Evaluating Free Energies ofEvaluating Free Energies ofBinding using Amber:Binding using Amber:

The MM-PBSA ApproachThe MM-PBSA Approach

Evaluating Free Energies ofEvaluating Free Energies ofBinding:Binding: MM-PBSAMM-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

Evaluating Free Energies ofEvaluating Free Energies ofBindingBinding

ΔGBind = ΔGAB – ΔGA - ΔGB

ΔGBind

A B AB

Solvent Solvent

Evaluating Free Energies ofEvaluating Free Energies ofBindingBinding

ΔGBind = ΔGAB – ΔGA - ΔGB

Approximate ΔGBind as

ΔGBind ≈ GAB – GA – GB

Where GX is the calculated average free energy

ΔGX = EMM + GSolv – TSMM

Evaluating Free Energies ofEvaluating Free Energies ofBindingBinding

ΔGX = EMM + GSolv – TSMM

Where EMM is the average molecular mechanical energy:

EMM = Ebond + Eangle + Etors + Evdw + Eelec

GSolv is the calculated solvation free energy

– TSMM is the solute entropy, which can be estimated by using

normal-mode analysis

Evaluating Free Energies ofEvaluating Free Energies ofBindingBinding

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.

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Evaluating Free Energies ofEvaluating Free Energies ofBinding: Calculating GBinding: Calculating GSolvSolv

Molecular solvent model gives gives correct representation of long-range electrostatic effects and correct geometry but could be hardly used to estimate solvation energy

Evaluating Free Energies ofEvaluating Free Energies ofBinding: Calculating GBinding: Calculating GSolvSolv

Continuum model gives fast estimate of the solvation energy but could be hardly used in Molecular Dynamics simulations

Evaluating Free Energies ofEvaluating Free Energies ofBindingBinding

Compromise:MD trajectory

One carries out a MD simulation in a periodic box with solvent

Snapshots of representativestructures

Evaluate EMM , GSolv and –TSMM for every saved snapshot

Evaluating Free Energies ofEvaluating Free Energies ofBinding: Two ApproachesBinding: Two Approaches

ΔGBind

A B AB

Solvent 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