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Cooperative binding pervades Nature. This review discusses the use of isothermal titration calorimetry (ITC) in the identification and characterisation of cooperativity in biological interactions. ITC has broad scope in the analysis of cooperativity as it determines binding stiochiometries, affinities and thermodynamic parameters, including enthalpy and entropy in a single experiment. Examples from the literature are used to demonstrate the applicability of ITC in the characterisation of cooperative systems.

Isothermal titration calorimetry (ITC) is a powerful and important technique for the study of the thermodynamics of macromolecular interactions. In an ITC experiment, two reactants are titrated against one another and the extent of binding is determined by direct measurement of heat exchange with the environment (a ubiquitous process in all biological interactions). It is the only technique where the binding constant (_{b}

ITC also allows for an accurate determination of the reaction stoichiometry that is independent of the binding affinity. The reaction stoichiometry is determined from the titration equivalence point. Given the suitability of ITC to determine reaction stoichiometry, it is increasingly used in the analysis of systems that involve multiple binding events, such as the formation of multiprotein complexes [

This review aims to illustrate the use of ITC in dissecting the thermodynamics of cooperativity, with examples taken from the literature. The use of correct experimental design and appropriate binding models are described as are recent advancements in fitting calorimetric data using global analysis and the synergy of ITC with NMR.

In a titration experiment, the ligand, _{0}) that is sensed calorimetrically. As the titration proceeds, each injection drives a volume of liquid out of the calorimetric cell that is equal to the injection volume, υ. Thus the concentration of the macromolecule decreases slightly after each injection. For analysis of the isotherms, it is necessary to correct for this displacement; the total concentrations of ligand, [_{t}_{t}_{0} and [_{0} are the initial concentrations of the macromolecule and the ligand, respectively. After each injection, a number of molecules of ligand have been added to a total amount of macromolecule [_{t}

The heat after each injection is derived by calculating the area under each peak. The size of the heat event is directly proportional to the amount of binding that occurs. As the macromolecule become saturated with the ligand, the magnitudes of the peaks decrease until the peak size reflects dilution and mechanical effects, resulting in a classical sigmoidal curve. The total heat content, _{0} is given by:

The successful extraction of thermodynamic parameters relies on the use of nonlinear least squares curve fitting while employing an appropriate model that describes the interaction under study. The simplest model is one where there is a single independent binding site, forming a 1:1 ligand/macromolecule complex (

The aim of the fitting procedure is to find those values of parameters which best describe the data. The fitting process is typically undertaken using a one-site model based on the Wiseman isotherm [_{b}_{d}_{b}

The shape of the isotherm varies according to the _{b}

Therefore, in a carefully designed ITC experiment, nonlinear least-squares fitting to the binding data using the one-site model determines the values of _{b}^{−1} K^{−1} is the ideal gas law constant [

However, in order to study the complex macromolecular interactions that display cooperativity, it is necessary to use alternative binding models that have been developed to take into account multiple binding sites and the possible cooperativity between the binding sites. Also, when studying complex macromolecular interactions, 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. For complex interactions to be accessible to ITC analysis, multiple titration experiments need to be performed in which the contents of the syringe and calorimetric cell are varied, so that the shape of the isotherm can be fully explored.

In a 1:1 interaction (_{j}_{j}

As the titration of multivalent macromolecule with ligand proceeds, the average number of ligand molecules bound per macromolecule,

Biological systems are complex networks that require careful regulation [

Consider a common case of cooperativity where one macromolecule,

If the binding is regulated by cooperativity, in that the binding of one ligand influences the binding of the second, then the association constants will differ by a unitless term defined as the cooperativity constant, _{X}_{Y}_{Y|X}_{X|Y}

Even for a macromolecule with just two binding sites there are at least six possible binding mechanisms. The binding sites may be; identical, but independent (

Cooperativity is often ascribed to conformational changes in macromolecular structure. However, it has been demonstrated that cooperative processes need not involve large conformation changes, but can by transmitted through subtle changes in protein motions [^{−1} can be easily achieved by a slight stiffening of a few of the many global dynamic modes of motion available to a protein [

