Biochemistry 530 NMR Theory and...
Transcript of Biochemistry 530 NMR Theory and...
Biochemistry 530
NMR Theory and Practice
Gabriele Varani
Department of Biochemistry
and
Department of Chemistry
University of Washington
Lecturer: Gabriele Varani
Biochemistry and Chemistry
Room J479 and Bagley 63
Phone: 543 7113
Email: [email protected]
Office Hours by arrangement
Lecture 1: Basic Principles of NMR
Lecture 2: 2D NMR
Lecture 3: NMR assignments/structure determination
Lecture 4: 2D and 3D heteronuclear NMR
Recommended NMR Textbooks
Derome, A. E. (1987)
Modern NMR Techniques for Chemistry Research, Pergamon Press
Wüthrich, K. (1986)
NMR of Proteins and Nucleic Acids , John Wiley and Sons
Roberts, G. C. K. (1993)
NMR of Macromolecules: A Practical Approach, Oxford Univ. Press
Cavanagh, J., et al. (1996)
Protein NMR Spectroscopy, Principles and Practice, Academic Press
Evans, J. N. S. (1999)
Biomolecular NMR Spectroscopy, Oxford Univ. Press
Useful websites
http://www.ch.ic.ac.uk/local/organic/nmr.html
NMR Spectroscopy. Principles and Application.
Six second year lectures given at Imperial College, U.K.
http://uic.unl.edu/nmr_theory.html
http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/nmr1.ht
m
Theoretical principles of NMR
Courtesy of Sheffield Hallam University, U.K.
http://www.nature.com/nsb/wilma/v4n10.875828203.html
links to various NMR and structural biology web sites
simulation and analysis software; NMR research groups, etc.
http://www.ch.ic.ac.uk/local/organic/nmr.html
NMR Spectroscopy. Principles and Application.
Six second year lectures given at Imperial College, U.K.
http://uic.unl.edu/nmr_theory.html
http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/n
mr1.htm
Theoretical principles of NMR
Courtesy of Sheffield Hallam University, U.K.
http://www.nature.com/nsb/wilma/v4n10.875828203.html
links to various NMR and structural biology web sites
simulation and analysis software; NMR research groups,
etc.
NMR spectrum of a protein: hundreds of
individual resonances resolved
1D spectrum
amides Ha Side chain CH2
Side chain CH3
NH2
Fourier-transform NMR (Ernst, 1965)
Signal - FID
(time domain)
Spectrum
(frequency domain)
2D NMR spectrum of a protein
2D projection
representation
2D contour
representation
RRM1 RRM2
ω2(1HMethyl) [ppm]
1(1
3C
Met
hyl )
[p
pm
]
13C methyl HMQC on selectively labeled protein
ω2(1HMethyl) [ppm]
1(1
3C
Met
hyl )
[p
pm
]
RRM1 RRM2
13C methyl HMQC on protein-RNA complex
ω2(1HMethyl) [ppm]
1(1
3C
Met
hyl )
[p
pm
]
Rna14
RRM1 RRM2 Rna15
L205d2
L274d1
V300g2
V247g2
V297g2
V185g2
I313d1 I228d1
I222d1
V217g1
V175g2
13C methyl HMQC on 300 kDa complex
Rna15
Hrp1
RNA
Rna14
180
Define and identify protein interaction sites in
large complexes
50100150200250
50
100
150
200
250
162
156
158
160
164 14 13 12 11
U68
U16,U70
U17
U71
U82
U28
U68
U16,U70
U17
U82
U40
U71
U41
U22
U77
U34
U25
U74
U49
U47
U39
U31
Standard (10 min)
50100150200250
50
100
150
200
250
162
156
158
160
164
14 13 12 11
Ultrafast NMR (2-3s)
Ultrafast acquisition of NMR spectra
Bound riboswitch
1212.212.412.612.81313.213.413.6
144
145
146
147
148
149
150
151
13 12
150
144
146
148
t = 0 sec
G81 G59
G43 G44
G57
G14
G78 G72
Conformation changes in real time
1212.212.412.612.81313.213.413.6
144
145
146
147
148
149
150
151t = 16 sec
G14
G78
G57
G81
G59
G43
G44
Conformation changes in real time
1212.212.412.612.81313.213.413.6
144
145
146
147
148
149
150
151t = 28 sec
G14
G78
G44
G57
G43
G38,G59
G32
G81
G37
G46
Conformation changes in real time
1212.212.412.612.81313.213.413.6
144
145
146
147
148
149
150
151
t = 58 sec
G14
G78
G43
G44 G57
G38,G59
G37
G32
G81
Conformation changes in real time
The Spectrometer: 1. A powerful magnet
AD
C
