NMR journey. Introduction to solution NMR. Alexandre Bonvin. Topics. Why use NMR...? Bijvoet Center for Biomolecular Research

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1 2 NMR journey Introduction to solution NMR Alexandre Bonvin Bijvoet Center for Biomolecular Research with thanks to Dr. Klaartje Houben EMBO Global Exchange course, CCMB, Hyderabad, India November 29th - December 6th, Topics Why use NMR for structural biology...? The very basics Multidimensional NMR (intro) Why use NMR...? Resonance assignment Structure parameters & calculations NMR relaxation & dynamics

2 NMR & Structural biology DYNAMICS NMR & Structural biology TRANSIENT COMPLEXES 6 a F helices F helices DBD CBD apo-cap CAP-cAMP 2 Dynamic activation of an allosteric regulatory protein Tzeng S-R & Kalodimos CG Nature (2009) Visualization of the Encounter Ensemble of the Transient Electron Transfer Complex of Cytochrome c and Cytochrome c Peroxidase Bashir Q. et al JACS (2010) NMR & Structural biology EXCITED STATES 7 NMR & Structural biology MEMBRANE PROTEINS 8 Structure and Dynamics of Pin1 During Catalysis by NMR Labeikovsky W. et al JMB (2007) Mechanisms of Proton Conduction and Gating in Influenza M2 Proton Channels from Solid-State NMR Hu F. et al Science (2010)

3 NMR & Structural biology AMYLOID FIBRILS 9 NMR & Structural biology IN-CELL NMR 10 Amyloid Fibrils of the HET-s( ) Prion Form a β Solenoid with a Triangular Hydrophobic Core Wasmer C. et al Science (2008) High-resolution multidimensional NMR spectroscopy of proteins in human cells Inomata K. et al Nature (2009) The NMR sample 11 isotope labeling 15 N, 13 C, 2 H selective labeling (e.g. only methyl groups) recombinant expression in E.coli sample pure, stable and high concentration 500 ul of 0.5 mm solution -> ~ 5 mg per sample preferably low salt, low ph no additives The very basics of NMR

4 Nuclear spin precession 13 Nuclear spin 14 E = µ B 0 (rad. T -1. s -1 ) Nuclear spin & radiowaves 1 H (I = 1/2) Larmor frequency m = -!! H = " HB 0 = 2#$ H 15 Boltzman distribution 1 H m = -! 16 m =! m =!

5 Net magnetization 17 Pulse 18 B 0 B 1 " B0 # = 0 2! ( " B # = 1 1 2! rotating frame: observe with frequency $0 Chemical shielding 19 Chemical shift # B $ = 0 1% 2" (! ) shielding constant 20 More conveniently expressed as part per million by comparison to a reference frequency: Local magnetic field is influenced by electronic environment! = 10 6 "# " ref " ref

6 21 22 Free induction decay (FID) FID: analogue vs digital Free Induction Decay (FID) Fourier Transform Relaxation Signal 0 FT Signal 0 NMR Relaxation Restores Boltzmann equilibrium time (ms) freq. (s -1 ) T2-relaxation (spin-spin) disappearance of transverse (x,y) magnetization 1/T2 ~ signal line-width FT T1-relaxation (spin-lattice) build-up of longitudinal (z) magnetization determines how long you should wait for the next experiment

7 Relaxation 25 Relaxation 26 Spin-spin relaxation (dephasing in xy plane) Spin-lattive relaxation (restoring of equilibrium magnetization) 1/T2 ~ signal line-width NMR spectral quality 27 Scalar coupling / J-coupling 28 Sensitivity Signal to noise ratio (S/N) Sample concentration Field strength.. Resolution Peak separation Line-width (T2) Field strength.. H3C - CH2 - Br 3 JHH

8 Why multidimensional NMR multidimensional NMR experiments resolve overlapping signals enables assignment of all signals Multidimensional NMR encode structural and/or dynamical information enables structure determination enables study of dynamics D NMR 3D NMR

