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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;

NMR 3- 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:

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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;

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  1. NMR 3- 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. Term paper:  Find a NMR paper and write a report on the subject related to the paper.

  2. 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)

  3. 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

  4. The Bloch Equations: dM/dt = M x B + relaxation terms • dMx(t) / dt =  [ My(t) * Bz - Mz(t) * By ] - Mx(t) / T2 --------- (1) • dMy(t) / dt =  [ Mz(t) * Bx - Mx(t) * Bz ] - My(t) / T2 --------- (2) • dMz(t) / dt =  [ Mx(t) * By - My(t) * Bx ] - ( Mz(t) - Mo ) / T1 ------ (3) • Rotating frame: • Let [dM(t)/dt]rot = [dM(t)/dt]lab+M(t) x  • = M(t) x [γB(t) + ] • Let Beff = B(t) + /γ------------------- (4) • Thus, if B(t) + /γ= 0, or B(t) = - , Beff = 0 •  dM(t)/dt = 0,  M(t) is time independent. • In the absence of RF field and B(t) = Bo or B(t) = -Bo = - o= Larmor frequency. • In a frame rotating at Larmor frequency the magnetization is static. • The Bloch equations become: • dMz(t) / dt = [ Mo- Mz(t)/ T1 -------------- (5) • dMx(t) / dt = - Mx(t) / T2 -------------- (6) • dMy(t) / dt = - My(t)/T2 -------------- (7) Z Bo= Bo- o/ Bo Y X

  5. Solutions: Mz = Mo – [Mo –Mz(0)]exp(-t/T1) -------------- (8) Mx = Mx(0)exp(-t/T2); -------------- (9) My = My(0)exp(-t/T2); -------------- (10) • T1 relaxation in the Z-direction and T2 relaxation on the xy-plane • If we obsere the spins in a frame which rotate at exactly the Larmor frequency then we see the spin state stationary (Static). • What if we observe the spin at a frequency which is  from the Larmor frequency ?  Both Mx and My will rotate at  Hz. Experimentally what is the rotating frame ? o Computer Probe Transmitter 106 – 109 Hz  Signal is in rotating frame (kHz) o - o Receiver Digitizer

  6. Effect of RF-field: • dMz(t)/dt = [Mx(t)Bry(t) – My(t)Brx(t)] – [Mz(t) – Mo]/T1 • dMx(t)/dt = - My(t) – Mz(t)Bry(t) – Mx(t)/T2 ----------- (11) • dMy(t)/dt = Mx(t) – Mz(t)Brx(t) – My(t)/T2 • where Brx(t) = Brocos and Bry(t) = Brosin •  = -γΔBo- rf = o - rfis the offset. • In a common experimental situation in pulse NMR, B1 • is applied for a time p<< T1, T2 and neither B1 nor  • is time dependent. Thus, during the time when B1 is on eq. 11 becomes: • dMz(t)/dt = Mx(t)Bry(t) – My(t)Brx(t) • dMx(t)/dt = - My(t) – Mz(t)Bry(t) ----------- (12) • dMy(t)/dt = Mx(t) – Mz(t)Brx(t) • The solution of eq. 12 is a series of rotations about the axis perpendicular • to the applied B1 field. The signal can be described as: • Mx(t) = Mosincos(t)exp(-t/T2) • My(t) = Mosinsin(t)exp(-t/T2) Bo Br B1

  7. Bloch Equations (Phenomenological equations): dMx/dt = (M x H)x – Mx/T2 -------------------- (1) dMy/dt = (M x H)y – My/T2 -------------------- (2) dMz/dt = (M x H)z – (Mo – Mz)/T1 ----------- (1) For H1 along the x-axis and H1 0 and in steady state i.e. dM/dt = 0 we can solve the above simultaneous Equations to get: Mx = o(oT2) -------- (3) (Lorenzian lineshape, absorption) My = o(oT2) -------- (4) (Dispersion) Mx My

  8. Fourier transformation (FT) FT  Function at  = 1/T2 exponential Lorenzian At zero Hz FT Lorenzian at  FT M Mx My  Absorption: Mx = Mo/[1 + ( - )2T22] Dispersion signal: My = Mo(-)/[1 + ( - )2T22]

