Experimental Molecular Biophysics

TIGP CBMB

Lou-sing Kan, Ph. D.

Institute of Chemistry, Academia Sinica

March 16, 2006

NMR(I)- NMR theory and experiments

The original of nuclear magnetic resonance

Nuclear spin

The Resonance Phenomenon

Magnetization

E = hBo/2 where h is Planck's constant (6.63 x 10-27 erg sec)

E = h

o = Bo/2 Larmor equation

o = 2o is the angular Larmor resonance frequency

The gyromagnetic ratio is a constant for any particular type of nucleus and is directly proportional to the strength of the tiny nuclear magnet.

Natural Gyromagnetic Sensitivity† Electric

Nucleus Spin Quantum Abundance Ratio (% vs. 1H) Quadrupole

Number (I) (%) (10-7rad/Tsec) Moment (Q)

(e·1024cm2)

1H 1/2 99.9844 26.7520 100.0

2H 1 0.0156 4.1067 0.965 0.00277

13C 1/2 1.108 6.7265 1.59

15N 1/2 0.365 -2.7108 0.104

19F 1/2 100 25.167 83.3

31P 1/2 100 10.829 6.63

Nupper/Nlower eE/ kT eh/ kT

k is the Boltzmann constant, and T is the absolute temperature (°K).

Boltzmann constant = 1.3806503 × 10-23 m2 kg s-2 K-1

9 8 7 6 5 4 3 2 1 ppm

O

HO

N

N N

N

OH

NH2

H H

OH

Chemical Shift

5mg Adenosine in DMSO, 0.035 M

= C10H13N4O4

= (/2)Blocal = (/2)(1-)

= ( - REF) x106 / REF

9 8 7 6 5 4 3 2 1 ppm

O

HO

N

N N

N

OH

NH2

H H

OH

O

HO

N

N N

N

OH

NH2

H H

OH

Protons Chemical shift (ppm)

H8 8.34

H2 8.13

NH2 7.33

H1’ 5.89

2’-OH 5.42

5’-OH 5.40

3’-OH 5.16

H2’ 4.60

H3’ 4.13

H4’ 3.95

H5’ 3.66

H5” 3.54

HDO 3.25

DMSO 2.49

Impurities 1.23

Spin-Spin Coupling (Splitting)

Observation: A nucleus with a magnetic moment may interact with other nuclear spins resulting in mutual splitting of the NMR signal from each nucleus into multiplets.

The number of components into which a signal is split is 2nI+1, where I is the spin quantum number and n is the number of other nuclei interacting with the nucleus.

For proton, I = 1/2

Neighbor group has one proton

Neighbor group has two protons

Neighbor group has three protons

Two neighbor groups have one proton each

9 8 7 6 5 4 3 2 1 ppm

35203540 Hz 27602780 Hz 24802500 Hz 3.95 ppm 22002220 Hz 21202140 Hz

3230324032503260 Hz 30903095310031053110 Hz O

HO

N

N N

N

OH

NH2

H H

OH

Assignment

35203540 Hz 27602780 Hz 24802500 Hz 3.95 ppm 22002220 Hz 21202140 Hz

35203540 Hz 27602780 Hz 24802500 Hz 3.95 ppm 22002220 Hz 21202140 Hz

10Hz

Karplus equation for determining dihedral angleCoupling consts. J, Hz

H1’-H2’ 5.9

H2’-H3’ 5.5

H3’-H4’ 3.0

H4’-H5’ 4.1

H4’-H5” 3.5

H5’-H5” 12.3

H2’-C2’-OH 6.6

H3’-C3’-OH 4.7

H5’-C5’-OH 7.2

H5”-C5’-OH 4.4

decoupled

7.907.958.008.058.108.158.208.258.308.358.408.458.50 ppm

7.907.958.008.058.108.158.208.258.308.358.408.458.50 ppm

7.907.958.008.058.108.158.208.258.308.358.408.458.50 ppm

Proton couples with other nuclei

O

HO

N

N N

N

OH

NH2

H H

OH

Peak intensity

9 8 7 6 5 4 3 2 1 ppm

0.582

2.479

0.981

1.003

1.029

1.010

1.000

1.035

2.087

1.075

2.096

1.049

1.065

O

HO

N

N N

N

OH

NH2

H H

OH

Summary

RelaxationRelaxation processes, which neither emit nor absorb radiation, permit the nuclear spin system to redistribute the population of nuclear spins. Some of these processes lead to the nonequilibrium spin distribution (Nlower – Nupper) exponentially approaching the equilibrium distribution.

(Nlower – Nupper) = (Nlower – Nupper)equil (1 – e-/T1)

Where the time constant for the exponential relaxation is T1, the spin-lattice relaxation time.

=3s

=2s

=0.5s

=0.25s

=0.005s

45678 ppm Inverse-recovery

dMz/dt = -(Mo-Mz)/T1 Mo-Mz

t = Aexp(-/T1) Mz = -MoMo

(Mo-Mt)/2Mo = exp(-/T1)a.u.

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 sec

-0.8

-0.6

-0.4

-0.2

0.8

0.6

0.4

0.2

0.0

ln[(Mo-Mt)/2Mo] = -/T1

Plot ln[(Mo-Mt)/2Mo] against , T1 equals to the minus reciproc

al of slope.

