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Nuclear Magnetic
Resonance:
October 2016
How it Works
How We Use it
NMR:
Further Reading
Modern NMR Techniques for Chemistry Research by Andrew E. Derome
(general principles and organic chemistry applications)
Understanding NMR Spectroscopy by James Keeler
(to help a user become an expert)
Parts of Chapters 2-5, 7
http://www-keeler.ch.cam.ac.uk/
Electromagnetic Radiation is a Sine Wave in 3
Dimensions
http://www.physics.gatech.edu/gcuo/UltrafastOptics/3803/OpticsI03Maxwell_sEqns.ppt
At any given point, as light propagates, the electric
and magnetic fields fluctuate sinusoidally
Quantum mechanically, the energy is hn (h is plank’s const.
and n is the frequency)
Magnetic Resonance uses
Radiofrequency Radiation
•Nuclei, especially
protons, are most visible
•Structural information
can be partial
(sometimes)
Nuclear Magnetic Resonance:
Observation
Sin wot
M (t)
t
z
FT
x
y
Ho
H1
O
H
H
w=-wo
w=0
w=+wo
2 “delta functions”
A More Realistic Example: A Sine Wave
with Exponential Decay
Sin wot exp(-at)
M (t)
z
x
y
Ho
H1
FT
a
O
H
H
n. b. we have tricks to get
rid of the negative signal
w=0
w=+wo
FT of exp(-at) = 1/{1 + ((w- wo )/a)2} (a “lorentzian”)
Line Width and Line Shape
M (t)
a
Sin wot exp(-at)
FT
Sin wot exp(-bt)
b>a
If signals come from the same molecule, integral
under the peak is equal
FT of exp(-at) = 1/{1 + (w/a)2}
A Molecule With Two Proton Signals
M (t)
Sin w1t + Sin w2t
+
z
X e-at
=
x
y
Ho
H
N
FT
H
N
H
N
H1
N
N
H
n. b. We add to
deuterated water:
NH2 is invisible
w=w1
w=w2
Where Does the NMR Signal Come
From?


1.
2.
We measure signals and mathematically
interpret them, then we form models to fit the
math
We must come up with a model which
Produces sinusoidal signals
Produces exponential decay
Electrons and Nuclei Have Magnetic
Moments
mm = gL (L = nuclear spin angular
momentum)
g = the magnetogyric ratio, characteristic of
the type of nucleus (see table 9-1 of Cantor
and Schimmel)
1H is the most sensitive of the natural
abundance nuclei
For organic molecules or biomolecules, 13C,
15N, 19F and 31P are most frequently detected
The Larmor Frequency
w = gH = “The Larmor frequency”
The Larmor Frequency Depends on:
• The gyromagnetic ratio (characteristic of the nucleus)
• The local magnetic field
1. Ho the External field
2. Local variations due to the chemical environment
In real situations, we measure the Larmor
frequency relative to a reference.
The frequency for a signal attached to a given
nucleus, relative to this reference, is called the
chemical shift
The Larmor Frequency
The Local Magnetic Field Depends on:
• Magnetic fields from neighboring nuclei
• Aromatic rings (ring currents)
• Coupling to other nuclei
1. Electronic structure of covalent bonds
2. Through space coupling (“dipolar interactions”)
(Nuclear Overhauser Enhancement (NOE)
proportional to r-6, r is the interproton distance
3. Residual dipolar splittings-arise from magnetic
dipole-dipole interactions-sensitive to the
alignment of the sample relative to the external
field
A “Classical” Picture to Explain NMR
Consider a spinning
charged body in a
magnetic field Ho
Current
Torque = t =
mm X H
These are all vector quantities
mm
Ho
Magnetic Moment
t = dL/dt = change in
angular momentum:
perpendicular to mm and
H
But mm =
gL
dL/dt = gL X H = -L X w
(mechanically you can observe the same with a “spinning top”)
Circular (Periodic) Motion
Cosine (x projections)
Sine (y projections)
Geometric Interpretation
A(t) = Snuclei rncos(wn t - fn) sum of harmonic
funtions
rn = “amplitude”
or “intensity”
y
wn = “frequency”
fn = “phase”
r
wt -f
0
The Fourier Transform extracts these harmonic functions from
the magnetization as a function of time (called the “free
induction decay” or “FID”) to obtain the frequency spectrum
x
Quantum Mechanical Aspects of NMR:
Practical Considerations
Nuclei have discrete (quantized) spin
states
Spin ½ nuclei: spin + 1/2, spin – 1/2
Spin 1 nuclei: spin + 1, spin 0, spin -1
 We observe xy magnetization signal when
there is a net movement of nuclei from
one spin state to another over the
ensemble of spins in the sample: Z
magnetization corresponds to a net
magnetic moment with the external field

