COURSE#1022: Biochemical Applications of NMR Spectroscopy
http://www.bioc.aecom.yu.edu/labs/girvlab/nmr/course/
Chemical Exchange in NMR Spectroscopy
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LAST UPDATE: 3/28/2012
References
• Bain, A. D. (2003). "Chemical exchange in NMR." Progress in Nuclear Magnetic Resonance
Spectroscopy 43(3-4): 63-103.
• L. Y. Lian & G. C. K. Roberts, Chapter 6 “Effects of chemical exchange on NMR spectra” in
NMR of Macromolecules, A Practical Approach (1993)
• Cavanagh, Fairbrother, Palmer, & Skelton, Chapter 5.6 “Chemical Exchange Effects in NMR
Spectroscopy”
• Evans, Chapter 1.3 “Kinetics”
• Sanders & Hunter, Chapter 7 “Connections through Chemical Exchange”
• R. Freeman, “Chemical Exchange” from A Handbook of NMR
• M. H. Levitt, Chapter 15 “Motion”
• P. J. Hore, Chapter 4 “Chemical Exchange” in NMR, Oxford Chemistry Primer #32
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Dynamics - Good or Bad for the
NMR Spectrocopist?
Dynamics in NMR can be a curse or rewarding – its influence can cause signals to
become invisible beyond detection or it can allow one to uncover a large range of
motional properties at every site within a molecule …
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Chemical Exchange in NMR
Chemical exchange in NMR refers to any process in which a nucleus exchanges between
two or more environments in which its NMR parameters (chemical shift, scalar coupling,
dipolar coupling, relaxation rate) differ.
These may be intermolecular or intramolecular processes.
Intramolecular exchange processes include:
• motions of protein side chains
• helix-coil transitions of nucleic acids
• unfolding of proteins
• conformational equilibria (conformational exchange)
• tautomerization
Intermolecular exchange processes include:
• binding of ligands to macromolecules
• protonation/deprotonation equilibria of ionizable groups
• isotope exchange processes (such as the exchange of labile protons of a
macromolecule with solvent)
• enzyme catalyzed reactions
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Information From Chemical Exchange
Studying chemical exchange can provide important kinetic and thermodynamic
parameters such as:
Kinetic Rate Constants:
• kon
• koff
Thermodynamic Constants:
• Kassoc or Kd
• G
• H
• S
• Gact
Characterizing Protein Dynamics: Parameters and Timescales
Dynamic processes can be studied with a variety of
NMR methods such as:
• Real Time NMR, RT NMR
• EXchange SpectroscopY, EXSY (zz-exchange)
• Lineshape analysis
• Carr–Purcell Meiboom–Gill Relaxation Dispersion,
CPMG
• Rotating Frame Relaxation Dispersion, RF RD
• Nuclear Spin Relaxation, NSR
Proteins sample a range of thermodynamically
• Residual Dipolar Coupling, RDC
accessible conformations within a hierarchy of
• Paramagnetic Relaxation Enhancement, PRE.
timescales owing to their intrinsic flexibility..
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Note: Multiple states are hard to detect by Xray crystallography
Exchange Rates and The NMR Time Scale
The “NMR time scale” refers to how fast an event happens relative to the NMR observables:
Time Scale
Slow
Intermediate
Fast
Range (Sec-1)
Chem. Shift (d)
k << A- B
k = A - B
k >> A - B
0 – 1000
Coupling Const. (J)
k << JA- JB
k = JA - J B
k >> JA- JB
0 –12
T2 relaxation
k << 1/ T2,A- 1/ T2,B
k = 1/ T2,A- 1/ T2,B
k >> 1/ T2,A- 1/ T2,B
1 - 20
Two resonances (A,B) for one atom
Populations ~ relative stability
“slow exchange”
kex <<  (A) –  (B)
“intermediate exchange”
kex ~  (A) -  (B)
“fast exchange”
kex >>  (A) -  (B)
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Two-Site Exchange:
Rotation about a partial double bond in dimethylformamide
Equal Population of Exchange Sites
40 Hz
Increasing Exchange Rate
slow
k = 0.1 s-1
k = 5 s-1
k = 10 s-1
k = 20 s-1
k = 40 s-1
coalescence
k = 88.8 s-1
k = 200 s-1
k = 400 s-1
k = 800 s-1
fast
k = 10,000 s-1
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Unequal Population of Exchange Sites:
obs = f11 + f22
f1 + f2 =1
where:
f1, f2 – mole fraction of each species
1,2 – chemical shift of each species 9
McConnell’s Modification of the Bloch Equations
Exchange effects on the lines can be simulated using the McConnell’s Modification of
the Bloch Equations. The McConnell equations combine the differential equations for a
simple two-state chemical exchange process with the Bloch differential equations for a
classical description of the behavior of nuclear spins in a magnetic field. This equation
system provides a useful starting point for the analysis of slow, intermediate and fast
chemical exchange studied using a variety of NMR experiments.
