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Biochemical Applications of NMR Spectroscopy (AECOM, 1998 - present)
*Introduction*
1. Introduction
General overview of NMR and its applications in biochemistry
Overview of the course
2. Basic Principles of NMR
Nuclear spin (I): who's got it, and how much
Magnetic moment (m & g).
Isolated spin in a magnetic field
B0, torque, and w0.
E, DE, Boltzman (and g)
The basic NMR experiment:
B1 (R.F.) and resonance
The rotating frame
The experiment: delay, pulse, observe
Application of a pulse
Effect
Flip angle
Description of signal (intensity, frequency, decay)
The Fourier Transform (FT)
Summary
3. Signal properties & data processing
Review
R.F. Pulse brings magnetization into transverse (x,y) plane.
Magnetization precesses at (w0+wi)
Rotating frame (and the "carrier" + "offset")
Free Induction Decay (FID), oscillates at wi
Mathematical description
Iz, Ix, Iy: components of magnetization (projections) along z, x, & y axes
Start with Iz=unity, Ix=0, Iy=0. (normalized; actual magnetization M depends on # spins, gamma, and B0)
Pulse rotates Iz through flip angle a around axis of pulse
e.g. a along y axis: aÎy (again = gB1t)
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- Result
- Izcos(a) + Ixsin(a). If a=90 , then simply have Ix, since cos(90)=0, sin(90)=1 With time (t), magnetization precesses in the x,y plane. This is the same as a rotation about the z axis of angle (wt). i.e. (wt)Îz So the signal (FID) can be described as: Ixcos(wt) + Iysin(wt) It decays in the x,y plane with a time constant T2 as exp(-t/T2): Ixcos(wt)exp(-t/T2) + Iysin(wt)exp(-t/T2) Can also write as complex exponential exp(iwt-t/T2) Sampled signal Use "quadrature detection" to observe the signal, and determine sign of precession relative to carrier Results in a "complex" signal (Ix + iIy) Discretely sampled Sampling rate: Dt or "dwell time" (DW). Nyquist theorem Spectral width (SW) in Hz = 1/(2Dt) Folding or aliasing The discrete fourier transform (DFT) Formula "Real" absorptive Lorentzian + "imaginary" dispersive Lorentzian signals (only look at absorptive) Linewidth & T2 Digital resolution Number of data points (TD) & noise Zero Filling (SI) Linear Prediction Window or apodization functions Truncation artifacts Exponential (EM) Matched filter Gaussian (GM) Sine bell (SB) Phase and phasing Origin of phase errors Receiver and transmitter phase errors: frequency independent (zero order) Initial sampling delay: frequency dependent (first order) Zero and first order correction procedure Signal & Noise Definition of signal to noise (S/N) Signal averaging Number of scans (NS) S/N proportional to (NS)1/2 Putting it all together for the 1D experiment: Relaxation delay , Pulse, Acquire Text file for pulse program Setup (ased) Pulse length (p1), relaxation delay (d1), SW, TD, SI, NS, O1, RG Acquire (ZG) Window (LB, EM) FT Phase
- Preview
- NMR spectral parameters: chemical shift, coupling, T1, T2
4. Chemical shift & spin-spin coupling; Introduction to T1 and T2.
Chemical Shift
Definition (B_local, shielding constant = sigma)
Field dependant (a reason for going to larger magnets - better resolution)
Field independent units: ppm
Reference standards
Indirect referencing JACS 106, 1939-1941 (1984); J. Biomol. NMR 6, 135-50 (1995)
Ranges for 1H 13C 31P 19F 15N
Origins:
Intrinsic ("chemical")
Electron density
Diamagnetic and paramagnetic components
Extrinsic ("environmental")
Ring current (also carbonyls, etc)
Leads to conformation-dependent chemical shifts in macromolecules
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- Note
- old scales and sign conventions Example uses of chemical shifts: Ionization states Protein secondary structure Stereochemistry Isotope shifts and reaction mechanisms Hydrogen bonds
Spin-spin coupling, two kinds.
Dipolar
Large, normally averaged out in solution
But - relatively recent work at high field (Tjandra & Bax Science 278,1111 1997)
Spin-spin coupling through bonding electrons
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- Multiplicities
- 2nI+1 Weak vs strong coupling Typical values Field independent
- Nomenclature
- nJAB, AMX
- , 2, & 3 bond Ranges for 1H, 13C, 15N, 31P Dependence on dihedral angle (Karplus) Use in assignments (Decoupling, and coherence transfer)
Relaxation - linewidth in spectrum, and intensity vs. relaxation delay
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- T1
- relaxation towards thermal equilibrium Qualitative description and overview of measurement
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- T2
- relaxation in the transverse plane. Qualitative description and overview of measurement Both depend on molecular motion
Lab 1: Introduction & basic 1D experiment
*Basic Experiments & Small Molecules*
5. Relaxation & the NOE
6. Product operator description & coherence transfer
7. A repertoire of one-dimensional methods
Review of the basic 1D experiment (zg, zg30) - note: phase cycle
Broadband decoupling (zgdc, zgdc30; BAUG pp. 37-40)
Homonuclear gated decoupling (zghd)
Solvent suppression
Why work in 1H solvent?
