Chemical Exchange
and Ligand Binding
•
•
•
•
•
NMR time scale
Fast exchange for binding constants
Slow exchange for tight binding
Single vs. multiple binding mode
Calcium binding process of calcium binding
proteins
• CaM regulation of gap junctions
Effects of Chemical Exchange on NMR Spectra
•Chemical exchange refers to any process in which a nucleus
exchanges between two or more environments in which its NMR
parameters (e.g. chemical shift, scalar coupling, or relaxation) differ.
•DNMR deals with the effects in a broad sense of chemical exchange
processes on NMR spectra; and conversely with the information
about the changes in the environment of magnetic nuclei that can be
derived from observation of NMR spectra.
Kex
Conformational
equilibrium
KB
Chemical
equilibrium
Types of Chemical Exchange
Intramolecular exchange
– Motions of sidechains in proteins
A
B
– Helix-coil transitions of nucleic acids
– Unfolding of proteins
– Conformational equilibria
Intermolecular exchange
– Binding of small molecules to
macromolecules
– Protonation/deprotonation equilibria
– Isotope exchange processes
M+L
ML
– Enzyme catalyzed reactions
Because NMR detects the molecular motion itself, rather the numbers
of molecules in different states, NMR is able to detect chemical
exchange even when the system is in equilibrium
Typical Motion Time Scale for
Physical Processes
NMR Time Scale
Time Scale Chem. Shift, d Coupling Const., J
Slow
k << dA- dB
Intermediate k = dA - dB
Fast
k >> dA - dB
Sec-1
0 – 1000
k << JA- JB
k = J A- 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
• NMR time-scale refers to the chemical shift timescale.
• The range of the rate can be studied 0.05-5000 s-1 for H
can be extended to faster rate using 19F, 13C and etc.
2-state First Order Exchange
A
k1
k-1
Lifetime of state A:
tA = 1/k+1
Lifetime of state B:
tB = 1/k-1
Use a single lifetime
1/ t =1/ tA + 1/tB
= k+1+ k-1
B
Rationale for Chemical Exchange
For slow exchange
FT
For fast exchange
FT
Bloch equation approach:
dMAX/dt = -(DωA)MAY - MAX/tA + MBX/tB
dMBX/dt = -(DωB)MBY - MBX/tB + MAX/tA
•
•
•
2-state 2nd Order Exchange
M+L
k+1
k-1
Kd = [M] [L]/[ML] = k-1/k+1
– 10-9 M
kon = k+1 ~ 108 M-1 s-1 (diffusion-limited)
k-1 ~ 10-1 – 10-5 s-1
Kd =10-3
Lifetime 1/
t =1/ tML + 1/tl
= k-1 (1+fML/fL)
fML and fL are the mole fractions of bound and free ligand,
respectively
ML
Slow Exchange k << δA -δB A
• Separate lines are observed for each state.
• The exchange rate can be readily measured
from the line widths of the resonances
• Like the apparent spin-spin relaxation rates,
1/T2i,obs
1/T2A,obs= 1/T2A+ 1/tA = 1/T2A+ 1/k1
1/T2B,obs= 1/T2B+ 1/tB = 1/T2B+ 1/k-1
line width Lw = 1/pT2 = 1/pT2 + k1/p
Each resonance is broadened by D Lw = k/p
Increasing temperature increases k, line width
increases
k1
k-1
B
Slow Exchange for M+L
k1
k-1
ML
• Separate resonances potentially are
observable for both the free and
bound states MF, MB, LF, and LB
• The addition of a ligand to a solution
of a protein can be used to determine
the stoichiometry of the complex.
• Once a stoichiometric mole ratio is
achieved, peaks from free ligand
appear with increasing intensity as
the excess of free ligand increases.
• Obtain spectra over a range of [L]/[M]
ratios from 1 to 10
k1
Slow Exchange for M+L k- ML
1
• For free form
1/T2L,obs= 1/T2L+ 1/tL = 1/T2L+ k-1 fML/fL
1/T2M,obs= 1/T2M+ 1/tM = 1/T2M+ k-1 fML/fM
For complex form
1/T2ML,obs= 1/T2ML+ 1/tML = 1/T2ML+ k-1
Measurements of line width during a titration can be
used to derive k-1 (koff).
19F
spectra of the enzyme-inhibitor complex at
various mole ratio of carbonic anhydrase:inhibitor
Free inhibitor
Bound ligand
•
1:4
1:3
1:2
1:1
1:0.5
•
At -6 ppm the broadened
peak for the bound ligand
is in slow exchange with
the peak from free ligand
at 0 ppm.
