Timescales of Protein Dynamics From Henzler-Wildman and Kern, Nature 2007
Summary of 1D Experiment time domain data Fourier Transform (FT) frequency domain data or
Transverse Relaxation Ensemble of Nuclear Spins Loss of NMR Signal T 2 Random Phase Phase Synchronization No NMR Signal NMR Signal!
Relaxation of populations @EQ After 90 deg pulse Energy Time constant for return to equilibrium is T1
The Frequency Dependence of Relexation Rates, T1 example! τ m θ H N After 90 deg pulse ω B 0 Efficient relaxation if!! ω = 1 / τ m
A Major Source of Relaxation is Brownian Rotational Diffusion! τ m θ H N d NH B local (t) t! τ m : rotational correlation time--the time to rotate through one radian B 0
Stokes-Einstein Equation for Rotational Diffusion And dependence of T1 and T2 on tumbling τ m = 4πηr3 3kT where: r = radius k = Boltzman constant h = viscosity coefficient Rule of thumb: For 20 kd at 298 K τ m (s) = 10ns! τ m (s)
The Inversion Recovery Experiment to measure T1 90y T t
Inversion Recovery Data
Analysis of Inversion Recovery Data Mz eq M z (t) Mz = Mz eq ( 1-2 e -T/T1 ) -Mz eq = Mz eq ( 1-2 e -R1*T ) with R1 = 1/T1
Summary of 1D Experiment time domain data Fourier Transform (FT) frequency domain data
Transverse Relaxation Ensemble of Nuclear Spins Loss of NMR Signal T 2 Random Phase Phase Synchronization No NMR Signal NMR Signal!
Tranverse Relaxation Affects Resonance Linewidth FWHM= 1 π T 2 T2 is short (rapid dephasing) T2 is long (slow dephasing) Transverse Relaxation Rate Constant : R 2 =1/T 2
The spin echo to measure R2 90 180 T T FT Resonance intensity weighted by exp(-r 2 2T)
Spin Echo Spectra at Variable t Delay T=40 ms T=20 ms 0 T=0
Extracting R2 from Spin-Echo Data I(t)! I(T)!=!exp(*R 2 2T) with R 2 =1/T 2 T
Protein Dynamics from NMR Show spies Amide Nitrogen Spies Report On Conformational Dynamics Amide Hydrogen
T1 and T2 inform on dynamics for each residue!
R1 and R2 are not uniform
Rigid amide groups
Detecting mobile amide groups
The Frequency Dependence of Relexation Rates, R1 example! τ m θ H N After 180 ω B 0 Efficient relaxation if!! ω = 1 / τ m
Relaxation Rates Depend on Amplitude and Frequency of Local Field Fluctuations! R 1 (N) = c 2 J(ω) Square of fluctuating local field! Spectral Density Function! Note-the Spectral Density Function, J, is the Fourier Transform of the C rot (t), the correlation function for rotational diffusion J(ω) = τ m 1+ ( ωτ m )2
15 N- 1 H spin pair has four energy states N H! ω H ββ! ω N βα αβ! ω N αα! ω H
( ) ( ) ( ) [ ] ( ) N N H N N H J c J J J d R ω ω ω ω ω ω 2 2 1 6 3 4 + + + + = ( ) ( ) ( ) ( ) ( ) [ ] ( ) ( ) [ ] 0 4 3 6 6 6 3 0 4 8 2 2 2 J J c J J J J J d R N N H H N N H + + + + + + + = ω ω ω ω ω ω ω 3 2 0 1 8 NH H N r h d = π γ γ µ = Δ 3 N c ω where Farrow et.al, (1995) J. Biomol. NMR 6, 153 Relaxation rates for spin-1/2 nucleus that has a dipolar interaction and chemical shift anisotropy Dipolar Coupling Chemical Shift Anisotropy
Model Free formalism accounts for internal motions J Lipari-Szabo (Model Free) ( ω) 2 5 2 ( 2 S τ 1 S ) τ ( ) ( ) m + 2 2 2 1+ ω τ m 1+ ω τ = 2! τ m! τ e H θ N where 1 τ 1 1 = + τ e τ m Requires rotational tumbling and local motions are not correlated B 0
Heteronuclear NOE measurements Measure saturated and unsaturated experiments and take the intensity ratio for each peak Farrow and Kay, Biochemistry, 1993
The heteronuclear NOE N H R 1H ββ R 1N M N (N αα - N βα ) + (N αβ - N ββ ) βα αβ M H (N αα - N αβ ) + (N βα - N ββ ) R 1N R 1H αα Saturation equalizes ββ and βα, αβ and αα à M H = 0 R 1 transitions are an independent return to equilibrium
N H The heteronuclear NOE ββ W 2NH M N (N αα - N βα ) + (N αβ - N ββ ) βα W 0NH αβ αα W 2 transitions increase N αα and decrease N ββ à M increases (positive NOE) M N decreases (negative NOE) W 0 transitions increase N βα and decrease N αβ à M decreases (negative NOE) M N increases (positive NOE) NOE= I(sat) I(unsat) =1+( γ H I(unsat) γ )d2 6J(ω +ω ) J(ω ω ) N N H N H /R 1 (N)
15 N-{ 1 H} Heteronuclear NOE versus rotational correlation time! I sat I unsat! τ m (s)
hnoe and Dcp2 Rigid GB1 Dcp2 Flexible Floor and Gross, unpub.