Add first order kinetics terms to the Bloch
equations for the change in magnetization over
time.
Can obtain a general equation for the real part of the
frequency domain signal arising from symmetric
chemical exchange.
• McConnell, H. M. (1958). "Reaction rates by nuclear magnetic resonance." Journal Of Chemical Physics 28: 430-431.
• Idiyatullin, D., S. Michaeli and M. Garwood (2004). "Product operator analysis of the influence of chemical exchange on
relaxation rates." Journal of Magnetic Resonance 171(2): 330-337.
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Symmetric Two-Site Exchange:
Measuring the Exchange Rate
k =  o2 /2(he - ho)
k = o / 21/2
k =  (o2 - e2)1/2/21/2
k =  (he-ho)
k – exchange rate
 – peak frequency
h – peak-width at half-height
e – with exchange
o – no exchange
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“Asymmetric” Two-Site Exchange
If the populations of A and B are different the position of the averaged peak is a
population-weighted average:
average = pAA + pBB
If the chemical shifts of the two species are known, then the position of the peak in
the fast exchange spectrum may be used to derive the equilibrium constant of the
reaction.
(he - ho) = 4pApB o2 /(kA+kB)
Fast Exchange
Coalescence
∆δ
Slow exchange
calculation of a two-site exchange system for the ratio
between the chemical shift difference ∆δ and the rate
constant 1/τ varying between 40 and 0.1
kA =  (he-ho)A
kB =  (he-ho)B
k – exchange rate
 – peak frequency
h – peak-width at half-height
e – with exchange
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o – no exchange
Diagnosis of the exchange regime
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Scenario: Two-Site Exchange in Fast Exchange Limit
Extra term is due to
exchange broadening
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Scenario: Two-Site Exchange in Limit of Slow Exchange
If see plot like this,
exchange is present: as
increase temp, LW will
initially decrease then
increase
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Scenario: Two-Site Exchange at Coalescence
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Two-Site Exchange:
Coalescence Temperature and
Measurement of Thermodynamic Parameters for Interconversion
Eyring relation used to determine ΔG‡ from the temperature dependence of k:
Arrhenius plot of
ln(LW) vs 1/T will
give Gact
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The NMR Advantage for Studying Dynamics
NMR is able to detect chemical exchange even when the system is in equilibrium –we
can perturb the magnetization in one state to study rates without perturbing the
chemical system.
Almost all other spectroscopic methods of measuring rates involve displacing the
system from equilibrium and following its return to equilibrium.
Timescale of UV/Vis/IR spectroscopy is very
small because lifetime of excited state is short –
spectrum of mixture is a sum of its individual
components
In NMR, spectrum of mix is not
necessarily a sum of spectra of
its individual components –
depends on timescale of
process.
B
A
C
A
Binding of a lanthanide complex to an oligonucleotide by UV/Vis
B
C
Proton NMR selective inversion experiment
on dimethylacetamide
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NMR Methods To Study Exchange: RT NMR
First and foremost, NMR provides access to site-specific probes of local structure and
dynamics with unmatched coverage across almost every atom in the protein
In this powerful yet simple approach, dynamic processes on the ~s timescale are directly detected
by quantifying the time-dependence of NMR signal intensities. Physical processes on this
timescale include:
•
•
•
protein folding
solvent hydrogen-exchange
relatively slow conformational changes
• cis-trans proline isomerization
• domain movements
The real-time (RT) NMR experiment is performed by initiating the physical process of interest then
rapidly acquiring a sequence of NMR spectra. A special injection apparatus or application of laser
light can streamline the initiation process within the NMR tube to study protein folding, ligand
binding or conformational changes. The signal intensities from a series of spectra as a function of
the time of acquisition are then fitted to an appropriate model such as exponential conversion from
A→B.