9 33 34 nd experiment 1D indirect dimensions direct dimension t1 preparation acquisition 1 FID of N points Encoding information mixing/magnetization transfer 2D preparation t1 evolution mixing t2 acquisition N FIDs of N points???? 3D preparation t1 evolution mixing t2 evolution mixing t3 acquisition NxN FIDs of N points proton A spin-spin interactions proton B Magnetization transfer homonuclear NMR Magnetic dipole interaction (NOE) Nuclear Overhauser Effect through space distance dependent (1/r6) NOESY -> distance restraints J-coupling interaction through 3-4 bonds max. chemical connectivities assignment also conformation dependent NOESY COSY TOCSY t1 t1 tm t1 mlev FID FID FID t2 t2 t2 magnetic dipole interaction crosspeak intensity ~1/r 6 up to 5 Å J-coupling interaction transfer over one J-coupling, i.e. max. 3-4 bonds J-coupling interaction transfer over several J-couplings, i.e. multiple steps over max. 3-4 bonds

10 38 2D NOESY Uses dipolar interaction (NOE) to transfer magnetization between protons cross-peak intensity ~ 1/r 6 distances (r) < 5Å Homonuclear scalar coupling diagonal H N 3 JHαHβ ~ 3-12 Hz H N cross-peak 3 JHNHα ~ 2-10 Hz D COSY & TOCSY homonuclear NMR ~Å 2D COSY 2D TOCSY NOESY t1 tm FID t2 proton A proton B A A (ωa) A A (ωa) (F1,F2) = ωa, ωa Hβ Hβ B B (ωb) (F1,F2) = ωa, ωb ωa ωb Hα Hα Diagonal HN HN F1 ωa Cross-peak F2

11 heteronuclear NMR 41 J coupling constants 42 1JCbCg = 35 Hz 1JCbHb = 130 Hz 1 H 15 N measure frequencies of different nuclei; e.g. 1 H, 15 N, 13 C no diagonal peaks mixing not possible using NOE, only via J 1JCaCb = 35 Hz 1JCaC = 1JNC = 1JCaN = 55 Hz -15 Hz -11 Hz 1JCaHa = 140 Hz 2JCaN = 7 Hz 1JHN = -92 Hz 2JNC < 1 Hz 15 N HSQC 43 1 H- 15 N HSQC: protein fingerprint 44 Backbone HN Side-chain NH and NH2

12 45 1 H- 15 N HSQC: protein fingerprint Relaxation & dynamics NMR relaxation Relaxation is caused by dynamics Return to equilibrium Spin-lattice relaxation Longitudinal relaxation T1 relaxation Return to z-axis B0 B1 Fluctuating magnetic fields Overall tumbling and local motions cause the local magnetic fields to fluctuate in time Spin-spin relaxation Transversal relaxation T2 relaxation Dephasing of magnetization in the x/y plane B0 B0 B1 Bloc

13 49 50 Relaxation is caused by dynamics Local fluctuating magnetic fields Fluctuating magnetic fields Overall tumbling and local motions cause the local magnetic fields to fluctuate in time Bloc(t) is thus time dependent If Bloc(t) is fluctuating with frequency components near ω0 then transitions may be induced that bring the spins back to equilibrium The efficiency of relaxation also depends on the amplitude of Bloc (t) Stationary random function, B loc (t) Bloc(t) = Bloc[iso] + Bloc(t)[aniso] Isotropic part is not time dependent chemical shift J-coupling Only the anisotropic part is time dependent chemical shift anisotropy (CSA) dipolar interaction (DD) B loc (t) e x 0 t B0 13 C anisotropic interactions r 2 <B loc (t)> = 0 <B loc (t)> 0 CSA dipole-dipole What are the frequency components of B (t)? Local fluctuating magnetic fields Components of the local field Bloc(t) = Bloc[iso] + Bloc(t)[aniso] Isotropic part is not time dependent chemical shift J-coupling Only the anisotropic part is time dependent chemical shift anisotropy (CSA) dipolar interaction (DD) Bloc(t) exy Transverse fluctuating fields Non-adiabatic: exchange of energy between the spin-system and the lattice [environment] α non-adiabatic transitions β α Only Bloc(t)[aniso] can cause relaxation Transverse fluctuating fields: Bloc(t) ex + Bloc(t) ey Longitudinal fluctuating fields: Bloc(t) ez β transitions between states restore Boltzman equilibrium T1 relaxation

