1

In the name of

GOD

2

Zeinab Mokhtari

10-Feb-2010

3

Isothermal titration calorimetry (ITC)

thermodynamics of macromolecular interactions in biological systems

direct measurement of heat exchange extent of binding

a single experiment : binding constant, Gibbs free energy, enthalpy and entropy

Advantages

can be performed in a physiologically relevant buffer

the interacting species do not require immobilisation or chemical modification

an accurate determination of the stoichiometry (independent of the binding affinity)

Introduction

R= 1.98 cal mol-1 K-1

from the titration equivalence point

4

analysis of systems involving multiple binding events:

formation of multiprotein complexes

binding of multivalent ligands

ligand

cooperativity

ITC for dissecting the thermodynamics of cooperativity

5

Selection of an Appropriate Binding Site Model

At the beginning of the experiment the calorimetric cell is filled with the macromolecule.

correction for displacement of liquid:

sensed calorimetrically

Normaltitration

6

nonlinear least squares curve fitting

necessary energy to maintain a constant temperature) in microcalories per second(

each injection binding heat exchangeinteraction

heat after each injection : the area under each peak

Heat α amount of binding

Saturation of macromolecule with the ligand

classical sigmoidal curve

decrease of the peaks magnitude until the peak size reflects dilution and mechanical effects

7

The simplest model:

a single independent binding site

1:1 ligand/macromolecule

Wiseman isotherm

It is only in c value ranges of approximately 1 to 1000 that isotherms can be accurately deconvoluted. nonlinear least squares curve fitting

n, Kb and ∆H

8

Complex macromolecular interactions that display cooperativity

alternative binding models:

multiple binding sites and the possible cooperativity between the binding sites

multiple titration experiments: The contents of the syringe and calorimetric cell are varied.

A single ITC experiment is often insufficient to sample the shape of the binding isotherm and may not allow derivation of the binding and cooperativity parameters.

9

Multiple Binding Sites

n multiple ligand binding sites

two different association constants:

the overall behaviour of the n sites (model dependent)

how binding occurs at each site (model dependent)

macroscopic

microscopic

1:1 interaction only one association constant

determined by ITC

Overall binding constant

Stepwise binding constant

10

Overall binding constant, βj

Stepwise binding constant, Kj

j :any integer between 0 and n

for ligation of the jth site:

ν : the average number of ligand molecules bound per macromolecule

For multivalent macromolecules

11

Cooperativity positive (synergistic)negative (interfering)

α : a unitless term defined as the cooperativity constant

)α < 1()α > 1( Noncooperative

(additive))α = 1(

Homotrophic

ligands

Figure 1. Reaction scheme for the binding of heterogeneous ligands, X and Y , to a macromolecule, M, containing two binding sites.

12

for a macromolecule with just two binding sites

at least six possible binding mechanisms

The binding sites may be:

IdenticalIndependent (Neutral cooperativity (α = 1))Negative cooperativity (α < 1)Positive cooperativity (α > 1)

nonidenticalIndependent (Neutral cooperativity (α = 1))Negative cooperativity (α < 1)Positive cooperativity (α > 1)

13

Cooperativity: Thermodynamics and Conformational Changes

conformational changes in macromolecular structurelarge conformation changes

subtle changes

reinforcement of the interactions between the ligand and the receptorEnthalpy

functional group interactions (ionic, hydrogen bonds, van der Waals interactions)conformational changespolarisation of the interacting groups

electrostatic complementarity

Entropy a measure of disorder in a system

Changes in the binding entropy reflect loss of motion caused by changes in internal rotations and vibrations of the molecules.

Desolvation and the release of counterions upon complex formation

entropy-enthalpy compensation

enthalpic chelate effectstructural tightening

classical entropic chelate effect

14

heterotropic binding to a macromolecule with two dependent binding sites

Gibbs–Helmholtz relationship Vel´azquez-Campoy

15

Type I : governed by entropytype II : governed by both entropy and enthalpytype III : predominantly enthalpic

Positive cooperativity can be both enthalpy- and entropy-driven.

Entropydriven positive cooperativity occurs when the combined entropic cost of the sequential binding events is lower than the summation of two independent events.

Enthalpy-driven positive cooperative occurs when binding of the first ligand results in a conformational change at the second binding site, rendering it higher affinity to the ligand.

Negative cooperativity : mainly entropy-driven and occur when binding results in a loss of configurational entropy.

Enthalpy-driven negative cooperativity : ligand binding leads to a conformationalchange that results in the dissociation of a complex.

homodimeric enzyme glycerol-3-phosphate:CTP transferase multivalent carbohydrates to legume lectins

dissociation of the trimeric G-protein

Negative cooperativity

three types of cooperativity

16

Reverse ITC ExperimentsIn order to fully resolve the binding and cooperative thermodynamics

to check the stoichiometry and the suitability of the binding model

1:1 biomolecular reactions: It is expected that the measured thermodynamic parameters are invariant when changing the orientation of the experiment .

