Malvern and AFFINImeter together, show how the latest advances in the field of ITC data analysis enable users to “squeeze” the ITC isotherm(s) to get more information than just thermodynamic data and to expand the range of applications of ITC.

1. How to gain insights into complex modes of
interaction with ITC
Adrian Velazquez-Campoy
ARAID-BIFI Researcher
Scientific advisor at AFFINImeter
Eva Muñoz
Senior Scientist at AFFINImeter

2. 0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
0 30 60 90 120 150 180
-0.3
0.0
0.3
0.6
0.9
time (min)
dQ/dt(cal/s)
[Fd]T
/[FNR]T
Q(kcal/molofinjectant)
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

3. Isothermal Titration Calorimetry:
Standard Model vs. Nonstandard Models
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
0 30 60 90 120 150 180
-0.3
0.0
0.3
0.6
0.9
time (min)
dQ/dt(cal/s)
[Fd]T
/[FNR]T
Q(kcal/molofinjectant)
Adrian Velazquez-Campoy
ARAID-BIFI Researcher

4. Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
ITC
Gold-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

5. ITC
Provides invaluable information:
Interaction? YES/NO
Ka , Kd , G
H, -TS
n
CP , nX
...
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models

6. 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

7. 0.0 0.5 1.0 1.5 2.0 2.5
-6.0
-4.0
-2.0
0.0
-0.04
-0.02
0.00
0 10 20 30 40 50
time (min)
dQ/dt(cal/s)
[Ligand]T
/[Macromolecule]T
Q(kcal/molofinjectant)
-10
-8
-6
-4
-2
0
2
kcal/mol
G
H
-TS
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
MolarFraction
[Ligand]T
/[Macromolecule]T
Standard model: 1:1
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models

8. 𝑛 = 1 ⇒ 𝑍 = 1 + 𝛽 𝑎𝑝𝑝 𝐿 = 1 + 𝐾𝑎
𝑎𝑝𝑝
𝐿
𝐾𝑎
𝑎𝑝𝑝
, ∆𝐻 𝑎𝑝𝑝
, 𝑛
∆𝐺 𝑎𝑝𝑝
, −𝑇∆𝑆 𝑎𝑝𝑝
• Conformational change coupled to binding
• Allosteric systems
• Polysteric systems
Quasi-simple approximation?
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Standard model: 1:1

9. 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
𝐾𝑎
𝑎𝑝𝑝
= 𝑓 𝐾𝑎 , 𝐾 𝑋, 𝛼, 𝑋

10. Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: 1:2
Cooperativity: homo- and heterotropy
𝐾 𝑎, ∆𝐻 𝑎
𝐾 𝑋, ∆𝐻 𝑋 𝐾 𝑎 𝛼, , ∆𝐻 𝑥 + Δℎ
𝐾 𝑋 𝛼, ∆𝐻 𝑥 + Δℎ𝑘1, ∆ℎ1
𝑘2, ∆ℎ2 𝑘1 𝛼, ∆ℎ1 + ∆𝜂
𝑘2 𝛼, ∆ℎ2 + ∆𝜂
𝑲 𝟏
∆𝑯 𝟏
𝑲 𝟐
∆𝑯 𝟐
Homotropic Interaction Heterotropic Interaction

11. Homotropy: The “stoichiometric model”
𝑍 =
𝑖=0
𝑛
𝑃𝐿𝑖
𝑃
=
𝑖=0
𝑛
𝛽𝑖 𝐿 𝑖
=
𝑖=0
𝑛
𝑗=1
𝑖
𝐾𝑗 𝐿 𝑖
𝑛 = 2 ⇒ 𝑍 = 1 + 𝐾1 𝐿 + 𝐾1 𝐾2 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

12. Kj’s are “ensemble” association constants
𝑍 = 1 + 𝐾1 𝐿 + 𝐾1 𝐾2 𝐿 2
𝑍 = 1 + 𝑘1 + 𝑘2 𝐿 + 𝑘1 𝑘2 𝛼 𝐿 2
No ordered binding mechanism is implied!
𝐾1 = 𝑘1 + 𝑘2 =
+
𝐾2 =
𝑘1 𝑘2 𝛼
𝑘1 + 𝑘2
=
( + )
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2

13. ∆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 + 𝐾1 𝐾2 𝐿 2
𝑍 = 1 + 𝑘1 + 𝑘2 𝐿 + 𝑘1 𝑘2 𝛼 𝐿 2

