Introduction to NMR for measuring structure and dynamics + = UCSF Macromolecular Interactions John Gross, Ph.D.
Nuclear Spins: Microscopic Bar Magnets H µ S N N + Protein Fragment Magnetic Moment Bar Magnet Magnetic moment µ = γs Angular Momentum The proportionality constant γ: strength of bar magnet
Equation of Motion dµ dt = γ B x µ Based on magnetic torque: d L dt = B L
Spin Precession µ Magnetic Field, Bo Precession frequency: γb 0 =ω o
Precessional Orbits Gravity Driving Forces for Precession + Applied magnetic field,b 0 Spinning Top Spinning Nucleus
Nuclear Spins Report Local Environment B total B applied + B local = B total determines precession
Detection of Spin Precession Z µ Y X Detector measures magnetic field on x-axis
Net Magnetization M x = M y = j µ x j = 0 j µ y j = 0 No Transverse Magnetization at equilibrium
Magnetic Energy E = µ B N µ E = -µ z B z S Static Magnetic Field Oriented Along Z-Axis
Energy Energy States (spin-1/2 nucleus)
Net Magnetization along Z Axis Z Z Y Y X X µ z j = M z j
Solution I: apply second field along y Axis Z Y Bo X If B1 >> Bo, Mz would rotate about B1. Leave B1 on until X axis reached ----> transverse magnetization Approach is not practical. B 1
Magnetic Resonance Z Y B1 1/ν 0 Bo X Turn B 1 on and off with a frequency matching the precessional frequency
Resonance Ensemble of Nuclear Spins Resonant RF Field Random Phase Phase Synchronization No NMR Signal NMR Signal!
Magnetization Vector Model Equilibrium Z After 90 degree pulse Z Y Y X X B z 90y: Resonant 90 Degree Pulse
Resonant Pulse in Real Time Z! X! Y! R.F. Field (applied at precession frequency)! Net magnetization rotated into transverse plane! Rotates due to static and local fields!
Summary of 1D Experiment Transverse Magnetization Decay constant T2 Amplitude propotional to amount magnetization prior to pulse time domain data Fourier Transform (FT) <--- Width of resonance--dynamical info Position of resonance ---> local magnetic environment frequency domain data or ω
J couplings contain information on structure
The J Coupling Consider two spin-1/2 nuclei (ie, 1 H and 15 N): 15 N e- 1 H Augments local field Diminishes local field Effect transmitted through electrons in intervening bonds
Vector View 15 N e- 1 H z y τ z y x (After 90y pulse) x Components rotate faster or slower than rotating frame by +- J/2
Spectrum with J coupling 1 J NH ~ 90 Hz -SW 2 -J 2 0 +J 2 SW 2 15 N Detected Spectrum
Protein NMR Spectroscopy
Periodic Table of NMR active Nuclei
Isotopic Labeling Proteins for NMR Bacterial expression: Minimal media, 15 N NH 4 Cl or 13 C glucose as sole nitrogen and carbon source Amino acid-type labeling Auxotrophic or standard strains (ei, BL21(DE3) depending on scheme Labeling post purification ; reductive methylation of lysines Results in additional spin-1/2 nuclei which can be used as probes
The HSQC is an NH chemical shift correlation map R! 15 N - C α - CO 15 N (ppm) H! 1 H (ppm)
An overview of the HSQC 1 H y Δ Δ Δ Δ t 2 15 N t 1 /2 t 1 /2 DEC Transfer to 15 N Transfer back to 1 H Encode 15 N chemical shift for time t 1 Bodenhausen & Ruben
2D Time-Domain Data t 1 t 2
The Spin Echo averages chemical shift evolution τ τ t Echo Forms After 2τ φ -φ φ=2πτδ
Spin-Echo Refocuses J and CS 90y Evolution τ τ t J XH only J Coupling Refocused J & CS J Coupling & Chemical Shift Refocused
90y τ Double Spin Echo τ t J Coupling Active Chemical Shift Refocused!
