lecture exchangedynamics 2012

7/30/2019 Lecture ExchangeDynamics 2012

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COURSE#1022: Biochemical Applications of NMR Spectroscopy

http://www.bioc.aecom.yu.edu/labs/girvlab/nmr/course/

Chemical Exchange in NMR Spectroscopy

1LAST UPDATE: 3/28/2012


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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 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

Dynamics - Good or Bad for the

NMR Spectrocopist?

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Chemical exchange in NMR refers to any process in which a nucleus exchanges betweentwo or more environments in which its NMR parameters (chemical shift, scalar coupling,

dipolar coupling, relaxation rate) differ.

These may be intermolecularorintramolecularprocesses.

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

Chemical Exchange in NMR

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Information From Chemical Exchange

Studying chemical exchange can provide important kinetic and thermodynamicparameters such as:

Kinetic Rate Constants:

kon

koff

Thermodynamic Constants:

Kassoc or Kd

G

H

S

Gact


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Characterizing Protein Dynamics: Parameters and Timescales

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Dynamic processes can be studied with a variety ofNMR methods such as:

Real Time NMR, RT NMR

EXchange SpectroscopY, EXSY (zz-exchange)

Lineshape analysis

CarrPurcell MeiboomGill Relaxation Dispersion,

CPMG

Rotating Frame Relaxation Dispersion, RF RD

Nuclear Spin Relaxation, NSR

Residual Dipolar Coupling, RDC

Paramagnetic Relaxation Enhancement, PRE.

Proteins sample a range of thermodynamically

accessible conformations within a hierarchy of

timescales owing to their intrinsic flexibility..Note: Multiple states are hard to detect by Xray crystallography


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The NMR time scale refers to how fast an event happens relative to the NMR observables:

Time Scale Chem. Shift (d) Coupling Const. (J) T2 relaxation

Slow k > JA- JB k >> 1/ T2,A- 1/ T2,BRange (Sec-1) 0 1000 0 12 1 - 20

Exchange Rates and The NMR Time Scale

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Two resonances (A,B) for one atom

Populations ~ relative stability

slow exchange

kex > (A) - (B)


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coalescence

k= 0.1 s-1

k= 5 s-1

k= 200 s-1

k= 88.8 s-1

k= 40 s-1

k= 20 s-1

k= 10 s-1

k= 400 s-1

k= 800 s-1

k= 10,000 s-1

40 Hz

I

ncreasingExch

angeRate

slow

fast

Equal Population of Exchange Sites

Two-Site Exchange:

Rotation about a partial double bond in dimethylformamide

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obs =f1 1 +f2 2

f1 +f2 =1where:

f1,f2 mole fraction of each species

1,

2 chemical shift of each species

Unequal Population of Exchange Sites:


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McConnells Modification of the Bloch Equations

Exchange effects on the lines can be simulated using the McConnells 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.

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.

Can obtain a general equation for the real part of the

frequency domain signal arising from symmetric

chemical exchange.

Add first order kinetics terms to the Bloch

equations for the change in magnetization over

time.

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k exchange rate

peak frequency

h peak-width at half-height

e with exchange

o no exchange

k =

(he-ho)

k = (o2 - e

2)1/2/21/2

k = o / 21/2

k = o2 /2(he - ho)

Symmetric Two-Site Exchange:

Measuring the Exchange Rate

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Asymmetric Two-Site Exchange

If the populations of A and B are different the position of the averaged peak is apopulation-weighted average:

average = pAA + pBB

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.

calculation of a two-site exchange system for the ratio

between the chemical shift difference and the rateconstant 1/ varying between 40 and 0.1

Slow exchange

Fast Exchange

Coalescence

kA = (he-ho)A

kB = (he-ho)B

(he - ho) = 4pApB o2 /(kA+kB)

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k exchange rate

peak frequency

h peak-width at half-height

e with exchangeo no exchange


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Diagnosis of the exchange regime

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Scenario: Two-Site Exchange in Fast Exchange Limit

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Extra term is due toexchange broadening


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Scenario: Two-Site Exchange in Limit of Slow Exchange

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If see plot like this,

exchange is present: asincrease temp, LW willinitially 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 G from the temperature dependence ofk:

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Arrhenius plot of

ln(LW) vs 1/Twill

give Gact


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Binding of a lanthanide complex to an oligonucleotide by UV/Vis

NMR is able to detect chemical exchange even when the system is in equilibrium wecan perturb the magnetization in one state to study rates withoutperturbing the

chemical system.

Almost all other spectroscopic methods of measuring rates involve displacing the

system from equilibrium and following its return to equilibrium.

The NMR Advantage for Studying Dynamics

Proton NMR selective inversion experimenton dimethylacetamide

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Timescale of UV/Vis/IR spectroscopy is verysmall because lifetime of excited state is short

spectrum of mixture is a sum of its individualcomponents

In NMR, spectrum of mix is notnecessarily a sum of spectra of

its individual components depends on timescale of

process.

A

B

C

A

B

C


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Hydrogen exchange (HX) is used to measure the exchange rate of thelabile protons in a macromolecule. For example, ifa protein is placed

in D2O, the amide signals due to1H 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):

RT NMR Example: Hydrogen Exchange (HX) vs. Protein Structure

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The amide exchange rate usually correlates with the

secondary structure in proteins. Can also use todetermine sites that are protected after complexation.


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EXchange SpectroscopY (EXSY), also known as the zz-exchange experiment, is used to

quantify dynamic processes in the 105000 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-transisomerization. EXSY requires that the dynamic process is in the slow exchange regime

where each structural probe reveals a unique set of signals (kex||).

NMR Methods To Study Exchange: Exchange Spectroscopy

Typically, a series of 2D spectra are acquired with different

values of tmix to generate build-up curves from the fourmeasured 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 ofinterest. For example, in studies of the 7 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 grouplabeling.

The authors concluded that the gating of this proteasome is controlled through highly dynamic N-

termini 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

out states.


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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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Lineshape analysis is a relatively straightforward approach to interpretation of NMR spectra

reporting exchange in the 10100 ms time window. Physical processes in this time window include:

binding events and slowintermediate 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:

NMR Methods To Study Exchange: Lineshape Analysis


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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

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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


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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

Measuring Binding Using NMR:

Chemical Shift Mapping (CSP-NMR)

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Chemical shift, pH and Measurement of pKa

-OOC-CH-CH3

NH2

HOOC-CH-CH3

NH2

= p1 p2

pH = pKa + logmax -

min

max shift under acidic conditions

min shift under basic conditions

Observed shift

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More to come .

Ligand conformations - Transferred nOe

Drug discovery/ Ligand screening based on STD

(Saturation Transfer Difference) and other methods

pKas

Enzyme kinetics

Protein folding/unfolding

Binding sites

H-bonding and Hydration

Exchange Influences NMR Spectroscopy In Many Ways

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lecture exchangedynamics 2012

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