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.

NMR II- 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

BBoo

Radio Wave hRadio Wave h

Larmor Equation: = Bo/ 2 = Larmor frequency; = nuclear gyric ratioBo = magnetic field strength (Telsla)

NMR SpectroscopyNMR Spectroscopy Biol. important nuclei: 1H, 2D, 13C, 15N, 19F, 31P

Energ

y

Bo= 0 Bo

E = h

Classical view

Quantum mechanical view

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

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.

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 3. (Dep. Nature of the bond ~ 1-105) HQ = Quadrupolar Interaction: Nuclear spins with surrounding electric field gradient. Path 3. (For I > ½ nuclei; 103 -107)

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 complexIn solution, many of the interaction vanishBut many more become orientational independent.

1. Chemical Shift Indices: 1. Chemical Shift Indices: Determining secondary structure.Determining secondary structure.

2. J-coupling: 2. J-coupling: Determine dihedral angles.Determine dihedral angles. (Karplus equation)(Karplus equation)

..

3. Nuclear Overhauser Effect (NOE): 3. Nuclear Overhauser Effect (NOE): Determine inter-atomic distances (NOE Determine inter-atomic distances (NOE R R-6-6)) ..

4. Residual dipolar coupling: 4. Residual dipolar coupling: Determine bond orientations.Determine bond orientations.

..

5. Relaxation rates (T 5. Relaxation rates (T11, T, T2 2 etc):etc): Determine macromolecular dynamics.Determine macromolecular dynamics.

NMR Parameters employed for determining protein structureNMR Parameters employed for determining protein structure

R 1H1H

15N

1H

BO

I

t

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)

Fourier transformation (FT)

FT

FT

•In addition, most molecules examined by NMR have several sets of nuclei, each with a different precession frequency.

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

234 233 232 231 230 229 228 227 226 225 224 223f1 ppm

•The FID (free induction decay) is then Fourier transform to frequency domain to obtain each vpression ( chemical shift) for different nuclei.

Time (sec)

frequency (Hz)

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

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.

How to suppress water signal ?

1. 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

tB1

0

1/

FT

Power

Sinx/x

1/

Power

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:

Receiver on(/2)-X

(/2)X

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

GZ

1H

Gradient causes

Homo/Hetero Nuclear 2D NMR

Basic 1D Experiment

Basic 2D Experiment

二維核磁共振基本原理 (HETCOR)

(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

2D-NMR Spectrum

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

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

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

二維核磁共振基本原理 (HETCOR)

Homonuclear: 同核 (1H); Heteronuclear: 異核 (1H, 13C, 15N etc)

Amide Proton Resonance Assignments of Thioesterase I

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.

1H Chemical Shift

13C

Chem

ical Sh

ift

15 N Shi

ft

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 !!!

II. DynamicsII. Dynamics4-dimensional structure4-dimensional structure

NMR RelaxationNMR Relaxation

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 = (ohN H/82)(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).

NMR Relaxation & Protein DynamicsNMR 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:

r

RF

Nuclear Overhauser Effect (NOE)(Energy transfer through dipolar effect)

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

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

I S

Modelfree ananlysisModelfree ananlysis

J() = ]2)'(1

')22(

2)'(1

')21(

2)(1

2[

52

s

sSfS

f

ffS

m

mS

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:

S2: Order parameters (Magnitude of motion)

R ex : Chemical exchange rate (Slow motion in ms or s regime)

: Correlation times (Speed of motion)

Fitting T1, T2 and NOE data to determine S2, and Rex which contain the dynamics information of the protein

1. Measured T1, T2 and (1H, 15N) NOE at 500 and 600 MHz at 310 K. 2. Total of 128 resonances were measured at 500 MHz and 134 resonances were determined at 600 MHz.. 3. Average:

R1 = 1.108 0.056 S-1 (1.506 0.096 S-1), R2 = 10.31 1.40 S-1(9.236 1.17 S-1) XNOE = 0.742 0.044 (0.705 0.039) at 14.09 T (11.74 T).

4. From the above data one can determine:. From the above data one can determine: a). Rotational diffusion constant. a). Rotational diffusion constant. b). Order parameter, S b). Order parameter, S2 2 Measure of the flexibility Measure of the flexibility.. c). Determine rate of local motion. c). Determine rate of local motion. d). Conformational exchange rates. d). Conformational exchange rates...

At atomic resolution At atomic resolution...

Dynamics of E. coli Thioesterase/protease I

Relaxation Data

Obtained in two fields:

: 500 MHz

: 600 MHz

Order parameter – Flexibility

S2av= 0.85

S = 1 rigid S = 0 random Mostly rigid

Flexible region

Correlation time – Residues with fast internal motion

Exchange rate – Residues with low motion

Radius of the susage 1/SLarge radius disordered region

Radius of the sausage Rex

Large radius Residues with slow motion

800 MHz

Thank You !