How to gain insights into complex modes of interaction with ITC

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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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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Adrian Velazquez-CampoyARAID-BIFI Researcher

http://bifi.es/index.php

http://bifi.es/index.php

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

...


ITC´s “Black legend”:• Prone to artifacts

• Difficult technique (data analysis)

• Time consuming

• Sample consuming

• Inadequate for extreme affinity


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[Ligand]T/[Macromolecule]

T

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-10

-8

-6

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-2

0

2

kcal/m

ol

G

H

-TS

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[Ligand]T/[Macromolecule]

T

Standard model: 1:1


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?


Standard model: 1:1

Cooperativity: homo- and heterotropy

Homotropic Interaction Heterotropic Interaction

𝐾1 = 𝑓 𝑘1, 𝑘2, 𝛼

𝐾2 = 𝑓 𝑘1, 𝑘2, 𝛼


Nonstandard model: 1:2


= 𝑓 𝐾𝑎 , 𝐾𝑋, 𝛼, 𝑋


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?


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=

( + )



∆𝐻1=𝑘1∆ℎ1 + 𝑘2∆ℎ2

𝑘1 + 𝑘2

∆𝐻2=𝑘2∆ℎ1 + 𝑘1∆ℎ2

𝑘1 + 𝑘2+ ∆𝜂



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



Different scenarios 𝜌 =4𝐾2

𝐾1



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

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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



Gorshkova et al. (1995) Journal of Biological Chemistry 270 21679-21683

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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



Buczek and Horvath. (2006) Journal of Molecular Biology 359 1217-1234


Nonstandard model: Homotropy 1:2 O. nova d(T4G4T4G4) + Telomere Binding Protein Subunit N-domain

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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


= 𝐾𝑎

1 + 𝛼𝐾𝑋 𝑋

1 + 𝐾𝑋 𝑋

𝐾𝑋, ∆𝐻𝑋


, ∆𝐻𝑎𝑎𝑝𝑝

𝐾𝑎 , ∆𝐻𝑎

∆𝐻𝑎𝑎𝑝𝑝

= ∆𝐻𝑎 − ∆𝐻𝑋

𝐾𝑋 𝑋

1 + 𝐾𝑋 𝑋+ ∆𝐻𝑋 + ∆ℎ

𝛼𝐾𝑋 𝑋

1 + 𝐾𝑋 𝑋


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


, ∆𝐻𝑎𝑎𝑝𝑝

𝐾𝑎/ 𝐾𝑎𝑎𝑝𝑝

, ∆𝐻𝑎 / ∆𝐻𝑎𝑎𝑝𝑝

𝛼, ∆ℎ



Test: Independent or cooperative binding?

𝛼 = 0∆ℎ = 0

↔𝐾𝑎

𝑎𝑝𝑝=

𝐾𝑎

1 + 𝐾𝑋 𝑋


= ∆𝐻𝑎 − ∆𝐻𝑋

𝐾𝑋 𝑋

1 + 𝐾𝑋 𝑋

Independent

Competitive

Otherwise… Cooperative𝛼 > 0, 𝛼 ≠ 1∆ℎ ≠ 0

𝛼 = 1∆ℎ = 0

↔ 𝐾𝑎

𝑎𝑝𝑝= 𝐾𝑎


= ∆𝐻𝑎



Test: Independent or cooperative binding?

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𝐾𝑎 = 1.1 ∙ 107 𝑀−1

∆𝐻𝑎 = −5.2 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙

𝐾𝑋 = 1.5 ∙ 105 𝑀−1

∆𝐻𝑋 = 3.1 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙


= 3.1 ∙ 105 𝑀−1


= −8.4 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙

𝑋 ≈ 200 𝜇𝑀

↓

𝛼 ≈ 0∆ℎ ≈ 0

Competitive Binding


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𝐾𝑎 = 9.2 ∙ 105 𝑀−1

∆𝐻𝑎 = 3.7 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙

𝐾𝑋 = 2.7 ∙ 105 𝑀−1

∆𝐻𝑋 = −2.1 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙


= 2.3 ∙ 105 𝑀−1


= 5.3 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙

𝑋 ≈ 40 𝜇𝑀

↓

𝛼 ≈ 0.18∆ℎ ≈ 1.6

Cooperative Binding


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 = ,


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


Tailored binding model


We need an easy tool to designour own binding models:

THE REACTION BUILDER




Drag and drop reactive species

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


< 3 fitting parameters/curve

GLOBAL FITTING


fitting parameters/curve: 6 - 7



GLOBAL FITTING


The species distribution plot


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)


Heparin – protein interactions

• Linear heterogeneous polysaccharide.• Involved in numerous biological events• Anticoagulant activity


Bioactive pentasaccharide (anticoagulant activity)

+

Antithrombin (AT)

HIGH AFFINITY

(Bioactive sequence)

Other sequences + Antithrombin (AT) LOW AFFINITY


Heparin – protein interactions

Heparin


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


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


Multiple site ligand binding


• 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)



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



CaMBD

CaM

k1

k2

k2

k1

k1 k2

Experimental setup


Stoichiometric equilibria approach Independent sites approach

Requirement of bindingindependency

k1 = k1; k2 = k2

k1

k1 k2

k2

Are S1 and S2 of CaMindependent?


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


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

How to gain insights into complex modes of interaction with ITC

Healthcare

Transcript of How to gain insights into complex modes of interaction with ITC