Evaluating Free Energies of Binding using Amber: The MM-PBSA Approach

1. Evaluating Free Energies ofBinding using Amber:The MM-PBSA Approach

2. Evaluating Free Energies ofBinding:MM-PBSA • The acronym MM-PBSA stands for Molecular Mechanics- Poisson Bolzmann Surface Area • The MM-PBSA approach represents the postprocessing method to evaluate free energies of binding or to calculate absolute free energies of molecules in solution. P.A. Kollman at al.,Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models, Acc. Chem. Res. 2000, 33, 889-897

3. ΔGBind A AB B Solvent Solvent Evaluating Free Energies ofBinding ΔGBind = ΔGAB – ΔGA - ΔGB

4. Evaluating Free Energies ofBinding ΔGBind = ΔGAB – ΔGA - ΔGB Approximate ΔGBindas ΔGBind ≈ GAB – GA – GB Where GX is the calculated average free energy ΔGX = EMM + GSolv – TSMM

5. Evaluating Free Energies ofBinding ΔGX =EMM + GSolv – TSMM WhereEMM is the average molecular mechanical energy: EMM = Ebond + Eangle + Etors + Evdw + Eelec GSolvis the calculated solvation free energy – TSMM is the solute entropy, which can be estimated by using normal-mode analysis

6. Evaluating Free Energies ofBinding ΔGX =EMM + GSolv – TSMM Could be easily calculated • In practice entropy contributions is usually neglected • Could be computationally expensive • Tend to have a large margin of error that introduces significant uncertainty in the result. ?

7. Evaluating Free Energies ofBinding: Calculating GSolv Molecular solvent model gives gives correct representation of long-range electrostatic effects and correct geometrybut could be hardly used to estimate solvation energy

8. Evaluating Free Energies ofBinding: Calculating GSolv Continuum model gives fast estimate of the solvation energybut could be hardly used in Molecular Dynamics simulations

9. Evaluating Free Energies ofBinding Compromise: MD trajectory One carries out a MD simulation in a periodic box with solvent Snapshots of representative structures Evaluate EMM , GSolv and –TSMM for every saved snapshot

10. ΔGBind A AB B Solvent Solvent Evaluating Free Energies ofBinding: Two Approaches • In general case, one carries out three independent MD simulations: for ligand, receptor, and complex • Single trajectory approach: one makes the approximation that no significant conformational changes occur upon binding so that the snapshots for all three species can be obtained from a single trajectory for a complex