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RT NMR Example: Hydrogen Exchange (HX) vs. Protein Structure
Hydrogen exchange (HX) is used to measure the exchange rate of the
labile protons in a macromolecule. For example, if a protein is placed
in D2O, the amide signals due to 1H nuclei will disappear over time
due to chemical exchange.
The observed NH intensity loss can usually be fit to a simple
exponential to measure a exchange rate (kex):
The amide exchange rate usually correlates with the
secondary structure in proteins. Can also use to
determine sites that are protected after complexation.
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RT NMR Example: Folding of Protein Upon pH Change
Study folding of the protein α-lactalbumin upon pH jump using a rapid-mixing apparatus..
After a post-mixing dead time of 2 s, each 2D spectrum was acquired in a mere 10 s,
revealing distinct signals from both the molten globule state and the folded state of the
protein:
Time-dependent intensities of 92
signals from the folded state and 5
signals from the molten globule state
fit well to a single-exponential with
τex=109±5 s, consistent with a global
two-state folding pathway:
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NMR Methods To Study Exchange: Exchange Spectroscopy
EXchange SpectroscopY (EXSY), also known as the zz-exchange experiment, is used to
quantify dynamic processes in the 10–5000 ms time window. Physical processes in this
time window include slow conformational changes such as domain movement, ligand
binding and release, topological interconversion of secondary structure and cis-trans
isomerization. EXSY requires that the dynamic process is in the slow exchange regime
where each structural probe reveals a unique set of signals (kex≪|Δν|).
Typically, a series of 2D spectra are acquired with different
values of tmix to generate “build-up curves” from the four
measured intensities. These data are fit to an exchange model to
extract kinetic rates of interconversion. For two-state exchange,
three equations describe the three unique build-up curves:
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EXSY Example: Catalytic Mechanism within the Proteasome
Practically though, many EXSY studies only require
a few structural probes to address the questions of
interest. For example, in studies of the α7 annulus of
the 20 S proteasome core particle, two crucial
methionine methyl probes were sufficient to provide
unique insight into motions vital to its catalytic
mechanism. Studying this massive 180 kDa complex
was made possible via special methyl group
labeling.
The authors concluded that the gating of this proteasome is controlled through highly dynamic Ntermini that interconvert between conformations that place them either outside or well inside the
antechamber, with rates of proteolysis that depend on the relative populations of termini in the “in” and
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“out” states.
Saturation Transfer:
A Method to Measure Kinetics Under Slow Exchange
Saturation of PCr signal causes the phosphate of ATP to decrease in intensity
and vice versa during metabolic flux
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Inversion Transfer:
A Method to Measure Kinetics Under Slow Exchange
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NMR Methods To Study Exchange: Lineshape Analysis
Lineshape analysis is a relatively straightforward approach to interpretation of NMR spectra
reporting exchange in the 10–100 ms time window. Physical processes in this time window include:
binding events and slow–intermediate conformational changes such as small domain movements that
could affect catalytic turnover rate and allostery.
Typically, a series of spectra are acquired along a titration coordinate such as ligand concentration,
temperature or pH to observe their incremental effect upon the NMR spectrum. The spectra in the
series may differ depending on the timescale of chemical exchange:
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Measuring the Binding Constant Under Fast Exchange
Titration of ligand binding to protein monitored
by 2D 15N-1H HSQC
Ligand Concentration
Plot chemical shift as a function of ligand
concentration to get Kd – really only accurate
under conditions of very fast exchange (see Lian &
Roberts)
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Ligand Binding Under Slow Exchange (k << A - B)
Generally more difficult to measure Kd under
conditions of slow exchange but can use intensity
changes
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Measuring Binding Using NMR:
Chemical Shift Mapping (CSP-NMR)
 Monitor the binding of ligands –
can be small molecules, drugs,
inhibitors, peptides, proteins, etc.
 Determine binding constants
 Site-specific
 Spatial distribution of responses can
be mapped on structure
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Chemical shift, pH and Measurement of pKa
HOOC-CH-CH3
-OOC-CH-CH
NH2
 = p1·  p2· 
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NH2
pH = pKa + log
max - 
 min
max  shift under acidic conditions
min  shift under basic conditions
  Observed shift
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Exchange Influences NMR Spectroscopy In Many Ways
More to come ….
 Ligand conformations - Transferred nOe
 Drug discovery/ Ligand screening based on STD
(Saturation Transfer Difference) and other methods
 pKa’s
 Enzyme kinetics
 Protein folding/unfolding
 Binding sites
 H-bonding and Hydration
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