ITC allows full thermodynamic characterisation of both the global (

In cases where the compensation of enthalpy and entropy is imprecise, then an increase in enthalpy can lead to a favourable contribution to the Gibbs free energy of binding, which has been termed the enthalpic chelate effect [

Continuing the above example of heterotropic binding to a macromolecule with two dependent binding sites, the Gibbs free energy associated with the formation of each complex can be determined from:

The cooperativity constant is a true equilibrium constant and is related to the interaction or cooperativity Gibbs free energy, enthalpy, and entropy by

Using these thermodynamic descriptors, three types of cooperativity have been defined; type I, II and III. Type I is governed by entropy, type II is governed by both entropy and enthalpy, and type III is predominantly enthalpic [

When macromolecules with multiple binding sites are titrated with ligands (or conversely, macromolecules with one site are titrated with multivalent ligands), the binding curve represents a description of the global energetics of the multisite system and may display multiple phases. The shape of the isotherm can differ significantly depending on whether the macromolecule or ligand is in the calorimetric cell. This is especially the case when multivalent systems display positive cooperativity and the intermediate state can be poorly populated. The isotherm is dominated by unsaturated and fully saturated states, with few singly-bound states, often giving a rather featureless binding curve [

In order to fully resolve the binding and cooperative thermodynamics, it is necessary to perform a reverse titration, where the titrant and titrand orientations are reversed. Reverse titrations should be conducted to check the stoichiometry and the suitability of the binding model [

In cases where normal and reverse titrations are insufficient to fully describe the microscopic binding constants, it may be necessary to attempt global fitting analysis or combine the ITC data with other biophysical data that can explore cooperativity, such as NMR (see below) and spectrofluorometry.

Suitable mathematical methods for analysing cooperative ITC data will now be described. These methods are either model independent (the binding polynomial) or model dependent, where the general binding mechanism under study is known. However, for all techniques, the general analysis procedure is very similar and can be thought to consist of six steps; (1) selection of an appropriate model/binding polynomial; (2) calculation of the total macromolecule and ligand concentrations for each injections using

Under equilibrium conditions, the binding of ligand by a multivalent macromolecule may be described by a binding polynomial [

The binding polynomial is defined as the partition function,

From the partition function, the fraction or population of each species _{j}

The use of the binding polynomial in the analysis of ITC is, perhaps, best illustrated through the use of an example. Consider a macromolecule with two binding sites for a homotropic ligand. The occupancy of the binding sites depends on the ligand concentration, the association constants and the presence or absence of a cooperativity factor. Calculation of the relative concentrations in each state depending on the binding model is given in

Binding polynomials for each model can be obtained by the summation of the relative concentrations for each state in that model,

The binding polynomial acts as the starting point for analysis of ITC data. Firstly, the total ligand concentration, [_{t}

The values of the macroscopic association constants (_{j}_{j}

Thus, analysis of the ITC data provides accurate values for _{j}_{j}_{j}_{j}

For cases where two different ligands bind a macromolecule, cooperativity may result through three mechanisms; (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; and (3) both ligands bind to binding sites distant to one another, but are coupled through a change in protein dynamics/conformation. An exact analysis has been developed that determines the thermodynamic parameters for cooperative binding with heterotropic ligands [

Consider the titration of ligand _{t}_{t}

Assuming values of the association and cooperativity constants it is possible to solve the set of nonlinear equations numerically by the Newton-Rhapson method giving the free concentrations of the reactants, [_{i}

The usefulness of this exact method is that only one titration experiment is required to determine the interaction parameters instead of a series of experiments, saving both time and material. Material can be significant in the study of multicomponent complexes where each experiment uses at least three species.

In ^{+} molecule through the formation of a transient ternary complex. The crystal structure of the 1:1 complex between Fd and FNR-NADP^{+} has been solved [

Titrations of FNR-NADP^{+} complex with Fd were performed and the data analysed using the binding formalism for heterotropic interactions [^{+} with a cooperativity constant, ^{+} is prebound to FNR. The thermodynamic parameters for the binding of Fd to FNR-NADP^{+} are shown in ^{+} causes strong negative cooperativity, corresponding to a Δ^{−1}. The cooperativity enthalpy is favourable (Δ^{−1}), whereas the entropy is unfavourable (-^{−1}). It is postulated that conformational changes that occur as a result of NADP^{+} being present regulates the cooperativity.