Pulsed NMR

In order to observe xy signal, we perturb
nuclei from their equilibrium positions
Magnetic
“Pulse” P(t) in
x or y direction
perturbs
equilibrium, by
setting up a
“resonance” at
the Larmor
frequency
Ho
Ho
equilibrium
perturbed
Two dimensional NMR
At least two magnetic pulses are required:
p1
p2
Input pulses
t1
t2
t1
t2
Magnetization measured as
function of time
Repeat experiment varying t1
M( t1, t2 )
Two fourier transforms (t1, t2 )
I( w1, w2)
Advantages of 2-d NMR
w1
Diagonal peaks occur
where w1 = w2
Cross peaks occur where
w1  w2
w2
•Increased resolution
•Cross peaks can reveal
structural information:
Through bond coupling
Through space coupling
(distances)
Chemical exchange
2d and 3d NMR Experiments
Commonly Used in Biology





COSY (Correlation Spectroscopy) Direct
Covalent bond required
NOESY (NOE Spectroscopy) Nuclei close in space
TOCSY (Total Correlation Spectroscopy)
Coupling transferred from one bond to another
HSQC (Heteronuclear Single Quantum
Coherence) Heteronuclear single bond coupling
(most often 1H-15N, also 1H-13C)
HNCA/HNCO/HNCACB (“Protein backbone
experiment”-3D) Proton-carbon-nitrogen
coupling
Application of NMR Data to
Biomolecules
1.
2.
3.
4.
5.
Collect data in magnet
Process Data (FT)
Assign the spectrum. Each peak = one proton
(or carbon or nitrogen, etc.)
Interpret data. For as many proton pairs as
possible, gather data on distance and
orientation.
Input distance, hydrogen bonding, and
orientation restraints into structure calculation,
together with covalent bonds, angles and
dihedrals
Molecular Dynamics Simulations

N atoms, 3N coordinates (Random Starting
Positions)
xn, yn, zn vnx, vny, vnz


Calculate position, velocity, acceleration for
each coordinate for time period, Δt
F = ma = Electrostatics + Covalent
bonds/angles + Solvent molecules, 3N
equations of motion
a=(Δvx/Δt)n, (Δvy/Δt)n , (Δvz/Δt)n

From new coordinates (after time Δt) repeat
Structure Calculation
Ep = S K1(r – ro)2 +S K2(q– qo)2 + S (V/2)[1 – cos(nf +
g) ] + Electrostatics + H-bond + L-J + data constraint
Data constraint (NOE) = KNOE (x – xo)2 if interproton
distance x > max xo from NOE, 0 otherwise
Similar terms are added for torsion angles from J-coupling
and for orientations of bonds from RDCs
1.
2.
3.
4.
5.
Generate many (~50) starting structures
Heat (in silico) and run molecular dynamics (iterative)
Cool, mimimize energy
Select suitable subset
Superimpose, look for convergence
Protein and nucleic acid 3D structure generation from NMR
NMR assignments
Distance (NOE) restraints
backbone-backbone-2Þ
sidechain-backbone
sidechain-sidechain 3Þ
}
Torsion angle restraints
Typical protocol for 3D
structure generation
from NMR data (1H
only)
H-bond restraints
Initial structures
Simulated annealing,
Restrained dynamics, or
Distance geometry
Convergence
Restrained dynamics, or
Restrained energy minimization
Iterative relaxation
matrix approach
How to judge the quality of an NMR structure?
Precision
≠
Accuracy
Root mean square
deviation (rmsd) as
measure of precision
2 possible explanations for variable regions: lack of
data and/or disorder
NMR and Structure-Based Drug Design
X-ray is higher resolution than NMR
 X-ray is faster than NMR (when the apostructure is easily crystallized) for a high
resolution structure
 The role of NMR in drug discovery has
changed