HSQC: guided tour 1 H y Δ Δ Δ Δ t 2 15 N t 1 /2 t 1 /2 DEC a b c d e f g h i
First transfer a) 1 H Δ=1/4J y NH Δ Δ a b c d 15 N e b) c) d) e) Morris & Freeman, INEPT 15 N transverse antiphase magnetization subject to 15 N chemical shift
15 N Chemical Shift Evolution 1 H y Δ Δ Δ Δ t 2 15 N e) f) t 1 /2 t 1 /2 e f g h i g) DEC j 2πδ N t 1 cos(2πδ N t 1 )
1 H y Δ Δ Detection Δ Δ t 2 15 N t 1 /2 t 1 /2 DEC i) t 2 e f g h i j S(t 1,t 2 ) = cos(2πδ N t 1 )exp( i2πδ H t 2 ) j) cos(2πδ N t 1 ) 2πδ H t 2
HSQC Signal 1 H y Δ Δ Δ Δ t 2 15 N t 1 /2 t 1 /2 DEC a b c d e f g h i j S(t 1,t 2 ) = cos(2πδ N t 1 )exp( i2πδ H t 2 )
Obtaining the Sine Component 1 H y Δ Δ Δ Δ t 2 15 N y t 1 /2 t 1 /2 DEC e f g h i j e) f) g) sin(2πδ N t 1 ) 2πδ N t 1 States, Ruben, Haberkorn
After Obtaining Im Part of Indirect Dimension... S c (t 1,ν 2 ) S s (t 1,ν 2 ) t 1 t 1 F 2 H N F 2 H N cos(2πδ N t 1 )[A 2 H + id2 H ] sin(2πδ N t1 )[A 2 H + id2 H ]
2D Fourier Transform: FT Direct Dimension S(t 1,t 2 ) = cos(2πδ N t 1 ) exp( i2πδ H t 2 ) FT Direct Dimension t 1 S(t 1,ν 2 ) = cos(2πδ N t 1 )[A 2 H + id2 H ] F 2 H N Re S(t 1,ν 2 ) is absorptive. But unable to discriminate sign of δ N
Some data shuffling then 2D FT =the HSQC Spectrum Re [S ' (ν 1,ν 2 )] = A 1 N A2 H N H N
3D NMR for Resonance Assignments N 3D HNCA CA H (amide)=hn
HNCA Pulse Sequence Correlates backbone HN, N and CA chemical shifts
Resonance assignments
Triple Resonance Pairs HNCOCA
Other Experiments for Backbone Assignments i-1 information i, i-1 information
THE RANGE OF 13 C CHEMICAL SHIFTS OBSERVED FOR EIGHT DIFFERENT PROTEINS Res. α β γ δ ε Gly 42-48 Ala 49-56 18-24 Ser 55-62 61-67 Thr 58-68 66-73 19-26 Val 57-67 30-37 16-25 Leu 51-60 39-48 22-29 21-28 Ile 55-66 34-47 25-31 14-22 9-16 Lys 52-61 29-37 21-26 27-34 40-43 Arg 50-60 28-35 25-30 41-45 Pro 60-67 27-35 24-29 49-53 Glu 52-62 27-34 32-38.................. WAGNER AND BRUHWILER, 1986 et al. Or http://www.bmrb.wisc.edu/ref_info/statsel.htm
Part II: Applications
NMR to monitor ligand binding ω b ω f k on ω b ω f Slow k off k ex <Δω k ex = k on [L]+ k off Δω = ω f ω b ω Intermediate k ex ~Δω Fast k ex >Δω
Binding of nucleotide to protein Chemical Shift (ppm) W43 m7gdp D47 m7gdp W43 GDP D47 GDP [Ligand] (mm) Dose dependent resonance shifts can be fit to obtain Kd
Fraction bound of labeled protein P b = ω ω f ω b ω f = [L] [L]+ K d ω : observed chemical shift
Shifts may be color coded onto surface to identify ligand binding site Caveats?
