NMR II- Pulse sequence and NMR experiments Instructor: Tai-huang Huang (黃太煌) 中央研究院生物醫學科學研究所 Tel. (886)-2-2652-3036; E. mail: bmthh@ibms.sinica.edu.tw Web site: www.nmr.ibms.sinica.edu.tw/~thh/biophysics/NMR-2.ppt Reference: Cavanagh, J. et al., “Protein NMR Spectroscopy-Principles and Practice”, Academic Press, 1996.

NMR II- Pulse sequence and NMR experiments Steps involved in determining protein structures by NMR 取得ＮＭＲ圖譜 圖譜分析 結構計算 液態樣品 ( hours/days to weeks) ( weeks to months) ( days to weeks)

NMR Spectroscopy Bo Radio Wave hn Larmor Equation: Biol. important nuclei: 1H, 2D, 13C, 15N, 19F, 31P Radio Wave hn Classical view Bo Quantum mechanical view Energy Larmor Equation: n =  Bo/ 2 n = Larmor frequency; = nuclear gyric ratio Bo = magnetic field strength (Telsla) E = hn Bo= 0 Bo

Ho Ho Basic Nuclear Spin Interactions Electrons Phonons Nuclear Spin j 6 Electrons 3 3 Nuclear Spin j Ho Ho Nuclear Spin i 1 2 1 5 4 4 Phonons 4 Dominant interactions: H = HZ + HD + HS + HQ . HZ = Zeeman Interaction HD = Dipolar Interactions HS = Chemical Shielding Interaction. HQ = Quadrupolar Interaction

Dominant interactions: . HZ = Zeeman Interaction : I with magnetic field. Path 1 ( BO ~ 109) HD = Dipolar Interactions: I with adjacent spins Path 2,3. ( ISR-3 ~103-5) HS = Chemical Shielding Interaction.: Nuclear spin with magnetic field but shielded by electrons. Path 6and 3. (Dep. Nature of the bond ~ 1-105) HQ = Quadrupolar Interaction: Nuclear spins with surrounding electric field gradient. Path 3. (For I > ½ nuclei; 103 -107) Total Interactions: H = HZ + HD + HS + HQ (All second order tensors) In solid the resonance frequency is orientation dependent and the spectrum will be very complex. There is often too much information to digest. In solution, many of the interactions average out to zero or scalar quantities (non-orientational independent). These remaining interactions contain rich structure-dynamic information. The trick is how to separate them and how to detect them.

In solid the resonance frequency is orientation dependent and the spectrum will be very complex In solution, many of the interaction vanish But many more become orientational independent.

NMR Parameters employed for determining protein structure 1. Chemical Shift Indices: Determining secondary structure. 2. J-coupling: Determine dihedral angles. (Karplus equation) . 3. Nuclear Overhauser Effect (NOE): Determine inter-atomic distances (NOE  R-6) . 4. Residual dipolar coupling: Determine bond orientations. . 5. Relaxation rates (T1, T2 etc): Determine macromolecular dynamics. 1H R 1H BO 1H  15N I t

 Collecting NMR signals NMR signal is detected on the xy plane. The oscillation of Mxy generate a current in a coil , which is the NMR signal. Due to the “relaxation process”, signal decay with time. This time dependent signal is called “free induction decay” (FID) Mxy time (if there’s no relaxation ) (the real case with T1 &T2) time

Fourier transformation (FT)

In addition, most molecules examined by NMR have several sets of nuclei, each with a different precession frequency. Time (sec) The FID (free induction decay) is then Fourier transform to frequency domain to obtain each vpression ( chemical shift) for different nuclei. frequency (Hz)

Pulsed NMR spectroscopy (only signal on X-Y plan is observable) 90o-pulse: Iz Iy  Sees a strong signal 180o-pulse: Iz -Iz  Sees no signal. 90x 90x FT Y Y X X 180x 180x FT Y Y X X

Pulsed NMR spectroscopy (only signal on X-Y plan is observable) -90o-pulse: Iz Iy  Sees a strong negative signal -180o-pulse: Iz -Iz  Sees no signal. 90x -90x (same as 270x) FT Y Y X X 180x -180x FT Y Y X X

