1. NMR Principles of Structure Determination
Hornak
Sheffield
U. Chicago
Biophysical Tools '04 -NMR Part A
9/22/2018

2. Energy levels and resonance
Magnetic moment of a nucleus:
m = g ħI
Energy of a magnetic dipole in magnetic field
E = -m Bo= -1/2għIz
Transitions between the levels
DE = hn =għIBo
Basic Principles
Spinning charge (i.e. charge possessing angular momentum J) has a magnetic moment (dipole m ) proportional to it:
M=gamma * angular momentum
The magnetic dipole interacts with the applied magnetic field Bo . Magnetic field exerts a torque on the magnetic dipole attempting to align it either parallel or antiparallel to itself. Quantization of nuclei does not allow parallel alignment but rather at a fixed angle q .
The interaction energy between the dipole m and the field Ho is given by:
E = mHosinq.
Transition between parallel and antiparallel orientations thus requires
DE = 2mHosinq.
Thus electromagnetic wave needed to flip the spins will have to be of frequency
Biophysical Tools '04 -NMR Part A
9/22/2018

3. Biophysical Tools '04 -NMR Part A
Sensitivity
Number of nuclei have a magnetic moment, the most sensitive are 1H and 19F.
Sensitivity is proportional to difference in populations at equilibrium:
Nupper/Nlower = e-DE/kt = e-g Ho / kt
the larger is g and the larger is the field (Ho) the greater is sensitivity.
Gyromagnetic ratio is fixed for a given nucleus, field can be increased at will (that’s why NHMFL)
Biophysical Tools '04 -NMR Part A
9/22/2018

4. Biophysical Tools '04 -NMR Part A
Measurement
NMR spectrometer
Fourier Transform NMR
Free Induction Decay (FID)
Fourier Transform
Biophysical Tools '04 -NMR Part A
9/22/2018

5. Biophysical Tools '04 -NMR Part A
Chemical Shift
Local fields induced by electrons
Chemical Shift
Electrons also interact with the magnetic field and by doing so (rotation about Ho ) electrons induce small local fields at the nucleus. The effect is small shielding of the external field which depends on the electrons surrounding the nucleus.
The effect is very small thus is expressed as a parts per million (ppm) shift with respect to a reference sample
Biophysical Tools '04 -NMR Part A
9/22/2018

6. Structure Determination
Spin-spin coupling
CH3 - CHO
Principles
resonances depend also on the environment e.g. who is:
(a) your family
(b) who is the neighbor
Spin-spin coupling
Nuclei talk to each other via bonding (paired) electrons. Each nucleus sees the small field of the other nucleus resulting in the multiplet splitting.
Biophysical Tools '04 -NMR Part A
9/22/2018

7. Biophysical Tools '04 -NMR Part A
2 Dimensional NMR
Connectivities
Resonance overlap
many overlapping resonances with various chemical shifts and spin-spin couplings
Old spy story: find connections:
solution: drop a plant and eavesdrop which resonances are being told the story
Biophysical Tools '04 -NMR Part A
9/22/2018

8. COSY: Residue identification
Ala
Glu
Arg
COSY
spin-spin (through bond) connectivities
ascribe the resonances to different spin systems
we know what connected to what but in what sequence ?!
Spin-spin connectivitites (thorugh bond)
Biophysical Tools '04 -NMR Part A
9/22/2018

9. NOESY: Distance information
Nuclear Overhauser Effect: NOE
dipolar - through space connectivity A B C D
NOESY
dipolar - through space connectivity
"talking" atoms - (nuclear Overhauser effect, NOE)
neighboring nuclei affect each other resonances, if close enough (> 5 Å) tickling one gets the other one laughing
off-diagonal cross peaks identify the H-H connectivity
the time-dependence of cross peak development is function of H-H proximity :
small proteins as NOE f(tc)/r6
competing movement of the protons limits the distance to a coarse estimate of the upper limit of H-H distance: strong, moderate, weak - 2.7; 3.3; 5 Å
can find distances but which resonance comes from which residues AD
Biophysical Tools '04 -NMR Part A
9/22/2018

10. Sequence specific assignments
all the peaks - thousands of them - have to be identified
simplest case: homonuclear 1.) intra-residue NH to Ca by COSY 2.) inter-residue Ca of i-th to NH of i+1-th by NOESY
heteronuclear/multidimensional NMR - RUBIK's cube
allow N nuclei and C nuclei "talk" to H bonded to neighboring atoms
connectivities between atoms established by simultaneous observation of 13C, 14N and H resonances
tracing a polypeptide chain: a game of Dominoes
Biophysical Tools '04 -NMR Part A
9/22/2018

11. Tracing a polypeptide chain
find a unique spin system (Gly, Val) in spectrum and 1o sequence.
Biophysical Tools '04 -NMR Part A
9/22/2018

12. Biophysical Tools '04 -NMR Part A
Contact plots
alpha helices: i to i+3 and i+4 contacts
beta strands: antiparallel : contacts perpendicular to diagonal parallel: i to N+i contacts
Biophysical Tools '04 -NMR Part A
9/22/2018

13. Structure Determination
Secondary Structure Determination
a helix: strong NH(i) - NH(i+1); moderate to weak CaH (i) - NH(i+3)
b strands: strong CaH (i) - NH(i+1) and interstrand Ca - NH
Tertiary structure determination
Distance Geometry Algorithms
ri = (xi,yi,zi)
and Lij < ri - rj < Uij
Refinement by Molecular Dynamics
Secondary Structure Determination
a helix: strong NH(i) - NH(i+1); moderate to weak CaH (i) - NH(i+3)
b strands: strong CaH (i) - NH(i+1) and interstrand Ca - NH
Tertiary structure determination
collect thousands of NOE distances and only few geometries will satisfy all distance constraints
molecular modeling by hand is impossible
Distance Geometry Algorithms
powerful mathematical algorithms which identify protein conformations in which each H nucleus has a position:
ri = (xi,yi,zi)
and satisfies NMR determined upper and lower bounds for observed distances between ith and jth atom:
Lij < ri - rj < Uij
structure is independent of the starting conditions or mathematical techniques
large dimensions calculated from very short distances
precision of the determined structure much better than the individual NOE distance
Refinement by Molecular Dynamics
Solution of the equation of motion for all atoms in the potential energy well which includes bond length, bond angle, electrostatics and van der Waals
Biophysical Tools '04 -NMR Part A
9/22/2018

14. Biophysical Tools '04 -NMR Part A
Summary
Assign the resonances
Determine proton-proton distances
Determine 2o structure from i  i+x NOE's and connectivities
Determine 3o structure by DG
Refine with MD
Assign the resonances
Determine proton-proton distances (torsion angles)
Determine 2o structure from i  i+x NOE's and connectivities
Determine 3o structure by DG
Refine with MD
(publish in Science)
Power of NMR structure determination
X-ray can do it too.... but NMR has an edge:
proteins in solution not in crystals; more relevant structure-function relationships
proteins do not have to crystallize, many will not
movement on biologically relevant timescale
Disadvantages:
small molecules < 20 kD
isotopic substitution, 13C and 14N are very rare, proteins have to be grown on media enriched in these isotopes
Biophysical Tools '04 -NMR Part A
9/22/2018