Post on 09-Aug-2015
How to gain insights into complex modes of interaction with ITC
Adrian Velazquez-CampoyARAID-BIFI Researcher
Scientific advisor at AFFINImeter
Eva MuñozSenior Scientist at AFFINImeter
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T
Q (
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l o
f in
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nt)
o Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
o Anlytical tools to gain insights into complex modes of interaction with ITC
• Complex binding models
• Global fitting
• Species distribution plot
OVERVIEW
Isothermal Titration Calorimetry:Standard Model vs. Nonstandard Models
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/dt
(cal/
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[Fd]T/[FNR]
T
Q (
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mo
l o
f in
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nt)
Adrian Velazquez-CampoyARAID-BIFI Researcher
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
ITCGold-standard for characterizing intermolecular interactions
• Simple experimental set-up
• Widespread use in BioLabs
• Invaluable information on interactions
But… many words of caution concerning:
• experimental set-up
• data analysis
• information accessible
ITCProvides invaluable information:
Interaction? YES/NOKa , Kd , GH, -TSnCP , nX
...
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
ITC´s “Black legend”:• Prone to artifacts
• Difficult technique (data analysis)
• Time consuming
• Sample consuming
• Inadequate for extreme affinity
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
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-0.04
-0.02
0.00
0 10 20 30 40 50
time (min)
dQ
/dt
(ca
l/s)
[Ligand]T/[Macromolecule]
T
Q (
kca
l/m
ol o
f in
jecta
nt)
-10
-8
-6
-4
-2
0
2
kcal/m
ol
G
H
-TS
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Mo
lar
Fra
ctio
n
[Ligand]T/[Macromolecule]
T
Standard model: 1:1
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
𝑛 = 1 ⇒ 𝑍 = 1 + 𝛽𝑎𝑝𝑝 𝐿 = 1 + 𝐾𝑎𝑎𝑝𝑝
𝐿
𝐾𝑎𝑎𝑝𝑝
, ∆𝐻𝑎𝑝𝑝, 𝑛
∆𝐺𝑎𝑝𝑝, −𝑇∆𝑆𝑎𝑝𝑝
• Conformational change coupled to binding
• Allosteric systems
• Polysteric systems
Quasi-simple approximation?
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Standard model: 1:1
Cooperativity: homo- and heterotropy
Homotropic Interaction Heterotropic Interaction
𝐾1 = 𝑓 𝑘1, 𝑘2, 𝛼
𝐾2 = 𝑓 𝑘1, 𝑘2, 𝛼
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: 1:2
𝐾𝑎𝑎𝑝𝑝
= 𝑓 𝐾𝑎 , 𝐾𝑋, 𝛼, 𝑋
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: 1:2
Cooperativity: homo- and heterotropy
𝐾𝑎 , ∆𝐻𝑎
𝐾𝑋, ∆𝐻𝑋 𝐾𝑎𝛼, , ∆𝐻𝑥 + Δℎ
𝐾𝑋𝛼, ∆𝐻𝑥 + Δℎ𝑘1, ∆ℎ1
𝑘2, ∆ℎ2 𝑘1𝛼, ∆ℎ1 + ∆𝜂
𝑘2𝛼, ∆ℎ2 + ∆𝜂
𝑲𝟏
∆𝑯𝟏
𝑲𝟐
∆𝑯𝟐
Homotropic Interaction Heterotropic Interaction
Homotropy: The “stoichiometric model”
𝑍 =
𝑖=0
𝑛𝑃𝐿𝑖𝑃
=
𝑖=0
𝑛
𝛽𝑖 𝐿𝑖 =
𝑖=0
𝑛
𝑗=1
𝑖
𝐾𝑗 𝐿 𝑖
𝑛 = 2 ⇒ 𝑍 = 1 + 𝐾1 𝐿 + 𝐾1𝐾2 𝐿 2
Ordered binding mechanism?
What is the meaning of Kj’s?