PRE-AMPRECEIVER DETECTOR
TRANSMITTER
CONTINUOUS REFERENCE
BINARY NUMBERS TO COMPUTERS
= 500 MHz = 500,000,000 Hz
499,995,000 < o < 500,005,000 Hz
sample
PROBE
Magnet
+-
+-5,000 Hzo- =
The Spectrometer: 2 A Radio station
• The transmitter generates short (<0.1 ms) RF pulses to the probe
• RF pulses stimulate nuclear spin transitions in the sample
• The emitted signal is measured by the receiver and digitized
• RF signals arising from the sample are all in the region of
500 MHz, differing only by the chemical shift range present
AD
C
PRE-AMPRECEIVER DETECTOR
TRANSMITTER
CONTINUOUS REFERENCE
BINARY NUMBERS TO COMPUTERS
= 500 MHz = 500,000,000 Hz
499,995,000 < o < 500,005,000 Hz
sample
PROBE
Magnet
+-
+-5,000 Hzo- =
For protons this is typically 10
ppm or 5000 Hz at 500 Mhz
If we subtract some reference
frequency ( = 500 MHz)
from the signal, we only digitize
the chemical shifts (o-)
(audiofrequencies)
Spectrometer performance: sensitivity and
stability
AD
C
PRE-AMPRECEIVER DETECTOR
TRANSMITTER
CONTINUOUS REFERENCE
BINARY NUMBERS TO COMPUTERS
= 500 MHz = 500,000,000 Hz
499,995,000 < o < 500,005,000 Hz
sample
PROBE
Magnet
+-
+-5,000 Hzo- =
• The probe is in many ways
the ‘heart’ of the spectrometer:
it determines s/n (e.g.
cryoprobes)
• Magnet homogeneity and
long term stability determine
resolution (1 part in 109)
• Stability of RF
amplifier/signal pre-
amplifier/frequency generation
units determine artifacts (1
part in 109)
Spectrometer performance: Magnetic field
strength provides increased resolution
500 Mhz (1 peak?)
750 Mhz (2 peaks?)
800 Mhz (2 peaks!)
The chemical shift scale
The frequency of absorption of the NMR signal depends on the
external field as we have seen
n0 = g B0/2p
Let us now introduce a quantity that describes the fact that
different nuclei in the sample experience slightly different
magnetic fields because of chemical structure and
conformation
n = (1-s) g B0
Finally, let us introduce a scale that is field-independent, so that we
can compare directly data recorded on different spectrometers:
d=(n-no)/n0x106
We use a standard sample (e.g. DSS) to reference all of our
spectra, so that we can report the resonance frequency for our
proton in a universal, field-independent manner
The NMR Signal and Spectrum
Signal - FID
(time domain)
Spectrum
(frequency domain)
The NMR Signal and Spectrum
• The emission signals are oscillatory and physically damped
(damped harmonic oscillations)
• This signal is called the Free Induction Decay or FID
• The actual spectrum is recovered from the FID via Fourier
transformation, which transforms the time interferogram into a
frequency spectrum
• Without FT NMR, it would take the square of the time to obtain an
equivalent signal/noise ration
Example: FID and a 1D spectrum
1D
spectrum
FID
Fourier Transform
Origin of the NMR signal
Nuclear subatomic particles have spin
1. If the number of neutrons and protons are both even
the nucleus has 0 spin
i.e. 12C (6 neutrons + 6 protons = 12) has I = Ø spin
2. If the number of neutrons plus protons is odd
the nucleus has a half-integer spin (1/2, 3/2, 5/2)
i.e. 13C (7 neutrons + 6 protons = 13) has I = 1/2 spin
3. If the number of neutrons and protons are both odd
then the nucleus has an integer spin (1, 2, 3)
i.e. 14N (7 neutrons + 7 protons = 14) has I = 1 spin; spin 1
nuclei are quadrupolar (relax fast)
For high resolution applications, we use spin ½ nuclei (1H, 13C, 15N, 31P in biology);
Nuclear spins and the energy levels in a magnetic
field
• A nucleus of spin I has 2I + 1 possible orientations
(a nucleus with spin 1/2 has 2 possible orientations)
• Each level is given a magnetic quantum number m
• The energy levels for a 1H nucleus are referred to as:
