Solubility Modelling in Condensed Matter Dielectric Continuum Theory and Nonlinear Response

iii Abstract Solubility Modelling in Condensed Matter. Dielectric Continuum Theory and Nonlinear Response. Lars Sandberg, Theoretical Biophysics Group, Department of Physics, Royal Institute of Technology, SE-106 91 Stockholm, SWEDEN.Solubility Modelling in Condensed Matter. Dielectric Continuum Theory and Nonlinear Response. Lars Sandberg, Theoretical Biophysics Group, Department of Physics, Royal Institute of Technology, SE-106 91 Stockholm, SWEDEN. The solubility of molecules in condensed matter is an important field in biophysics with applications in the food and pharmaceutical industry. Moreover, a good model description of electrostatic interactions is fundamental to the understanding of structure and function of biological macromolecules. This thesis presents my research on implicit solvation models where the solvent is described by a dielectric continuum. Nonlinear response effects like dielectric saturation and electrostriction are studied. Rigorous electrostatic theory is developed to estimate hydration free energies for ionic and molecular solvation in water. Approximate screened electrostatic potentials are used to derive theoretical hydrophobicity scales. Furthermore, they are applied to polyampholytes to determine the acidity equilibrium of ionizable groups in proteins at different pH values. The main conclusions are: Dielectric continuum theory that includes nonlinear response effects can quantitatively model the hydration of ions with valency 1 to 4. For monovalent ions the electrostriction work is at least 10 times smaller than the saturation contribution, but the nonlinearity is negligible compared to the ionic hydration free energy. Nonlinear effects are important to small organic polar molecules for which the hydration free energies are smaller. Dielectric saturation reduces the average error of calculated hydration free energies by 25% to a value twice the experimental uncertainty of kJ/mol with the use of a standard force field. The screened multipole potential approach in the dipole approximation is successful to describe octanol-water partitioning of amino acid side chains. However, the dielectric saturation effect is crucial to include in the implicit solvation model. A screened Coulomb potential model is equally good as and at least 100 times faster than the linear Poisson-Boltzmann model to predict p a values of ionizable groups in proteins. However, the electrostatic screening must be treated differently in the protein core and in the solvent interfacial region. Moreover, for buried isolated groups the electrostatic self-energy becomes important. Numerically calculated p as by linear response models are extremely sensitive to the specific choice of the low dielectric constant value of the macromolecule. Furthermore, time averaged p a values are stabilized over a time interval of about 100 ps along a molecular dynamics trajectory.