The Basis for Biological NMR

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The Basis for Biological NMR
Equilibrium is disrupted by a second radiofrequenc
y wave B1. When the frequency of B1 is at
the Larmor frequency of the spins, can achieve
resonant conditions.
The applied wave B1 and the net magnetization
vector Mo will interact and the system will
absorb energy. The net magnetization vector is
now along the xy plane (call it Mxy).
After the populations have been affected, the B1
wave is turned off. The net magnetization
vector Mxy will return to the z-axis.
However, it will precess as it goes back to the
equilibrium position.
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Spin-Spin Coupling (J Coupling)
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Spin-Lattice Coupling (Nuclear Overhauser Effect)
Two nuclear spins within about 5 Å will interact
with each other through space. This
interaction is called cross-relaxation, and it
gives rise to the nuclear Overhauser effect
(NOE). Two spins have 4 energy levels, and the
transitions along the edges correspond to
transitions of one or the other spin alone.
W2 and W0 are the cross-relaxation pathways,
which depend on the tumbling of the molecule.
Nuclear spins can also cross-relax through
dipole-dipole interactions and other mechanisms.
This cross relaxation causes changes in one spin
through perturbations of the other
spin. Intensity of the NOE is proportional to
r-6 (r is distance between 2 spins).
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Spin-Lattice Coupling (Nuclear Overhauser Effect)
When two nuclear spins are within 5 Å, they will
cross-relax. If one spin (S) is saturated (red
lines along the edge), the system is not in
equilibrium anymore. Magnetization will
either flow from the top to the bottom (W2
active) or from the right to left (W0 active).
The difference in energy between bb and aa is
twice the spectrometer frequency, and molecular
motions about that frequency are required for
the transition. The difference between ab and
ba is very small, and very slow molecular
motions (e.g. proteins) will excite that
transition.
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The Pulse FT NMR Experiment
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Typical 1H Spectrum of a Protein

Each 1H resonates at a well defined chemical
shift. This 76 residue protein has a
well-defined structure.
Regions where Protons from Amino Acid Side Chains
Resonate
ppm
downfield, less shielding
upfield, more shielding
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2D Nuclear Magnetic Resonance
In order to resolve spectral overlaps, a second
dimension can be added to the basic 1D NMR
experiment. Shown below is a spectrum which
correlates 1H bound directly to the amide 15N in
the protein backbone (and some side chains).
15N-1H HSQC
-15N - Ca- CO -15N - Ca
H
H
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2D Nuclear Magnetic Resonance
The Spin-Echo Sequence
In the spin-echo pulse sequence, a 90o pulse is
first applied to the spin system.
The 90o degree pulse rotates the magnetization
down into the X'Y' plane. The transverse
magnetization begins to dephase.
At some point in time after the 90o pulse, a
180o pulse is applied. This pulse rotates the
magnetization by 180o about the X' axis.
The 180o pulse causes the magnetization to at
least partially rephase and to produce a signal
called an echo.
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2D Nuclear Magnetic Resonance
When a molecule with J coupling (spin-spin
coupling) is subjected to a spin-echo sequence,
something unique but predictable occurs.
Molecule A2-C-C-B where A and B are spin-1/2
nuclei experiencing resonance.
The NMR spectrum from a 90-FID sequence looks
like this
With a spin-echo sequence this same molecule
gives a rather peculiar spectrum.
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2D Nuclear Magnetic Resonance
To understand what is happening, consider the
magnetization vectors from the A nuclei. There
are two absorptions lines in the spectrum from
the A nuclei, one at ?J/2 and one at ? -J/2.
At equilibrium, the magnetization vectors from
the ? J/2 and ?-J/2 lines in the spectrum are
both along Z.
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2D Nuclear Magnetic Resonance
90 degree pulse
A 90 degree pulse rotates both magnetization
vectors to the XY plane.
Assuming a rotating frame of reference at ?o ?
, the vectors precess according to their Larmor
frequency and dephase due to T2.
Precession and dephasing
When the 180 degree pulse is applied, it rotates
the magnetization vectors by 180 degrees about
the X' axis.