  9. 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

  10. 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

  11. Spin-echo pulse:90o--180o--detection 1. Refocus chemical shift. 2. Decouple of heteronuclear J-coupleing 180x 90x   Detection FT (Dephasing) (Excitation)  90x Y Y Y X X X 180x (Inversion) (Refocusing) (Detection)   Y Y X X

  12. Pulse of finite length Sinx/x • 1. Long weak pulse: • Square waver  SINC function (sinx/x) • If  is very short then one will excite a broad spectral region. • Long pulse excite only finite region of the spectrum. 2. Shape pulse: • SINC function (sinx/x)  Square wave • Gaussian  Gaussian Power B1 FT  t  0 1/ Power  1/

  13. 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

  14. 3. 1-1 pulse:  =  0 to 1/to 1/to   4. 1331 pulse: Similar to 11 pulse but more complicated 5. Gradient enhanced pulse sequence (Watergate): (/2)X (/2)-Y (/2)-Y (/2)-X   1H Receiver on GZ Gradient causes

  15. Homo Nuclear 2D NMR – Need two variable times Basic 1D Experiment Basic 2D Experiment

  16. Homo Nuclear 2D NMR – Need two variable times • Needs two time variables t1 and t2 for chemical shift to evolve. • Needs to decide what interaction do you wish to observe ? • J-coupling – short and long range coupling. • Take place on x-y plane only. • NOE – Take place when magnetization is in Z-direction. • In heterouclear NMR one needs a way to transfer magnetization • between nuclei. • J-coupling (the larger the easier to transfer magnetization). • Need to adjust the time duration of the coupling (Maximum • when coupling time  = 1/2J. If J = 100 Hz,  = 5 ms)

  17. three-bond one-bond 1 H 1 3 C J (Hz) bb 1 1 H H I S ab ba S I I S aa  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. • 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.

  18. 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

  19. Heteronuclear 2D NMR (HETCOR) – (Need ways to couple different nuclei)

  20. FT (t1) Transpose (t2) t1 t11 t21 t31 t41 FT (t2) 2 1

  21. 2D-NMR Spectrum – stack plot

  22. 2D spectrum (Countour plot)

  23. Determining Macromolecular Structures (3) Assign NMR resonances (1) Prepare NMR samples 2H, 13C and/or 15N- Labeled (2) Obtain NMR spectra- ( 1D, 2D, 3D & 4D) (4) Obtain NMR restraints distances, dihedral angles bond orientations (5) Structure Calculation and refinement

  24. Determining Macromolecular Structures (3) Assign NMR resonances • Assign all resonances to a specific amino acid. • Assign to a specific nucleus. • Proton resonances are most important for structure determination. • Homonuclear 2D NMR for small proteins (< 10kDa). • Heteronuclar NMR are required for larger proteins (> 10 kDa) • Deuteration is needed for protein > 30 kDa.

  25. Homonuclear NMR – small protein 1000 protons to assign. 1D clear is unable to do the job.

  26. (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)

  27. COSY: (MQF-COSY; DQF-COSY) • Off-diagonal resonances due to 1JNHC onebond 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.

  28. RC-RNase DQF-COSY (Fingerprint region)

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

  30. 1H – 1H NOESY of RC-RNase

  31. 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

  32. Larger proteins(> 10 kDa) • Need to label the protein with 13C and 15N, and may be 2H. • Need to do heteronuclear multidiemnsional NMR (3D or 4D) • Heteronculear has larger chemical shift dispersion, thus • better resolution. (13C ~ 200 ppm; 15N ~ 300 ppm) • Energy transfer between heteronuclei by J-coupling.

  33. 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

  34. 13C Chemical Shift 15N Shift 1H Chemical Shift

  35. 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.

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

  37. 2D 15N-1H Heteronuclear Single Quantum Correlation Spectroscopy) (15N-HSQC) 90x 90x 90x 180x 180x 180x    t2 1H 180x 90x 180x t1 15N Decoupling Magnetization transfer from 1H to 15N 15N chemical shift evolution 1H detection Magnetization transfer from 15N to 1H Efficientcy  sin(2J) Maximum transfer when 2J = /2. or  = 1/4J = 1/4x94 = 2.5 ms

  38. Amide Proton Resonance Assignments of Thioesterase I

  39. 3D NOESY-HSQC 90x 90x 90x 90x 90x 180x 180x 180x    t1 t3 NOE 1H 180x 90x 180x t2 15N Dec Decoupling NOESY 15N-HSQC

  40. 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

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