.

24. RC-RNase
DQF-COSY (Fingerprint region)

25. TOCSY (Spin System Identification) RC-RNase
1. J-Coupling: HN→Hα→Hβ…….2. Identify Spin System(a.a. type)
δ1/ppm

27. 1H – 1H NOESY of RC-RNase

28. r XNOE  r-6 RF XNOE = 1 + (d2/4)(H/ N)[6J(H + N) – J(H - N)] T1
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

30. Cγ χ2 H Cβ H H χ1 Cα C’ N ω Ψ ψ C’ Cα N O H
J-coupling of backbone nuclei (Hz)
3J(HN-CA) = 4 – 11 Hz depends
on secondary structure.
< 6 Hz  -helix
> 8 Hz  -stand Cγ 35 χ2 H
140 Cβ H H χ1 35 94
2J(13C15N) = 9 Cα C’ N 55 11 15 11 ω Ψ 15 ψ C’ Cα N 94 O H

31. Homonuclear: 同核 (1H); Heteronuclear: 異核 (1H, 13C, 15N etc)
二維核磁共振基本原理(HETCOR)
Homonuclear: 同核 (1H); Heteronuclear: 異核 (1H, 13C, 15N etc)

32. Amide Proton Resonance Assignments of Thioesterase I

33. Advantages of heteronuclear NMR:
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:
Must label the protein with 13C and/or 15N.
a). Expensive.
b). Time consuming.
Technically much more complicated.
More demanding on spectrometers.
Much larger data size.

38. 13C Chemical Shift
15N Shift
1H Chemical Shift

42. 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 !!!

44. II. Dynamics
4-dimensional structure

45. NMR Relaxation

46. NMR Relaxation & Protein Dynamics
Under current magnetic field strength the relaxation rates are dominated by dipolar interaction and chemical shift anisotropic interaction, and is related to the correlation time, J(), by the following equations:
R1 =1/T1 = (d2/4)[J(H - N) + 3J(N) + 6J(H + N)] + c2J(N) (1)
R2 =1/T2 = (d2/8)[4J(0) + J(H - N) + 3J(N) + 6J(H) + 6J(H + N)]
+ (c2/6)[4J(0) + 3J(N)] + Rex (2)
where d = (ohN  H/82)(rNH-3), c = N(σ‖- σ)/3.
o : permeability constant of free space; h: Planck constant;
i : magnetogyric ratio of spin i; i: Larmor frequency of spin i;
rNH = 1.02 Å: length of the NH bond vector; Rex: exchange rate;
σ‖- σ = -170 ppm (size of the CSA tensor of the backbone amide nitrogen).

47. r RF XNOE = 1 + (d2/4)(H/ N)[6J(H + N) - J(H - N)]T1
Nuclear Overhauser Effect (NOE)
(Energy transfer through dipolar effect) 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),

48. Modelfree ananlysis
The spins are assumed to be attached to a rigid macromolecule undergoing Browian motion with a rotational correlation time m. In addition, the spins also undergo internal motion with rotational correlation time s. Under this assumption the spectral density function, J() is given by:
J() =
S2: Order parameters (Magnitude of motion)
 : Correlation times (Speed of motion)
R ex : Chemical exchange rate (Slow motion in ms or s regime)
Fitting T1, T2 and NOE data to determine S2,  and Rex
which contain the dynamics information of the protein

49. Dynamics of E. coli Thioesterase/protease I
1. Measured T1, T2 and (1H, 15N) NOE at 500 and 600 MHz at 310 K Total of 128 resonances were measured at 500 MHz and 134 resonances were determined at 600 MHz Average: R1 =  S-1 (  S-1), R2 =  1.40 S-1(  1.17 S-1) XNOE =  (  0.039) at T (11.74 T) From the above data one can determine: a). Rotational diffusion constant b). Order parameter, S2  Measure of the flexibility c). Determine rate of local motion d). Conformational exchange rates  At atomic resolution . . .

51. Relaxation Data
Obtained in two fields:
: 500 MHz
: 600 MHz

52. Order parameter – Flexibility
S2av= 0.85
S = 1 rigid
S = 0 random
Mostly rigid
Flexible region

53. Correlation time – Residues with fast internal motion

54. Exchange rate – Residues with low motion

55. Radius of the susage  1/S
Large radius  disordered region

56. Radius of the sausage  Rex
Large radius  Residues with slow motion

57. Thank You !
800 MHz