Presaturation (zgpr)
Gradient methods
Introduction to gradients
Selective pulses (selzg; BAUG pp. 83-100)
Watergate (p3919gp)
Jump and return, a.k.a. 1:1 (p11)
T1 - inversion recovery (t1ir; BAUG pp. 71-81)
T2 - spin echo, Carr-Purcell-Meiboom-Gill (cpmg)
Steady-state NOE
Homonuclear - NOE difference (noedif)
Heteronuclear
Transient NOE
Initial rate approximation
Distances
TOE (noedif; BAUG pp. 101-111)
Heteronuclear coherence transfer: DEPT (dept; BAUG pp. 65-70)
Doddrell et al, J. Magn. Reson. 48, 323 (1982)
Signal to noise enhancement
Spectral editing
Lab 2: 1D homonuclear and heteronuclear experiments
8. Introduction to two-dimensional NMR
Building blocks:
INEPT
reverse INEPT
INEPT-revINEPT, as a filter
The second dimension, via the HSQC (INEPT-t1-reverse INEPT)
Quadrature in t1
Practical issues
9. 2D Heteronuclear experiments
10. 2D Homonuclear experiments
Introduction
The three most important homonuclear experiments:
COSY - cross peaks between protons <= 3 bonds apart
TOCSY - cross peaks from all members of a spin system
NOESY - cross peaks from through-space dipolar coupling
COSY & TOCSY - assignment of resonances
NOESY - conformation (distances between assigned spins)
Together provide sufficient data to determine the complete structures of
small proteins and nucleic acids - important experiments indeed.
- COSY
- COrrelation SpectroscopY? Aue, Bartoli, & Ernst J. Chem. Phys. 64, 2229-46 (1976) First 2D experiment ever proposed (1971) Cross peaks from scalar coupled 1H <= 3 bonds apart. Example spectrum (R2-CH-CH2-CH3) Pulse sequence: ____|___t1___| \/\/\/\/\/\/\/\/ Looks simple, but - Results of product operator analysis
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- Note
- here both I and S are protons Start on Iz as usual
- Îx -> -Iy During t1, both chemical shift evolution (wt1Îz) and coupling (pJt1Î1zÎ2z) I->S transfer builds up over t1 as sin(pJt1) ¿ so no cross peak signal in initial FIDs Terms leading to diagonal and cross peaks Properties of cross-peak and diagonal Diagonal - in-phase doublet Cross peaks - anti-phase doublet The two are 90 degrees out of phase with each other Can get cancellation in cross peaks for molecules with large linewidths
Examples
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- Variant
- DQF-COSY - Double Quantum Filtered COSY Rance et al, BBRC 117, 479-485 (1983) Pulse sequence: ___|__t1__| | \/\/\/\/\/\/\/\/ Final pulse converts MQ term in COSY into observable magnetization Diagonal and cross peaks simultaneously in phase Reduced contributions from "peaks without partners" - e.g. H2O But, lose factor of 2 in signal Usually worth the tradeoff & this is the standard COSY experiment Processing, phasing Final Note: caution about coupling constants from COSY Mutual cancellation and distortion. (E. COSY: "Exclusive COSY") Resonance overlap - a problem even in 2D NMR (example). A helpful experiment is: .... and so on for:
- TOCSY
- TOtal Correlation SpectroscopY? (a.k.a. "HOHAHA") NOESY (via the Transient 1D NOE) ROESY EXSY
Lab 3: 2D Correlation experiments
11. Pulsed field gradients, Solvent suppression, and Selfdiffusion
*Macromolecular Structure*
Small Proteins and Nucleic Acids
12. Resonance assignments
14. Structural Constraints
Lab 4: 23 residue antibiotic peptide: 2D correlation spectra & assignments
15. Structure calculation & refinement
16. Structure evaluation
17. Nucleic Acids: assignments, constraints & structure
Lab 5: 2D NOESY spectrum & analysis
18. Representative protein and nucleic acid NMR structure determinations
19. Conformation of ligands on macromolecules
Lab 6: Structure calculation & analysis
Larger Proteins & Nucleic Acids - Isotopic labeling & 3D experiments
20. Introduction to 3D NMR (via NOESY-HSQC and TOCSY-HSQC)
21. Triple resonance experiment and stucture determination, Part I
Lab7: 2D & 3D 1H15N spectra of labeled proteins
22. Triple resonance experiments and stucture determination, Part II
... including labeling, deuteration, and example 3D structure determination
23. On to larger (> 30kD) proteins
*Biochemical Applications*
Ligands, Kinetics & Mechanism
24. Water & hydrogen bonds
25. Ionization states & pK_a's
Lab 8: Triple resonance experiments
26. NMR-Based Screening in Drug Discovery
27. "Fun with Enzymes": k_on, k_off, K_eq, K_eq', PIX, etc.
28. Folding of proteins & nucleic acids
Lab 9: Titration of histidine pK_a's in ribonuclease
*Dynamics*
29. Metabolic studies in cells
30. Exchange & measuring dynamic processes
Lab 10: Substrate k_on and k_off from saturation transfer
31. Heteronuclear relaxation & Macromolecular dynamics |
