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How to gain insights into complex modes of interaction with ITC

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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.

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How to gain insights into complex modes of interaction with ITC

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 24. Analytical tools to gain insights into complex modes of interactions with ITC Eva Muñoz Senior Scientist at AFFINImeter
  25. 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. 26. EDTA +M Ca+2 Ba+2 M = , Analytical tools to gain insights into complex modes of interactions with ITC
  27. 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. 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. 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. 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. 31. Click on “Free Species” to add another equilibrium
  32. 32. Competitive model
  33. 33. Competitive model, bivalent receptor
  34. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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