Table 1.

The binding thermodynamics of methane for the various model hydrophobic enclosures as computed from DSF theory and FEP theory. E_hs was the hydration site system interaction energy, S^e_hs was the hydration site solute-water correlation entropy, ΔSASA was the buried solvent accessible surface area using a 1.4 Å radius probe, ΔE_LJ was the Lennard Jones interaction energy of the bound methane with the rest of the enclosure, DSF-ΔG_bind was the predicted binding free energy of the methane molecule for the model enclosure as computed from DSF theory, N_eff was scaling coefficient derived by determining the expectation value of the number of water molecules occupying a volume in the bulk fluid equal to the volume of the methane probe molecule, and FEP-ΔG_bind was the predicted binding free energy of the methane molecule for the model enclosure as computed from FEP theory. Note that the standard deviation of the E_hs values reported below were found to be uniformly less than 0.4 kcal/mol (as obtained from block averaging), and the standard errors of the FEP-ΔGbind values were uniformly less than 0.02 kcal/mol.

Model Enclosure*	Ehs (kcal/mol)	Sehs (cal/mol* K)	Δ SASA (Å2)	ΔMSA(Å2)	ΔELJ (kcal/mol)	DSF-ΔGbind (kcal/mol)	Neff* DSF-ΔGbind (kcal/mol)	FEP-ΔGbind (kcal/mol)
bulk	−19.8	0	0	0	0	0	0	0
A	−19.6	−1.2	−59.45	−3.84	0	−0.5	−0.46	−0.61
B	−18.9	−2.0	−118.9	−7.67	0	−1.5	−1.28	−1.15
C	−19.2	−1.8	−98.21	−10.49	0	−1.1	−0.97	−1.41
D	−18.7	−1.2	−91.32	−13.51	−1.41	−1.5	−1.26	−1.66
E	−17.7	−2.3	−151.15	−17.35	−1.41	−2.8	−2.39	−2.17
F	−17.3	−1.5	−117.52	−24.06	−1.41	−2.9	−2.5	−2.63
G	−16.0	−3.0	−156.39	−30.7	−1.41	−4.7	−4	−3.41
H	−15.6	−1.2	−132.41	−37.35	−1.41	−4.6	−3.92	−3.43
I	−15.6	−1.8	−143.71	−34.6	−1.41	−4.8	−4.05	−3.47
J	−17.8	−2.6	−182.65	−27.02	−2.82	−2.8	−2.41	−2.86
K	−15.5	−2.1	−175.59	−44.27	−2.82	−4.9	−4.17	−4.59
L	−13.0	0.3	−166.61	−64.21	−2.82	−6.8	−5.74	−5.24
M	−13.3	−0.1	−168.52	−61.51	−2.82	−6.6	−5.6	−5.45
R2 versus FEP:	0.94	0.16	0.76(a)	0.92(b)	0.73	0.95	0.95	N/A
MAE versus FEP	0.61	N/A	0.54(a)	0.47(b)	1.41	0.66	0.36	N/A
RMSE versus FEP	0.75	N/A	0.74(a)	0.58(b)	1.63	0.85	0.40	N/A

^*the enclosures are labeled as described in figure 3.

^(a)these values correspond to the correlation between the buried SASA/LJ interaction with optimized surface tension coefficient (γ =0.044 kcal/mol*Ų) and the FEP reference data.

^(b)these values correspond to the correlation between the buried MSA/LJ interaction with optimized surface tension coefficient (γ =0.011 kcal/mol*Ų) and the FEP reference data.