Introduction to solution NMR 1 Alexandre Bonvin Bijvoet Center for Biomolecular Research with thanks to Dr. Klaartje Houben Bente%Vestergaard% The NMR research group Prof. Marc Baldus Prof. Rolf Boelens Solution NMR: 950, 950(in 900-cryo, progress) 750, 900-cryo, 600-cryo, 750, 600US, 600-cryo, 2x500600US, MHz 2017?: 2x500 MHz 1.2 GHz Solid-state NMR: 800WB-DNP, 400WB-DNP, 700US, 500WB MHz e-infrastructure: >1900 CPU cores + EGI grid (>110 000 (>100 000 CPU cores) 2017?: 1.2 GHz Prof. Alexandre Bonvin National and European infrastructure http://www.uu.nl/nmr
5 6 NMR journey Topics Why use NMR for structural biology...? The very basics Multidimensional NMR (intro) Resonance assignment (lecture Banci) Structure parameters & calculations (lecture Banci) NMR relaxation & dynamics NMR & Structural biology DYNAMICS Why use NMR...? a F helices DBD F helices CBD apo-cap CAP-cAMP 2 Dynamic activation of an allosteric regulatory protein Tzeng S-R & Kalodimos CG Nature (2009)
NMR & Structural biology Allosteric regulation DYNAMICS Dynamic interaction between ligand-binding & DNA binding site NMR & Structural biology Biomolecular interactions Even weak and transient complexes can be studied Dynamic activation of an allosteric regulatory protein Tzeng S-R & Kalodimos CG Nature (2009) 11 12 NMR & Structural biology EXCITED STATES NMR & Structural biology MEMBRANE PROTEINS Native like environment Structural changes due to lipid environment Shekhar & Kay PNAS 2013 van der Cruijsen,... & Baldus PNAS 2013
NMR & Structural biology AMYLOID FIBRILS 13 NMR & Structural biology IN-CELL NMR Study proteins in their native cellular environment Outermembrane protein in bacterial cell envelop 14 Amyloid Fibrils of the HET-s(218 289) Prion Form a β Solenoid with a Triangular Hydrophobic Core Wasmer C. et al Science (2008) Renault M,... & Baldus PNAS 2012 The NMR sample 16 The very basics of NMR 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
17 18 Nuclear spin precession Nuclear spin E = µ B 0 (rad. T -1. s -1 ) 19 20 Nuclear spin Nuclear spin & radiowaves Nuclear magnetic resonance Only nuclei with non-zero spin quantum number are magnets Commonly used spins are spin ½ nuclei: 1 H, 13 C, 15 N, 31 P etc. NMR a non invasive technique Low energy radiowaves quantum number I = ½ magnetic field strength B0 α β -½ ½ β α ΔE = γħb0 gyromagnetic ratio (different for each type of nucleus) Larmor frequency ν = (γb 0)/2π
Boltzman distribution 21 Net magnetization 22 1 H m = -½ m = ½ Example - 20.001 spins - Only 1 more spin in lower energy state 24 Pulse Radio frequency pulses Turn on an amplifier for a certain amount of time & certain amount of power (B 1 field) Chemical shielding B 0 γ B0 ν = 0 2 π B 1 γ B ν = 1 1 2π only rotation around B1 is observed rotating frame: observe with frequency ν 0 Local magnetic field is influenced by electronic environment ==> frequencies of nuclei will differ
Chemical shift γ B ν = 0 1 2π ( σ ) shielding constant 25 The spectrometer 26 More conveniently expressed as part per million by comparison to a reference frequency:! = 10 6 "# " ref " ref 27 28 Free induction decay (FID) FID: analogue vs digital Free Induction Decay (FID)
29 30 Fourier Transform Relaxation Signal 0 FT Signal 0 NMR Relaxation Restores Boltzmann equilibrium 0 25 50 75 100 125 150 175 200 time (ms) 0 5 10 15 20 25 30 35 40 freq. (s -1 ) T2-relaxation (transverse relaxation)spin-spin) disappearance of transverse (x,y) magnetization contributions from spin-spin and T1 relaxation 1/T2 ~ signal line-width FT T1-relaxation (longitudinal relaxation / spin-lattice) build-up of longitudinal (z) magnetization determines how long you should wait for the next experiment 31 32 Relaxation Restoring Boltzmann equilibrium T 2 relaxation: disappearance of transverse (x,y) magnetization Relaxation Restoring Boltzmann equilibrium T 1 relaxation: build-up of longitudinal (z) magnetization!! 1/T2 ~ signal line-width!!!! T1 determines when to start the next experiment!!