Fragment-Based Lead Discovery:
History
“SAR by NMR” (Fesik) as Means of Identifying
and Linking Functional Groups
Step 1: Identify
small mw binder
(Ki1~10-3-10-6)
Step 2:Screen for 2nd
site binder in presence
of first (Ki2~10-3-10-6)
Step 3: Chemically link
moieties (Ki~ Ki *K i2)
two
1
Fragment Library Design
Fragments must be “lead-like” not “druglike”
 MW < 250, allows compound to “grow”
 Weak binding affinity (will add affinity with
growth)
 Contain polar groups




Insures solubility
Polar groups are reactive
Pick up hydrogen bonding interactions
Correlation Times and Dynamics in
NMR
We define the Relaxation times T1 and T2 such
that M(t) is proportional to exp (-t/T1(2))
T1 = Longitudinal relaxation time (rate of decay of z magnetization)
T2 = Transverse relaxation time (xy plane)
Decay occurs due to many factors, including tumbling/dynamics
of the molecule
Fluctuations in molecular conformation/position,
described by the correlation function, lead to decay
G(t) = <f(t)f(t + t)> = exp(-t/tc)
CPMG (Carr-Purcell-Meiboom Gill) Experiment
Takes Advantage of T2 Relaxation
Introduce “T2 filter”
Mixture of Small Molecule With Large
Molecule: We can Distinguish Free from
Bound

CPMG Experiments
1.2
2mM Linezolid
1
0.8
0.6
2mM Linezolid, 1mM 70S
0.4
0.2
0
0
100
200
300
400
T/ms
Small Molecule
Macromolecule
500
600
Saturation Transfer to Detect Ligand
Binding by NMR
NOE
•Sign of NOE
Transfer
Depends on
Tumbling (MW)
(as
measured
in STD or
LOGSY
exp)
0.0
~800
•Sign of Ligand
MW
Signal Inverts
upon Binding to N. B. Magnitude of High MW (+) NOE >>
Protein
Low MW (-) NOE
Identification of Binding Site by Displacement (HSP90)
Cpd B
1D 1H NMR
Water-LOGSY
(all signals positive)
Pos = Bound
Neg=Free
Protein Added
Control Competitor Added
Cpd A
SeeDs – Overall process
Target
Structure by X-Ray
NMR Competitive
Binding Experiment
Rapid
- NMR filter in <1 weeks
- X-ray structures in 2-3 weeks
Fragment Library
Use information
about fragment
binding to discover
or design new hit
compounds
Conclusions/Summary
NMR structure determination is built from
interproton distances and orientations of
internuclear bond vectors
 Large proteins are challenging by NMR
using relatively new techniques (TROSY)
 Partial information regarding ligand
binding and dynamics can be obtained
from the rate of signal buildup/decay.

Correlations Times and Relaxation
G(t) = <f (t)f (t + t)> = exp(-t/tc)
 This gives rise to resonances leading to decay of
magnetization
J(w) = FT{G(t)} = 2tc/(1 + w2tc2) (the spectral
density)



For large tc, (slowly tumbling (big) molecules)
rate of decay of signal is very rapid
TROSY Transverse Relaxation Spectroscopy
minimizes Decay of Signal for Large Molecules
For a Given Protein, Measuring T1 and T2 for Each
Backbone Amide Gives Information about
Internal Dynamics