2 Relaxation- Return to Equilibrium x,y planez axisTransverseLongitudinal11tt22E-t/T21-e-t/T188Transverse always faster!
3 magnetization vector's trajectory Relaxationmagnetization vector's trajectoryThe initial vector, Mo, evolves under the effects of T1 & T2 relaxation and from the influence of an applied rf-field. Here, the magnetization vector M(t) precesses about an effective field axis at a frequency determined by its offset. It's ends up at a "steady state" position as depicted in the lower plot of x- and y- magnetizations.
4 RelaxationThe T2 relaxation causes the horizontal (xy) magnetisation to decay. T1 relaxation re-establishes the z-magnetisation. Note that T1 relaxation is often slower than T2 relaxation.
7 Spin-lattice Relaxation time (Longitudinal) T1 Relaxation mechanisms:1. Dipole-Dipole interaction "through space"2. Electric Quadrupolar Relaxation3. Paramagnetic Relaxation4. Scalar Relaxation5. Chemical Shift Anisotropy Relaxation6. Spin Rotation
8 RelaxationSpin-lattice relaxation converts the excess energy into translational, rotational, and vibrational energy of the surrounding atoms and molecules (the lattice).Spin-spin relaxation transfers the excess energy to other magnetic nuclei in the sample.
9 Longitudinal Relaxation time T1 Inversion-Recovery Experiment180y (or x)90ytD
12 Range of interaction (Hz) relevant parametersDipolar coupling- abundance of magnetically active nuclei - size of the magnetogyric ratioQuadrupolar coupling- size of quadrupolar coupling constant - electric field gradient at the nucleusParamagneticconcentration of paramagnetic impuritiesScalar couplingsize of the scalar coupling constantsChemical Shift Anisotropy (CSA)- size of the chemical shift anisotropy - symmetry at the nuclear site6- Spin rotation
13 Spin-spin relaxation (Transverse) T2 T2 represents the lifetime of the signal in the transverse plane (XY plane)T2 is the relaxation time that is responsible for the line width.line width at half-height=1/T2
14 Spin-spin relaxation (Transverse) T2 Two factors contribute to the decay of transverse magnetization.molecular interactions( lead to a pure pure T2 molecular effect)variations in Bo( lead to an inhomogeneous T2 effect)
21 T1 and T2 In non-viscous liquids, usually T2 = T1. But some process like scalar coupling with quadrupolar nuclei, chemical exchange, interaction with a paramagnetic center, can accelerate the T2 relaxation such that T2 becomes shorter than T1.
23 Relaxation and correlation time For peptides in aqueous solutions the dipole-dipole spin-lattice and spin-spin relaxation process are mainly mediated by other nearby protons
24 Why The Interest In Dynamics? Function requires motion/kinetic energyEntropic contributions to binding eventsProtein Folding/UnfoldingUncertainty in NMR and crystal structuresEffect on NMR experiments- spin relaxation is dependent on rate of motions know dynamics to predict outcomes and design new experimentsQuantum mechanics/prediction (masochism)
27 Characterizing Protein Dynamics: Parameters/Timescales Relaxation
28 NMR Parameters That Report On Dynamics of Molecules Number of signals per atom: multiple signals for slow exchange between conformational statesLinewidths: narrow = faster motion, wide = slower; dependent on MW and conformational statesExchange of NH with solvent: requires local and/or global unfolding events slow timescalesHeteronuclear relaxation measurementsR1 (1/T1) spin-lattice- reports on fast motionsR2 (1/T2) spin-spin- reports on fast & slowHeteronuclear NOE- reports on fast & some slow
29 Linewidth is Dependent on MW ABSmall(Fast)Big(Slow)1H15NLinewidth determined by size of particleFragments have narrower linewidths