**3.1 Experimental methods**

Many experimental techniques have been developed to study various aspects of ligandprotein thermodynamics. X-ray crystallography provides very valuable information about the enthalpic contribution (hydrogen and halogen bonds, electrostatic interactions, etc). Although it focuses on static structures of ligand-receptor complexes, it also yields some information on entropic contribution. B-factors (temperature factors), obtainable for heavy (non-hydrogen) atoms of the complex under investigation, are sensitive to the mean square displacements of atoms because of thermal motions, therefore they reflect on ligand-protein dynamics. However, B-factors do not distinguish time scales of the motions and their interpretation is not straightforward. X-ray (Makowski *et al.*, 2011) and neutron scattering (Frauenfelder and Mezei, 2010) also reflect on ligand-protein dynamics. The former one focuses on global changes in protein size and shape in a time-resolved manner, while the latter reports on motion amplitudes and time scales for positions of hydrogen atoms. Another technique useful in understanding protein dynamics both in unbound (apo) and bound (holo) forms is fluorescence spectroscopy (Weiss, 2000). Single molecule techniques

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.

Many experimental techniques have been developed to study various aspects of ligandprotein thermodynamics. X-ray crystallography provides very valuable information about the enthalpic contribution (hydrogen and halogen bonds, electrostatic interactions, etc). Although it focuses on static structures of ligand-receptor complexes, it also yields some information on entropic contribution. B-factors (temperature factors), obtainable for heavy (non-hydrogen) atoms of the complex under investigation, are sensitive to the mean square displacements of atoms because of thermal motions, therefore they reflect on ligand-protein dynamics. However, B-factors do not distinguish time scales of the motions and their interpretation is not straightforward. X-ray (Makowski *et al.*, 2011) and neutron scattering (Frauenfelder and Mezei, 2010) also reflect on ligand-protein dynamics. The former one focuses on global changes in protein size and shape in a time-resolved manner, while the latter reports on motion amplitudes and time scales for positions of hydrogen atoms. Another technique useful in understanding protein dynamics both in unbound (apo) and bound (holo) forms is fluorescence spectroscopy (Weiss, 2000). Single molecule techniques

**3. Methods** 

**3.1 Experimental methods** 

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 its applications to study biological systems.

### **3.1.1 Isothermal titration calorimetry (ITC)**

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 ( *G* ), enthalpy ( *H* ) and entropy ( *S* ) can be determined in a single experiment (Perozzo *et al.*, 2004). ITC experiments performed at different temperatures are used to estimate the heat capacity change ( *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

with a stronger binder of interest. However, this method requires precise knowledge of binding constants of those weak binders. The experimental setup of the displacement assay is often challenging, as there are several factors increasing the error of measurements.

Fig. 2. An example of ITC data. Raw data, representing observed changes in heat resulting from interactions are shown in the upper panel. The resulting binding curve is displayed in the lower panel (from MicroCal materials http://www.microcal.com/technology/itc.asp). It is worth remembering that ITC experiment not only measures the heat absorbed or released during binding reactions, but it also detects the total heat effect in the calorimetric cell upon titration of ligand. Thus, the experimental data contain contributions arising from non-specific effects, such as dilution of ligand and protein, mixing two solutions of slightly different compositions, temperature differences between the ITC cell and the titrating syringe, and so forth. In order to determine these contributions the control experiments need

to be performed in order to extract the heat of ligand-protein complex formation.

*G* determines the stability of any ligand-protein complex of interest, which makes it very useful for studies and predictions of structure–activity relationships. The conventional analysis of ITC data involves fitting an appropriate model (*i.e.* single- or two-site binding model) to the data, and obtaining the binding constant. Quite often, though, more sophisticated models (such as multiple interacting-site models) must be applied, if the

**3.1.1.2 Thermodynamic content of ITC data** 

behaviour of the system is more complex.

The 

techniques: the experiments can be performed in a physiologically relevant buffer, no surface effects have to be taken into account, and the interacting species do not require immobilisation or labelling.

ITC is also used for determination of binding affinity-independent reaction stoichiometry. The reaction stoichiometry is estimated from the titration equivalence point. Provided this, ITC is increasingly used in the analysis of macromolecular complexes involving multiple binding events (e.g. protein aggregation or the formation of multi-protein complexes). Systems that involve multiple binding events that occur at two or more interacting sites often demonstrate cooperativity, which is an important mechanism of regulation in biological systems (Brown, 2009).