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2D Nuclear Magnetic Resonance
Precession and dephasing
When the 180 degree pulse is applied, it rotates
the magnetization vectors by 180 degrees about
the X' axis.
In addition the ?J/2 and ? -J/2 magnetization
vectors change places because the 180 degree
pulse also flips the spin state of the B nucleus
which is causing the splitting of the A spectral
lines.
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2D Nuclear Magnetic Resonance
Spins states flip
Refocussing
The two groups of vectors will refocus as they
evolve at their own Larmor frequency. In this
example the precession in the XY plane has been
stopped when the vectors have refocussed. You
will notice that the two groups of vectors do
not refocus on the -Y axis. The phase of the
two vectors on refocussing varies as a function
of TE. This phase varies as a function of TE at
a rate equal to the size of the spin-spin
coupling frequency. Therefore, measuring this
rate of change of phase will give us the size of
the spin-spin coupling constant. This is the
basis of one type of two-dimensional (2-D) NMR
spectroscopy.
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2D Exchange NMR
t1
t2
FT in t1 will give 2D frequency spectrum
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The 2D NMR Pulse Sequence

1D 1D 2D
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Anatomy of a 2D NMR Experiment
In this example, the second 90 degree pulse acts
only on the Y component of magnetization in the
XY plane.
Look at the off resonance singlets (?o) for
different values of t1.
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Anatomy of a 2D NMR Experiment
The spectra are plotted on a stacked plot. Have
the frequency data along one axis (this is just
like the 1D case) and a time domain on the second
axis.
Since the variations of the amplitudes along the
time axis is also periodic, can build a
pseudo-FID if we look at the point at each
frequency along f2. If we plot the FID from the
frequency data (like in 1D NMR) with
the variations in the signal over time, we get a
2D plot. Get cross peaks in the 2D maps where the
two lines intercept.
For simplicity, look at
the plot from above and draw it as a contour plot.
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2D Nuclear Magnetic Resonance
The basic 2D experiment involves repeating a
multiple-pulse 1D sequence. The 1D
pulse-sequences are systematically varied over a
delay time tD and the resultant spectra is
plotted as stacks.
There are now two time domains, one that
originates during the acquisition as usual and
the second that comes from the delay time tD.
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2D NMR Coupling is the Key
Like all 2D sequences, t1 is the variable time to
collect frequency information in the indirect
dimension. The delay t is fixed and is the time
during which the NOE builds up.
2D detect signals twice (before/after coupling)
90º pulse
t1
t2
Transfers between coupled spins
Same as 1D experiment
t1
t2
Chemical exchange can also happen during this
time, and it is possible to confuse an NOE peak
with a chemical exchange peak, but techniques
have been developed to figure out which is which.
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2D Nuclear Magnetic Resonance
The J-resolved Experiment
In a 2-D J-resolved NMR experiment, time domain
data is recorded as a function of TE and time.
These two time dimensions will referred to as t1
and t2. For the A2-C-C-B molecule, the
complete time domain signals look like this.
This data is Fourier transformed first in the t2
direction to give an f2 dimension
and then in the t1 direction to give an f1
dimension.
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2D Nuclear Magnetic Resonance
The J-resolved Experiment
Displaying the data as shaded contours, we have
the following two-dimensional data set.
The f1 dimension gives us J coupling information
while the f2 dimension gives chemical shift
information. This type of experiment is called
homonuclear J-Resolved 2-D NMR.
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The 2D NMR Spectrum
Pulse Sequence
Spectrum
Before mixing
Coupled spins
After mixing
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The Power of 2D NMRResolving Overlapping Signals
1D
2 signals overlapped
2D
2 cross peaks resolved
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COrrelation SpectroscopY (COSY)
Two 90 degree pulses are applied in sequence.
The time t1 is the time between the first and
second pulse.
The signal will vary with the time between the
pulses (t1).
In a 2D COSY spectrum, cross-peaks will exist
where there is spin-spin coupling between nuclei.
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Case Study 2D NMR Spectrum of Ethanol
The 2-D hydrogen correlated chemical shift
spectrum of ethanol
There are cross peaks between the OH and CH2
hydrogens and the CH2 And CH3 hydrogens due to J
coupling. There are no cross peaks between The
CH3 and OH hydrogens.
