Download Multinuclear NMR Notes

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Multinuclear NMR Notes
4/1/2010
NOTE: We will be discussing a paper on sodium MR in cartilage from the MRI lab in
the final section of class. This reference is as follows.
Shapiro et. al. “Sodium Visibility and Quantation in Intact Bovine Articular Cartilage
Using High Field 23NA MRI and MRS”. Journal of Magnetic Resonance. 142, 24-31
(2000)
I. Properties of NMR-Active Nuclei
1H and 13C are the most commonly used nuclei in NMR, but almost all elements
have stable NMR-active nuclei. Not all nuclei, however, are equally easy to observe.
There are several factors that influence signal strength:
A) Isotopic abundance—if the abundance of an isotope is too low, it won’t give a signal.
You may need to isotopically enrich the sample.
B) Chemical shift range—if the chemical shift range is too large, that means that the
nucleus is very sensitive to its environment; relatively minor inhomogeneities in the
sample (such as a temperature gradient) can create significant line broadening. The
chemical shift range of 1H is about 10 ppm (low extreme), and that of Pb is about 20000
ppm (high extreme).
C) T2 length—since line width equals 1/(πT2), a short T2 will give a broad line width,
and may not be very useful.
D) Receptivity—also called sensitivity, the relative signal strength of a nucleus as
compared to 1H or 13C under the same conditions. Receptivity of nuclide X (RX) is given
by
RX = A∙|γ3|∙I(I+1)
Receptivity has a cubic dependence on γ because γ is proportional to |M0|, ΔE,
and ω0, as shown in the equations below.
1) M= γ∙P, where M is the total magnetization of the sample and P is the total spin
angular momentum.
2) ΔE=h γ B0, where h is Planck’s constant, B0 is the magnitude of the applied magnetic
field, and ΔE is the energy difference between spin states.
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3) ω0=-γ B0, where ω0 is the Larmor frequency.
Equations 1) and 2) above influence the magnitude of the magnetization that is detected,
and equation 3) is relevant because the induced current in the coil is proportional to the
rate of change of the magnetic moment, so a faster Larmor frequency gives a stronger
signal.
Below is a table containing relative receptivities. (DP is sensitivity relative to 1H, and DC
is sensitivity relative to 13C.) This table is from
http://www.stanford.edu/group/chem-NMR/chem235_lecture_notes/lecture_1.pdf
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E)
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Nuclear Electric Quadrupole Moment—a nuclear quadrupole broadens the line width.
Not all nuclei are spheres. Some have prolate or oblate shapes. Only non-spherical
nuclei have quadrupoles. The charge distribution of a nucleus can be described by a
superposition of electric multipoles. These multipoles have the same shapes as s, p, d,
etc. atomic orbitals. C(r) represents the charge distribution of the nucleus.
C(r)
=
C(0)(r)
+
(total charge)
C(1)(r)
(dipole)
+
C(2)(r)
(quadrupole)
Note:
• No nuclide has an electric dipole moment
• The spherical C(0)(r) term has no direct significance in NMR
• C(n)(r) = 0 for n > 2I
All spin-1/2 nuclei . . .
– behave exactly like point charges located at the nuclear center (as far as
electrical effects)
– have a spherical charge distribution
– have no nuclear electric dipole, quadrupole, etc.
– lack electric energy terms that depend on orientation
Nuclides with I>1/2 . . .
– are termed “quadrupolar”
– have non-spherical charge distribution
– have an electric energy that is dependent on orientation in an electric field
gradient
The degree of broadening due to the quadrupole moment can be measured by the
linewidth factor, l, according to
l=Q2(2I+3)
I2(2I-1)
A nuclide can assume 2I+1 different orientations in a magnetic field.
For quadrupolar interactions, the energy separation between states is given by
ΔE = 2πe2qQ(3cos2θ-1)/(h∙4), where e=elementary charge, q=electric field gradient,
Q=quadrupole moment, and θ=angle between q and B0.
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II) Discussion of several multi-quantum NMR experiments. This section offers a
quick overview of several 2d and 3d NMR experiments for determination of molecular
structure. For each experiment we will discuss the pulse sequences and resultant data.
Homonuclear (1H, multi-dimensional) and Heteronuclear (1H plus one or more additional
nuclei) experiments will be addressed. We emphasize solution protein NMR, but in
principle these techniques can be applied to other organic as molecules as well.
