Todays Lecture

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Todays Lecture

• 3) Mon, Oct 6 Introduction to NMR Parameters
• Review of Bloch equations
• Chemical shiftBMRB database
• c. J couplingKarplus equation
• d. T1
• e. T2

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Bloch Equations
In the Bloch equations, magnetic fields along the
x and y axes create B1 fields or pulses. These
are typically applied for short durations, and
the length of time the pulse is turned on is
adjusted to give a desired rotation (such as 90
or 180 degrees).
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RF Pulses
In our simulation of the Bloch equations, we
showed that for protons (g2p26.7107 Hz/T) and
a B1 field of 9.310-5 T, it takes 40ms to rotate
the magnetization one time around the x or y
axis. The relationship between rf field
strength and pulse length is simply
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What range of frequencies can be covered with a
given rf pulse?
This says that a 40 ms 3600 pulse will create an
effective field strength (gB1/2p) of 25000 Hz.
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What range of frequencies can be covered with a
given rf pulse?
Since a wide range of frequencies can be covered
by a pulse, do they all behave the same? NO
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A 90 degree pulse followed by turning on the
detector leads to a Free Induction Decay (FID)
13C NMR FID of Methyl a-D-Arabinofuranoside in
CD3CN. Collected at 11.7 T by Jim Rocca in AMRIS.
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Expansion of previous FID
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Fourier Transform of previous FID
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Expansion of big peaks
The width of this peak is about 10 Hz. This is
R2 (or 1/T2). The indicates that it is the
natural linewidth experimental sources of
inhomogeneities. This comes from the rapidly
relaxing part of the FID.
The value for the J coupling is the inverse of
the spacing between beats on the FID!
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Hz vs ppm
PROBLEM A given molecule has different values
of w0 for different magnetic fields. How can we
compare results at different field strengths?
ANSWER Normalize the results to make them
independent of magnetic field. The value of a
chemical shift in Hz (referenced to some standard
value) is divided by the base spectrometer
frequency (in MHz). The units of this conversion
are Hz/MHz or parts per million. Because w0 gB0
is linear, 1H data at 500 MHz (26.7107/(2p) Hz/T
11.72 T) has the same ppm value at any other
field strength.
For example, two chemical shifts separated by 1
ppm on a 600 MHz magnet have 600 Hz between them.
The same two shifts at 500 MHz are still 1 ppm
apart but are only separated by 500 Hz.
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Chemical Shifts
Chemical shifts are influenced by the electronic
environment. Therefore, they are diagnostic for
particular types of molecular structures. The
following figure indicates average ranges of
chemical shifts for different types of molecules.
Table from http//www.cem.msu.edu/reusch/OrgPag
e/nmr.htm
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Chemical Shifts
Chemical shifts are particularly important in
biomolecular NMR, because many they have been
shown to be sensitive to secondary structure in
proteins. They have a wealth of tertiary
structural information also, but we currently do
not have a theory that is refined enough to
interpret very small (but significant) changes.
One of the best resources for chemical shifts and
other parameters in protein NMR is the BioMagRes
data Bank (BMRB) at University of
Wisconsin http//www.bmrb.wisc.edu/
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Chemical Shift Index (CSI)
The CSI was developed by researchers who were
working with the BMRB database. They noticed
that several chemical shifts in peptides had
different values when they were in an a-helix or
b-sheet. The CSI is computed for each type of
amino acid, because each amino acid has a
different base chemical environment. For
example, an 1Ha in alanine is different from an
1Ha in glycine. Here is a partial table that
allows for the determination of the CSI.
Complete details and additional references can be
found in the reference below.
These are average chemical shifts (in ppm) in
different secondary structures relative to random
coil values of certain nuclei in amino acids.
Wishart and Sykes Chemical shifts as a tool for
structure determination Methods in Enzymology
239, pp 363-392 (1994).
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J coupling and chemical shift example
All of the splittings are J couplings
1H NMR 1D spectra of Methyl a-D-Arabinofuranoside
in CD3CN. Collected at 11.7 T by Jim Rocca in
AMRIS.
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J coupling
Decouple 4.05 ppm
Decouple 4.93 ppm
Normal spectrum
J coupling allows you to identify atoms within 3
(sometimes more) covalent chemical bonds. This
will be even more powerful when we get to 2D NMR
experiments.
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Why are J coupling values different?
Martin Karplus showed that J from vicinal coupled
1H atoms depends on the dihedral angle between
the protons. This relationship can be
approximated by the famous Karplus equation
A, B, and C are empirically derived parameters.
J couplings provide an estimation of molecular
conformation!
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T1 and T2
T1 is the time constant for magnetization to
relax along the z-axis. R11/T1 is the rate
constant for the same phenomena. T2 and R2 are
the corresponding constants for relaxation in the
x-y plane. Why are they important?
We have seen that chemical shifts (d) are
influenced by the electronic environment of the
molecule. Because of w0gB0, it is clear that
the magnetic field must be different for
different chemical shifts. The electronic
environments create these different magnetic
fields. When molecules move, either as a rigid
rotor or from internal motions, these same
electronic environments can also act like rf
pulses with one big difference rf pulses are
coherent and molecular motions are
incoherent. The difference is important and is
essentially the difference between a group
effort where everything happens together and in
a controlled manner (coherent) vs. individuals
doing their own thing randomly and whenever
they want (incoherent). The incoherent motions
cause transitions between states which lead to
relaxation.
Quantitative details on T1 and T2 will be given
in a later lecture.
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Homework for Friday
In a 1H NMR experiment, the carrier frequency is
typically placed in the center of the spectrum.
(This coincidentally corresponds pretty closely
to water in aqueous samples.) For a particular
NMR experiment at 11.7T (500 MHz), the carrier
frequency was placed at 4.8 ppm and a 90 degree
pulse length was found to be 8 ms. Calculate the
following a) What is the rf field strength
(gB1/2?) on resonance? b) What is the effective
field strength at 1.2 ppm? c) Relative to the
axis of the applied B1 field, what is the angle
of the axis of rotation for the resonance at 1.2
ppm? d) Repeat a, b, and c for a 90 degree pulse
length of 60 ms on the same magnet. e) Repeat a,
b, and c for a 90 degree pulse length of 60 ms on
a 14.1 T (600 MHz) magnet. Is the answer the
same as d?