NMR spectral quality 33 Scalar coupling / J-coupling 34 Sensitivity Signal to noise ratio (S/N) Sample concentration Field strength.. Resolution Peak separation Line-width (T2) Field strength.. H3C - CH2 - Br 3 JHH Key concepts NMR Nuclear magnetic resonance In a magnetic field magnetic nuclei will resonate with a specific frequency FT-NMR Pulse, rotating frame, FID Chemical shift Electronic environment influences local magnetic field -> frequency NMR relaxation T 1 & T 2 J-coupling 35 Multidimensional NMR
Why multidimensional NMR Resolve overlapping signals observe signals from different nuclei separately Correlate chemical shifts of different nuclei needed for assignment of the chemical shifts Encoding structural and/or dynamical information enables structure determination enables study of dynamics 2D NMR 38 39 40 3D NMR nd experiment 1D indirect dimensions direct dimension t1 preparation acquisition 1 FID of N points 2D t1 preparation evolution mixing t2 acquisition N FIDs of N points 3D preparation t1 evolution mixing t2 evolution mixing t3 acquisition NxN FIDs of N points
41 42 Encoding information Magnetization transfer dipole-dipole interaction mixing/magnetization transfer???? Magnetic dipole interaction (NOE) Nuclear Overhauser Effect through space distance dependent (1/r6) NOESY -> distance restraints proton A spin-spin interactions proton B J-coupling interaction through 3-4 bonds max. chemical connectivities assignment also conformation dependent 43 homonuclear NMR NOESY t1 tm t2 FID magnetic dipole interaction crosspeak intensity ~1/r 6 up to 5 Å 2D NOESY Uses dipolar interaction (NOE) to transfer magnetization between protons cross-peak intensity ~ 1/r 6 distances (r) < 5Å COSY t1 FID t2 J-coupling interaction transfer over one J-coupling, i.e. max. 3-4 bonds diagonal H N TOCSY t1 mlev FID t2 J-coupling interaction transfer over several J- couplings, i.e. multiple steps over max. 3-4 bonds H N cross-peak 44
45 46 Homonuclear scalar coupling 2D COSY & TOCSY 2D COSY 2D TOCSY H β H β 3 JHαHβ ~ 3-12 Hz H α H α 3 JHNHα ~ 2-10 Hz HN HN 47 48 homonuclear NMR ~Å heteronuclear NMR NOESY t1 tm FID t2 proton A proton B A A (ωa) A A (ωa) B B (ωb) F1 ωa ωa ωb (F1,F2) = ωa, ωa (F1,F2) = ωa, ωb Diagonal Cross-peak 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 F2
J coupling constants 49 15 N HSQC Backbone HN Side-chain NH and NH2 50 1JCbCg = 35 Hz 1JCbHb = 130 Hz 1JCaCb = 35 Hz 1JCaC = 1JNC = 1JCaN = 55 Hz -15 Hz -11 Hz 1JCaHa = 140 Hz 2JCaN = 7 Hz 1JHN = -92 Hz 2JNC < 1 Hz 51 52 1 H- 15 N HSQC: protein fingerprint 1 H- 15 N HSQC: protein fingerprint
53 Key concepts multidimensional NMR Resolve overlapping signals Mixing/magnetization transfer NOESY, TOCSY, COSY Relaxation & dynamics HSQC 3D NOESY-HSQC, 3D TOCSY-HSQC Triple resonance 55 56 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 + return to z-axis B0 B1 B0 Bloc
57 58 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)? 59 60 Local fluctuating magnetic fields Components of the local field B loc(t) = B loc[iso] + B loc(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) Only Bloc(t)[aniso] can cause relaxation Transverse fluctuating fields: Bloc(t) ex + Bloc(t) ey Longitudinal fluctuating fields: Bloc(t) ez B loc(t) e xy Transverse fluctuating fields Non-adiabatic: exchange of energy between the spin-system and the lattice [environment] α β transitions between states restore Boltzman equilibrium T1 relaxation non-adiabatic transitions β α
61 62 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] Heisenberg s uncertainty relationship: shorter lifetimes broadening of energy levels non-adiabatic transitions variations of ω0 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 loc(t) e z: frequency ω 0 varies due to local changes in B 0 B loc(t) e xy: transitions between states reduce phase coherence B 0 Bloc(t) ez adiabatic variations of ω0 T2 relaxation 63 64 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 <B loc (t)> = 0 2 <B loc (t)> 0 Time correlation function, C(τ) C(τ) = <B loc (t)b loc (t+τ)> = <B loc (0)B loc (τ)> 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) 1 0.8 0.6 0.4 0.2 2 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
65 66 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) Small molecules (or high temperature): smaller (shorter) correlation times (fast tumbling), J(w) extends to higher frequencies - spectrum is flatter Can be characterized by a rotational correlation time τc τc is the time needed for the rms deflection of the molecules to be ~ 1 radian (60 ) 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 67 68 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 relaxation dispersion real time NMR J-couplings H/D exchange RDC
Protein backbone dynamics 69 Protein backbone dynamics 70 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 Relaxation rates 71 Lipari-Szabo MODELFREE 72 C(τ) 1 S 2 effective internal motion, τ int e overall rotation, τ c Overall and local motion are considered to be uncorrelated S 2 = order-parameter τ
73 74 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 J-couplings real time NMR H/D exchange RDC 75 76 Conformational exchange Conformational exchange Causes line-broadening of the signals R2,eff = R2 + Rex
H/D exchange 77 Key concepts relaxation time scales 78 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 The End Thank you for your attention!