**2.5 Enthalpy-entropy compensation, binding cooperativity, and protein flexibility**

The enthalpic and entropic contributions are related. An increase in enthalpy by tighter binding may directly affect the entropy by the restriction of mobility of the interacting molecules (Dunitz, 1995). This phenomenon, referred to as enthalpy-entropy compensation, is widely observed, although its relevance is disputed (Ford, 2005). Such compensation, although frequently observed, is not a requirement: if it was, meaning that changes in *H* were always compensated by opposing changes in *T S* , optimisation of binding affinities would not be possible, which is clearly not the case.

In connection to the enthalpy-entropy compensation, ligand-protein interactions can be cooperative, which means the binding energy associated with them is different than the sum of the individual contributions to the binding free energies. Cooperativity provides a medium to transfer information, enhance or attenuate a response to changes in local concentration and regulate the overall signalling/reaction pathway. Its effects are either positive (synergistic) or negative (interfering), depending on whether the binding of the first ligand increases or decreases the affinity for subsequent ligands. Noncooperative (additive) binding does not affect the affinity for remaining ligands and the subsequent binding sites can be regarded as independent.

Cooperativity is often linked to pronounced conformational changes in the structure of the protein. It can be, in some cases, caused by structural tightening through the presence of additional interactions; inter-atomic distances become shorter and interaction becomes

also offer an opportunity to measure contributions to binding events from interacting partners individually. Hydrogen-deuterium exchange mass spectrometry (HX-MS) and related methods, have been very successful in studying protein dynamics in large supramolecular complexes (Wales and Engen, 2006). The motion of the entire complex and individual contributors, and the dynamics of the binding events can be investigated by timeresolved HX-MS (Graf *et al.*, 2009). Another technique frequently used to study binding events is surface plasmon resonance (SPR), which allows for straightforward determination of equilibrium binding constants (Alves *et al.*, 2005). Terahertz spectroscopy is a relatively new technique, used primarily to probe solvation of macromolecules and their complexes (Ebbinghaus *et al.,* 2007). It is very sensitive to changes of the collective water network dynamics at the at the macromolecule-water interface. Terahertz absorption spectroscopy can also be used to probe collective modes in ligand-protein complexes (Xu et al., 2006). There are two groups of methods that deserve special attention in the context of thermodynamics of binding events and will be discussed more in details in the following part of this chapter. One of these is NMR spectroscopy, especially powerful for the study of ligand-protein dynamics, hence the entropic contribution to the binding free energy (Meyer and Peters, 2003). The other group contains calorimetric techniques, which are very important for the study of biological systems, their stability, and the thermodynamics of macromolecular interactions. Currently, two most popular techniques applied to investigate biological systems are differential scanning calorimetry (DSC) and isothermal titration calorimetry (ITC). The former quantifies the heat capacity and enthalpy of thermal denaturation, the latter measures the heat exchanged during macromolecular association. While DSC provides the way to estimate the stability of the system (protein, nucleic acid, ligand-protein complex, etc), ITC is an excellent tool to study the thermodynamics of binding events (Perozzo *et al.*, 2004). Since this chapter is dedicated to the thermodynamics of macromolecular associations, in the course of this chapter I will focus mainly on ITC and

ITC measures the heat evolved during macromolecular association events. In an ITC experiment, one binding partner (ligand) is titrated into a solution containing another binding partner (protein), and the extent of binding is determined by direct measurement of heat exchange (whether heat is being generated or absorbed upon the binding). ITC is the only experimental technique where the binding constant ( *Kd )*, Gibbs free energy of binding

*et al.*, 2004). ITC experiments performed at different temperatures are used to estimate the

*Cp* of the binding event (Perozzo *et al.*, 2004). During last few decades, ITC has attracted interest of broader scientific community, as a powerful technique when applied in life sciences. Several practical designs emerged, but the greatest advances have happened during last 10 years. Development of sensitive, stable, and – last but not least - affordable calorimeters made calorimetry a very popular analytical procedure and ITC became the gold standard in estimations of macromolecular interactions. Given the ability of ITC to obtain a full thermodynamic description of the system studied, the technique has found widespread applicability in the study of biological systems. Apart from its versatility and simple experimental setup, ITC also has advantages over some other

*S* ) can be determined in a single experiment (Perozzo

its applications to study biological systems.

**3.1.1 Isothermal titration calorimetry (ITC)** 

*H* ) and entropy (

( 

*G* ), enthalpy (

heat capacity change (

enthalpically more favorable. Evidence for such a mechanism has been reported for many ligand-protein complexes; biotin-streptavidin being one of the most extensively studied (Williams *et al.*, 2003). In other cases, cooperativity can occur in the absence of any conformational changes of the protein, and be driven solely by changes in protein dynamics (Homans, 2005, Wand, 2001). Catabolite-activated protein (CAP) is a very good example of such dynamic allostery. CAP is a transcriptional activator that exists as a homodimer in solution, with each subunit comprising a ligand-binding domain at the N-terminal domain and a DNA-binding domain at the C-terminal domain (Harman, 2001). Two cyclic AMP (cAMP) molecules bind to CAP dimer, and this binding increases affinity of CAP for DNA (Harman, 2001). Binding of each cAMP molecule shows negative cooperativity, i.e. binding of the first cAMP molecule decreases affinity of binding of the second cAMP molecule to CAP. This is accompanied by absence of long-range structural changes. Thermodynamic analysis, performed by a combination of ITC and solution NMR, confirmed that the observed negative cooperativity was entirely driven by changes in protein entropy (Popovych *et al.*, 2009). Thus, it is more appropriate to describe the phenomenon of cooperativity in terms of thermodynamics rather than merely conformational changes (if any such changes can be observed), since it is fundamentally thermodynamic in its nature. Examples above illustrate the importance of protein dynamics in binding events. Proteins tend to compensate the unfavourable entropic contribution to ligand binding by increasing

their dynamics in regions distant from the ligand binding site (Evans and Bronowska, 2010, MacRaild *et al.*, 2007) Flexible binding sites may require more flexible ligand moieties than 'stiffer' ones. The traditional focus on the enthalpic term (direct and specific interactions) and dominance of the 'induced fit' model has led to an overly enthalpic view of the world that neglects protein flexibility. Such view of the ligand-protein binding events, although very intuitive, is flawed by neglect of entropic contributions and – as a consequence – an impairment to correct predictions of free binding energy. Although it is true that tighter interactions make binding more favourable, the thermodynamic signature of a "good" binder does not need to be dominated by an enthalpic term.
