Biophysical Tools '04 - NMR part II Experimental parameters that can be measured by NMR: - chemical shifts - linewidth - signal decay times - splittings Experimental parameters that can be measured by NMR: - chemical shifts - linewidth - signal decay times - splittings Biophysical Tools '04 - NMR part II 9/17/2018
Biophysical Tools '04 - NMR part II Precession NMR: Part II Net magnetization precesses incoherently in xy-plane Fluctuating magnetic field in xy-plane with frequency inducing the resonance brings the spins into coherence. Pulses 90o and 180o pulses contain all the frequencies and tip the all vectors (resonances) into y- or z-axis Larmor frequency wL = -g B0 Biophysical Tools '04 - NMR part II 9/17/2018
Biophysical Tools '04 - NMR part II Larmor Frequency Biophysical Tools '04 - NMR part II 9/17/2018
Biophysical Tools '04 - NMR part II Free Induction Decay Biophysical Tools '04 - NMR part II 9/17/2018
Fourier Transform of FID Transient response: Free Induction Decay Dephasing of the vectors due to different Larmor frequencies Rate of dephasing ~ 1/T2 Decaying magnetization will oscillate with characteristic frequencies: Larmor frequencies of the resonating spins = FID FT of the time signal - FID gives frequency spectrum Biophysical Tools '04 - NMR part II 9/17/2018
Applications: Dynamics - T1 relaxation relaxation due to fluctuating fields in the sample which induce transitions from excited to ground state decay of magnatization modulation of the dipole-dipole interactions is a function of correlation time thus the T1 is function of correlation time can obtain correlation time from T1 Biophysical Tools '04 - NMR part II 9/17/2018
Applications: Structure - J-coupling Karplus equations The extent (strength) of splitting J is related to the bonds and the angles between the bonds. For example for CH-CH the coupling is 17cos2f +1.1 where is the torsion angle of C-C bond. Tim Cross uses Biophysical Tools '04 - NMR part II 9/17/2018
Applications: Binding - Chemical exchange Slow exchange: k << Dw Fast exchange: k >> Dw 1/T2obs = 1/T2 + k Chemical exchange If one spin lives exchanges between two environments giving two different resonant frequencies then the spectrum will be affected by the exchange rate. slow exchange for exchange rate k smaller than the Dw Fast exchange if k is much greater than Dw the average Larmor frequency (resonance position) will be Dw/2 relaxation time: 1/T2obs = 1/T2 + Dw2/8k From the linewidth broadening, relaxation rates or from averaging of the resonance positions can obtain the exchange time: - ligand on- and off-rates - binding equilibria - diffusion between different environments or conformations Ligand binding For spin ensemble, in limits of fast exchange the observed lineshape is a mole-weighted average: dobs = fAdA + fBdB shift in the resonance is used to calculate fraction of the spins in each environment Applications: Rotational rates On-, off rates Ligand binding Biophysical Tools '04 - NMR part II 9/17/2018
Biophysical Tools '04 - NMR part II Intracellular pH pH dependence Shift of ionizable groups: histidines and phosphate Biophysical Tools '04 - NMR part II 9/17/2018
Biophysical Tools '04 - NMR part II Metabolism Glucose metabolism Energetics Metabolism Biophysical Tools '04 - NMR part II 9/17/2018
Biophysical Tools '04 - NMR part II Molecular Ordering Molecular ordering: tensors Scalars, vectors and tensors isotropic: Ax = Ay = Az cylindrical: Ax = Ay Az orthorhombic tensors: Ax Ay Az Orientational sensitivity Can determine orientation of spins (lipids) in the membrane Biophysical Tools '04 - NMR part II 9/17/2018
Biophysical Tools '04 - NMR part II NMR Imaging Magnetic Resonance Imaging Larmor frequency is defined by the field strength. Different fields give different resonant frequencies even for the same nuclei. Encode the spatial position in frequency by having a defined field gradient Translate the frequencies into position: back-projection Get 3D picture by collecting spectra with gradients in various directions Spectroscopy on a small volume: combine imaging with spectroscopy to get the metabolism in that volume !!! Biophysical Tools '04 - NMR part II 9/17/2018