Water suppression is an important issue Dynamic range problem. Types of NMR Experiments Homo Nuclear: Detect proton. Heteronuclear – Other nuclei, 13C, 15N, 31P etc. Water suppression is an important issue Dynamic range problem. Huge Water signal (110 M compare to 1 mM for normal protein sample) 1D one pulse 1H Aromatic & Amide Aliphatic

How to suppress water signal ? Sinx/x Presaturation: 1. Long weak pulse: Square waver  SINC function (sinx/x) If  is very short then one will excite a broad spectral region. SINC function (sinx/x)  Square wave 2. Shape pulse: Gaussian  Gaussian Power B1 FT  t  1/ Power  1/

4. 1331 pulse: Similar to 11 pulse but more complicated =   to 1/to 1/to   4. 1331 pulse: Similar to 11 pulse but more complicated 5. Gradient enhanced pulse sequence: (/2)X (/2)-X (/2)-Y (/2)-Y 1H   Receiver on GZ Gradient causes

Homo/Hetero Nuclear 2D NMR Basic 1D Experiment Basic 2D Experiment

二維核磁共振基本原理(HETCOR)

(Nuclear Overhauser Effect SpectroscopY) Through space dipolar effect Determine NOE Measuring distance Assign resonances (COrrelated SpectroscopY) Through bond J-coupling Assign adjacent resonances (Multiple Quantum Filtered COrrelated SpectroscopY) Through bond J-coupling similar to COSY Assign adjacent resonances More sensitive (Homonuclear HAtman-HAhn spectroscopY) (TOtal Correlated SpectroscopY) (TOC SY) Through bond relayed J-coupling Assign full spin system (residues type)

2D-NMR Spectrum

aa ab ba bb I S S I  J-coupling Nuclei which are bonded to one another could cause an influence on each other's effective magnetic field. This is called spin-spin coupling or J coupling. 1 3 C H one-bond three-bond Each spin now seems to has two energy ‘sub-levels’ depending on the state of the spin it is coupled to: The magnitude of the separation is called coupling constant (J) and has units of Hz. aa ab ba bb I S S I J (Hz)

Cγ χ2 H Cβ H H χ1 Cα C’ N ω Ψ ψ C’ Cα N O H J-coupling of backbone nuclei (Hz) 3J(HN-CA) = 4 – 11 Hz depends on secondary structure. < 6 Hz  -helix > 8 Hz  -stand Cγ 35 χ2 H 140 Cβ H H χ1 35 94 2J(13C15N) = 9 Cα C’ N 55 11 15 11 ω Ψ 15 ψ C’ Cα N 94 O H

COSY: (MQF-COSY; DQF-COSY) Off-diagonal resonances due to 1JNHC one bond J-coupling. Assign adjacent resonances. One can select a magnetization transfer pathway (efficiency) by varying the evolution time. TOCSY: ( HOHAHA) Off-diagonal resonances due to relayed J-coupling. Magnetization transfer thru Hartmann-Hahn cross polarization. Assign long range correlated resonances (Whole a.a. system). NOESY: Off-diagonal resonances due to NOE. Magnetization transfer thru energy transfer due to thru space dipolar effect. I  R-6  Determine distances. 3. Sequential resonance assignments.

RC-RNase DQF-COSY (Fingerprint region)

TOCSY (Spin System Identification) RC-RNase 1. J-Coupling: HN→Hα→Hβ…….2. Identify Spin System(a.a. type) δ1/ppm

1H – 1H NOESY of RC-RNase

r XNOE  r-6 RF XNOE = 1 + (d2/4)(H/ N)[6J(H + N) – J(H - N)] T1 Nuclear Overhauser Effect (NOE) RF r I S XNOE = 1 + (d2/4)(H/ N)[6J(H + N) – J(H - N)] T1 where d = (ohN  H/82)(rNH-3), XNOE  r-6

Cγ χ2 H Cβ H H χ1 Cα C’ N ω Ψ ψ C’ Cα N O H J-coupling of backbone nuclei (Hz) 3J(HN-CA) = 4 – 11 Hz depends on secondary structure. < 6 Hz  -helix > 8 Hz  -stand Cγ 35 χ2 H 140 Cβ H H χ1 35 94 2J(13C15N) = 9 Cα C’ N 55 11 15 11 ω Ψ 15 ψ C’ Cα N 94 O H