14. Different scenarios 𝜌 =
4𝐾2
𝐾1
identical & independent
nonidentical & independent
identical & cooperative
nonidentical & cooperative
𝑘1 = 𝑘2 = 𝑘, 𝛼 = 𝜌 = 1
Δℎ1 = Δℎ2 = Δℎ, ∆𝜂 = 0
𝑘1 ≠ 𝑘2,𝛼 = 1, 𝜌 < 1
Δℎ1 ≠ Δℎ2, ∆𝜂 = 0
𝑘1 = 𝑘2 = 𝑘, 𝛼 = 𝜌 ≠ 1
Δℎ1 = Δℎ2 = Δℎ, ∆𝜂 ≠ 0
𝑘1 ≠ 𝑘2,𝛼 ≠ 1, 𝜌 ≠ 1
Δℎ1 ≠ Δℎ2, ∆𝜂 ≠ 0
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2

15. Different scenarios 𝜌 =
4𝐾2
𝐾1
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Homotropy 1:2
4𝐾2 ≠ 𝐾1,𝛼 ≠ 1, 𝜌 ≠ 1
Δ𝐻2 ≠ Δ𝐻1, ∆𝜂 ≠ 0
4𝐾2 ≠ 𝐾1, 𝛼 = 𝜌 ≠ 1
Δ𝐻2 ≠ Δ𝐻1, ∆𝜂 ≠ 0
4𝐾2 < 𝐾1,𝛼 = 1, 𝜌 < 1
Δ𝐻2 ≠ Δ𝐻1, ∆𝜂 = 0
4𝐾2 = 𝐾1, 𝛼 = 𝜌 = 1
Δ𝐻2 = Δ𝐻1, ∆𝜂 = 0
identical & independent
nonidentical & independent
identical & cooperative
nonidentical & cooperative

16. 0 1 2 3 4
-10
-5
0
Q(kcal/molofinjectant)
Molar Ratio
K1 3.0·106 M-1
H1 -10.1 kcal/mol
K2 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

17. Gorshkova et al. (1995) Journal of Biological Chemistry 270 21679-21683
0 1 2 3 4 5
0
2
4
6
Q(kcal/molofinjectant)
Molar Ratio
K1 5.5·104 M-1
H1 -1.9 kcal/mol
K2 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

18. 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
5Q(kcal/molofinjectant)
Molar Ratio
K1 2.5·107 M-1
H1 3.4 kcal/mol
K2 1.3·105 M-1
H2 -5.9 kcal/mol
 0.021

19. Heterotropy
𝐾 𝑎
𝑎𝑝𝑝
= 𝐾 𝑎
1 + 𝛼𝐾 𝑋 𝑋
1 + 𝐾 𝑋 𝑋
𝐾 𝑋, ∆𝐻 𝑋
𝐾𝑎
𝑎𝑝𝑝
, ∆𝐻 𝑎
𝑎𝑝𝑝
𝐾𝑎 , ∆𝐻 𝑎
∆𝐻 𝑎
𝑎𝑝𝑝
= ∆𝐻 𝑎 − ∆𝐻 𝑋
𝐾 𝑋 𝑋
1 + 𝐾 𝑋 𝑋
+ ∆𝐻 𝑋 + ∆ℎ
𝛼𝐾 𝑋 𝑋
1 + 𝐾 𝑋 𝑋
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Heterotropy 1:2

20. • Perform titrations with both ligands
• Perform titration with one ligand in the presence of the other ligand
• Compare and calculate
𝐾𝑎, ∆𝐻 𝑎 𝐾 𝑋, ∆𝐻 𝑋
𝐾𝑎
𝑎𝑝𝑝
, ∆𝐻 𝑎
𝑎𝑝𝑝
𝐾𝑎/ 𝐾𝑎
𝑎𝑝𝑝
, ∆𝐻 𝑎 / ∆𝐻 𝑎
𝑎𝑝𝑝
𝛼, ∆ℎ
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Heterotropy 1:2
Test: Independent or cooperative binding?

21. 𝛼 = 0
∆ℎ = 0
↔
𝐾 𝑎
𝑎𝑝𝑝
=
𝐾 𝑎
1 + 𝐾 𝑋 𝑋
∆𝐻 𝑎
𝑎𝑝𝑝
= ∆𝐻 𝑎 − ∆𝐻 𝑋
𝐾 𝑋 𝑋
1 + 𝐾 𝑋 𝑋
Independent
Competitive
Otherwise… Cooperative𝛼 > 0, 𝛼 ≠ 1
∆ℎ ≠ 0
𝛼 = 1
∆ℎ = 0
↔
𝐾 𝑎
𝑎𝑝𝑝
= 𝐾 𝑎
∆𝐻 𝑎
𝑎𝑝𝑝
= ∆𝐻 𝑎
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models
Nonstandard model: Heterotropy 1:2
Test: Independent or cooperative binding?

