Doctor of Philosophy / Department of Chemistry / Paul E. Smith / In the past several decades, molecular dynamics (MD) simulations have played an important role in providing atomic details for phenomena of interest. The force field used in MD simulations is a critical factor determining the quality of the simulations. Kirkwood-Buff (KB) theory has been applied to study preferential interactions and to develop a new force field. KB theory provides a path from quantities determined from simulation data to the corresponding thermodynamic data. Here we combine KB theory and molecular simulations to study a variety of intermolecular interactions in solution. First, a force field for the computer simulation of aqueous solutions of alcohols is presented. The force field is designed to reproduce the experimentally observed density and KB integrals for a series of alcohols, allowing for an accurate description of alcohols’ activity. Other properties such as the translational diffusion constant and heat of mixing are also well reproduced. Second, the newly developed force field is then extended to more complicated systems, such as peptide or mini-proteins, to determine backbone dihedral potentials energetics. The models developed here provide a basis for an accurate force field for peptides and proteins. Third, we have then studied the surface tension of a variety water models. Results showed that different simulation conditions can affect the final values of surface tension. Finally, by using the Kirkwood-Buff theory of solution and surface probability distributions, we attempted to characterize the properties of the Gas/Liquid interface region. The same approach is then used to understand the relationship between changes in surface tension, the degree of surface adsorption or depletion, and the bulk solution properties.

Doctor of Philosophy / Department of Chemistry / Paul Edward Smith / The activity and function of many macromolecules in cellular environments are coupled with the binding of ions such as alkaline earth metal ions and poly oxo anions. These ions are involved in the regulation of important processes such as protein crystallization, nucleic acid and protein stability, enzyme activity, and many others. The exact mechanism of ion specificity is still elusive. In principle, computer simulations can be used to help provide a molecular level understanding of the dynamics of hydrated ions and their interactions with the biomolecules. However, most of the force fields available today often fail to accurately reproduce the properties of ions in aqueous environments. Here we develop a classical non polarizable force field for aqueous alkaline earth metal halides (MX₂) where M = Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺ and X = Cl⁻, Br⁻, I⁻, and for some biologically important oxo anions which are NO₃⁻, ClO₄⁻, H₂PO₄⁻ and SO₄²⁻, for use in biomolecular simulations. The new force field parameters are developed to reproduce the experimental Kirkwood-Buff integrals. The Kirkwood-Buff integrals can be used to quantify the affinity between molecular species in solution. This helps to capture the fine balance between the interactions of ions and water. Since this new force field can reproduce the experimental Kirkwood-Buff integrals for most concentrations of the respective salts, they are capable of reproduce the experimental activity derivatives, partial molar volumes, and excess coordination numbers. Use of these new models in MD simulations also leads to reasonable diffusion constants and dielectric decrements. Attempts to develop force field parameters for CO₃²⁻, HPO₄²⁻ and PO₄³⁻ ions were unsuccessful due to an excessive aggregation behavior in the simulations. Therefore, in an effort to overcome this aggregation behavior in the simulations, we have investigated scaling the anion to water interaction strength, and also the possibility of using a high frequency permittivity in the simulations. The strategy of increasing relative permittivity of the system to mimic electronic screening effects are particularly promising for decreasing the excessive ion clustering observed in the MD simulations.

Doctor of Philosophy / Department of Chemistry / Paul E. Smith / The Kirkwood-Buff (KB) theory of solutions, published in 1951, established a route from integrals over radial (pair) distribution functions (RDFs) in the grand canonical ensemble to a set of thermodynamic quantities in an equivalent closed ensemble. These “KB integrals” (KBIs) can also be expressed in terms of the particle-particle (i.e., concentration or density) fluctuations within grand canonical ensemble regions. Contributions by Ben-Naim in 1977 provided the means to obtain the KBIs if one already knew the set of thermodynamic quantities for the mixture of interest; that is, he provided the inversion procedure. Thus, KB theory provides a two-way bridge between local (microscopic) and global (bulk/thermodynamic) properties. Due to its lack of approximations, its wide ranging applicability, and the absence of a competitive theory for rigorously understanding liquid mixtures, it has been used to understand solution microheterogeneity, solute solubility, cosolvent effects on biomolecules, preferential solvation, etc. Here, after using KB theory to test the accuracy of pair potentials, we present and illustrate two extensions of the theory, resulting in a general Fluctuation Solution Theory (FST). First, we generalize KB theory to include two-way relationships between the grand canonical ensemble’s particle-energy and energy-energy fluctuations and additional thermodynamic quantities. This extension allows for non-isothermal conditions to be considered, unlike traditional KB theory. We illustrate these new relationships using analyses of experimental data and molecular dynamics (MD) simulations for pure liquids and binary mixtures. Furthermore, we use it to obtain conformation-specific infinitely dilute partial molar volumes and compressibilities for proteins (other properties will follow) from MD simulations and compare the method to a non-FST method for obtaining the same properties. The second extension of KB theory involves moving beyond doublet particle fluctuations to additionally consider triplet and quadruplet particle fluctuations, which are related to derivatives of the thermodynamic properties involved in regular KB theory. We present these higher order fluctuations obtained from experiment and simulation for pure liquids and binary mixtures. Using the newfound experimental third and fourth cumulants of the distribution of particles in solution, which can be extracted from bulk thermodynamic data using this extension, we also probe particle distributions’ non-Gaussian nature.

A technology for optimization of potential parameters from condensed phase simulations (POP) is discussed and illustrated. It is based on direct calculations of the derivatives of macroscopic observables with respect to the potential parameters. The derivatives are used in a local minimization scheme, comparing simulated and experimental data. In particular, we show that the Newton Trust-Region protocol allows for accurate and robust optimization. POP is illustrated for a toy problem of alanine dipeptide and is applied to folding of the peptide WAAAH. The helix fraction is highly sensitive to the potential parameters while the slope of the melting curve is not. The sensitivity variations make it difficult to satisfy both observations simultaneously. We conjecture that there is no set of parameters that reproduces experimental melting curves of short peptides that are modeled with the usual functional form of a force field. We then apply the newly developed technology to study the liquid mixture of tert-butanol and water. We are able to obtain, after 4 iterations, the correct phase behavior and accurately predict the value of the Kirkwood Buff (KB) integrals. We further illustrate that a potential that is determined solely by KB information, or the pair correlation function, is not necessarily unique. / text

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