NMR in Biophysical Chemistry Preview: Ligand Binding and ...

ENC-tutorial 2006:Erik RP Zuiderweg, U Michigan

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NMR in BiophysicalChemistry

Erik Zuiderweg and David Case

Preview:

Ligand Binding andAllosterics


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Simple Ligand Binding:Two-site exchange


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fA=fB=0.5 kex=10-1 s-1


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fA=fB=0.5 kex=100 s-1


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fA=fB=0.5 kex=101 s-1


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fA=fB=0.5 kex=102 s-1


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fA=fB=0.5 kex=103 s-1


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fA=fB=0.5 kex=104 s-1


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fA=fB=0.5 kex=105 s-1


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fA=fB=0.5 kex=106 s-1


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Fast exchange titration


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kex=106 s-1 fA=1.00 fB=0.00

! = fFREE!BOUND + fBOUND!BOUND


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kex=106 s-1 fA=0.67 fB=0.33



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kex=106 s-1 fA=0.50 fB=0.50



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kex=106 s-1 fA=0.33 fB=0.67



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kex=106 s-1 fA=0.00 fB=1.00



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SIMPLE USE:Chemical Shift Mapping

Complex:15N-2H Flavodoxin 14N-1H Methionine

SynthaseAmide H

Amide

15N

15N

14N

15N

14N


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Quantitating Fast Exchange Binding Constants

[LP] =[L]

TOT+ [P]

TOT+ K

D( ) ± [L]TOT

+ [P]TOT

+ KD( )

2

! 4[L]TOT[P]

TOT

2


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Slow exchange Titration


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kex=0.1 s-1 fA=1.00 fB=0.00

IA = fFREE IFREE IB = fBOUNDIBOUND


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kex=0.1 s-1 fA=0.67 fB=0.33



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kex=0.1 s-1 fA=0.50 fB=0.50



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kex=0.1 s-1 fA=0.33 fB=0.67



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kex=0.1 s-1 fA=0.00 fB=1.00



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Quantitating Slow Exchange Binding Constants

Saturation =IBOUND

IBOUND

+ IFREE


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Range of Quantitation


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Intermediate exchangetitration


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kex=103 fA=1.0 fB=0.0

LW = fALWA + fBLWB + fA fB!A "!A( )

2

kex


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kex=103 fA=0.9 fB=0.1


2

kex


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kex=103 fA=0.8 fB=0.2


2

kex


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kex=103 fA=0.5 fB=0.5


2

kex


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kex=103 fA=0.2 fB=0.8


2

kex


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kex=103 fA=0.1 fB=0.9


2

kex


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kex=103 fA=0.0 fB=1.0


2

kex


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Quantitating Kinetics

Slow Exchange : Upper limit on kex (typical: kex << 10 s-1)

Fast Exchange : Lower limit on kex (typical: kex >> 104 s-1)

Intermediate Exchange : quantify kex

(typical: 102 s-1 < kex < 104 s-1)


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Simulating two-site exchange

dMx

A(t)

dt= !"AMy

A(t) ! R

2

A+ kAB( )Mx

A(t) + kBAMx

B(t)

dMy

A(t)

dt= +"AMx

A(t) ! R

2

A+ kAB( )My

A(t) + kBAMy

B(t)

dMx

B(t)

dt= !"BMy

B(t) ! R

2

B+ kBA( )Mx

B(t) + kABMx

A(t)

dMy

B(t)

dt= +"BMx

B(t) ! R

2

B+ kBA( )My

B(t) + kABMy

A(t)


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i!A " R2A " kAB kBA

kAB i!B " R2B " kBA

#

$%&

'(M

+

A

M+

B

#

$%&

'(=

pAMtot

pBMtot

#$%

&'(

Steady-state solution


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S !( ) = Im Mtot

pA ! "!!B( ) + pB ! "

!!A( ) + i kAB + kBA( )

! "!!A( ) + ikAB( ) ! "

!!B( ) + ikBA( ) + kABkBA

#$%

&%

'(%

)%

Steady-state solution


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More Possibilities in 2D


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Ligand Binding:Three-site exchange


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Curved traces insequential 3-site exchange

2L + P ! " L + LP ! "L2P

P PL PL2


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Sometimes, a two-site exchange

must be three-site exchange

KD=10-9 M

Δω=200 r/s

IHPFree

IHPBound

31P NMR


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kon_max =108 M-1 s-1

KD =10-9 M

koff_max =0.1 s-1

!" =100 rs-1

IHP

Hemoglobin

IHP

Hemoglobin


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Sometimes, a two-site exchange

must be three-site exchange

KD=10-9 M

Δω=200 r/s

IHPFree

IHPBound

31P NMR


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k =108 M-1 s-1

KD =10-9

M

k =104 s-1

KDa =10-4 M

k =104 s-1

k =10 9 s-1

KDb =10-5

Solution: one ligand,

two consecutive fast processes

“entry site”


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Simulating three-siteexchange

d

dt

M+

A(t)

M+

B(t)

M+

C(t)

!