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Some More Examples of 2D Spectra
(CH3)2CHOH
C6H5CH2CH3
CH3CH2CH2OH
Homonuclear
Heteronuclear
Scalar Coupling
COSY
HSQC
TOCSY
Hetero-TOCSY
HMQC
Dipolar Coupling
NOESY
NOESY-HSQC
NOESY-HMQC
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Through Space Correlation (NOESY)
Looking at J-coupled systems through COSY will
tell us about the chemical structure of the
system but does not tell much about
stereochemistry or Conformation.
Recall that if a nuclei in the system was
hit with a pulse so as to cause saturation, it
will relax by either zero- or double-quantum proce
sses and would enhance the signals from nuclei
that were close by. This was the NOE.
Relaxation could take place either through W2IS
or W0IS, depending on the size of the system (the
rate of tumbling).
The spins will stay aligned with the external
magnetic field Bo while the molecule tumbles in
solution.
This generates magnetic fields (fluctuating
dipoles) at the rate of tumbling. The fluctuating
dipoles allow the spins to release energy.
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Through Space Correlation (NOESY)
Need a way to analyze how the molecule move in
solution.
Define the correlation function as the average of
how the molecules are oriented at some time t and
a little while after that (t ?)
This function basically correlates the
orientation of the molecule at two different
times. This gives information about the rate of
tumbling. The correlation function is in the
time domain. This function can be Fourier
transformed into the frequency domain to give the
spectral density function. Here ?c is defined as
the tumbling rate.
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Through Space Correlation (NOESY)
Depending on how fast the molecule is tumbling
(as defined by ?c) the movement of the system
will be composed of frequencies faster, slower or
equal to the Larmor frequency.
Since the probability of a transition depends on
the different frequencies that the system has
(i.e. the spectral density), the W terms
are proportional to the spectral density
function. Since we need to have two magnetic
dipoles to get dipolar coupling, the NOE depends
on the strength of the two dipoles involved. The
strength of a dipole is proportional to r-3, thus
the NOE varies as r-6. The NOE decays very fast
as the two nuclei are pulled away from each
other. For protons, this is about 5-6 Å
separation.
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Steady State NOE
In order to estimate the distance between protons
in a molecule, can saturate one nuclei and look
at the relative enhancement of other
nuclei. Take two spectra, the first without any
irradiation and the second with. Subtracting the
two spectra will give the enhancements. This is
used to estimate distances.
In the case of a molecule with three protons, two
at fixed distances (CH2).
Since the two protons (Ha and Hb) on CH2 are
fixed, they are references. The NOE effect from
these two protons can be used a reference
to calculate the distance between the other
protons (Ha and Hc, Hb and Hc)
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Transient NOE
With steady state NOE, have to continuously
irradiate the system to achieve saturation. This
is fine for small molecules but with
larger molecules, get spin diffusion
The energy that is transferred from nuclei I to
nuclei S is then transferred to other
nuclei. This will give signal enhancement even
for nuclei far away from the center of
irradiation.
For larger molecules, the amount of time that the
spins are saturated must be limited (otherwise
get spin diffusion). Also, working on one proton
at a time for larger molecules would be
time consuming. Have to do a 2D experiment where
all proton are studied.
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NOE Spectroscopy
The first two pulses are an inversion for
all protons. We label everything with chemical
shifts and couplings.
The magnetization component that ends up in the
-Z axis evolves during the mixing time tm and
dipolar coupled spins will undergo NOE. The 2D
spectrum will have chemical shifts in f1 and
f2. The cross peaks are for nuclei that are
dipolar coupled.
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NOE Spectroscopy
The cross peaks are for nuclei that are dipolar
coupled. The size of the cross peaks will depend
on the distance between the (through-space)
coupled nuclei. These distances are measured
relative to a standard for which the distance is
already known.
COSY gives information on through-bond coupling
(chemical structure). NOESY gives information
on through-space coupling (stereochemistry and
configuration).
