Protein Dynamics from NMRProtein Dynamics from NMR

03/19/02

Protein and Peptide Drug Analysis, pages 714-716

Amide proton exchange

Heteronuclear relaxation

Application to determine the mechanism of cooperativity in binding of Ca2+ by calbindin D9k

Why The Interest In Dynamics? 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: Characterizing Protein Dynamics: Parameters/TimescalesParameters/Timescales

Relaxation

NMR Parameters That Report On NMR Parameters That Report On Dynamics of MoleculesDynamics 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 measurementsR1 (1/T1) spin-lattice- reports on fast motionsR2 (1/T2) spin-spin- reports on fast & slowHeteronuclear NOE- reports on fast & some slow

Relaxation- Return to EquilibriumRelaxation- Return to Equilibrium

t

z axisx,y plane

0

1

2

t

0

1

2

8 8

E-t/T2

t

1-e-t/T1

t

LongitudinalTransverse

Transverse always faster!

Longitudinal (TLongitudinal (T11) Relaxation) RelaxationMECHANISMMolecular 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

dMz/dt = Meq – Mz/T1

Mz(t) = Meq (1-e-t/T1) Mz(t) Meq

FastSlow

Transverse (TTransverse (T22) Relaxation) Relaxation

t

MECHANISMMagnetic 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

dMx,y/dt = Mx,y/T2

Linewidthtime

FastSlow

Linewidth is Dependent on MW

A B A B

1H

1H

15N

15N

1H

15N Linewidth determined by size of particle

Fragments have narrower linewidths

Small(Fast)

Big(Slow)

Amide Proton Exchange(secminhoursdaysmonths)

•Peptides/unfolded proteins exchange rapidly

•Folded proteins protected: solvent accesibility, H-bonds

-N-H

D-O-D

OH-N

H-bonded amides: exchange occurs via local or global unfolding events

Heteronuclear Relaxation(psecnsec & secmsec)

•15N relaxation dominated by 1H

•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” (S2) most common

-15N-

H-1

5 N-

H -15N-

H

Dynamics To Probe The OriginDynamics To Probe The OriginOf Structural UncertaintyOf Structural Uncertainty

Measurements show if high RMSD is due to high flexibility (low S2)

Strong correlation

Weak correlation