**1. Introduction**

Biologically relevant macromolecules, such as proteins, do not operate as static, isolated entities. On the contrary, they are involved in numerous interactions with other species, such as proteins, nucleic acid, membranes, small molecule ligands, and also, critically, solvent molecules. These interactions often display a remarkable degree of specificity and high affinity. Fundamentally, the biological processes rely on molecular organisation and recognition events. Binding between two interacting partners has both enthalpic (*H*) and entropic (-*TS*) components, which means the recognition event is associated with changes of both the structure and dynamics of each counterpart. Like any other spontaneous process, binding occurs only when it is associated with a negative Gibbs' free energy of binding ( *G* ), which may have differing thermodynamic signatures, varying from enthalpy- to entropy-driven. Thus, the understanding of the forces driving the recognition and interaction require a detailed description of the binding thermodynamics, and a correlation of the thermodynamic parameters with the structures of interacting partners. Such an understanding of the nature of the recognition phenomena is of a great importance for medicinal chemistry and material research, since it enables truly rational structure-based molecular design.

This chapter is organised in the following way. The first part of it introduces general principles which govern macromolecular associations under equilibrium conditions: the free energy of binding and its enthalpic and entropic components, the contributions from both interacting partners, interaction energy of the association, and specific types of interactions – such as hydrogen bonding or van der Waals interactions, ligand and protein flexibility, and ultimately solvent effects (e.g. solute-solvent interactions, solvent reorganisation). The second part is dedicated to methods applied to assess particular contributions, experimental as well as computational. Specifically, there will be a focus on isothermal titrational calorimetry (ITC), solution nuclear magnetic resonance (NMR), and a discussion of computational approaches to the estimation of enthalpic and entropic contributions to the binding free energy. I will discuss the applicability of these methods, the approximations behind them, and their limitations. In the third part of this chapter, I will provide the reader several examples of ligand-protein interactions and focus on the forces driving the associations, which can be very different from case to case. Finally, I will address several practical aspects of assessing the thermodynamic parameters in molecular design, the

conformational entropy associated with the measured motions (Yang and Kay, 1996). It has been shown that for a wide range of motion models, the functional dependence of the conformational entropy on the order parameter is similar, suggesting that changes in order parameters can be related to changes in entropy in a model-independent manner. I will introduce the application of this model-free formalism to MD simulation, for the study of dynamical behaviour of ligand-protein complexes and the estimation of changes in the conformational entropy upon ligand-protein association. The MD simulations, performed on several proteins in complexes with their cognate ligands, indicate that the molecular ensembles provide a picture of the protein backbone dynamics that show a remarkably high degree of consistency with NMR relaxation data, regardless of the protein's size and

In this chapter I will also address the enthalpy-entropy compensation phenomenon and the challenges it imposes on molecular design. The generality of this phenomenon have been a subject of debate for many years. Although this compensation is not a thermodynamic requirement as such (Ford, 2005, Sharp, 2001), it has been very frequently observed in protein-ligand interactions (Whitesides and Krishnamurthy, 2005). Briefly, stronger and more directed interactions are less entropically favourable, since the tight binding constricts molecular motions. The detailed mechanism of enthalpy-entropy compensation is, nonetheless, highly system-dependent, and this compensation does not obey a single functional form. An example of enthalpy-entropy compensation and its consequences to the

A discussion of the thermodynamics of protein-ligand interactions would not be complete without commenting on dynamic allostery and cooperativity. The mechanism of allostery plays a prominent role in control of protein biological activity, and it is becoming accepted that protein conformational dynamics play an important role in allosteric function. Changes of protein flexibility upon ligand binding affect the entropic cost of binding at distant protein regions. Counter-intuitively, proteins can increase their conformational entropy upon ligand binding, thus reducing the entropic cost of the binding event (MacRaild *et al*., 2007). I will discuss these phenomena, illustrating them through several examples of

The overall aim of this chapter is to introduce the forces driving binding events, and to make the reader familiar with some general rules governing molecular recognition processes and equally to raise awareness of the limitations of these rules. Combining the structural information with equilibrium thermodynamic data does not yield an understanding of the binding energetics under non-equilibrium conditions, and global parameters, obtained during ITC experiments, do not enable us to assess the individual contributions to the binding free energy. Certain contributions, such as entropy, may behave in a strongly non-additive and highly correlated manner (Dill, 1997). This chapter will

discuss the boundaries of rational molecular design guided by thermodynamic data.

A non-covalent association of two macromolecules is governed by general thermodynamics. Similarly to any other binding event (or – in a broader context – to any spontaneous process), it occurs only when it is coupled with a negative Gibbs' binding free energy (1),

**2.1 Enthalpic and entropic components of free binding energy** 

which is the sum of an enthalpic, and an entropic, terms:

structure (Schowalter and Brüschweiler, 2007).

biologically-relevant protein-ligand interactions.

design process will be provided.

**2. Principles** 

bottlenecks of methods employed in such process, and the directions for future development.

The information content provided by thermodynamic parameters is vast. It plays a prominent role in the elucidation of the molecular mechanism of the binding phenomenon, and – through the link to structural data – enables the establishment of the structure-activity relationships, which may eventually lead to rational design. However, the deconvolution of the thermodynamic data and particular contributions is not a straightforward process; in particular, assessing the entropic contributions is often very challenging.

