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NMR

This is a more challenging and less directed project than the usual weekly assignments. To complete it should take two weeks. At the end, the team may be selected to give a short 20-30 minute presentation.

Nuclear Magnetic Resonance (NMR) has a number of very important applications to biology and medicine. There are two main applications that you can focus on:

  • MRI imaging techniques and applications
  • Macromolecular structure prediction

They both share the same basic physics, so the first week will be spent learning the basic physics. Then the second will concentrate on one of the two areas listed above.

Note that the second application, that of macromolecular structure prediction is extremely complicated technically, even in comparison with MRI imaging. It is very hard to understand it well in two weeks. MRI imaging is difficult, but a basic understanding of it does not rely on as many subtle complicated effects.

Week 1

There are good resources available on the web, and some recommended ones are compiled at the above nmr link. By the end of the first week, you should familiarize yourself with:

  • spin and its energy levels in a magnetic field
  • how transitions are made between different levels by the absorption or emission of photons, and how this is related to NMR.
  • The different relaxation processes (denoted T1 and T2).
  • Precession and the Bloch equation(s)
  • How to use pulsed magnetic fields to change the orientation of spins.

hw2/nmr in the code zip ball Download code zip ball allows you to investigate the behavior of the magnetic moment under the application of a time varying magnetic field using the Bloch equations. You should try to understand this code, and then modify to implement the code to simulate the Bloch equations in the "rotating frame".

Within one week, the team should upload their progress report, obtaining answers to the above questions, including implementation of the python code.

Week 2

In this week you can concentrate on MRI imaging or using NMR for protein structure prediction.

MRI Imaging

You want to be able to learn the basic physics and math of this technique. This requires a good understanding of Fourier Transforms, as well as understanding the behavior of the Bloch equations. At the end you should do the following:

  • What interesting biological questions can be addressed with this techniques, or variations of it, such as FMRI?
  • Explain how by applying to appropriate sequence of magnetic fields, including ones with slow spatial variation, you can relate the time dependent magnetization to the Fourier Transform of the spin density, and how this can be used to do medical imaging.
  • Describe what are the limits of sensitivity and spatial resolution that you expect from this technique.
  • Now you should look for at least one new advance in NMR imaging in the recent literature.

NMR Spectroscopy Applied to Biological Macromolecules

There are a large variety of sophisticated techniques that used NMR to determine the structure of large macromolecules such as proteins. Some of the physical involved in this is quite complex, and require an advanced understanding of quantum statistical mechanics. So some of the phenomena used, such as NOESY (the Nuclear Overhauser Effect) should be taken for granted and you should not attempt to derive it. Putting together the various phenomena used in NMR, is still challenging, and these are the things you should pursue:

  • First, give examples of structures that have been solved by NMR and when it should be used as an alternative to X-ray crystallography.
  • The chemical shift.
  • How coupling between spins affects energy levels
  • How does "Spin Echo" work?
  • Understand the basics of two dimensional NMR techniques.
  • How is this data used in conjunction with a physical model of a moving protein to predict its three dimensional structure?