Cooperativity?
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
Kj’s are “ensemble” association constants
𝑍 = 1 + 𝐾1 𝐿 + 𝐾1𝐾2 𝐿 2
𝑍 = 1 + 𝑘1 + 𝑘2 𝐿 + 𝑘1𝑘2𝛼 𝐿 2
No ordered binding mechanism is implied!
𝐾1 = 𝑘1 + 𝑘2 =+
𝐾2 =𝑘1𝑘2𝛼
𝑘1 + 𝑘2=
( + )
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
∆𝐻1=𝑘1∆ℎ1 + 𝑘2∆ℎ2
𝑘1 + 𝑘2
∆𝐻2=𝑘2∆ℎ1 + 𝑘1∆ℎ2
𝑘1 + 𝑘2+ ∆𝜂
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
Kj’s are “ensemble” association constants
𝑍 = 1 + 𝐾1 𝐿 + 𝐾1𝐾2 𝐿 2
𝑍 = 1 + 𝑘1 + 𝑘2 𝐿 + 𝑘1𝑘2𝛼 𝐿 2
Different scenarios 𝜌 =4𝐾2
𝐾1
identical & independent
nonidentical & independent
identical & cooperative
nonidentical & cooperative
𝑘1 = 𝑘2 = 𝑘, 𝛼 = 𝜌 = 1Δℎ1 = Δℎ2 = Δℎ, ∆𝜂 = 0
𝑘1 ≠ 𝑘2,𝛼 = 1, 𝜌 < 1Δℎ1 ≠ Δℎ2, ∆𝜂 = 0
𝑘1 = 𝑘2 = 𝑘, 𝛼 = 𝜌 ≠ 1Δℎ1 = Δℎ2 = Δℎ, ∆𝜂 ≠ 0
𝑘1 ≠ 𝑘2,𝛼 ≠ 1, 𝜌 ≠ 1Δℎ1 ≠ Δℎ2, ∆𝜂 ≠ 0
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
Different scenarios 𝜌 =4𝐾2
𝐾1
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
4𝐾2 ≠ 𝐾1,𝛼 ≠ 1, 𝜌 ≠ 1Δ𝐻2 ≠ Δ𝐻1, ∆𝜂 ≠ 0
4𝐾2 ≠ 𝐾1, 𝛼 = 𝜌 ≠ 1Δ𝐻2 ≠ Δ𝐻1, ∆𝜂 ≠ 0
4𝐾2 < 𝐾1,𝛼 = 1, 𝜌 < 1Δ𝐻2 ≠ Δ𝐻1, ∆𝜂 = 0
4𝐾2 = 𝐾1, 𝛼 = 𝜌 = 1Δ𝐻2 = Δ𝐻1, ∆𝜂 = 0
identical & independent
nonidentical & independent
identical & cooperative
nonidentical & cooperative
0 1 2 3 4
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0
Q (
kca
l/m
ol o
f in
jecta
nt)
Molar Ratio
K1 3.0·106 M-1
H1 -10.1 kcal/molK2 8.0·105 M-1
H2 -9.0 kcal/mol
1.1
R. solanacearum Lectin + -Methyl-Fucoside
Kostlanova et al. (2005) Journal of Biological Chemistry 280 27839-27849
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
Gorshkova et al. (1995) Journal of Biological Chemistry 270 21679-21683
0 1 2 3 4 5
0
2
4
6
Q (
kca
l/m
ol o
f in
jecta
nt)
Molar Ratio
K1 5.5·104 M-1
H1 -1.9 kcal/molK2 7.6·104 M-1
H2 11.8 kcal/mol
5.5
cAMP Receptor Protein + cAMP
ML
M ML2
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
Buczek and Horvath. (2006) Journal of Molecular Biology 359 1217-1234
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2 O. nova d(T4G4T4G4) + Telomere Binding Protein Subunit N-domain
0 1 2 3 4
-5
0
5
Q (
kca
l/m
ol o
f in
jecta
nt)
Molar Ratio