"

###

$

%

&&&=

i'A( R

2

A ( kAB( k

ACkBA

kCA

kAB

i'B( R

2

B ( kBA( k

BCkCB

kAC

kBC

i'C( R

2

C ( kCA

( kCB

!

"

###

$

%

&&&

M+

A(t)

M+

B(t)

M+

C(t)

!

"

###

$

%

&&&


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Solution


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Ligand Binding:four-site exchange


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Ligand-binding-induced conformationalchange = 4-site exchange

k =105 M-1 s-1

k =108 M-1 s-1

k =103 s-1

k =103 s-1

k =10-2 s-1 k =10-1 s-1

k =10-1 s-1 k =10-3 s-1


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k =105 M-1 s-1

k =108 M-1 s-1

k =103 s-1

k =103 s-1

k =10-2 s-1 k =10-1 s-1

k =10-1 s-1 k =10-3 s-1


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k =105 M-1 s-1

k =108 M-1 s-1

k =103 s-1

k =103 s-1

k =10-2 s-1 k =10-1 s-1

k =10-1 s-1 k =10-3 s-1


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k =105 M-1 s-1

k =108 M-1 s-1

k =103 s-1

k =103 s-1

k =10-2 s-1 k =10-1 s-1

k =10-1 s-1 k =10-3 s-1


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Allosterics


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Allosterics is wide-spread

•Site “b” knows whether site “a” is occupied

•“Intra-molecular signal transduction”


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e.g. signal transduction

NMR allows delineation of theallosteric mechanism of a

cytidylyltransferase

Stevens, S.Y., Sanker, S., Kent, C. and Zuiderweg, E.R.P.,

Nature Structural Biology 8, 947-952 (2001)


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Crystal structure of CTP:glycerol-3-phosphate cytidylyltransferase

(GCTase)+ 2CTP

Courtesy ofMartha LudwigChris Weber


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An Allosteric Enzyme

CTP

CTP CTP

CTP CTP

CTP CTP

G3P

G3P G3P

G3P

G3P

G3P G3P

G3P

CTP

G3P

G3P

CTP

1 µM

(1 µM)

300 µM (300 µM)

(1500 µM)

(100 µM) (100 µM)


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CTP

CTP CTP

CTP CTP

CTP CTP

G3P

G3P G3P

G3P

G3P

G3P G3P

G3P

CTP

G3P

G3P

CTP

1 µM

(1 µM)

300 µM (300 µM)

(1500 µM)

(100 µM) (100 µM)


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CTP CHEMICAL SHIFT MAPPING

First CTPKD < 5 µM

Second CTPKD = 500 µM


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CTP

CTP CTP


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+S

+S

or

or

or

DEFINING THE KNF-ALLOSTERIC MODEL


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Where is the negative cooperativitycoming from?

First CTPΔG = -7.3 Kcal/M

Second CTPΔG = -4.6 Kcal/M


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First CTPΔG = -7.3 Kcal/M

Second CTPΔG = -4.6 Kcal/M

Binding sites identical,Expect identical localbinding free energies

Thus:2.7 Kcal/M of bindingfree energy lost on

interface


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15N R2 relaxation with and without exchange broadening suppression

GCT GCT(CTP)2GCT(CTP)


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Therefore, the allosteric free energyof negative cooperativity

has an entropic component.

GCT

Dynamic

GCT(CTP)2GCT(CTP)

Dynamic Rigid

ΔS = 0 ΔS = neg

Other example:Allosteric energy is (partially)

dynamic in origin

Mäler, L., Blankenship, J., Rance, M. & Chazin, W. J. Nature Struct. Biol. 7, 245 – 250 (2000).


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1 2L


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The allosteric free energy ofpositive cooperativity

has an entropic component.

Calb

Dynamic

Calb(Ca2+)2Calb(Ca2+)

Rigid Rigid

ΔS = 0ΔS = neg


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Cooper A, Dryden DT: Allostery without conformational change. A plausible model.

Eur Biophys J 1984, 11:103-109.


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Thank you for your attentionI hope this was useful…

NMR in Biophysical Chemistry Preview: Ligand Binding and ...

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