Using ITC it is also possible to study protonation effects, in cases when protein-ligand binding is coupled to changes in the protonation state of the system. If the formation of the complex changes the protonation state of ligand as well as that of the protein (whether free or bound), proton transfer with the solvent occurs. As a result, the signal measured by ITC will contain the heat effect of protonation/ deprotonation, contributing to the overall heat of binding. Repeating the experiment at the same pH in buffers with different ionisation enthalpies but otherwise under the same conditions allows for the determination of the number of protons released/ accepted by buffer solution. From this, the intrinsic binding enthalpy corrected by protonation heats, can be established (4).

$$
\Delta H\_{obs} = \Delta H\_{bind} + nH + \Delta H\_{ion} \tag{4}
$$

ITC can also provide information about solvation effects. If *H* is determined at a range of temperatures, the change in the constant pressure heat capacity ( *Cp* ) for an interaction is given by the slope of the linear regression analysis of *Hobs* plotted vs. temperature. There is a strong correlation between *Cp* and the amount of desolvated (buried) surface area of a macromolecular complex. Thus, for the ligand-protein binding events, *Cp* is most often negative, when the complex is regarded as a reference state. Through this correlation, changes in *Cp* are measure of solvation state of the macromolecule and involvement of solvent effects in binding event (Perozzo *et al.*, 2004).

#### **3.1.1.1 Experimental setup**

In a typical ITC experiment, a solution of ligand is injected (titrated) into a solution of the protein, in small volumes, over the time. During that time, the changes in heat resulting from the interaction are monitored (Figure 2, upper panel). Each peak represents a heat change associated with the injection of a ligand sample into the protein solution inside the ITC reaction cell. Concentrations of both ligand and protein in their respective solutions are known. As the ligand-protein system reaches saturation, the heat changes diminish until only heats of dilution are observed. A binding curve is then obtained from a plot of the heats from each titration against the ratio of ligand and protein inside the ITC cell (Figure 2, lower panel). The binding curve is analysed with the appropriate binding model to determine the thermodynamic parameters.

ITC is a straightforward technique to accurately measure binding events with affinity range from mM up to high-nM. Problems occur when the ligand binds very tightly, in a singledigit nM and below. This is due to the titration curve becoming too steep to fit accurately. In such cases, the displacement experiments are commonly used. Such experimental setup consists of binding a low-affinity binding ligand first and then displacing it during titration

techniques: the experiments can be performed in a physiologically relevant buffer, no surface effects have to be taken into account, and the interacting species do not require

ITC is also used for determination of binding affinity-independent reaction stoichiometry. The reaction stoichiometry is estimated from the titration equivalence point. Provided this, ITC is increasingly used in the analysis of macromolecular complexes involving multiple binding events (e.g. protein aggregation or the formation of multi-protein complexes). Systems that involve multiple binding events that occur at two or more interacting sites often demonstrate cooperativity, which is an important mechanism of regulation in

Using ITC it is also possible to study protonation effects, in cases when protein-ligand binding is coupled to changes in the protonation state of the system. If the formation of the complex changes the protonation state of ligand as well as that of the protein (whether free or bound), proton transfer with the solvent occurs. As a result, the signal measured by ITC will contain the heat effect of protonation/ deprotonation, contributing to the overall heat of binding. Repeating the experiment at the same pH in buffers with different ionisation enthalpies but otherwise under the same conditions allows for the determination of the number of protons released/ accepted by buffer solution. From this, the intrinsic binding

negative, when the complex is regarded as a reference state. Through this correlation,

In a typical ITC experiment, a solution of ligand is injected (titrated) into a solution of the protein, in small volumes, over the time. During that time, the changes in heat resulting from the interaction are monitored (Figure 2, upper panel). Each peak represents a heat change associated with the injection of a ligand sample into the protein solution inside the ITC reaction cell. Concentrations of both ligand and protein in their respective solutions are known. As the ligand-protein system reaches saturation, the heat changes diminish until only heats of dilution are observed. A binding curve is then obtained from a plot of the heats from each titration against the ratio of ligand and protein inside the ITC cell (Figure 2, lower panel). The binding curve is analysed with the appropriate binding model to determine the

ITC is a straightforward technique to accurately measure binding events with affinity range from mM up to high-nM. Problems occur when the ligand binds very tightly, in a singledigit nM and below. This is due to the titration curve becoming too steep to fit accurately. In such cases, the displacement experiments are commonly used. Such experimental setup consists of binding a low-affinity binding ligand first and then displacing it during titration

 

*Cp* are measure of solvation state of the macromolecule and involvement of

*H H nH H obs bind ion* (4)

*H* is determined at a range of

*Hobs* plotted vs. temperature. There

*Cp* ) for an interaction is

*Cp* is most often

*Cp* and the amount of desolvated (buried) surface area of a

enthalpy corrected by protonation heats, can be established (4).