K1 2.5·107 M-1
H1 3.4 kcal/molK2 1.3·105 M-1
H2 -5.9 kcal/mol
0.021
Heterotropy
𝐾𝑎𝑎𝑝𝑝
= 𝐾𝑎
1 + 𝛼𝐾𝑋 𝑋
1 + 𝐾𝑋 𝑋
𝐾𝑋, ∆𝐻𝑋
𝐾𝑎𝑎𝑝𝑝
, ∆𝐻𝑎𝑎𝑝𝑝
𝐾𝑎 , ∆𝐻𝑎
∆𝐻𝑎𝑎𝑝𝑝
= ∆𝐻𝑎 − ∆𝐻𝑋
𝐾𝑋 𝑋
1 + 𝐾𝑋 𝑋+ ∆𝐻𝑋 + ∆ℎ
𝛼𝐾𝑋 𝑋
1 + 𝐾𝑋 𝑋
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Heterotropy 1:2
• Perform titrations with both ligands
• Perform titration with one ligand in the presence of the other ligand
• Compare and calculate
𝐾𝑎, ∆𝐻𝑎 𝐾𝑋, ∆𝐻𝑋
𝐾𝑎𝑎𝑝𝑝
, ∆𝐻𝑎𝑎𝑝𝑝
𝐾𝑎/ 𝐾𝑎𝑎𝑝𝑝
, ∆𝐻𝑎 / ∆𝐻𝑎𝑎𝑝𝑝
𝛼, ∆ℎ
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Heterotropy 1:2
Test: Independent or cooperative binding?
𝛼 = 0∆ℎ = 0
↔𝐾𝑎
𝑎𝑝𝑝=
𝐾𝑎
1 + 𝐾𝑋 𝑋
∆𝐻𝑎𝑎𝑝𝑝
= ∆𝐻𝑎 − ∆𝐻𝑋
𝐾𝑋 𝑋
1 + 𝐾𝑋 𝑋
Independent
Competitive
Otherwise… Cooperative𝛼 > 0, 𝛼 ≠ 1∆ℎ ≠ 0
𝛼 = 1∆ℎ = 0
↔ 𝐾𝑎
𝑎𝑝𝑝= 𝐾𝑎
∆𝐻𝑎𝑎𝑝𝑝
= ∆𝐻𝑎
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Heterotropy 1:2
Test: Independent or cooperative binding?
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-1
0
0 30 60 90 120
time (min)
dQ
/dt
(ca
l/s)
M+L1
M/L2+L1
Molar Ratio
Q (
kca
l/m
ol o
f in
jecta
nt)
𝐾𝑎 = 1.1 ∙ 107 𝑀−1
∆𝐻𝑎 = −5.2 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾𝑋 = 1.5 ∙ 105 𝑀−1
∆𝐻𝑋 = 3.1 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾𝑎𝑎𝑝𝑝
= 3.1 ∙ 105 𝑀−1
∆𝐻𝑎𝑎𝑝𝑝
= −8.4 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝑋 ≈ 200 𝜇𝑀
↓
𝛼 ≈ 0∆ℎ ≈ 0
Competitive Binding
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
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0.0
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0.4
0 30 60 90 120 150 180 210
time (min)
dQ
/dt
(ca
l/s) M+L1
M/L2+L1
Molar Ratio
Q (
kca
l/m
ol o
f in
jecta
nt)
𝐾𝑎 = 9.2 ∙ 105 𝑀−1
∆𝐻𝑎 = 3.7 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾𝑋 = 2.7 ∙ 105 𝑀−1
∆𝐻𝑋 = −2.1 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾𝑎𝑎𝑝𝑝
= 2.3 ∙ 105 𝑀−1
∆𝐻𝑎𝑎𝑝𝑝
= 5.3 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝑋 ≈ 40 𝜇𝑀
↓
𝛼 ≈ 0.18∆ℎ ≈ 1.6
Cooperative Binding
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Analytical toolsto gain insights into complex modes of
interactions with ITCEva Muñoz
Senior Scientist at AFFINImeter
Competitive experiments.
