1. The Role of Entropy in Biomolecular Modelling Three Examples 1.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 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 individual solvent or co-solvent molecules 2. Partitioning of Solutes between various Solvent Mixtures Solvation of small molecules: H S Enthalpy co-act or may depending on mixture and solute S S Entropycounteract Continium methods will not catch these entropic effects

3. Four Ways to Compute Entropy Differences Coupling Parameters approach Hamiltonian is made function of : Free energy depends on : 1.Entropy Difference via Thermodynamic Intergration (TI) Free Energy Difference and End States Energy Difference accurate not so acc u rate

4. Four Ways to Compute Entropy Differences using and 2. Entropy Difference directly via TI correlation betweenandnot so accurate only -dependent terms all 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 only solute-solvent terms not so accurate all solvent terms solvent: v solute: u

6. Comparison of 1. Excess Free Energy, Entropy of Water 2. Hydration Free Energy, Entropy of Water Using four different Methods Three Models or Hamiltonians: 1.SPC Model: Coulomb plus van der Waals interaction 2.SPC nc Model: no Coulomb interaction 3.SPC nn Model: no (non-bonded) interaction Christine Peter Thermodynamic CycleSystem 1000 H 2 O molecules periodic boundary conditions T = 280K, 300K, 320K simulations = 100-600ps NVT NPT Change: 1 H 2 O  hydration all H 2 O  excessmore accurate SPC (liquid) SPC nc (liquid, no Coulomb) SPC nn (ideal gas) G, S, H = 0

7. Free Energy and Entropy of Water Reference: J.Chem.Phys. (2004) method 2144

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

9. All 1000 H 2 O Molecules Changed TI

10. A Single H 2 O Molecule Changed  A via TI S via TI S uv via TI NVT NPT same pattern as for 1000 H 2 O changed erratic not converged same pattern as for 1000 H 2 O changed