Simulation systems

The simulated protein/ligand complexes are listed in Table ​Table1.1. For the trypsin/benzamine complex, the crystal structure [PDB ID: 3atl] was immersed in a cubic water box with an edge length of 111 Å and containing KCl at a concentration of 150 mM (approximately 140,000 atoms, Fig. 1a). Protonation states at pH 7 were chosen using PDB2PQR [35]. For the FKBP/FK506 complex, the crystal structure [PDB ID: 1fkf] was placed in a cubic water box with an edge length of 117 Å and containing NaCl at a concentration of 150 mM (~120,000 atoms, Fig. 2a). Protonation states were chosen using AmberTools [36]. For the A_2A/T4E complex, the crystal structure [PDB ID: 3uzc] was embedded in a membrane using CHARMM-GUI [37], which contains 210 DMPC lipid molecules. The initial box size was 82×82×138 ų. The Amber ff14SB force field [38] and the SPC/E_b water model [39] were used for all simulations. The ligand parameters were generated using the Antechamber module in the AmberTools package with GAFF and AM1-BCC [40, 41].

Binding free energy calculation for the trypsin/benzamidine complex. (a) Initial configuration of the complex, ions, and water oxygen in the simulation box. A close-up view of benzamidine with trypsin is shown in the inset. (b) The distance between the center-of-mass (COM) positions of trypsin and benzamidine, d, plotted as a function of the PaCS-MD cycles. Three independent simulations are shown in different colors. The dashed line indicates the average value of d where the complex totally dissociated. (c) Representative dissociation pathways of benzamidine from trypsin obtained by PaCS-MD simulations. Colored lines show the trace of the benzamidine COM position along representative concatenated trajectories. Colors are the same as in (b). The initial and final structures of benzamidine in the first PaCS-MD trial are shown in the stick model, and in transparent color for the other trials. (d) Free energy profile against d calculated by PaCS-MD/MSM. The error bars indicate the standard deviation of three PaCS-MD/MSM trials. Green lines indicate the experimentally determined values of the binding free energy. The inset shows a close-up view of a benzamidine structure with d=21.1 Å In this paper, the molecular structure was visualized using VMD [64].

Binding free energy calculation for the FKBP/FK506 complex, shown in a similar manner to that for the trypsin/benzamidine complex in Fig. 1. (a) Overall view of the system simulated. (b) Evolution of d against the PaCS-MD cycles. (c) Dissociation pathways obtained by three PaCS-MD simulations. (d) The average free energy profile from three independent PaCS-MD/MSM calculations. The experimentally determined binding free energy is indicated by a green line.

Free energies calculated by dPaCS-MD/MSM and comparison with experimental values

The values after ‘±’ indicate standard errors.