22. 0.0 0.5 1.0 1.5 2.0
-9
-6
-3
0
-2
-1
0
0 30 60 90 120
time (min)
dQ/dt(cal/s)
M+L1
M/L2+L1
Molar Ratio
Q(kcal/molofinjectant)
𝐾 𝑎 = 1.1 ∙ 107
𝑀−1
∆𝐻 𝑎 = −5.2 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾 𝑋 = 1.5 ∙ 105
𝑀−1
∆𝐻 𝑋 = 3.1 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾 𝑎
𝑎𝑝𝑝
= 3.1 ∙ 105
𝑀−1
∆𝐻 𝑎
𝑎𝑝𝑝
= −8.4 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝑋 ≈ 200 𝜇𝑀
↓
𝛼 ≈ 0
∆ℎ ≈ 0
Competitive Binding
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models

23. 0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0 30 60 90 120 150 180 210
time (min)
dQ/dt(cal/s)
M+L1
M/L2+L1
Molar Ratio
Q(kcal/molofinjectant)
𝐾 𝑎 = 9.2 ∙ 105 𝑀−1
∆𝐻 𝑎 = 3.7 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾 𝑋 = 2.7 ∙ 105
𝑀−1
∆𝐻 𝑋 = −2.1 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝐾 𝑎
𝑎𝑝𝑝
= 2.3 ∙ 105
𝑀−1
∆𝐻 𝑎
𝑎𝑝𝑝
= 5.3 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙
𝑋 ≈ 40 𝜇𝑀
↓
𝛼 ≈ 0.18
∆ℎ ≈ 1.6
Cooperative Binding
Isothermal Titration Calorimetry: Standard model vs. Nonstandard models

24. Analytical tools
to gain insights into complex modes of
interactions with ITC
Eva Muñoz
Senior Scientist at AFFINImeter

25. 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

26. EDTA
+M
Ca+2 Ba+2
M = ,
Analytical tools to gain insights into complex modes of interactions with ITC

27. EDTA Ca+2Ba+2
EDTA
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

28. Analytical tools to gain insights into complex modes of interactions with ITC
We need an easy tool to design
our own binding models:
THE REACTION BUILDER

29. Analytical tools to gain insights into complex modes of interactions with ITC
We need an easy tool to design
our own binding models:
THE REACTION BUILDER
Drag and drop reactive species

30. Analytical tools to gain insights into complex modes of interactions with ITC
We need an easy tool to design
our own binding models:
THE REACTION BUILDER

31. Click on “Free Species” to add another equilibrium

32. Competitive model

33. Competitive model,
bivalent receptor

34. 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

35. < 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

36. ITC isotherms of Ba2+/Ca2+ mixtures binding to EDTA
GLOBAL FITTING
Analytical tools to gain insights into complex modes of interactions with ITC

37. 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

38. 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

39. 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

40. 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

41. Percentage of Ps: 46 %
SPECIES DISTRIBUTION PLOT
rA and rB: correction factors for
concentration of Ps and La
Ps
La
FITTING
COMPETITIVEBINDINGMODEL
Pentasaccharide Low affinitysequences
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
Ps
La
Analytical tools to gain insights into complex modes of interactions with ITC

42. 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-8LMW-1
Application in the pharmaceutical industry
GLOBAL FITTING
Analytical tools to gain insights into complex modes of interactions with ITC

43. 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.

44. 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 by
Maria João Carvalho
João Morais-Cabral
Institute for molecular and
cell biology, Porto

45. 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

46. Experimental setup
Analytical tools to gain insights into complex modes of interactions with ITC
Stoichiometric equilibria approach Independent sites approach
Requirement of binding
independency
k1 = k1; k2 = k2
k1
k1 k2
k2
Are S1 and S2 of CaM
independent?

47. Analytical tools to gain insights into complex modes of interactions with ITC
Stoichiometric equilibria approach Independent sites approach
Requirement of binding
independency
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
𝑲 𝟏 = 𝒌 𝟏 + 𝒌 𝟐
𝑲 𝟐 =
𝒌 𝟏 · 𝒌 𝟐
𝒌 𝟏 + 𝒌 𝟐
Relationship between Ks and Hs
∆𝑯 𝟏=
𝒌 𝟏∆𝒉 𝟏 + 𝒌 𝟐∆𝒉 𝟐
𝒌 𝟏 + 𝒌 𝟐
k1 = k1; k2 = k2
k1
k1 k2
k2
∆𝑯 𝟐=
𝒌 𝟐∆𝒉 𝟏 + 𝒌 𝟏∆𝒉 𝟐
𝒌 𝟏 + 𝒌 𝟐
S1 and S2 of CaM
independent

48. s1
s2
CaM into CaMBD
Single-site titrations
GLOBAL 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

49. 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