**2.4 Classical and non-classical hydrophobic effect**

10 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

the bulk upon ligand binding. Such displacement may affect the thermodynamic signature of the binding event in a dramatic way. It is generally assumed that the release of a water molecule from a rigid environment should be entropically favorable. The upper limit of the entropy gained for transferring a water molecule from a protein to bulk solvent was estimated to be 2 kcal/mol at room temperature (Dunitz, 1994). This gain would be compensated by loss of enthalpy, so the total contribution to the free energy (as a sum of its enthalpic and entropic terms) of a single water molecule released from the protein to the bulk is difficult to guess. Moreover, in order to reach this 2 kcal/mol limit the water molecule would have to be fixed very rigidly while bound. This is often not the case, and it has been observed in numerous occasions that even very tightly bound, "structural" waters may retain a significant amount of residual mobility (Denisov *et al.*, 1997, Fischer and

"Structural" water molecules affect their surrounding not only via direct interactions (such as hydrogen-bonding network), but also by influencing the dynamical behaviour of their environment. Numerous cases have been reported when binding of the structural water affected protein flexibility (Fischer and Verma, 1999, Smith *et al.*, 2004). The direction of such influence cannot be predicted by simple rules, as it is heavily dependent on the details of the binding site – some protein become more dynamic upon water binding (Fischer and Verma, 1999), while other ones become more rigid (Mao *et al.*, 2000). Yet ignoring those water effects is likely to lead to substantial errors in the free energy predictions. The importance of the contributions of "structural" water molecules to binding events and its implications for drug

The traditional, enthalpy-dominated view of ligand-protein association largely neglects solvation effects, which strongly affect the thermodynamic profile of a binding event. Recently it became clear that studying the hydration state of a protein binding pocket in the apo (unbound) state should be a routine procedure in rational drug design, as the role of solvation in tuning binding affinity is critical. Solvation costs are a plausible reason why some ligands, despite fitting into a binding site, fail during experimental tests as inhibitors. Young and coworkers showed that an optimised inhibitor of factor Xa turns virtually inactive when the isopropyl group interacting in the S4 pocket of factor Xa is substituted by hydrogen: The compound (PDB code 2J4I) is characterised by Ki of 1 nM. Replacing the isopropyl group by hydrogen reduces its affinity to 39 M. Substitution of this group by hydrogen, apart from reducing the number of favourable hydrophobic interactions, leads to unfavourable solvation of the binding pocket (Young *et al*., 2007, and references therein). Desolvation of the ligand itself may sometimes control the binding free energy. For highly hydrophilic ligands, the desolvation costs may be very high and make unfavourable contributions to the binding (Daranas *et al.* 2004, MacRaild *et al.*, 2007, Syme *et al.*, 2010). The calorimetric study of -galactose derivatives binding to arabinose binding protein (ABP) showed dramatic differences in binding free energy between several deoxy derivatives (Daranas *et al.*, 2004). The most likely reason of 4-deoxygalactose failing to bind to ABP is

design have been emphasised in a study by Michel et al (Michel *et al.*, 2009).

the unfavourable desolvation cost (Bronowska and Homans, unpublished data).

terahertz spectroscopy results (Ebbinghaus *et al.*, 2007, Heugen *et al.*, 2006).

Spectroscopic evidence shows that (1) water molecules in the first solvation shell (surrounding the hydrophobic solute) are more flexible that it was originally thought (Finney and Soper, 1994) and (2) hydrogen bonds at hydrophobic surfaces are weaker than it was assumed (Scatena *et al.*, 2001). In addition, the properties of the water molecules from first two solvation shells are very different from these of bulk water, as emerged from

Verma, 1999, Matthews and Liu, 2009, Smith *et al.*, 2004).

The concept of the classical hydrophobic effect relies on a hydrophobic solute disrupting the structure of bulk water. This decreases entropy due to ordering of water molecules around the hydrophobic entity. Such unfavourable effects can be minimised if solute molecules aggregate. Upon aggregation, water molecules form one larger "cage" surrounding the hydrophobic aggregate, and the surface area of such aggregate is smaller than the sum of surface areas of individual (non-aggregated) solutes. This makes the entropic contribution less unfavourable and hence makes the free energy more favourable (Homans, 2007).

If this mechanism was the sole driving force for a protein-ligand interaction, all binding events involving hydrophobic ligands would be entropy-driven. This is not the case. Several years ago, in the group of Steve Homans (University of Leeds), we studied the thermodynamics signature of ligand binding by the mouse major urinary protein (MUP). This protein is characterised by a strongly hydrophobic binding pocket and it binds a handful of very different hydrophobic ligands – long-chain alcohols and pyrazine derivatives, among others. Surprisingly, the ITC data showed that the binding was enthalpy-driven (Barratt *et al.*, 2005). This was combined with a negative change in heat capacity upon binding - a hallmark of the hydrophobic effect.

In order to elucidate the molecular origin of this unusual binding signature, we employed computational methods, such as molecular dynamics (MD) simulations. I will discuss the results in more details later in this chapter. The data showed that the key to this favorable enthalpy of binding of ligands to MUP seems to be the sub-optimal solvation of the binding pocket in apo (unbound) state: only a few water molecules remained there prior to ligand binding. The favourable enthalpic component was, thus, largely determined by ligand desolvation, with only a minor contribution from desolvation of the protein. Such complexation thermodynamics driven by enthalpic components have been referred to as the "non-classical hydrophobic effect".