14 53 54 Components of the local field Components of the local field Bloc(t) exy Transverse fluctuating fields Non-adiabatic: exchange of energy between the spin-system and the lattice [environment] non-adiabatic transitions β α Bloc(t) ez Longitudinal fluctuating fields Adiabatic: NO exchange of energy between the spin-system and the lattice Effective field along z-axis varies frequency ω0 varies B 0 Bloc(t) ez adiabatic variations of ω0 Heisenberg s uncertainty relationship: shorter lifetimes broadening of energy levels variations of ω0 Bloc(t) ez: frequency ω0 varies due to local changes in B0 Bloc(t) exy: transitions between states reduce phase coherence T2 relaxation Correlation function Spectral density function Describes the fluctuating magnetic fields correlation function C(τ) decays exponentially with a characteristic time τc B loc (t) e x ^ Stationary random function, B loc (t) 0 t Time correlation function, C(τ) C(τ) = <B loc (t)b loc (t+τ)> = <B loc (0)B loc (τ)> <B loc (t)> = 0 2 <B loc (t)> 0 Frequencies of the random fluctuating fields Spectral density function J(ω) is the Fourier transform of the correlation function C(τ) J(ω) describes if a certain frequency can induce relaxation and whether it is efficient J(ω) J(ω) = τ c /(1+ω 2 τ c 2 ) C(τ) C(0) = <B loc (t)> τ c C(τ) = exp( τ/τ c ) C( ) = <B loc (t)> = 0 τ 2 τc 5 ns 10 ns 20 ns ω

15 57 58 Link to rotational motions in liquids Link to rotational motions in liquids Molecules in solution tumble (rotational diffusion combining rotations and collisions with other molecules) Can be characterized by a rotational correlation time!c!c is the time needed for the rms deflection of the molecules to be ~ 1 radian (60 ) Small molecules (or high temperature): smaller (shorter) correlation times (fast tumbling), J(w) extends to higher frequencies - spectrum is flatter Large molecules (or low temperature): larger (longer) correlation times (slow tumbling) J(w) larger close to 0 J(ω) = τ c /(1+ω 2 τ 2 c ) J(ω) τc 5 ns 10 ns 20 ns ω Relaxation NMR time scales relaxation time is related to rate of motion R1 = 1/T1 R2 = 1/T2 protein dynamics protein folding domain motions loop motions side chain motions bond vibrations overall tumbling enzyme catalysis; allosterics fs ps ns s ms s NMR R 1,R 2,NOE RDC relaxation dispersion J-couplings real time NMR H/D exchange

16 61 62 Protein backbone dynamics Protein backbone dynamics 15 N relaxation to describe ps-ns dynamics R1: longitudinal relaxation rate R2: transversal relaxation rate hetero-nuclear NOE: { 1 H}- 15 N 15 N relaxation to describe ps-ns dynamics R1: longitudinal relaxation rate R2: transversal relaxation rate hetero-nuclear NOE: { 1 H}- 15 N dipole interaction chemical shift anisotropy Measured as a 2D 1 H- 15 N spectrum R1,R2: Repeat experiment several times with increasing relaxationdelay Fit the signal intensity as a function of the relaxation delay I0. exp(-rt) { 1 H}- 15 N NOE: Intensity ratio between saturated and non-saturated experiment FAST (ps-ns): rotation correlation time 63 Relaxation rates 64

17 65 66 Relaxation rates Lipari-Szabo MODELFREE C(τ) 1 S 2 effective internal motion, τ int e overall rotation, τ c τ Overall and local motion are considered to be uncorrelated S 2 = order-parameter Modelfree analysis NMR time scales τc = 7.3 ns S 2 protein dynamics protein folding domain motions loop motions side chain motions bond vibrations overall tumbling enzyme catalysis; allosterics fs ps ns s ms s NMR R 1,R 2,NOE relaxation dispersion real time NMR J-couplings H/D exchange RDC

18 Conformational exchange 69 Conformational exchange 70 Causes line-broadening of the signals R2,eff = R2 + Rex H/D exchange 71 Key concepts relaxation time scales 72 Lac headpiece Kalodimos et al. Science fluctuating magnetic fields correlation function, spectral density function molecular motions rotational correlation time (ns) protected in the free state protected only in the DNA-bound state fast time scale flexibility (ps-ns) slow time scale (μs-ms): conformational exchange