ITC is often used to measure the interactions between ligands and long-chain macromolecules (often considered one-dimensional lattices) such as nucleic acids and carbohydrates. These long-chain macromolecules consist of repeating units that form a number of potential binding sites (_{b}_{t}

Also, in a homogenous lattice with no bound ligand, any particular residue can potentially initiate a ligand binding site. Thus, the actual number of free ligand binding sites on an unoccupied lattice is (

As shown previously, transformation of binding data to a linear representation can facilitate data analysis. Therefore in a transformation to a Scatchard plot

Firstly, consider a long-chain molecule with homogenous non-cooperative ligand binding sites. In this instance, it is not necessary to take into account a cooperativity factor:

This model assumes an infinite polymer. ITC experiments will generally be performed with polymers of known finite length and end effects,

In practice, to solve this equation using the information present in the ITC experiment, it is necessary to express [_{t}_{t}

Knowing the ligand and macromolecule concentrations, it is possible to solve _{i}

Introduction of a cooperativity factor,

Again the equation can be written as a polynomial equation with [

The heat exchange associated with each injection can be evaluated using

The total binding parameter is actually the summation of the partial binding numbers (υ_{isol}_{sc}_{dc}

The nature of the cooperativity dictates how the binding modes change during the course of the titration. In a non-cooperative system, isolated ligands will bind initially, followed by singly contiguous ligands and finally doubly contiguous ligands with two nearest neighbours. In contrast, in a positively cooperative system, the ligands will immediately cluster forming doubly contiguous ligands. The opposite would happen in a system regulated by negative cooperativity. 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.

As mentioned previously, reverse titrations can be used to fully characterise the binding isotherms. The same applies for the binding of ligands to lattice-like macromolecules. The binding polynomials used are the same, but the roles of the ligand and macromolecule reversed.

An alternative method of implementing the noncooperative McGhee–von Hippel model in the analysis of ITC data has been proposed by Shriver and coworkers [_{b,i}

The concentration of bound protein, [_{b,i}

Sac7d is a 7 kDa chromatin protein from the hyperthermophile ^{−1}), with a unfavourable enthalpic contribution (9.2 kcal mol^{−1}). The role of entropy in the interaction was attributed to the polyelectrolyte effect which is known to play an important role in promoting binding to DNA. The unfavourable enthalpy was attributed to the energy needed to distort DNA, which is generally believed to be considerable [

Recently, global analysis of ITC data has become increasingly popular as it allows multiple titrations, such as normal and reverse titrations, to be compiled into a single dataset from which the thermodynamic parameters can be calculated [

However, global analysis departs with the floating parameter

A protocol for the global analysis of ITC data for multisite and cooperative binding using the

Global analysis of ITC data was used to examine the role of cooperativity in the assembly of a three-component multiprotein complex involved in signal transduction after T-cell receptor (TCR) activation [^{pY}^{191} can bind one Grb2 molecule, which in turn can bind one Sos1NT molecule.

Two titrations were performed: LAT^{pY}^{191} into Grb2 alone and LAT^{pY}^{191} into a stoichiometrically mixed 1:1 Grb2-Sos1NT solution. The best fit parameters for the binding of LAT phosphopeptide to Grb2 from a global model for the ternary interaction were _{d}^{−1} and Δ^{−1}. In the presence of Sos1NT, the cooperativity factor (^{−1} and Δ^{−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 ^{2} of the fit.

NMR spectroscopy is one of the few experimental techniques capable of measuring the occupancies of individual binding sites on proteins and therefore determining the microscopic binding affinities. Coupling this site-specific data with the macroscopic binding data from ITC allows a complete description of the binding properties of the system. A method of determining cooperativity using NMR spectroscopy has been described using the isotope-enriched two-dimensional heteronuclear single-quantum coherence experiment (2D HSQC) [^{1}H and ^{13}C or ^{15}N) whilst the macromolecule remains unenriched. Spectra are recorded at different molar ratios and the peak volumes are integrated. Isotherms are generated by plotting the peak volume integration against molar ratio. The data is then fitted to site-specific binding models to obtain the thermodynamic parameters.

