experimental molecular biophysics tigp cbmb lou-sing kan, ph. d. institute of chemistry, academia...
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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