Monitoring Protein/Protein Interactions by HSQC
ILV labeling Selectively label R group methyls with C-13 (NMR visible) Isoleucine Leucine Valine (add alpha-ketoacid precursors to ILV 30 minutes prior to induction )
13 C- 1 H HSQC of ILV labeled protein Ile Val Leu
Measuring pka by NMR (ph 4.5-9.5) I199 I136 I199 I136 I136 (Stephen Floor) pka of 7.2, elevated for Glu
ph dependence disappears in E152Q mutant (ph 4.5-9.5) I199 I136 I199 E152Q I136
Preview: folding, dynamics and catalysis
Timescales of Protein Dynamics From Henzler-Wildman and Kern, Nature 2007
Fast Dynamics Show spies Amide Nitrogen Nuclear Spies Report Dynamics Amide Hydrogen
Tranverse Relaxation Effects Resonance Linewidth 1 π T 2 = (d CH ) 2 * τ c Immobile τ c large Mobile τ c small Rate constant : R 2 =1/T 2
Transverse Relaxation Ensemble of Nuclear Spins Loss of NMR Signal 1/T 2 Random Phase Phase Synchronization No NMR Signal NMR Signal!
A Major Source of Relaxation is Brownian Rotational Diffusion N θ H d NH B local (t) t τ m : rotational correlation time--the time to rotate through one radian B 0
The spin echo to measure R2 90 180 τ τ FT Resonance intensity weighted by exp(-r 2 2τ)
Spin Echo Spectra at Variable τ Delay Re S(ν) τ=40 ms τ=20 ms 0 τ=0
Extracting R2 from Spin-Echo Data I(τ) I(τ) = exp(-r 2 τ) τ This can be thought of as a type of 2D NMR Experiment
Relaxation of populations Before 180 @EQ After 180 Energy
The Inversion Recovery Experiment to measure R1 90y τ t Note lack of CS evolution during delay
Inversion Recovery Data
Analysis of Inversion Recovery Data Mz eq M z (t) Mz = Mz eq ( 1-2 e -tr1 ) -Mz eq
The Frequency Dependence of Relexation Rates, R1 example τ c θ N H After 180 ω B 0 Efficient relaxation if 1/τ c =ω!
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! J(ω) = τ m 1+ ( ωτ m )2
15 N- 1 H spin pair has four states N H ω H ββ ω N βα ω N ω H αβ αα
( ) ( ) ( ) [ ] ( ) 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 Spectral Density Functions
Rigid amide groups
Detecting mobile amide groups
R1 and R2 are not uniform
Model Free formalism accounts for internal motions τ e Lipari-Szabo (Model Free) τ m θ H J ( ω) 2 5 2 ( 2 S τ 1 S ) τ ( ) ( ) m + 2 2 2 1+ ω τ m 1+ ω τ = 2 N where 1 τ 1 1 = + τ e τ m 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 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 M increases (positive NOE) M N decreases (negative NOE) W 0 transitions increase N βα and decrease N αβ M decreases (negative NOE) M N increases (positive NOE) NOE = I(sat) I(unsat) I(unsat) =1+ ( γ H )d 2 { 6J(ω + ω ) J(ω ω )} γ / R N H N H 1 (N) N
hnoe and Dcp2 Rigid GB1 Dcp2 Flexible Floor and Gross, unpub.
hnoe versus structure 180 Low NOE (dynamic) High NOE (rigid)
R1, R2 and NH-NOE: three relaxation rates -> three fit parameters: τ m,τ e, S 2
Timescales of Protein Dynamics From Henzler-Wildman and Kern, Nature 2007
Spectral Manifestations of Exchange ω a k f k ex = k f + k r ω a ω b Slow k r Δω=ω a -ω b ω b k ex <Δω Intermediate ω k ex ~Δω Fast k ex >Δω
Methionine Specific Labeling Inhibition of KSHV Pr stabilizes the dimeric conformation Slow interconversion between monomer and dimer Marnett A. B. et.al. PNAS 2004;101:6870-6875
Tyrosine specific labeling 15 N TYR HSQC GB1-yDCP2-NB 7 out of 8 resonances detected
Slow Exchange Reported by Unnatural Amino Acid Lampe et al, JACS 2008
Monitoring unfolded states by NMR Gross et al, Cell 2003 Unstructured regions fluctuate from fast (ns-ps) to slow ms-us timescales