A) HSQC: Heteronuclear Single Quantum Coherence. This 2d experiment
measures coherence between protons and a single directly-bonded heteronucleus.
Typically, the amide nitrogen and hydrogen in the protein backbone will be
measured. This is sometimes referred to as a “protein fingerprint”. The results
allow one to estimate which residues as present, and can be used as a “sanity
check” to match a protein sequence obtained through biochemical methods. The
HSQC does not provide information on residue order or three-dimensional
structure.
B) COSY: Correlation Spectroscopy. Ravi covered this method in class on 3/30.
COSY is a 2-d homonuclear experiment to measure J-coupling between protons
separated by up to 3 bonds. The two dimensions (t1 and t2) of the resultant
spectrum refer to the “evolution time” between two pulses, and the “detection
time” after the second pulse. The experiment is carried out as a series of 1d FID
measurement, each with a slightly different and carefully controlled value for the
evolution time.
COSY can be used to estimate the phi angles between amide N and alpha C in the
protein backbone.
C) TOCSY: Totally Correlated Spectroscopy. This 2d homonuclear experiment
can be viewed as a “longer-range COSY.” It incorporates a spin-lock pulse to
extend coherence beyond 3 bonds. This is useful in molecules containing carbon
rings such as sugars.
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D) NOESY: Nuclear Overhauser Effect Spectroscopy. Another 2-d homonuclear
experiment. This adds a third pulse to the COSY pulse sequence, allowing
nuclear spins to cohere through space rather than through bonds. The throughspace coupling falls off with the 6th power of distance and generally extends to
about 5 nm. NOESY is useful on examining 3d structure, as it allows one to
observe protons that are spatially close but perhaps widely separated in sequence.
Such information provides insight into protein tertiary structure.
E) NOESY – HSQC: A 3d experiment combining both thru-space proton coupling
and heteronuclear J-coupling. Similar 3d experiments can by devised by
combining other 2d homonuclear and 2d heteronuclear methods to obtain a 3d
spectrum.
F) Triple Resonance Experiments. A variety of experiments can be carried out to
examine coherence between 1H, 13C, and 15N nuclei. Using 3 frequencies rather
than 2 makes the spectrum simpler to interpret by reducing “overlap” in the data.
The nomenclature for these experiments describes the pattern of spin coherence
that they measure. Consider the example CBCA(CO)NH. Spin is transferred as
follows:
C on side-chain  C in backbone  carboxyl C  amide N (across
peptide bond)  amide H.
II)
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Na Imaging in Cartilage
Shapiro et. al. “Sodium Visibility and Quantation in Intact Bovine Articular Cartilage
Using High Field 23NA MRI and MRS”. Journal of Magnetic Resonance. 142, 24-31
(2000)
This study examines a novel imaging technique based on sodium magnetic resonance. It
is not a multi-quantum technique per se, but it does illustrate an interesting application
taking advantage of the properties of a “different” nucleus.
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Osteoarthritis is a disease characterized by the degradation of cartilage, specifically loss
of proteoglycan (PG) in the extracellular matrix. PG contains a large number of negative
charges which are balanced though electrostatic interactions with intercellular sodium.
Osmotic forces then lead water to “follow” the Na+ into the tissue. This study
demonstrates an MRI method to provide a map of sodium concentration in tissue. A
decline in sodium density may correlate to proteoglycan loss, a precursor to osteoarthritis.
A major question is the “visibility” of sodium in cartilage – for a given concentration of
sodium, what is the intensity of the MR signal in tissue vs. simple solution? Association
with biomolecules may enhance T2 decay, decreasing visibility. For other tissues,
sodium visibility has been shown to be significantly less than 100%
•
•
•
Muscle: ~40%
Cartilage: ~100% (but method was questionable)
Some others: ~40-90%
Sodium NMR was run on solid cartilage plugs. The plugs were then liquefied in acid and
the experiment repeated. The results implied the same sodium quantities in each,
illustrating that sodium visibility does not decrease in cartilage vs. solution.
Phantoms were constructed consisting of agarose (to simulate proteoglycan) and saline.
These were used to calibrate MRI to obtain sodium concentration at various location in
bovine patellae, as shown below: