Difference: EinsteinSyllabus (2 vs. 3)

*Introduction*

1. Introduction

1. General overview of NMR and its applications in biochemistry
2. Overview of the course

2. Basic Principles of NMR

1. Nuclear spin (I): who's got it, and how much
2. Magnetic moment (m & g).
3. Isolated spin in a magnetic field
4. B0, torque, and w0.
5. E, DE, Boltzman (and g)
6. The basic NMR experiment:
   1. B1 (R.F.) and resonance
   2. The rotating frame
   3. The experiment: delay, pulse, observe
   4. Application of a pulse
   5. Effect
   6. Flip angle
   7. Description of signal (intensity, frequency, decay)
   8. The Fourier Transform (FT)
7. Summary

3. Signal properties & data processing

1. Review
   1. .F. Pulse brings magnetization into transverse (x,y) plane.
   2. Magnetization precesses at (w0+wi)
   3. Rotating frame (and the "carrier" + "offset")
   4. Free Induction Decay (FID), oscillates at wi
   5. Mathematical description
      1. Iz, Ix, Iy: components of magnetization (projections) along z, x, & y axes
      2. Start with Iz=unity, Ix=0, Iy=0. (normalized; actual magnetization M depends on # spins, gamma, and B0)
      3. Pulse rotates Iz through flip angle a around axis of pulse e.g. a along y axis: aÎy (again = gB1t)
      4. Result: Izcos(a) + Ixsin(a). If a=90 , then simply have Ix, since cos(90)=0, sin(90)=1
   6. With time (t), magnetization precesses in the x,y plane.
      1. This is the same as a rotation about the z axis of angle (wt). i.e. (wt)Îz
      2. So the signal (FID) can be described as:
      3. Ixcos(wt) + Iysin(wt)
      4. It decays in the x,y plane with a time constant T2 as exp(-t/T2):
      5. Ixcos(wt)exp(-t/T2) + Iysin(wt)exp(-t/T2)
      6. Can also write as complex exponential exp(iwt-t/T2)
   7. Sampled signal
      1. Use "quadrature detection" to observe the signal, and determine sign of precession relative to carrier
      2. Results in a "complex" signal (Ix + iIy)
      3. Discretely sampled
      4. Sampling rate: Dt or "dwell time" (DW).
      5. Nyquist theorem
      6. Spectral width (SW) in Hz = 1/(2Dt)
      7. Folding or aliasing
   8. 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
      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
         Multiplicities: 2nI+1
         Weak vs strong coupling
         Typical values
         Field independent
         Nomenclature: nJAB, AMX
         1, 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
      T1: relaxation towards thermal equilibrium
         Qualitative description and overview of measurement

      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
         Note: here both I and S are protons
         Start on Iz as usual
         90Îx -> -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
      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