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

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Evaluating Free Energies of Binding: 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

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Evaluating Free Energies of Binding Δ G Bind = Δ G AB – Δ G A - Δ G B Δ G Bind A B AB Solvent

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Evaluating Free Energies of Binding Δ G Bind = Δ G AB – Δ G A - Δ G B Approximate Δ G Bind as Δ G Bind ≈ G AB – G A – G B Where G X is the calculated average free energy Δ G X = E MM + G Solv – TS MM

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Evaluating Free Energies of Binding Δ G X = E MM + G Solv – TS MM Where E MM is the average molecular mechanical energy: E MM = E bond + E angle + E tors + E vdw + E elec G Solv is the calculated solvation free energy – TS MM is the solute entropy, which can be estimated by using normal-mode analysis

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Evaluating Free Energies of Binding Δ G X = E MM + G Solv – TS MM 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. ?

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Evaluating Free Energies of Binding: Calculating G Solv Molecular solvent model gives gives correct representation of long-range electrostatic effects and correct geometry but could be hardly used to estimate solvation energy

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Evaluating Free Energies of Binding: Calculating G Solv Continuum model gives fast estimate of the solvation energy but could be hardly used in Molecular Dynamics simulations

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Evaluating Free Energies of Binding Compromise: MD trajectory One carries out a MD simulation in a periodic box with solvent Snapshots of representative structures Evaluate E MM, G Solv and –TS MM for every saved snapshot

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Evaluating Free Energies of Binding: Two Approaches Δ G Bind A B AB Solvent 1.In general case, one carries out three independent MD simulations: for ligand, receptor, and complex 2.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

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