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)

Biomolecular NMR: primarily spin 1/2 nuclei (1H, 13C, 15N, 31P) 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... (1H) Nuclei with even mass numbers and an even number of protons have I=0 (12C) Nuclei with even mass numbers and an odd number of protons have I=1,2,3… (2H) Biomolecular NMR: primarily spin 1/2 nuclei (1H, 13C, 15N, 31P)

Nuclei With Non-Zero Spin Align in Magnetic Fields DE = h g Ho Efficiency factor- nucleus Constants Strength of magnet Ho anti-parallel parallel Alignment Energy

NMR: The Bar Magnet Analogy p p p ap ap ap + - + - + - + - Ho = - + - + + - - + - + - + - + - + - + + - + - + - 1. force non-alignment 2. release

Resonance: Perturb Equilibrium ap 1. equilibrium DE Ho DE = h g Ho Efficiency factor- nucleus Constants Strength of magnet hn = DE H1 2. pump in energy p ap 3. non-equilibrium

Return to Equilibrium (Relax): Read Out Signals p ap DE 3. Non-equilibrium hn = DE 4. release energy (detect) p ap 5. equilibrium

Magnetic Resonance Sensitivity Np Nap = e -DE/kT Sensitivity (S) ~ D(population) S ~ DN = DE = h g Ho Efficiency factor- nucleus Constants Strength of magnet DE is small At room temp., DN ~ 1:105 Intrinsically low sensitivity Need lots of sample Increase sensitivity by increasing magnetic field strength

Intrinsic Sensitivity of Nuclei Nucleus g % Natural Relative Abundance Sensitivity 1H 2.7 x 108 99.98 1.0 13C 6.7 x 107 1.11 0.004 15N -2.7 x 107 0.36 0.0004 31P 1.1 x 108 100. 0.5

The Classical Treatment: Nuclear Spin Angular Momentum Two spins All spins  Sum Bulk Magnetization excess facing down Ho anti-parallel parallel Torque + int. motion = precession Precession around Z axis Larmor frequency (): DE = hgHo  DE = hn  n = H0 = 

Pulse Fourier Transform NMR 90ºx RF pulse =  =  B0 Bo Bo A t Fourier Transform f  NMR frequency Variation of signal at X axis vs. time

The Power of Fourier Transform 90ºx RF pulse + 1 =  B0 2 =  B0 A t Fourier Transform f 2 1 NMR frequency domain Spectrum of frequencies NMR time domain Variation in amplitude vs time

The Pulse FT NMR Experiment equilibration 90º pulse detection of signals Experiment (t) Data Analysis Fourier Transform Time domain (t)

NMR Terminology Chemical Shift & Linewidth The exact resonance frequency (chemical shift) is determined by the electronic environment of the nucleus