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Unformatted text preview: 7. Nuclear Magnetic Resonance Nuclear Magnetic Resonance (NMR) is another method besides crystallography that can be used to find structures of proteins. NMR spectroscopy is the observation of spins of atoms and electrons in a molecule that is placed in a magnetic field. The spins precess at a frequency in the radio frequency range and the frequency can be detected by the electrical signal that it generates. We briefly discuss the physics of NMR, and then describe distance geometry , a mathematical theory that can be used to find the protein structure from some types of NMR data. 7.1. Larmor frequency. Spins placed in a magnetic field precess; they wobble like a spinning top. Only certain isotopes of molecules found in organic compounds have spins that react to the magnetic field; the most common ones used in proteins are 1 H, 13 C, 15 N. The isotopes 13 C and 15 N are not in common abundance, so specially prepared protein samples must be used. Figure 1. An NMR experiment is the observation of the pre- cession of nuclear spins in the presence of a magnetic field. The large arrow represents the magnetic field of the magnet, the small arrow represents magnetic field of the nucleus which is precessing like a spinning top as the tip of the arrow moves on the indicated circle. The frequency of precession is called the Larmor frequency and it is determined mainly by the type of atom and the strength of the magnetic field. The basic NMR 1 2 equation is, (1) = B where = the Larmor frequency, i.e., the angular frequency of the precession in radians per second = gyromagnetic ratio, a constant depending on the type of the atom B = the intensity of the magnetic field 7.2. Splitting and chemical shift. Equation (1) assumes that the detected fre- quency depends only on the atom and the intensity of the magnetic field. There is another factor, however. The magnetic field intensity B is not the same everywhere in the molecule; it is affected by neighboring atoms and electrons. Neighboring spins have their own magnetic field and this perturbs the field of the magnet and changes the frequency of precession. This is illustrated by the NMR spectrum of the hydrogen atoms in the molecule Toluene (figure 2). The spectrum is a Fourier transform of the electrical signal showing the intensities (vertical axis) of certain frequencies (horizontal axis). The spectrum can be thought of as the absolute values of Fourier coefficients for the function giving the signal as a function of time. It the signal is the real part of s ( t ) = n j =1 a j e 2 i j t then the spectrum gives absolute values | a j | , j = 1 ...n at frequencies j cycles per second....
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- Fall '11