Relaxation Time Phenomenon & Application NMR Spectroscopy Relaxation Time Phenomenon & Application

Relaxation- Return to Equilibrium x,y plane z axis Transverse Longitudinal 1 1 t t 2 2 E-t/T2 1-e-t/T1 8 8 Transverse always faster!

magnetization vector's trajectory Relaxation magnetization vector's trajectory The 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. http://gamma.magnet.fsu.edu/info/tour/bloch/index.html

Relaxation                       The 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.

Relaxation time – Bloch Equation

Relaxation time – Bloch equation

Spin-lattice Relaxation time (Longitudinal) T1 Relaxation mechanisms: 1. Dipole-Dipole interaction "through space" 2. Electric Quadrupolar Relaxation 3. Paramagnetic Relaxation 4. Scalar Relaxation 5. Chemical Shift Anisotropy Relaxation 6. Spin Rotation

Relaxation Spin-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.

Longitudinal Relaxation time T1 Inversion-Recovery Experiment 180y (or x) 90y tD

T1 relaxation

Range of interaction (Hz) relevant parameters Dipolar coupling 104 - 105 - abundance of magnetically active nuclei - size of the magnetogyric ratio Quadrupolar coupling 106 - 109 - size of quadrupolar coupling constant - electric field gradient at the nucleus Paramagnetic 107 -108 concentration of paramagnetic impurities Scalar coupling 10 - 103 size of the scalar coupling constants Chemical Shift Anisotropy (CSA) 10 - 104 - size of the chemical shift anisotropy - symmetry at the nuclear site 6- Spin rotation

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

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)

Spin-spin relaxation (Transverse) T2 90y 180y (or x) tD tD signal width at half-height (line-width )= (pi * T2)-1

Spin-spin relaxation (Transverse) T2

Spin-Echo Experiment

Spin-Echo experiment

MXY =MXYo e-t/T2

Carr-Purcell-Meiboom-Gill sequence

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.

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

Why The Interest In Dynamics? Function requires motion/kinetic energy Entropic contributions to binding events Protein Folding/Unfolding Uncertainty in NMR and crystal structures Effect on NMR experiments- spin relaxation is dependent on rate of motions  know dynamics to predict outcomes and design new experiments Quantum mechanics/prediction (masochism)

Application

Characterizing Protein Dynamics: Parameters/Timescales Relaxation

NMR Parameters That Report On Dynamics of Molecules Number of signals per atom: multiple signals for slow exchange between conformational states Linewidths: narrow = faster motion, wide = slower; dependent on MW and conformational states Exchange of NH with solvent: requires local and/or global unfolding events  slow timescales Heteronuclear relaxation measurements R1 (1/T1) spin-lattice- reports on fast motions R2 (1/T2) spin-spin- reports on fast & slow Heteronuclear NOE- reports on fast & some slow

Linewidth is Dependent on MW A B Small (Fast) Big (Slow) 1H 15N Linewidth determined by size of particle Fragments have narrower linewidths