Human ileal bile acid binding protein (I-BABP) has two binding sites for glycocholate, the physiologically most abundant bile salt [

The cooperativity in this system was analysed using ITC and heteronuclear 2D HSQC NMR spectroscopy [^{1}H-^{15}N; I-BABP was not labeled. ^{1}H-^{15}N spectrum were recorded at different molar ratios. In each spectrum three main resonance peaks were observed, corresponding to unbound glycocholate, glycocholate bound at site 1 and glycocholate bound at site 2. Binding curves for each site were generated by plotting the peak volume integrations against molar ratio. The NMR curves were then fitted using a site-specific binding model, as described by Tochtrop

From the NMR binding curves, the microscopic affinities were calculated as 1.5 mM for site 1 and 2.1 mM for site 2. The cooperativity constant,

Whilst the example illustrates cooperativity between two sites, the experiment can be extended to systems with multiple sites as long as NMR peaks corresponding to each site can be resolved. Also, by using unique isotope enrichment for different ligands, it is possible to study systems with multiple ligands [

ITC provides information rich data with kinetic, thermodynamic and stoichiometric parameters defined in a single experiment. As one of the few biophysical techniques able to dissect the thermodynamics of a binding event, it has rapidly become an important tool in the study of biological interactions, including those involved in ternary complex formation and the binding of multivalent ligands. Assemblies of such systems are often regulated by cooperativity. Cooperativity is best understood in terms of thermodynamics, as not all cooperative systems undergo conformational changes that are often associated with allosteric modulation. Thus, ITC is the ideal technique to ascertain the origin and underlying mechanisms of cooperativity.

To obtain full thermodynamic characterisation of the cooperativity, multiple complementary titrations are often necessary to define binding and cooperativity parameters. The importance of correct experimental design and selection of suitable binding models cannot be understated. The recent application of model-independent binding polynomial formalism to analyse ITC data should reduce the number of examples in the literature where incorrect or insufficient binding models are used.

The example of glycocholate binding to I-BABP illustrates the abundant information that can be obtained from the combination of ITC with other biophysical techniques (full characterisation of the microscopic and macroscopic binding affinities). Global analysis offers the possibility of combining ITC with data from other techniques such as surface plasmon resonance [

I would like to thank Tom Blundell for his thoughtful comments on the manuscript. A.B. is funded by a BBSRC DTA studentship and the work supported by Wellcome Trust Programme Grant RG44650 “The structural biology of cell signaling and regulation: multiple systems and the achievement of high signal-to-noise ratios”.

Reaction scheme for the binding of heterogeneous ligands, _{X}_{Y}_{X}_{|}_{Y}_{Y|X}

Global and cooperative thermodynamic parameters associated with the negatively cooperative binding of Fd to FNR-NADP^{+}.

The three distinguishable types of ligand binding sites: isolated (iso), singly contiguous (sc) and doubly contiguous (dc). The potential number of binding sites is given by (

The crystal structure of chromatin protein Sac7d bound to a nucleic acid fragment (PDB ID: 1AZP) demonstrates that binding induces a 66° kink in the structure of DNA. Thermodynamics of the binding event determined by application of the non-cooperative McGhee–von Hippel model to ITC data demonstrates that binding is characterised by a favourable entropy term and an unfavourable enthalpy term attributed to the energetic penalty of kinking DNA.

A macromolecule with two binding sites is capable of existing in three states: unbound, singly bound or doubly bound. The relative concentration of these states depends on whether the macromolecular binding sites are identical and whether they are independent. The binding polynomial for each model is obtained by the summation of the terms in each column.

Binding state | General | Identical independent | Nonidentical independent | Cooperative |
---|---|---|---|---|

Unbound | 1 | 1 | 1 | 1 |

Singly bound | _{1}[ |
2 |
_{1}[_{2}[ |
2 |

Doubly bound | _{2}[^{2} |
^{2}[^{2} |
_{1}_{2}[^{2} |
^{2}[^{2} |