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The Role of Entropy in Biomolecular Modelling

The Role of Entropy in Biomolecular Modelling. Three Examples. Force Field Development How to parametrise non-bonded interaction terms? Include Entropy. of variety of solutes. Simulation at finite T. The Role of Entropy in Biomolecular Modelling.

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The Role of Entropy in Biomolecular Modelling

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  1. The Role of Entropy in Biomolecular Modelling Three Examples • Force Field Development • How to parametrise non-bonded interaction terms? • Include Entropy of variety of solutes Simulation at finite T

  2. The Role of Entropy in Biomolecular Modelling 2. Partitioning of Solutes between various Solvent Mixtures Solvation of small molecules: DHS Enthalpy co-act or may depending on mixture and solute DSS Entropy counteract Continium methods will not catch these entropic effects 3. Protein-Ligand Complexation: Ligand binding to the Estrogen Receptor: A variety of configurations (ensemble) contributes to binding, both in the protein and in water Continuum representation of the solvent is unable to mimic binding subtleties of individualsolvent or co-solvent molecules

  3. Four Ways to Compute Entropy Differences Coupling Parameters l approach Hamiltonian is made function of l: Free energy depends on l: • Entropy Difference via Thermodynamic Intergration (TI) • Free Energy Difference and End States Energy Difference accurate not so accurate

  4. Four Ways to Compute Entropy Differences 2. Entropy Difference directly via TI using and correlation between and not so accurate all terms only l-dependent terms 3. Entropy Difference via finite Temperature Difference using difference between almost equal accurate values

  5. Four Ways to Compute Entropy Differences 4 . Solvation Entropy Difference via Solute-Solvent Entropy Difference (using TI) and End States Solvent-Solvent Energy Difference accurate not so accurate solvent: v solute: u only solute-solvent terms all solvent terms

  6. Comparison of1. Excess Free Energy, Entropy of Water2. Hydration Free Energy, Entropy of WaterUsing four different Methods Christine Peter • Three Models or Hamiltonians: • SPC Model: Coulomb plus van der Waals interaction • SPCnc Model: no Coulomb interaction • SPCnn Model: no (non-bonded) interaction Thermodynamic Cycle System 1000 H2O molecules periodic boundary conditions T = 280K, 300K, 320K simulations = 100-600ps NVT n NPT Change: 1 H2O g hydration all H2O g excess more accurate SPC (liquid) SPCnn (ideal gas) DG, DS, DH = 0 SPCnc (liquid, no Coulomb)

  7. Free Energy and Entropy of Water method 2 1 4 4 Reference: J.Chem.Phys. (2004)

  8. Free Energy and Entropy of Water method 3 close 63 Reference: J. Chem. Phys. (2004)

  9. All 1000 H2O Molecules Changed TI TI

  10. A Single H2O Molecule Changed DA via TI DS via TI DSuv via TI NVT NPT same pattern as for 1000 H2O changed erratic not converged same pattern as for 1000 H2O changed

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