ITC can also provide information about solvation effects. If

given by the slope of the linear regression analysis of

solvent effects in binding event (Perozzo *et al.*, 2004).

temperatures, the change in the constant pressure heat capacity (

macromolecular complex. Thus, for the ligand-protein binding events,

immobilisation or labelling.

biological systems (Brown, 2009).

is a strong correlation between

**3.1.1.1 Experimental setup** 

thermodynamic parameters.

changes in

with a stronger binder of interest. However, this method requires precise knowledge of binding constants of those weak binders. The experimental setup of the displacement assay is often challenging, as there are several factors increasing the error of measurements.

Fig. 2. An example of ITC data. Raw data, representing observed changes in heat resulting from interactions are shown in the upper panel. The resulting binding curve is displayed in the lower panel (from MicroCal materials http://www.microcal.com/technology/itc.asp).

It is worth remembering that ITC experiment not only measures the heat absorbed or released during binding reactions, but it also detects the total heat effect in the calorimetric cell upon titration of ligand. Thus, the experimental data contain contributions arising from non-specific effects, such as dilution of ligand and protein, mixing two solutions of slightly different compositions, temperature differences between the ITC cell and the titrating syringe, and so forth. In order to determine these contributions the control experiments need to be performed in order to extract the heat of ligand-protein complex formation.

## **3.1.1.2 Thermodynamic content of ITC data**

The *G* determines the stability of any ligand-protein complex of interest, which makes it very useful for studies and predictions of structure–activity relationships. The conventional analysis of ITC data involves fitting an appropriate model (*i.e.* single- or two-site binding model) to the data, and obtaining the binding constant. Quite often, though, more sophisticated models (such as multiple interacting-site models) must be applied, if the behaviour of the system is more complex.

with ligand-protein binding can, at a given temperature, be expressed as the sum of several contributing effects. The main one is related to solvent effects. The burial of water-accessible surface area upon binding event should result in release of confined or interfacial water molecules to the bulk. This should contribute favourably to the total entropy of interaction. A positive entropy change is usually a strong indication that water molecules have been released from the complex surface (Jelesarov and Bosshard, 1999). On the other hand, interfacial water remaining upon binding can also contribute positively to the total entropy

Another important entropic contribution is related to the reduction of conformational (rotational and vibrational) degrees of freedom of protein side-chains. In addition to these, the ligand loses translational degrees of freedom upon binding. All these contribute unfavourably to the overall entropy of interaction. However, in some cases the protein increases the number of conformational degrees of freedom upon ligand binding, as observed by NMR and deduced from MD simulations (MacRaild *et al*., 2007, Stoeckmann *et al.*, 2008). This is likely to happen in order to partly offset the unfavourable entropic contribution from ligand binding and thus to reduce the overall thermodynamic cost of that

As mentioned in the previous section of this chapter, this phenomenon is described by the linear relationship between the change in enthalpy and the change in entropy. This means that favourable changes in binding enthalpy are compensated by opposite changes in binding entropy and vice versa, resulting in very small changes in overall free binding energy. Enthalpy–entropy compensation is an illustration of the 'motion opposes binding' rule, and it is believed to be a consequence of altering the weak inter-molecular interactions

Enthalpy-entropy compensation is a difficult problem to address in the context of rational molecular design. In such framework, the goal is to maximise the binding affinity of a complex of the designed compound and the protein target. The optimisation strategy requires simultaneous minimisation of both enthalpic and entropic penalties. However,

Thermodynamics of biologically-relevant macromolecules and their complexes can be characterised by measurements using NMR spectroscopy. The basis of NMR spectroscopy is the non-zero nuclear magnetic moment of many elements, such as 1H, 13C, 15N, or 19F. When put into an external static magnetic field (B), the different nuclear spin states of these elements become quantised with energies proportional to their projections onto vector B. The energy differences are also proportional to the field strength and dependent on the chemical environment of the element, which makes NMR an ideal technique to study 3D

A variety of NMR methods have been introduced to study ligand-protein interactions. These methods include one-, two- and three-dimensional NMR experiments. Many studies, to date, proved the power of stable-isotope labelling and isotope-edited NMR in the investigation of ligand-protein interactions. Recent development of techniques allowed for

*H* and *S* are connected to

*Cp* , the

of the interaction (Fischer and Verma, 1999).