BUTOne species may display greater aggregation when concentrated.

If normal and reverse titrations are insufficient to fully describe the microscopic binding constants

Combination of the ITC data with other biophysical data that can explore cooperativity, such as NMR and spectrofluorometry.

global fitting analysis

17

(1) Selection of an appropriate model/binding polynomial

(2) Calculation of the total macromolecule and ligand concentrations for each injections

(3) Solvation of the the ligand conservation equation for each experimental point assuming certain values

(4) Calculation of the concentrations of each different complex or bound state

(5 )Calculation of the expected signal, assuming certain values for the binding enthalpies

(6) Obtaining the optimal constants and enthalpies that reproduce the experimental data using an iterative method, i.e., nonlinear least squares regression

General Analysis Procedure

mathematical methods for analysing cooperative ITC data

18

Analysis of Cooperativity Using the Binding PolynomialFreire et al.

major advantage : model independent

equilibrium conditions : the binding of ligand by a multivalent macromolecule may be described by a binding polynomial

The number of binding sites should be known or fixed prior to analysis.

macroscopic association constants and enthalpy values

model specific constants

determining the correct model

starting point for data analysis in the absence of a validated binding model

19

partition function, P, of the system

summation of the different concentrations of bound

species relative to the free macromolecule concentration,

orsummation of the

concentration of free ligand in terms of the macroscopic

association constantfraction or population of each species

average number of ligand molecules bound per macromolecule

average excess molar enthalpy

average Gibbs free energy

model independent

20

three states for a macromolecule with two binding sites

identical

binding polynomial for each model : summation of the terms in each column

relative concentration of the statesindependent

general binding polynomial

21

a macromolecule with two binding sites for a homotropic ligand

example

Occupancy of the binding sites

ligand concentration

association constants

cooperativity factor

nonlinear least squares regression analysis of the experimentally-determined heat event

22

accurate values for βj and ∆Hj

thermodynamic parameters

cooperativity factor

The value of the cooperativity parameter provides a very strong indication of the true binding model.

relate the macroscopic binding parameters to the microscopic binding parameters

23

Heterotropic Interactions

two different ligands

)1( both ligands bind to the same binding site

)2( both ligands bind to sites very close to one another, so that the ligands themselves or binding site residues in the macromolecule interact

)3( both ligands bind to binding sites distant to one another, but are coupled through a change in protein dynamics/conformation

Three mechanisms of cooperativity

24

titration of ligand X into a calorimetric cell containing both macromolecule, [M]t and ligand [Y ]t

assuming values of the association and cooperativity constants

free concentrations of the reactants, [M], [X] and [Y ]

concentrations of the complexes, [MX], [MY ] and [MXY ]

mass action law

solving the set of nonlinear equations numerically by the Newton-Rhapson method:

25

Only one titration experiment is required to determine the interaction parameters instead of a series of experiments, saving both time and material.

evaluating the heat effect, qi ,associated with each injection by

nonlinear least squares fitting

26

Figure 2. Global and cooperative thermodynamic parameters associated with the negatively cooperative binding of Fd to FNR-NADP.+

strong negative cooperativity

unfavourable entropy

favourable enthalpy

Titrations of FNR-NADP+ complex with Fd

α = 0.17

Binding affinity is reduced by sixfold when NADP+ is prebound to FNR.

27

Cooperativity of Long-Chain Macromolecules with Multiple Binding Sites

one-dimensional latticesnucleic acids and carbohydrates

footprint :

the minimal number of repeating units necessary to support binding (l)

characterisation of protein-lattice systems

affinity of the interaction

how the affinity varies with lattice heterogeneity

the binding site size (l)

whether ligand binding is cooperative

potential binding site overlap cooperativity between neighbouring ligands

Ligands can bind to lattices in three ways:

isolated binding

singly contiguous binding

doubly contiguous binding

intrinsic association constant

in the presence of neighbouring ligands

cooperativity factor, α

28

homogenous lattice

actual number of free ligand binding sites on an unoccupied lattice

N - l + 1

Figure 3. The three distinguishable types of ligand binding sites

29

Scatchard plota linear representation to facilitate data analysis

only linear when l = 1 and the binding sites are equivalent and independent

McGhee and von Hippelany size of ligand footprint

cooperative interactions between contiguously bound ligands

infinite polymer

Extended by Tosodikov et al. : finite lattices

When l > 1, positive curvature reflecting the entropic resistance to saturation

30

Introduction of a cooperativity factor, α

Scatchard plot is affected both by the entropic resistance to saturation and the cooperativity parameter, α.