hnoe versus structure 180 Low NOE (dynamic) High NOE (rigid)
Model Free formalism accounts for internal motions J Lipari-Szabo (Model Free) ( ω) 2 5 2 ( 2 S τ 1 S ) τ ( ) ( ) m + 2 2 2 1+ ω τ m 1+ ω τ = 2! τ m! τ e H θ N where 1 τ 1 1 = + τ e τ m!s 2 and! τ m and! τ e obtained by fitting against R1, R2 and heteronuclear NOE B 0
Determining Structures by NMR
A Real 2D NOE Experiment of a Small Peptide A projection through both dimensions gives a 1D spectrum HN-Haliph crosspeaks HN-Ha crosspeaks 1H, ppm HN-HN crosspeaks 1H, ppm
Interpretation of NOESY Spectra Crosspeaks are a measure of NOE between two spins. Intensity proportional to The intensity of the crosspeak is used to quantify the interaction. 1H ppm 1H ppm
Higher Dimensionality 3 and 4D Heteronuclear Experiments on Isotopically Labeled (15N-13C) Proteins 2D NOESY of a 76 residue protein homodimer (effectively 18kD) in D2O 1H, ppm 1H, ppm In practice, even small proteins have very crowded 2D spectra making assignment very difficult. In this case the fact that it is in D2O simplifies the spectra because the amide protons exchange for deuterium and are not visible.
Benefit of C13 and N15 labeling of Proteins for NMR Higher Dimensionality (3 and 4D) Experiments Reduce Overlap Compared to 2D Experiments 1H! 15N! 1H! 1H! 1H! 2D noe Expt. on unlabeled protein 3D noe Expt. on N15-labeled protein Many More Types of Experiments Can be Done on Isotopically Labeled Protein 15N-1H! 1H-13C! noes between Protons Attached to N15 and Protons Attached to 13C 13C-1H! 1H-13C! noes between Protons Attached to 13C and Protons and Attached to 13C
Side-chain protein assignments R H-C-H H-C-H R N--C--C--N--C--C-- H H O H H O R H-C-H R H-C-H --N--C--C--N--C--C-- H H O H H O H(CCO)NH i - 1 res. All Carbon s H s at i-1 to N-H pair. 15N-TOCSY i res. All H s at i to N-H pair.
Close interatomic distances in secondary structures alpha-helix parallel beta-sheet antiparallel beta-sheet type I turn type II turn
H a chemical shifts and secondary structure the figure at right shows distributions of H a chemical shifts observed in sheets (lighter bars) and helices (darker bars). H a chemical shifts in a-helices are on average 0.39 ppm below random coil values, while b-sheet values are 0.37 ppm above random coil values. Wishart, Sykes & Richards J Mol Biol (1991) 222, 311.
Chemical shift index (CSI) trends like these led to the development of the concept of the chemical shift index* as a tool for assigning secondary structure using chemical shift values. one starts with a table of reference values for each aminoacid type, which is essentially a table of random coil H a values CSI s are then assigned as follows: exp tl H a shift rel. to reference assigned CSI within ± 0.1 ppm 0 >0.1 ppm lower -1 >0.1 ppm higher +1 *Wishart, Sykes & Richards Biochemistry (1992) 31, 1647-51.
Chemical shift indices CSI residue # any dense grouping of four or more -1 s, uninterrupted by 1 s is assigned as a helix, while any dense grouping of three or more 1 s, uninterrupted by -1 s, is assigned as a sheet. a dense grouping means at least 70% nonzero CSI s. other one regions are assigned as coil this simple technique assigns 2ndary structure w/90-95% accuracy similar useful relationships exist for 13 C a, 13 C C=O shifts
NMR provides information about structure chemical shifts <=> local electronic environment coupling constants <=> torsion angles NOE, ROE <=> interproton distances residual dipolar couplings <=> bond orientation and dynamics relaxation times NOE, ROE Most of the data describe local environment of the protons relative to each other not the global conformation of the molecule
Distance NOE: The distance between i and j is a function of the NOE intensity D ij ~ C(NOE ij ) -6 H-bonds: Identified by slowly exchanging amide H N protons Angles Side Chain and backbone torsion angles identified from J-coupling experiments Chemical Shift also gives Angular Information Residual Dipolar Couplings Bond Orientations Relative to an Alignment Tensor
Molecular Dynamics with Simulated Annealing starting from random coordinates Goal is to minimize the hybrid energy function Additional Unambiguous Experimental Restraints E-ForceField E-NOEs E-Angles E-H_bonds E-Chemical_shift E-Dipolar_couplings
Key problem is ambiguity in NOE assignments Need for higher dimensional data: 3D & 4D Need for heteronuclear data Need for better calculational strategies that can deal with ambiguous data
# residues # restraints/residue
Paper Discussion
P21 RAS(1-166) GDP structure determined by NMR Poorly Defined Loop Ensemble of structures: backbone RMSD in Switch 2
Loop containing critical residues for catalysis poorly defined RMSD
Disorder from lack of restraints or mobility?
What does T2 tell us about the Switch 2 loop containing Q61?! τ m (s)
Is the heteronuclear NOE consistent with fast ps-ns motions in active site?! τ m (s)
T1/T2 Proportional to! τ m for each resid
Mapping relaxation data onto structure S 2
Dynamic Switches as a handle for regulatory factors GEF Catalyzes product release Sondek and coworkers Nature, 2000
Order-disorder transitions accompany GEF activation Paper for Friday Aghazadeh et al, Cell 2000