3290 J. Chem. Theory Comput., Vol. 6, No. 11, 2010 Wereszczynski and McCammon Figure 4. (a) Distribution of boost potentials applied during the 50 ns simulations, showing an increased range of ∆ V values throughout the all-dihedral aMD simulation relative to the selective dihedral aMD. (b) Percent of the total weight from the simulations relative to the percent of frames that contributed this weight. The lower ranges of boosts in the selective aMD produce more uniform sampling relative to the all-dihedral aMD, which tends to be dominated by a small subset of the conﬁgurations. Figure 5. Free energies for the decoupling of oseltamivir from the neuraminidase active site as computed by alchemical transformation with classical MD (a) and selectively applied aMD (b). For each set of simulations three possible equilibration times were chosen; however, for only the longest equilibration period does the calculated free energy remain stable with increased sampling. The aMD results converged to values comparable to the cMD results with signiﬁcantly less simulation time. The time scale on the x axis includes the equilibration time for which free energy values are not calculated. was repeated three times (with different initial velocities). An equilibration period is typically discarded from the BAR calculations, the length of which is determined by several factors, including molecular rigidity, the slow motions of loops which are relevant to free energy differences, and the amount of computational time available.50 In Figure 5a we show the time evolution of the mean free energies for three equilibration times, 1000, 2000, and 3000 ps, along with the associated errors. The 3000 ps of equilibration curve is the only one which does not have a mean that changes ap- preciably with increased sampling, suggesting that for this initial conﬁguration of this complex a full 3 ns per window is required for each of the λ windows to equilibrate to their new Hamiltonians. The free energy of 66.9 ( 1.2 kcal/mol is calculated by using 3 ns for equilibration and the remaining 2 ns for sampling, as shown in Table 2. Note that this is not the free energy of binding in solution; rather it is only one leg of the thermodynamic cycle required for that calculation. Examination of individual BAR runs shows that increased sampling decreases both the variance between the three runs and the bootstrap errors associated with each (Figure S1, Supporting Information). BAR results from simulations using selective aMD (with the ﬁrst 200 ps utilizing all-dihedral aMD) are presented in Figure 5b. As in the cMD calculations, we have chosen three Table 2. Free Energies for the Decoupling of Oseltamivir from the Neuraminidase Active Site As Calculated with cMD and Selective aMD for Varying Equilibration and Sampling Periods simulation type cMD aMD equilibration time 1 ns 2 ns 3 ns 250 ps 500 ps 750 ps sampling time 1 ns 2 ns 3 ns 4 ns 1 ns 2 ns 3 ns 1 ns 2 ns 500 ps 750 ps 1000 ps 1250 ps 500 ps 750 ps 1000 ps 500 ps 750 ps free energy (kcal/mol) 71.0 ( 1.4 70.5 ( 1.5 69.5 ( 1.6 68.4 ( 1.3 69.6 ( 2.2 68.5 ( 2.0 67.6 ( 1.5 66.8 ( 1.8 66.9 ( 1.2 70.5 ( 1.4 69.4 ( 1.0 69.2 ( 1.2 68.7 ( 1.1 69.2 ( 1.2 69.0 ( 1.1 68.3 ( 1.2 67.9 ( 1.4 67.3 ( 1.5 equilibration times, 250, 500, and 750 ps, and the mean value of the free energy does not remain constant with increased sampling unless the longest of these equilibration times is discarded. With 750 ps of equilibration and 750 ps of sampling