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Interpretation of 2D NMR Spectra
Crosspeaks are a measure of some type of
interaction between 2 spins (NOE,
J-coupling....) The intensity of the crosspeak
often quantifies the interaction. A
heteronuclear experiment (1H-15N) would not have
diagonal crosspeaks.
1H ppm
1H ppm
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Assignment of Resonance
A homonuclear TOCSY experiment (Total
Correlation Spectroscopy) Crosspeaks occur
between 1H that are within a network of
J-coupled spins (in practice within a residue)
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NOESY for Sequential Assignments
1H J-couplings are Too Small to Detect
Interactions across Peptide Bond One advantage
of heteronuclear experiments is the large
coupling constants -- can use hetero TOCSY and
COSY like experiments to get across the peptide
bond (see cbcannh and cbca(co)nnh experiments
later.
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1H-based Resonance Assignments
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Steps in Structure Determination Using NMR
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Total Correlation Spectroscopy (TOCSY)
TOCSY (Total Correlation Spectroscopy) is capable
of correlating all spins in a coupled
network. The working end of the TOCSY pulse
sequence is an isotropic mixing sequence that is
a sequence of pulses that are designed to remove
all chemical shift differences and create a
strong coupling environment. This is called the
Hartmann-Hahn condition. Sometimes the TOCSY
experiment is called HOHAHA (Homonuclear
Hartmann-Hahn). The strong coupling product
operator is similar to the regular (weak)
coupling operator but it includes IxSx and IySy
terms. The net result of the TOCSY mixing
sequence is the transfer of magnetization from I
to S along the same axis (e.g. Iz to Sz or Ix to
Sx or Iy to Sy). The transfer depends on the
coupling constant but is fairly complicated
because S can transfer to another spin, R, and so
on.
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Total Correlation Spectroscopy (TOCSY)
Like the 1D COSY, the 2D TOCSY experiment relies
on scalar or J couplings.
The idea behind the TOCSY experiment is the
connection of all spins that can be linked up by
J-couplings. Remember that J coupling
between nuclei that are more than 3 bond lengths
away is very weak.
If we look at the amino acids in a protein, we
notice that within an amino acid there usually
always three covalent bonds between two protons
giving rise to a 3J proton proton coupling and
thus sufficient to be used in a TOCSY experiment.
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Spin Systems
Any set of protons in a chain of unbroken
J-coupling interactions will give rise to sets of
TOCSY cross peaks. For example, each of the 3
sets of peaks shown above will be correlated in a
2D TOCSY spectrum.
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Total Correlation Spectroscopy (TOCSY)
Groups of nuclei linked by J-couplings are
usually referred to as spin systems. Individual
amino acids therefore appear as a single or in
some cases several spin systems. The amino
acid aspartic acid contains an amide proton, ?
proton and two b protons. All of these four
protons are linked by 3J or 2J couplings and
thus form a spin system.

• There is no effective coupling between the amide
  proton and the b protons
• because they are four bonds apart. But as both b
  and amide protons have
• 3J couplings with the ? protons they are all part
  of one spin system.
• In phenylalanine, there are 2 spin systems. The
  first comprising the amide,
• and two ? protons. The second is made up of the
  aromatic ring protons,
• H?, H ? and H ?. The two spin systems of
  phenylalanine are not coupled.

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Total Correlation Spectroscopy (TOCSY)
TOCSY Between the Hb protons and the Hd protons
of phenylalanine are four covalent bonds.
J-coupling over 4 covalent bonds is extremely
weak and practically non-existent.
Along the backbone we have a similar situation.
As there are only two protons in the backbone
portion we would have to cover at least four
bonds to move from residue to residue along the
backbone.
The number  of protons that can be linked up in
a 2D TOCSY spectrum is therefore limited to all
those protons within an amino acid.
For some amino acids, e.g. phenylalanine, there
is a further lack of connection within the amino
acid. Such amino acids contain two or more spin
systems.
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Total Correlation Spectroscopy (TOCSY)
The TOCSY spectra of Asp and Phe are shown
below. These patterns are characteristic for
each amino acid. As they are neither affected
by the linkage of amino acids along the
backbone nor by the structure of the protein
they will always allow the identification of the
type of amino acid.