The stoichiometry of the
complex is 2:1. No signal
from the free ligand is
visible until more than 2
moles of inhibitor are
present.
Coalescence Rate
• For AB equal
concentrations, there will be a
rate of interchange where the
separate lines for two species
are no longer discernible
• The coalescence rate
kc = p Dd / √2 = 2.22 Dd
Dd is the chemical shift
difference between the two
signals in the unit of Hz.
Dd depends on the magnetic field
Coalescence Temperature
• Since the rate depends on
the DG of the inversion,
and the DG is affected by
T, higher temperature will
T
TC
make things go faster.
• Tc is the temperature at
which fast and slow
we can calculate the DG‡ of the process
exchange meet.
• T>Tc, fast exchange
DG‡ = R * TC* [ 22.96 + ln ( TC / Dd ) ]
• T<Tc, slow exchange
Fast Exchange k >> δA -δB
A
k1
k-1
B
• A single resonance is observed, whose
chemical shift is the weight average of the
chemical shifts of the two individual states
δobs = fAδA +fBδB, fA + fB = 1
For very fast limit
1/T2,obs= fA/T2A+ fB/T2B
For moderately fast
1/T2,obs= fA/T2A+ fB/T2B + fAfB2 4p (DdAB)2/ k-1
Maximal line broadening is observed when
fA = fB = 0.5
Fast Exchange k >> δA -δB
M+L
k+1
ML
k-1
For M δM,obs = fMδM +fMLδML
For L δL.obs = fLδL +fMLδML
1/T2,obs= fML/T2,ML+ fL/T2,L + fMLfL2 4p
(dML-dL)2/ k-1
• A maximum in the line broadening
of ligand or protein resonances
occurs during the titration at a mole
ratio of approx. ligand:protein 1:3
• The dissociation constant for the
complex can be obtained by
measuring the chemical shift of the
ligand resonance at a series of [L].
Integration of Calcium Signaling Via CaSR
site5
Site 4
LB1
LB2
Site 1
Site 2
Site 3
Identification of Ca2+
binding sites in ECD of
CaSR
How can CaSR sense
the change of Ca2+o
within a narrow range?
(multiple sites?
cooperativity?)
Identification of
CaM binding region
in c-tail of CaSR
Y. Huang, JJ Yang, J Biol Chem. 2007; Yun Huang.. JJ Yang Biochemistry 2009; Y Hang, … JJ Yang, JBC 2010
Subdomain Approach
LB
1
LB2
site4
site2
site1
site3
site2
site5
site3
Yun Huang.. JJ Yang Biochemistry 2009
Relative change of chemical shift
Two Distinct Ca2+-Binding Processes Revealed by NMR
1
0.8
0.6
0.4
Kd: 1.6 ± 0.1 mM
0.2
nHill: 2.3 ± 0.3
0
0
1
2
3
2+
4
5
6
7
[Ca ] (mM)
6
1.2 10
1.2
ANS + Protein + Ca2+
6
site3
site2
1
ANS + Protein
5
8.0 10
5
6.0 10
ANS
5
4.0 10
Relative change
site1
Fluorescence Intensity
1.0 10
0.8
0.6
Kd1 = 0.7 ± 0.1 mM
0.4
Kd2 = 6.4 ± 0.8 mM
0.2
5
2.0 10
n hill = 2.9 ± 1.2
0
0.0
Yun Huang.. JJ Yang Biochemistry 2009;
440 460 480 500 520 540 560 580 600
wavelength (nm)
0
5
10
15
20
2+
[Ca ] mM
25
30
35
Developing Calcium Sensors by Design
1. Highly targeting specificity
2. Simple stoichiometric
interaction mode to ease
calibration
3. Tunable affinities, selectivity
& kinetics
4. Minimal perturbation on
signaling without using
natural calcium binding
proteins
JACS, 2002, 2005, 2007 Biochem, 2005, 2006, PEDS, 2007,
protein science 2008
J. Zhou, A. Hofer, J.J. Yang, Biochem, 2007
A.Holder, … J.J. Yang, Biotech 2009
S. Tang,….O. Delbano J.J. Yang, PNAS, 2011