H Peak(ppm) T1(s)

8 8.362 2.0272 8.151 4.511

NH2 7.374 0.427

1' 5.89 1.8352'-OH 5.468 1.2815'-OH 5.457 1.1843'-OH 5.218 1.349

2' 4.624 0.9163' 4.163 0.9354' 3.979 1.2185' 3.673 0.4745" 3.568 0.476

H2O 3.395 1.316

There are additional relaxation processes that adiabatically redistribute any absorbed energy among the many nuclei in a particular spin system without the spin system as a whole losing energy. Therefore, the lifetime for any particular nucleus in the higher energy state may be decreased, but the total number of nuclei in that state will be unchanged. This also occurs exponentially and has a time constant T2, the spin-spin relaxation time. Under some circumstances,the linewidth of an NMR signal at half-height, W1/2, can be related to T2 by W1/2 = 1/(T2)

Rate of proton exchange

Mxy = Mxyoexp(-/T2)

Spin-echo

Nuclear Overhauser enhancement (NOE)

When two nuclei are in sufficiently close spatial proximity, there may be an interaction between the two dipole moments. The interaction between a nuclear dipole moment and the magnetic field generated by another was already noted to provide a mechanism for relaxation. The nuclear dipole-dipole coupling thus leads to the NOE as well as T1 relaxation. If there is any mechanism other than from nuclear dipole-dipole interactions leading to relaxation, e.g., from an unpaired electron, the NOE will be diminished – perhaps annihilated.

Summary:

Parameters generated by NMR

Chemical shift

Coupling constant

Peak area

Spin-lattice relaxation

Spin-spin relaxation

Nuclear Overhauser enhancement

Experimental Methods

Pulse NMR

Fourier transform

Faster

Measure dilute solution or less materials

Measure relaxation times

Do 2D and multidimensional NMR

FID

The meanings of pulse angle

9 8 7 6 5 4 3 2 1 ppm

0.582

2.479

0.981

1.003

1.029

1.010

1.000

1.035

2.087

1.075

2.096

1.049

1.065

9 8 7 6 5 4 3 2 1 ppm

0.563

4.488

1.013

1.001

0.913

0.991

1.000

0.886

1.786

0.811

2.019

0.458

0.785

Right intensity

Wrong intensity

2D NMR

Experiments that irradiate the sample with two rediofrequency fields.For examples: chemical shifts and coupling constants.

ppm

3.63.84.04.24.44.64.85.05.25.45.65.8 ppm

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.030

0.025

0.020

0.015

0.010

0.005

0.000

O

HO

N

N N

N

OH

NH2

H H

OH

ppm

3.63.84.04.24.44.64.85.05.25.45.65.8 ppm

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.030

0.025

0.020

0.015

0.010

0.005

0.000

1’ 2’2’-OH 5’-OH 3’-OH

3’ 4’ 5’ 5’’

35203540 Hz 27602780 Hz 24802500 Hz 3.95 ppm 22002220 Hz 21202140 Hz

By 2D J-res

2D COSY (correlation spectroscopy)

ppm

3.63.84.04.24.44.64.85.05.25.45.65.86.0 ppm

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

6.0

6.2

O

HO

N

N N

N

OH

NH2

H H

OH

O

HO

N

N N

N

OH

NH2

H H

OH

The frequent used 2D pulse programs.

Carbon-13 NMR

405060708090100110120130140150 ppm

405060708090100110120130140150 ppm

C2C8

C1’

C4’

C2’

C3’

C5’

C4C5

C6

DEPT (distortionless enhancement by polarization transfer)

405060708090100110120130140150 ppm

405060708090100110120130140150 ppm

2D HSQC (Heteronuclear single quantum coherence)

  ppm 1JCH , Hz

C2 152.9 200

C4 149.6

C5 119.9

C6 156.7

C8 140.4 211

C1’ 88.4 166

C2’ 74.0 148

C3’ 71.2 148

C4’ 86.4 148

C5’ 71.2 141

The chemical shifts and one bond C-H coupling

constant of adenosine.The chemical shift range of

selected function groups.

Conclusion:

(Homework: Please write a conclusion of this course.)

References

Edwin D. BeckerHigh Resolution NMR, Theory and Chemical Applications, 3rd EditionAcademic Press, 2000.Ray FreemanMagnetic Resonance in Chemistry And MedicineOxford, 2003Joseph P. HornakThe Basic of NMRhttp://www.cis.rit.edu/htbooks/nmr/bnmr.htm

General

T.C. FarrarAn Introduction To Pulse NMR SpectroscopyFarragut Press, Chicago, 1987.H. Gunther"Modern pulse methods in high-resolution NMR spectroscopy."Angew. Chem.. Int. Ed. Engl.22:350-380 (1983)

Basic Pulse NMR

Ad BaxTwo-Dimensional Nuclear Magnetic Resonance in LiquidDelft University Press, 1982Richard R. Ernst, Geoffrey Bodenhausen, Alexander WokaunPriciples of NMR in One and Two DimensionsOxford, 1987

2D NMR

Peter BiglerNMR Spectroscopy Processing StrategiesVCH, 1997

Data Process

H. Duddeck, W. DietrichStructure Elucidation by Modern NMR, A WorkbookSpringer-Verlag, 1989

Application: small molecules

Kurt WuthrichNMR of Proteins and Nucleic AcidsJohn Wiley & Sons, 1986

C. A. G. HaasnootNMR in Conformation Analysis of Bio-organic Molecules

Application: Peptides and Proteins

Application: Nucleic Acids

G. C. K. RobertsNMR of Macromolecules, A Practical ApproachIRL Press, 1995.

Application: Others

S. Braun, H.-O. Kalinowske, S. Berger100 and More Basic NMR ExperimentsVCH, 1996S. W. HomansA Dictionary of Concepts in NMROxford, 1992Handbook of High Resolution Multinuclear NMRJohn Wiley & Sons, 1981

Dictionary