a (m = +1/2) and b (m = -1/2)
In the absence of an external magnetic field, these orientations have
equal energy; if a magnetic field is applied, energy levels are split
The a state is the energetically preferred orientation
(magnetic moment parallel with the applied magnetic field)
The b state has higher energy
(magnetic moment anti-parallel to the applied magnetic field)
Nuclear spins and the energy levels in a magnetic
field
The energy of a particular level is given by:
E = g h m Bo
where: g is the the gyromagnetic ratio, a nuclear property
(a measure of the polarizability of the nucleus)
h is Planck's constant divided by 2p (h = h/2p )
Bo is the strength of the magnetic field
The difference in energy between levels (the transition energy)
DE = g h Bo
If the magnetic field is increased, so is DE
(as DE increases, so does sensitivity)
NMR properties of nuclei of common use in
biology
Isotope Spin Abundance Magnetogyric ratio NMR frequency
(I) g/107 rad T-1s-1 MHz (2.3 T magnet)
1H 1/2 99.985 % 26.7519 100.000000 2H 1 0.015 4.1066 15.351 13C 1/2 1.108 6.7283 25.145 14N 1 99.63 1.9338 7.228 15N 1/2 0.37 -2.712 10.136783 17O 5/2 0.037 -3.6279 13.561 19F 1/2 100 25.181 94.094003 23Na 3/2 100 7.08013 26.466 31P 1/2 100 10.841 40.480737 113Cd 1/2 12.26 -5.9550 22.193173
Nuclear precession in a magnetic field: semi-
classical description
y
Bo
x
z The nucleus has a positive charge
and spins
This generates a small magnetic
field
The nucleus possesses a magnetic
moment m proportional to its spin I
• In a magnetic field, the axis of rotation will precess about
the magnetic field Bo
• The frequency of precession (o Larmor frequency)
is identical to the transition frequency (o = -gBo)
• The precession may be clockwise or anticlockwise
depending on the sign of the gyromagnetic ratio (+g or -g)
Origin of a macroscopic (observable) NMR signal
Out of a large collection of
moments, a surplus have
their z component aligned
with the applied field, so
the sample becomes
magnetized in the direction
of the main field Bo
• The parallel orientation is of lower energy than the antiparallel
• At equilibrium, spins will be distributed according to Boltzmann
distribution between the two energy states
• A net magnetization parallel to the applied magnetic field arises
because of the small population difference between states
z
Bo
y
x
Mo
Sensitivity of NMR experiment
Nuclei populate energy levels according to Boltzmann distribution
n1/n2 = exp (-DE/kT)
If we irradiate the system on resonance (DE=hn), the probability of
signal absorption will be proportional to the population
difference:
n2-n1
If DE>>kT (e.g. optical spectroscopy) then all dipoles are in the
ground state
If DE<kT (NMR), then the net absorption of energy will be small
because n2=n1 and stimulated emission/absorption are equally
probable
The only thing you can do is increase the magnetic field,
because
DE = g h Bo
S/N in NMR is poor because energy levels are so
close
According to Boltzmann’ distribution:
kTEEe
n
n /)(
2
1 21
If the system is exposed to a frequency: h
EEv 12
then the energy absorbed is proportional to the difference
(as is the case for optical spectroscopy), then essentially
all the molecules will be in their ground state configuration
if kTE D 12 nn
S/N in NMR is poor because energy levels are so
close
kTEEe
n
n /)(
2
1 21
(as is the case for NMR spectroscopy), then the net
absorption of energy will be very small because the rate of
upward transitions is equal to the rate of downward
transitions
For this reason, we use magnets of increasing strength to
separate energy level more and increase the sensitivity of
the experiment
If instead kTE D21 nn