Catcher: Ca2+ Sensor for Detecting High Concentration
Normalized absorbance
E147
Ca2+
R
R
Y66
H
O
-
O
Neutral
1.5
1.2
EGFP
D8
D9
D10
CatchER
D12
Normalized fluorescence
E225
E223
E204
D202
0.9
0.6
0.3
Y66
x-
x-
Ca2+
x- xDesigned Ca2+ binding site
Normalized fluorescence
x-
0.8
0.6
0.4
6.0 mM Ca2+
1.0
0.5
0.1
100
0
0.2
S. Tang,….O. Delbano J.J. Yang, PNAS, 2011
0
500
ormalized fluorescence (%)
chromophore
1.0
520 540 560 580
Wavelength (nm)
600
F488; 10 M EGTA
0.8
F488; 5 mM Ca
F395; 10 M EGTA
0.6
F395; 5 mM Ca
0.4
0.2
0
0
250 300 350 400 450 500 550
Wavelength (nm)
Anionic
1.0
80
60
40
20
0
2+
2+
fluorescence
Normalized fluorescence
1.0
0.8
0.6
0.4
Relative amount of Ca-bound CatchER
CatchER: Ca2+ binding capability
3.5
F
F
3.0
Equilibrium dialysis
coupled with ICP-OES
488
395
A
488
2.5
2.0
1.5
10
15
25
[CatchER] M
0.2
0
500
20
520 540 560 580
Wavelength (nm)
600
1H, 15N-HSQC
S. Tang,….O. Delbano J.J. Yang, PNAS, 2011
30
Fast Kinetics of CatchER
100
1000
80
500
300
200
60
100
40
50
20
0
0
0
0.02 0.04 0.06 0.08
time (s)
0.1
kon = koff/Kd= 3.9 x 106 M-1s-1
S. Tang,….O. Delbano J.J. Yang, PNAS, 2011
normalized fluorescence (%)
normalized fluorescence (%)
[Ca2+] µM
[EGTA]
µM
0
100
80
60
40
20
200
0
0
0.1
0.2 0.3
time (s)
0.4
0.5
Fast Kinetics: koff = 700 s-1
CatchER’s Ca2+ Induced Chemical Shift Changes
Y182
S. Tang,….O. Delbano J.J. Yang, PNAS, 2011
G228
The Connexin Family Tree
31
Söhl et al., Nat. Rev. Neurosci. 6: 191-200, 2005
Identifying CaM Binding Region in Gap
Junction Connexins
NH2
Score
COOH
Cx50_m
145
Cx46_h
136
Cx44_s
133
Cx43_h
142
CaMKI_h
294
CaMKII_h
289
789999999999999876
TKKFRLEGTLLRTYVCHI
789999999999987654
RGRVRMAGALLRTYVFNI
899999999999766543
RGKVRIAGALLRTYVFNI
479999999999999999
HGKVKMRGGLLRTYIISI
000999999999999999
FAKSKWKQAFNATAVVRH
000999999999999999
NARRKLKGAILTTMLATR
xxBxB#xxx#xxxx#xxx
1
5
10
162
153
150
161
315
310
Y. Zhou. JJ Yang JBC. 2007; Zhou Y, Yang JJ. Biophys J. 2009 ; Y. Chen, .. JJ Yang Biochem J. 2011
Monitoring Cx Peptide and Calmodulin
[Cx44]/[CaM]
[Cx43]/[CaM]
0:1
0.4:1
0.8:1
1.2:1
9.2
9.1
9.0
T117
0.6:1
0.2
0.9:1
Dppm-H
K94
D64
G33
G61
G25
K148
A57
0
1.2:1
-0.1
T29
-0.2
0
0.5
1
1.5
[Cx43]/[CaM]
T117
9.2
1H
9.1
(ppm)
133
115
134
113
132
114
133
115
134
113
132
114
133
115
134
113
132
114
133
115
134
113
132
114
133
115
134
113
132
A57
133
115
2
Y. Zhou. JJ Yang JBC. 2007
A57
114
2.0:1
8.3
132
114
0.3:1
0.1
8.4
113
T29
0:1
8.5
9.0
134
8.5
1H
33
8.4
(ppm)
8.3
HSQC Spectra of Holo-CaM with Cx50 Peptide
Holo-CaM
Holo-CaM + Cx50p
G33
T29
G134
T70
T117
F19
A128
L116
V136
I27
I130
K21
K148
K94
A147
I100
N137
D64
A57
34
Y. Chen, .. JJ Yang Biochem J. 2011
Strong Binding Indication by Slow Exchange
CaM :
Cx50p
1:0
Free G33
105.2
105.4
105.6
8.70
8.65
8.60
CaM +
Cx43p
8.55
105.2
1 : 0.4
105.4
105.6
8.70
8.65
8.60
8.55
8.70
8.65
8.60
8.55
8.65
8.60
8.55
105.2
1:1
105.4
105.6
105.2
1:
1.2
105.4
105.6
bound
8.70
35
Y. Chen, .. JJ Yang Biochem J. 2011
Residues in the linker of Calmodulin underwent
sequential phases of conformational change
O R Raren, MA Shea Biochem, 2002