1. NMR in Medicine and Biology MRI- Magnetic Resonance Imaging (water) In-vivo spectroscopy (metabolites) Solid-state NMR (large structures) Solution NMR –Bioanalytical, primary structure –Three-dimensional structure –Molecular motions –Molecular interactions- binding, reactions Ligand screening (Pharma)

2. Nuclear Spin Nuclear spin angular momentum is a quantized property of the nucleus in each atom, which arises from the sub-atomic properties of neutrons and protons The nuclear spin angular momentum of each atom is represented by a nuclear spin quantum number (I) All nuclei with odd mass numbers have I=1/2,3/2... Nuclei with even mass numbers and an even number of protons have I=0 Nuclei with even mass numbers and an odd number of protons have I=1,2,3… Biomolecular NMR: primarily spin 1/2 nuclei ( 1 H, 13 C, 15 N, 31 P)

3. Nuclei With Non-Zero Spin Align in Magnetic Fields HoHo anti-parallel parallel Alignment Energy  E = h  H o Efficiency factor- nucleus ConstantsStrength of magnet

4. NMR: The Bar Magnet Analogy +-+- H o = +-+- +-+- +-+- +-+- +-+- +-+- +-+- +-+- +-+- +-+- +-+- +-+- 1. force non-alignment2. release p ap p p +-+- +-+- +-+-

5. Resonance: Perturb Equilibrium HoHo h  E H1H1 2. pump in energy  E = h  H o Efficiency factor- nucleus ConstantsStrength of magnet p ap 1. equilibrium EE p ap 3. non-equilibrium

6. Return to Equilibrium (Relax): Read Out Signals p ap 5. equilibrium h  E 4. release energy (detect) p ap EE 3. Non-equilibrium

7. Magnetic Resonance Sensitivity  E is small At room temp.,  N ~ 1:10 5 Intrinsically low sensitivity  Need lots of sample  E = h  H o Efficiency factor- nucleus ConstantsStrength of magnet N p N ap = e -  E/kT Sensitivity (S) ~  population) S ~  N = Increase sensitivity by increasing magnetic field strength

8. Intrinsic Sensitivity of Nuclei Nucleus  Natural Relative Abundance Sensitivity 1 H2.7 x 10 8 99.98 1.0 13 C6.7 x 10 7 1.11 0.004 15 N -2.7 x 10 7 0.36 0.0004 31 P1.1 x 10 8 100. 0.5

9. The Classical Treatment: Nuclear Spin Angular Momentum HoHo anti-parallel parallel  Torque + int. motion = precession  Precession around Z axis  Larmor frequency (  ):  E = h  H o   E = h  =  H 0 =  Two spins All spins  Sum Bulk Magnetization excess facing down