Two groups of computational methods, which are particularly useful in assessment of the thermodynamics of molecular recognition events, will be discussed. One of them are methods based on molecular dynamics (MD) simulations, provide detailed insights into the nature of ligand-protein interactions by representing the interacting species as a conformational ensemble that follows the laws of statistical thermodynamics. As such, these are very valuable tools in the assessment of the dynamics of such complexes on short (typically, picosecond to tens of nanosecond, occasionally microsecond) time scales. I will give an overview of free energy perturbation (FEP) methods, thermodynamic integration (TI), and enhanced sampling techniques. The second group of computational methods relies on very accurate determinations of energies of the macromolecular systems studied, employing calculations based on approximate solutions of the Schrödinger equation. The spectrum of these quantum chemical (QM) methods applied to study ligand-protein interactions is vast, containing high-level ab initio calculations: from Hartree-Fock, through perturbational calculations, to coupled-clusters methods; DFT and methods based on it (including "frozen" DFT and SCC-DFTTB tight binding approaches); to semi-empirical Hamiltonians (such as AM1, PM3, PM6, just to mention the most popular ones) (Piela, 2007, Stewart, 2009). Computational schemes based the hybrid quantum mechanical –molecular mechanical (QM/MM) regimes will also be introduced. Due to the strong dependence of the molecular dynamics simulations on the applied force field, and due to the dependence of both MD simulations and QM calculations on the correct structure of the complex, validation of results obtained by these methodologies against experimental data is crucial.

Isothermal titration calorimetry (ITC) is one of the techniques commonly used in such validations. This technique allows for the direct measurement of all components of the Gibbs' equation simultaneously, at a given temperature, thus obtaining information on all the components of free binding energy during a single experiment. Yet since these are *de facto* global parameters, the decomposition of the factors driving the association, and investigation of the origin of force that drives the binding is usually of limited value. Nonetheless, the ITC remains the primary tool for description of the thermodynamics of ligand-protein binding (Perozzo *et al*., 2004). In this chapter, I will give a brief overview of ITC and its applicability in the description of recognition events and to molecular design.

Another experimental technique, which has proven very useful in the experimental validation of computational results, is NMR relaxation. These measurements are extremely valuable, as they specifically investigate protein dynamics on the same time scales as MD simulations. As such, the results obtained can be directly compared with simulation outputs. In addition, the Lipari-Szabo model-free formalism (Lipari and Szabo, 1982) is relatively free of assumptions regarding the physical model describing the molecular motions. The only requirement is the internal dynamics being uncorrelated with the global tumbling of the system under investigation. The results of the Lipari–Szabo analysis, in the form of generalised order parameters ( <sup>2</sup> *SLS* ), can be readily interpreted in terms of the conformational entropy associated with the measured motions (Yang and Kay, 1996). It has been shown that for a wide range of motion models, the functional dependence of the conformational entropy on the order parameter is similar, suggesting that changes in order parameters can be related to changes in entropy in a model-independent manner. I will introduce the application of this model-free formalism to MD simulation, for the study of dynamical behaviour of ligand-protein complexes and the estimation of changes in the conformational entropy upon ligand-protein association. The MD simulations, performed on several proteins in complexes with their cognate ligands, indicate that the molecular ensembles provide a picture of the protein backbone dynamics that show a remarkably high degree of consistency with NMR relaxation data, regardless of the protein's size and structure (Schowalter and Brüschweiler, 2007).

In this chapter I will also address the enthalpy-entropy compensation phenomenon and the challenges it imposes on molecular design. The generality of this phenomenon have been a subject of debate for many years. Although this compensation is not a thermodynamic requirement as such (Ford, 2005, Sharp, 2001), it has been very frequently observed in protein-ligand interactions (Whitesides and Krishnamurthy, 2005). Briefly, stronger and more directed interactions are less entropically favourable, since the tight binding constricts molecular motions. The detailed mechanism of enthalpy-entropy compensation is, nonetheless, highly system-dependent, and this compensation does not obey a single functional form. An example of enthalpy-entropy compensation and its consequences to the design process will be provided.

A discussion of the thermodynamics of protein-ligand interactions would not be complete without commenting on dynamic allostery and cooperativity. The mechanism of allostery plays a prominent role in control of protein biological activity, and it is becoming accepted that protein conformational dynamics play an important role in allosteric function. Changes of protein flexibility upon ligand binding affect the entropic cost of binding at distant protein regions. Counter-intuitively, proteins can increase their conformational entropy upon ligand binding, thus reducing the entropic cost of the binding event (MacRaild *et al*., 2007). I will discuss these phenomena, illustrating them through several examples of biologically-relevant protein-ligand interactions.

The overall aim of this chapter is to introduce the forces driving binding events, and to make the reader familiar with some general rules governing molecular recognition processes and equally to raise awareness of the limitations of these rules. Combining the structural information with equilibrium thermodynamic data does not yield an understanding of the binding energetics under non-equilibrium conditions, and global parameters, obtained during ITC experiments, do not enable us to assess the individual contributions to the binding free energy. Certain contributions, such as entropy, may behave in a strongly non-additive and highly correlated manner (Dill, 1997). This chapter will discuss the boundaries of rational molecular design guided by thermodynamic data.