*3.1.1.2.3 Enthalpy-entropy compensation* 

as well as being related to solvent effects. Since both

reducing one of them usually means increasing the other.

**3.1.2 Nuclear Magnetic Resonance (NMR) spectroscopy** 

structural and dynamical properties of the systems.

correlation between enthalpy/entropy and heat capacity changes is clear.

process.

As mentioned earlier, observed overall *G* can be very similar regardless of the driving force, which can be very different from one case to another. *G* can be the same for an interaction with positive *S* and *H* (entropy-driven, binding signature dominated by the classical hydrophobic effect), an interaction with negative *S* and *H* (enthalpy-driven binding signature), or all sort of combinations of negative *H* and positive *S* . As described in the previous section, ligand-protein complexes tend to compensate for enthalpic and entropic contributions, making changes in *G* less sensitive to the molecular details of the interactions. Therefore, dissection of *G* into enthalpic and entropic contributions is of a fundamental importance for understanding of the binding energetics.

#### *3.1.1.2.1 Enthalpic contributions*

The change in the enthalpy represents the changes in energy associated with specific, noncovalent interaction. However, such an interpretation is too simplistic to describe experimental *H* values, and the physical meaning of observed *H* seems to be more complex. The measured changes in enthalpy are the result of the formation and breaking of many individual bonds; it reflects the loss of protein–solvent hydrogen bonds and van der Waals interactions, the loss of ligand-solvent interactions, the formation of ligand-protein bonds, salt bridges and van der Waals contacts, the re-organisation of the intra-molecular hydrogen-bonding network of the protein, solvent reorganisation near the protein surface, conformational changes at the binding site due to the binding event, and many more. These individual components may produce either favourable or unfavourable contributions, depending on the system.

The treatment of each component individually is very challenging since the global heat effect of a particular interaction is a balance between the enthalpy of the ligand binding to the protein and to the solvent. Several approaches have been employed to investigate the energetics of individual bonds, including alanine scanning mutagenesis (Perozzo *et al*., 2004 and references therein), and removal of particular hydrogen bonds at the binding site (Connelly *et al.*, 1994). However, these approaches suffer from the major bottleneck, resulting from the fact that a direct relation between the change in enthalpy and the removal of the corresponding specific interactions cannot be made *a priori*.

A large part of the observed *H* is due to a bulk hydration effect, as emerged from ITC studies carried out in water and deuterium (Connelly *et al.*, 1993). Frequently, water molecules are located at complex interfaces, improving the complementarity of the surfaces and extending hydrogen-bonding networks. This should contribute favourably to the enthalpy, but it may be offset by an unfavourable entropic contribution (Perozzo *et al.*, 2004). The role of interfacial water was studied by lowering water activity by adding osmolytes such as glycerol to the solution. It was found that complexes with a low degree of surface complementarity and no change in hydration are tolerant to osmotic pressure (Perozzo *et al.,* 2004, and references therein).

#### *3.1.1.2.2 Entropic contributions*

*S* may be calculated directly from *G* and *H* , according to the Gibbs' equation. Its physical representation is not straightforward. It is often related to the dynamics and flexibility of the system (Diehl *et al.*, 2010, Homans, 2007), sometimes dubbed as a 'measure of the system's disorder' (which is incorrect). It has been proposed that the *S* associated with ligand-protein binding can, at a given temperature, be expressed as the sum of several contributing effects. The main one is related to solvent effects. The burial of water-accessible surface area upon binding event should result in release of confined or interfacial water molecules to the bulk. This should contribute favourably to the total entropy of interaction. A positive entropy change is usually a strong indication that water molecules have been released from the complex surface (Jelesarov and Bosshard, 1999). On the other hand, interfacial water remaining upon binding can also contribute positively to the total entropy of the interaction (Fischer and Verma, 1999).

Another important entropic contribution is related to the reduction of conformational (rotational and vibrational) degrees of freedom of protein side-chains. In addition to these, the ligand loses translational degrees of freedom upon binding. All these contribute unfavourably to the overall entropy of interaction. However, in some cases the protein increases the number of conformational degrees of freedom upon ligand binding, as observed by NMR and deduced from MD simulations (MacRaild *et al*., 2007, Stoeckmann *et al.*, 2008). This is likely to happen in order to partly offset the unfavourable entropic contribution from ligand binding and thus to reduce the overall thermodynamic cost of that process.
