2868 J. Chem. Theory Comput., Vol. 6, No. 9, 2010 The water contribution to the total Gibbs free energy was obtained as GW( ) ) G( ) - UCL( ), where UCL is the direct ligand-cavity interaction. Ligand-water, ULW, and cavity- water, UCW, interaction energies were calculated using force ﬁeld terms with 1.2 nm cutoff as ensemble averages over MD trajectories at values discretized into 0.01 nm bins. The water-water interaction energy was obtained as UWW( ) ) H( ) - ULW( ) - UCW( ) - UCL( ). The standard formula T G(T) ) H0 + Cp(T - T0) - TS0 - TCpln T0 expressessfor a given system at constant pressuresthe temperature dependence of G as a function of the system heat capacity, Cp. Assuming constant Cp for the considered temperature range, such equation can be rewritten in a parametric form as Differentiating with respect to T gives G(T) ) ATln T + BT + C -S(T) ) Aln T + A + B The results presented throughout this article correspond to S( ) numerical estimate for T ) 298 K, obtained from optimal A and B values to ﬁt eq 3 using ﬁve G( ) values. Uncertainties on G and S estimates were determined as δX ) N ∑ (Xi - X˜)2 i)1 N(N - 1) where X˜ is a value obtained using all data points, while Xi corresponds to N ) 5 independent simulation blocks. Uncertainties δX for G, H, and -TS proﬁles along are reported as vertical error bars (Figures 3 and 4). We note that the uncertainties for entropic and enthalpic components for T ) 298 K are larger than for T ) 318 K, the midpoint of the considered temperature range (see the Supporting Information). Nevertheless, as no qualitative difference in the resulting signatures is observed at the two temperatures, we focused on the thermodynamic data for T ) 298 K in order to remain in line with the majority of other studies conducted at this temperature. We stress that all conclusions of this study regarding the cavity-ligand binding process are independent of this choice. 3. Results 3.1. Hydrophobic Hydration. First, let us focus on the hydration of the ligand and the binding pocket when they are far from each other. Two clearly distinguishable hydration shells are formed around the ligand, in agreement with the expected picture for small-length scale hydration, as inferred from the water density map for ) 1.1 nm (Figure 2). In contrast, average water density inside the pocket gradually vanishes, indicating that dewetting takes place (Figure 3A). This can be attributed exclusively to the concave topography of pocket walls, as the water potential energy due to interaction with the solutes is lower at the pocket bottom (2) (3) (4) (5) Setny et al. Figure 2. Water density distribution maps for key snapshots along . Color coding is normalized such that F* ) 1 corresponds to bulk water density of 998 g/L. Figure 3. (Thermo)dynamics of pocket hydration. (A) Aver- age cavity occupancy along . <N> is the average number of water oxygens located at Z < 0. (B) Free energy and its entropy component as functions of pocket occupancy, N (note different energy scale for each proﬁle). (-4.6 kJ mol-1 minimum) than around the ligand (-0.9 kJ mol-1 minimum). A previous analysis of pocket hydration revealed that the observed average water density results from intermittent expansions and retractions of the liquid phase rather than uncorrelated diffusion of individual water molecules char- acteristic of a “vapor-like” phase.52 In order to quantify the thermodynamic effects due to pocket hydration, we calcu- lated the system free energy, F, as a function of pocket occupancy, N, using the relation F(N) ) -kBT ln P(N), where N is the number of water molecules with an oxygen atom located at z < 0, P(N) corresponds to its probability distribution obtained from MD trajectories with the ligand at g 10 nm, T is the temperature, and kB is the Boltzmann