Hydrophobic Association Figure 4. Thermodynamic contributions along the binding coordinate. (A) Relative Gibbs free energy, G (red), enthalpy, H (blue), and entropic term, -TS (green), and their uncertain- ties (vertical bars; eq 5). (B) Water contribution to the Gibbs free energy, GW (orange), and decomposed interaction ener- gies: cavity-ligand, UCL (thin black), ligand-water, ULW (green), cavity-water, UCW (black), and water-water, UWW (cyan). constant. The F proﬁle reveals series of metastable states extending from N ) 0 (empty pocket) through N = 6 (average occupancy) to N ) 11 (close to bulk-like density), indicating no apparent free energy change for pocket dehydration (Figure 3B). The corresponding entropy changes were derived using the temperature dependence of the free energy based on MD simulations at ﬁve different tempera- tures (see Methods Section). They show that complete pocket dehydration, starting from the average water occupancy, is entropically unfavorable. This observation agrees with the fact that solvent ﬂuctuations are eliminated upon dehydration. At the same time, the free energy plateau reveals a perfect entropy-enthalpy compensation, indicating the favorable enthalpic effect due to the displacement of water molecules from the hydrophobic cavity interior to the bulk. 3.2. Cavity-Ligand Association. The obtained free energy proﬁle for the ligand approaching the cavity is ﬂat until ∼ 0.4 nm. At shorter distances, it decreases monotonically indicating a steady mean force toward binding (Figure 4A). The free energy minimum is reached at ) -0.35 nm and corresponds to a direct contact between the ligand and the pocket bottom. The overall free-energy change upon binding, ∆ G ) -16.5 ( 0.6 kJ mol-1, is dominated by water-related contributions, ∆ GW ) -10.6 ( 0.6 kJ mol-1, as direct cavity-ligand interaction energy ∆ UCL is only -5.9 kJ mol-1 (Figure 4B). Differently from what is found for other processes driven by hydrophobic interactions, nonpolar cavity-ligand binding is driven here by a large change in enthalpy, ∆ H ) -29.1 ( 17.3 kJ mol-1, with an opposing entropic contribution, -T∆ S ) 12.6 ( 17.3 kJ mol-1. J. Chem. Theory Comput., Vol. 6, No. 9, 2010 2869 A relatively simple shape of the free energy proﬁle covers substantial, compensating changes in enthalpy and entropy components as the ligand moves toward the cavity. A local maximum in H of 15.2 ( 6.1 kJ mol-1, mirrored by a minimum in -TS of -14.6 ( 6.1 kJ mol-1, is observed already around ) 0.55 nm. A comparison between water density maps for ) 0.55 and 1.1 nm (Figure 2) indicates that the reason for the observed changes is the partial destruction of the ligands second hydration shell, leaving the ﬁrst hydration shell exposed to the weakly hydrated pocket region. Accordingly, a major contribution to the increasing enthalpy arises from the change in water-water interaction energy (UWW), with marginal effects due to cavity-water (UCW) and ligand-water (ULW) interactions. The trends of enthalpic and entropic components suddenly invert as the ligand moves closer to the pocket, leading to a substantial decrease in H until ) 0.3 nm, with a subsequent plateau, and the formation of a -TS maximum (Figure 4A). These changes correspond to almost complete dehydration of the region between the cavity and the ligand (Figures 2 and 3A). The sizable enthalpy change observed is due to favorable contribution from water-water interactions that dominate unfavorable energetic effects of cavity and ligand dehydration. It is worth noting that no simultaneous change in free energy occurs, in agreement with the free energy proﬁle for cavity dehydration described in the previous section. In addition, the change in the entropic component of PMF for the ligand moving from ) 0.55 to 0.3 nm (34 ( 11 kJ mol-1) is comparable with the entropic effect of changing the cavity occupancy from the average value to N ) 1 (33 ( 28 kJ mol-1). This agreement might be partially fortuitous and should be treated semiquantitatively because of a number of factors. First, the cavity dehydration upon ligand binding and dewetting due to spontaneous ﬂuctuations are different processes. Second, at ) 0.3 nm, the dehydra- tion is not fully complete. Third, large uncertainties are associated with -TS values. Yet, the observed correspon- dence seems to conﬁrm the overall interpretation of the described thermodynamic effects. Further ligand translocation into the pocket corresponds to the gradual withdrawal of a hydrophobic object from an aqueous environment. It is accompanied by a steady decrease in free energy, initially driven by favorable changes in entropy. At the same time, no apparent change in enthalpy takes place, due to compensation between the increase in ULW and the decrease in UCW. For < -2.5 nm, any extra ligand dehydration is limited. Increasingly favorable cavity- water interactions together with increasingly strong direct cavity-ligand attraction lead to a favorable enthalpy change. The moderate increase in the entropy component around the equilibrium binding distance (∼3 kJ mol-1) can be explained considering ligand immobilization due to direct contact with the wall. 4. Discussion Our results demonstrate the determinant role of pocket (de)hydration upon hydrophobic cavity-ligand binding on the underlying thermodynamic signature. The favorable, driving enthalpy change results from the release of water