Only linear if the apparent negative cooperativity due to the entropic resistance to saturation is compensated by real positive cooperativity.

the enthalpy associated with the interaction between two adjacent bound ligands

31

32

nature of the cooperativity

Change of the binding modes during the course of the titration

Non-cooperative system

Isolated ligands will bind initially, followed by singly contiguous ligands and finally doubly contiguous ligands with two nearest neighbours.

Positively cooperative system

The ligands will immediately cluster forming doubly contiguous ligands.

Negatively cooperative system

Isolated ligands would form initially, and only when ligand accumulated would singly contiguous ligands be observed. Ligands with two neighbours would only accumulate at very high ligand concentration.

Reverse titrationsto fully characterise the binding isotherms

the roles of the ligand and macromolecule reversed

33

An alternative method of implementing theNon-cooperative McGhee–von Hippel model

Shriver

change in concentration of bound protein as the result of the ith injection

the heat of dilution observed with each injection after saturation of the binding sites at the end of titration

can be solved for values of k and l

34

Example: Chromatin Protein Sac7d Binding to DNA

Binds non-cooperatively and non-specifically to the minor groove of duplex DNA

induces a significant kink (66°) in the DNA structure

Titrations: Sac7d and poly(dGdC)

non-cooperative McGhee–von Hippel model

ITC data

25° Cmoderate intrinsic affinity )approximately 833 nM(

ligand footprint of 4.3 base pairs

entropy driven (17.5 kcal mol¡1)

unfavourable enthalpic contribution (9.2 kcal mol¡1)polyelectrolyte

effect

energy needed todistort DNA

Kinking is associated with base-pair unstacking, unwinding and bending, which leads to widening of the minor groove as well the release of water and counterions (which would contribute to the favourable entropy term) due to backbone charge redistribution.

35

Global Analysis multiple titrations, such as normal and reverse titrations

increase the information and precision of the parameters as long as unrecognised systematic errors are not introduced

temperature and pH dependence

floating parameter n : Reaction stoichiometry and concentration errors

n is often a non-integer

In global analysis only integral values reflecting the stoichiometry are permitted. Therefore it is necessary to accurately determine the stoichiometry prior to global analysis by alternative biophysical techniques.

multisite and cooperative bindingSEDPHAT

Houtman et al.global analysis of data from a variety of biophysical techniques

36

Figure 4. Thermodynamics of the binding event determined by application of the non-cooperative McGhee–von Hippel model to ITC data

Favourable entropy

Unfavourableenthalpy

energetic penalty of kinking DNA

37

Global analysis of ITC data

role of cooperativity in the assembly of a threecomponent multiprotein complex

Example: LAT, Grb2 and Sos1 Ternary Complex Assembly

To reduce the complexity: LATpY 191 can bind one Grb2 molecule, which in turn can bind one Sos1NT molecule.

Two titrations were performed:LATpY 191 into Grb2 alone and LATpY 191 into a stoichiometrically mixed 1:1 Grb2-Sos1NT solution

global model for the ternary interaction

Kd = 286 nM

∆G = -8.9 kcal mol-1

∆H = -3.9 kcal mol-1

In the presence of Sos1NT:

α = 0.54

∆g = 0.37 kcal mol-1

∆h = -3.9 kcal mol-1

A model without permitting cooperativity was unable to account for systematic difference in the initial heats of injection for LAT phosphopeptide to Grb2 in the presence and absence of Sos1NT and resulted in an almost threefold increase in the χ2 of the fit.

38

Combination of ITC and NMR to Study CooperativityNMR spectroscopy

measuring the occupancies of individual binding sites

determining the microscopic binding affinities

site-specific data

macroscopic binding data from ITC

Full characterisation of the microscopic and macroscopic binding affinities

)2D HSQC(isotope-enriched two-dimensional heteronuclear single-quantum coherence experiment

)A method of determining cooperativity using NMR spectroscopy(

isotopically labeled ligands (usually 1H and 13C or 15N) unenriched macromolecule

Isotherms are generated by plotting the peak volume integration against molar ratio.

site-specific binding models

Coupling

39

Example: Glycocholate Binding to I-BABP

Human ileal bile acid binding protein (I-BABP)

two binding sites for glycocholatethe physiologically most abundant bile salt

intrinsically weak affinity extremely strong positive cooperativityBut

low ligand–protein ratios : a significant amount of glycocholate remains unboundhigh ligand–protein ratios : more ligand is bound

ITC and heteronuclear 2D HSQC NMR

sequential model

glycocholate was isotopically labeled

three main resonance peaks: unbound glycocholate, glycocholate bound at site 1 and glycocholate bound at site 2

site-specific binding model

NMR : microscopic affinities , cooperativity constant

multiple sites different ligands

40 Thanks

Photo luminescence in coral