Physique S1. classes of p53-MDM2 (murine double minute 2) inhibitors. The absolute binding free energy calculations for MDMX (murine double minute X) resulted in a mean absolute error value of 0.816 kcal/mol while it is 3.08 kcal/mol for MDM2, a highly flexible protein compared to MDMX. With the integration of the free energy landscape method, the mean absolute error for MDM2 is usually improved to 1 1.95 kcal/mol. of the thermodynamic cycle (E- F, Physique 6). For each windows, 5000 energy minimization actions were carried out using the steepest descent algorithm. The system was subjected to NVT equilibration for 100 picoseconds. Temperature was coupled using Langevin dynamics  with Bismuth Subcitrate Potassium reference temperature set to 298 Kelvin. Subsequently, NPT equilibration was carried out for 100 picoseconds using Parrinello-Rahman scheme. For all those simulations the Particle Mesh Ewald (PME) algorithm was used to treat electrostatic interactions . The LINCS constraint algorithm was used for H-bonds . For production run 1 ns of simulation was carried out for each windows and the data was collected. The binding free energy was calculated as sum of free energy change of formation of protein-ligand complex and the free energy of desolvating the ligand. The analytical correction term for adding restraints to decoupled ligand was also added to it. It can be expressed as: is usually calculated using the Boresch equation . (D) Electrostatic and van der Waals interactions turned on for restrained ligand in complex with protein MDM2. (E) The ligand-protein complex with full interactions but restrained ligand. (F) Restraints removed resulting in fully interacting ligand in complex with protein MDM2. Protein and ligand were taken from PDB accession code: 4MDQ for representation of this cycle while the arrows represent the direction of cycle. The binding free energy calculations were done for all the ligand-MDM2/MDMX complexes used in this study. 3.3. Restraints Rabbit Polyclonal to WEE2 In order to hold the position and orientation of the ligands with respect to protein, restraint terms were used. It allowed the ligand to adopt different conformations while keeping it in the binding site such that it does not freely move out of partially interacting protein ligand system as the interactions are gradually turned off during the simulation. However, there is an entropic cost of the ligand for not allowing the free wandering throughout the simulation cell. Following the method proposed by Boresch et al.  the entropic cost was calculated analytically for six point restraint of the ligand in the binding site. The free energy term associated with ligand restraints as Bismuth Subcitrate Potassium interactions are turned off as: refers to ideal gas constant, is usually heat in Kelvin, is usually standard system volume for 1 molar concentration, is usually reference distance for restraints, and are reference angles for restraints, refers to strength constant of distance (and can be calculated as represents the Fermi function: denotes to Boltzmann constant, is usually temperature. and represent the Hamiltonians for the says and The value of C is usually iteratively calculated to fulfill and can be calculated as: and represent the number of co-ordinate frames at j and k says . The BAR method implemented in alchemical_analysis.py python tool  was used to calculate free energy for two end says. 3.5. Free Energy Landscape Generation The apo state of MDM2 is usually highly flexible and significant conformational changes are observed upon ligand binding. Therefore, in order to get thorough sampling of conformational space of apo MDM2 and thereof to estimate Gibbs free energies based on the Bismuth Subcitrate Potassium population, two-dimensional free energy scenery was generated. The unliganded structure for MDM2 was collected from protein databank (PDBID:1Z1M) . The residues 26C110 were used as start structure for 500 ns long simulation. The system was solvated in a cubic box with TIP3P water molecules at 12 ? marginal radii. At physiological pH, the structure was found to have positive charge, thus, to make the system electrically neutral, six chloride ions were added in the simulation box using the genion tool. Then whole molecular systems were subjected to energy minimization by steepest descent minimization algorithm. Subsequently, the system was equilibrated using NVT and NPT ensemble for 100 ps each. Isotropic pressure coupling was performed using Parrinello-Rahman method. Electrostatic interactions were computed using Particle Mesh Ewald method. VdW and coulomb interactions were truncated at 1.0 nm. Conformations were stored every 10 ps. Finally, the system was subjected to production run for 500 ns. Free energy scenery was obtained by computing the joint probability distribution from radius of gyration and the root mean square deviation from the first frame of production run used as reference structure. In theory, a two-dimensional free energy landscape of the apo MDM2 is usually proposed to provide correction term for the bias in alchemical free energy calculations due to undersampling of the apo state when the ligand stops interacting within the binding site. The.