Homonuclear: 同核 (1H); Heteronuclear: 異核 (1H, 13C, 15N etc) 二維核磁共振基本原理(HETCOR) Homonuclear: 同核 (1H); Heteronuclear: 異核 (1H, 13C, 15N etc)

Amide Proton Resonance Assignments of Thioesterase I

Advantages of heteronuclear NMR: Large chemical shift dispersion  Increased resolution. Large coupling constant (Easy to transfer magnetization. Thru bond connectivity  Easy assignments. Permit easier analysis of protein dynamics. Permit determining the structure of larger proteins (> 100 kDa). Disadvantages of heteronuclear NMR: Must label the protein with 13C and/or 15N. a). Expensive. b). Time consuming. Technically much more complicated. More demanding on spectrometers. Much larger data size.

13C Chemical Shift 15N Shift 1H Chemical Shift

Heteronuclear multidimensional NMR experiments for resonance assignments Magnetization transfer pathway: 1H  15N  13C  15N  1H  1H Detection Detect 1H, 13C, 15N resonances Permit sequential correlation of backbone 1H-13C-15N resonances !!!

II. Dynamics 4-dimensional structure

NMR Relaxation

NMR Relaxation & Protein Dynamics Under current magnetic field strength the relaxation rates are dominated by dipolar interaction and chemical shift anisotropic interaction, and is related to the correlation time, J(), by the following equations: R1 =1/T1 = (d2/4)[J(H - N) + 3J(N) + 6J(H + N)] + c2J(N) ----------- (1) R2 =1/T2 = (d2/8)[4J(0) + J(H - N) + 3J(N) + 6J(H) + 6J(H + N)] + (c2/6)[4J(0) + 3J(N)] + Rex ---------------------------------- (2) where d = (ohN  H/82)(rNH-3), c = N(σ‖- σ)/3. o : permeability constant of free space; h: Planck constant; i : magnetogyric ratio of spin i; i: Larmor frequency of spin i; rNH = 1.02 Å: length of the NH bond vector; Rex: exchange rate; σ‖- σ = -170 ppm (size of the CSA tensor of the backbone amide nitrogen).

r RF XNOE = 1 + (d2/4)(H/ N)[6J(H + N) - J(H - N)]T1 Nuclear Overhauser Effect (NOE) (Energy transfer through dipolar effect) RF r I S XNOE = 1 + (d2/4)(H/ N)[6J(H + N) - J(H - N)]T1 where d = (ohN  H/82)(rNH-3),

Modelfree ananlysis The spins are assumed to be attached to a rigid macromolecule undergoing Browian motion with a rotational correlation time m. In addition, the spins also undergo internal motion with rotational correlation time s. Under this assumption the spectral density function, J() is given by: J() = S2: Order parameters (Magnitude of motion)  : Correlation times (Speed of motion) R ex : Chemical exchange rate (Slow motion in ms or s regime) Fitting T1, T2 and NOE data to determine S2,  and Rex which contain the dynamics information of the protein

Dynamics of E. coli Thioesterase/protease I 1. Measured T1, T2 and (1H, 15N) NOE at 500 and 600 MHz at 310 K. 2. Total of 128 resonances were measured at 500 MHz and 134 resonances were determined at 600 MHz. . 3. Average: R1 = 1.108  0.056 S-1 (1.506  0.096 S-1), R2 = 10.31  1.40 S-1(9.236  1.17 S-1) XNOE = 0.742  0.044 (0.705  0.039) at 14.09 T (11.74 T). 4. From the above data one can determine: a). Rotational diffusion constant. b). Order parameter, S2  Measure of the flexibility. c). Determine rate of local motion. d). Conformational exchange rates. .  At atomic resolution . . .

Relaxation Data Obtained in two fields: : 500 MHz : 600 MHz

Order parameter – Flexibility S2av= 0.85 S = 1 rigid S = 0 random Mostly rigid Flexible region

Correlation time – Residues with fast internal motion

Exchange rate – Residues with low motion

Radius of the susage  1/S Large radius  disordered region

Radius of the sausage  Rex Large radius  Residues with slow motion

Thank You ! 800 MHz