Heterogeneous mixtures of ligands
Analytical tools to gain insights into complex modes of interactions with ITC
Mixtures two ligands difficult to separate
Analytical tools:
Tailored binding models.
Global analysis of several isotherms.
Tools to interpret the results: species distribution plot.
Mixture of ligands
Receptor
EDTA
+ M
Ca+2 Ba+2M = ,
Analytical tools to gain insights into complex modes of interactions with ITC
EDTA Ca+2Ba+2EDTA
Competitive binding model
Ca+2
Ba+2
EDTA
Experimental setup
M = compound in cell
A = compound in syringe
B = third species (competitor)
DIRECT TITRATION
Analytical tools to gain insights into complex modes of interactions with ITC
Tailored binding model
Analytical tools to gain insights into complex modes of interactions with ITC
We need an easy tool to designour own binding models:
THE REACTION BUILDER
Analytical tools to gain insights into complex modes of interactions with ITC
We need an easy tool to designour own binding models:
THE REACTION BUILDER
Drag and drop reactive species
Analytical tools to gain insights into complex modes of interactions with ITC
We need an easy tool to designour own binding models:
THE REACTION BUILDER
Click on “Free Species” to add another equilibrium
Competitive model
Competitive model,
bivalent receptor
ITC isotherms of Ba2+/Ca2+ mixtures binding to EDTA
6-7 fitting parameters/curve
INDIVIDUAL FITTING
Analytical tools to gain insights into complex modes of interactions with ITC
< 3 fitting parameters/curve
GLOBAL FITTING
ITC isotherms of Ba2+/Ca2+ mixtures binding to EDTA
fitting parameters/curve: 6 - 7
Analytical tools to gain insights into complex modes of interactions with ITC
ITC isotherms of Ba2+/Ca2+ mixtures binding to EDTA
GLOBAL FITTING
Analytical tools to gain insights into complex modes of interactions with ITC
The species distribution plot
Analytical tools to gain insights into complex modes of interactions with ITC
Ca2+-EDTA
Ba2+-EDTA
Visualizes the population of each species through the titration
Ca2+/Ba2+ 1:1
Ca2+-EDTA
Ba2+-EDTA
Ca2+/Ba2+ 1:3
Ca+2
Ba+2
EDTA
Heparin
Bioactive pentasaccharide (anticoagulant activity)
+
Antithrombin (AT)
HIGH AFFINITY
(Bioactive sequence)
Heterogeneous mixtures of ligands
Heparin – protein interactions
• Linear heterogeneous polysaccharide.• Involved in numerous biological events• Anticoagulant activity
Analytical tools to gain insights into complex modes of interactions with ITC
Bioactive pentasaccharide (anticoagulant activity)
+
Antithrombin (AT)
HIGH AFFINITY
(Bioactive sequence)
Other sequences + Antithrombin (AT) LOW AFFINITY
Heterogeneous mixtures of ligands
Heparin – protein interactions
Heparin
Analytical tools to gain insights into complex modes of interactions with ITC
Bioactive pentasaccharide (anticoagulant activity)
+
Antithrombin (AT)
HIGH AFFINITY
(Bioactive sequence)
Other sequences + Antithrombin (AT) LOW AFFINITY
Heterogeneous mixtures of ligands
Heparin – protein interactions
Heparin
Analytical tools to gain insights into complex modes of interactions with ITC
Percentage of Ps: 46 %
SPECIES DISTRIBUTION PLOT
rA and rB: correction factors forconcentration of Ps and La
Ps
La
FITTING
COMPETITIVE BINDING MODEL
Pentasaccharide Low affinity sequences
KA (106 M-1) H(Kcal/mol) KA (103 M-1) H (Kcal/mol)
19.20 -11.14 352 -1.98
Tailored binding model
AT-PsAT-La
Ps La
Ps = pentasaccharide (high affinity)
La = Low affinity sequences
AT
Experimental setup
PsLa
Analytical tools to gain insights into complex modes of interactions with ITC
Laboratorios
farmacéuticos ROVI
• Determination of percentage of pentasaccharide in Low Molecular Weight Heparins.
