Protein Dynamics from NMR 03/19/02 Protein and Peptide Drug Analysis, pages Amide proton exchange Heteronuclear relaxation Application to determine the mechanism of cooperativity in binding of Ca 2+ by calbindin D 9k

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)

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  R 1 (1/T 1 ) spin-lattice- reports on fast motions  R 2 (1/T 2 ) spin-spin- reports on fast & slow  Heteronuclear NOE- reports on fast & some slow

Relaxation- Return to Equilibrium t z axisx,y plane t E -t/T 2 t 1-e -t/T 1 t Longitudinal Transverse Transverse always faster!

Longitudinal (T 1 ) Relaxation MECHANISM  Molecular motions cause the nuclear magnets to fluctuate relative to a fixed point in space  Fluctuating magnetic fields promote spins to flip between states [Induced by the lattice!!]  Over time, spin flips cause a return to equilibrium  Slow motions make effect more efficient t dM z /dt = M eq – M z /T 1 M z (t) = M eq (1-e -t/T 1 ) M z (t)  M eq Fast Slow

Transverse (T 2 ) Relaxation t MECHANISM  Magnetic field is not homogenous to an infinite degree  Each spin comprising the bulk magnetization will feel a slightly different field  Over time, the spin fan out (lose coherence)  Slow motions make effect more efficient dM x,y /dt = M x,y /T 2  Linewidth time Fast Slow

Linewidth is Dependent on MW A B A B 1H1H 1H1H 15 N 1H1H  Linewidth determined by size of particle  Fragments have narrower linewidths Small (Fast) Big (Slow)

Amide Proton Exchange (sec  min  hours  days  months) Peptides/unfolded proteins exchange rapidly Folded proteins protected: solvent accesibility, H-bonds -N- H D-O-D O  H-N  H-bonded amides: exchange occurs via local or global unfolding events

Heteronuclear Relaxation (psec  nsec &  sec  msec) 15 N relaxation dominated by 1 H N-H distance fixed, variation in relaxation due to differences in motional properties Overall tumbling, internal motions  Must fit relaxation parameters to a motional model: Lipari-Szabo “order parameter” (S 2 ) most common - 15 N- H H H

Dynamics To Probe The Origin Of Structural Uncertainty  Measurements show if high RMSD is due to high flexibility (low S 2 ) Strong correlation Weak correlation     