1. Topics for today:
1) A few comments on using NMR to investigate internal motions
in biomolecules.
2) “MRI”, or Magnetic Resonance Imaging
(The last day to talk about NMR!)

2. 1) Using NMR to investigate internal motions in proteins, nucleic acids, etc.
NMR is perhaps the most powerful experimental method for obtaining information regarding motions in biomolecules.
(another method that was maybe mentioned earlier in the course is fluorescence anisotropy).

3. Proteins (and nucleic acids) in solution are not rigid structures.
They can be thought of as being in equilibrium between multiple conformations, where the population of each conformation is determined by its free energy.
The “native” or “folded” conformation refers to the most populated
(or most stable) one of these multiple conformations.
Protein motions include side chain motions, as well as transient global unfolding.

4. One way to gain information on protein dynamics is to investigate the rates at which amide (N-H) protons exchange with the solvent water.
This provides information about H-bond opening frequencies.
H2O H H
Amide (N-H) protons exchange rapidly with solvent when they are not in hydrogen bonds.
Protons bonded to carbon (C-H) do not exchange with protons in solvent.

5. N-H protons that are well protected from exchange with solvent can be identified in NMR spectra obtained after transfer of the protein to D2O solvent.
1H -15N 2-D spectrum obtained 14 minutes
after transfer of protein to D2O solvent.
NMR signals are from H that are protected from exchange with deuterium for > 14 minutes.

6. Amide (N-H) protons that exchange with the solvent H2O within 1 second can be detected by irradiating the sample at the NMR frequency of the solvent water, and measuring changes in the intensities of NMR signals from N-H protons.
1 sec pulse of RF at
NMR frequency of H2O
H2O H H
Intensity change in the NMR signal from N-H protons if they exchange with protons from water in < 1 sec.

7. Times for backbone N-H protons to exchange with solvent protons, measured by NMR:
Red: milliseconds
Yellow: seconds
Green: minutes
Blue: hours to days
Hydrogen bonds will protect N-H groups from exchange with solvent, so slow exchange indicates the presence of hydrogen bonds that open infrequently (located in relatively rigid parts of the protein).

8. Next - discuss NMR as an imaging method (MRI).
Several recent Nobel prizes are associated with NMR, including: Richard Ernst (1992) Multi-dimensional NMR, and Fourier transform NMR Kurt Wuthrich (2002) Determination of protein structure using NMR Paul Lauterbur, Peter Mansfield (2003) NMR imaging (a.k.a. MRI, or “magnetic resonance imaging”)

11. d
1010 Gauss
1007 Gauss
1004 Gauss
1000 Gauss

12. What does the 1H NMR spectrum of cube of water look like, in this
non-uniform magnetic field?

15. What does the 1H NMR spectrum of sphere of water look like, in a
non-uniform magnetic field?
How about the 1H NMR cube of of water with a cube-shaped empty cavity
at its center, in a non-uniform magnetic field?

16. In NMR imaging, 1H NMR spectra are obtained for a sample placed in
a non-uniform magnetic field.
The spectrum is interpreted, to answer the question:
What distribution of water in the sample would account for the observed NMR
spectrum?
In practice, a large number NMR spectra of the sample are obtained, with
different orientations of the magnetic field gradient.

17. Object being
imaged.
NMR spectrum

18. Introduce “contrast agents” for MRI (which can be used to enhance images).
To understand how contrast agents work, it is helpful to:
Review how NMR spectra are obtained;
and,
introduce “T1 relaxation time” and “T2 relaxation time”.

19. How NMR spectra are obtained:

20. What is recorded in an FT-NMR experiment:

21. M eventually returns back to equilibrium, along the z-direction.
The process of M returning to equilibrium is called “relaxation”.
The time required for the z-component of M to decay to 1/e of its initial value is called the “T1 relaxation time”.
The time required for the x- and y-components of M to decay to 1/e of their initial values is called the “T2 relaxation time”.

22. How does relaxation influence NMR spectra?
An NMR signal with a very long T2 relaxation time
(little decay of signal).
NMR frequency spectrum with sharp line:

23. An NMR signal with a shorter T2 relaxation time
(some decay of signal).
1/ p T2

24. An NMR signal with a very short T2 relaxation time gives a spectrum with a very broad line:
1/ p T2

25. A contrast agent, such as gadolinium, interacts with water in the sample and greatly reduces its relaxation time, and broadens (reduces) the observable NMR signal.
When introduced into the circulatory system, the contrast agent enhances relaxation of H2O in regions where the contrast agent is present.

26. Short quiz:
1) Make a qualitative sketch of the 1H NMR spectrum of a cube of water with a small sphere-shaped empty cavity at its center, a uniform magnetic field. (2 points)
2) Make a qualitative sketch of the 1H NMR spectrum of a cube of water with a small sphere-shaped empty cavity at its center, a magnetic field that increases along the z-direction, as shown below. (3 points) o