LMW-2 LMW-3 LMW-4 LMW-5 LMW-6 LMW-7 LMW-8 LMW-1
Application in the pharmaceutical industry
GLOBAL FITTING
Analytical tools to gain insights into complex modes of interactions with ITC
Multiple site ligand binding
Analytical tools to gain insights into complex modes of interactions with ITC
• Higher level of complexity: many equilibria, intermediate complex species.
• Cooperavitity?
Receptor with several binding sites
Analytical tools:
• Tailored binding models.
• Global fitting.
• Stoichiometric equilibria vs. independent sites approach.
Based on Site constants
k1
k2
k2
k1
k1 k2
Interaction of Calmodulin (CaM) with a Calmodulin binding protein (CaMBD)
Analytical tools to gain insights into complex modes of interactions with ITC
Multiple site ligand binding
CaMBD
CaM
x
Data Kindly provided byMaria João CarvalhoJoão Morais-Cabral
Institute for molecular and cell biology, Porto
Interaction of Calmodulin (CaM) with a Calmodulin binding protein (CaMBD)
Based on Site constants
Based on Stoichiometric constants
Analytical tools to gain insights into complex modes of interactions with ITC
Multiple site ligand binding
CaMBD
CaM
k1
k2
k2
k1
k1 k2
Experimental setup
Analytical tools to gain insights into complex modes of interactions with ITC
Stoichiometric equilibria approach Independent sites approach
Requirement of bindingindependency
k1 = k1; k2 = k2
k1
k1 k2
k2
Are S1 and S2 of CaMindependent?
Analytical tools to gain insights into complex modes of interactions with ITC
Stoichiometric equilibria approach Independent sites approach
Requirement of bindingindependency
STOICHIOMETRIC EQUILIBRIA
Equilibrium 1 Equilibrium 2
K1
(108 M-1)
H
(Kcal/mol)
K2
(105 M-1)
H
(Kcal/mol)
1.1123 - 12.245 6.0342 - 4.053
INDEPENDENT SITES
S1 S2
k1
(108 M-1)
h1
(Kcal/mol)
k2
(105 M-1)
h2
(Kcal/mol)
1.1062 - 12.290 6.0673 - 4.008
𝑲𝟏 = 𝒌𝟏 + 𝒌𝟐
𝑲𝟐 =𝒌𝟏 · 𝒌𝟐
𝒌𝟏 + 𝒌𝟐
Relationship between Ks and Hs
∆𝑯𝟏=𝒌𝟏∆𝒉𝟏 + 𝒌𝟐∆𝒉𝟐
𝒌𝟏 + 𝒌𝟐
k1 = k1; k2 = k2
k1
k1 k2
k2
∆𝑯𝟐=𝒌𝟐∆𝒉𝟏 + 𝒌𝟏∆𝒉𝟐
𝒌𝟏 + 𝒌𝟐
S1 and S2 of CaMindependent
s1
s2
CaM into CaMBD
Single-site titrationsGLOBAL FITTING (INDEPENDENT SITES)
s1 s2
k1
(108 M-1)
h1
(Kcal/mol)
k2
(105 M-1)
h2
(Kcal/mol)
0.30 - 10.97 5.09 - 5.09
Analytical tools to gain insights into complex modes of interactions with ITC
GLOBAL FITTING
Species distribution plot
GLOBAL FITTING
Tailored binding models
SUMMARY
How to gain insights into complex modes of interaction with ITC?
An understanding of standard models vs. nonstandard
models