Master of Science / Department of Biochemistry / Paul E. Smith / We are developing a force field (FF) for molecular dynamics (MD) simulations of peptides and small proteins that is grounded in the Kirkwood-Buff theory of solutions. Here we present the Kirkwood-Buff Force Field (KBFF) parameters for the aromatic amino acids, based upon simulations of binary mixtures of small molecules representative of these amino acids over their entire composition ranges (excluding Histidine). Many aromatics are not fully soluble in water, so they have instead been studied in solvents of methanol or toluene. The parameters were developed by studying the following binary solutions: Phenylalanine − benzene + methanol, toluene + methanol, and toluene + benzene; Tyrosine − toluene + phenol and toluene + p-Cresol; Tryptophan − pyrrole + methanol and indole + methanol; Histidine − pyrrole + methanol, pyridine + methanol, pyridine + water, histidine + water (at 0.25 molal), and histidine monohydrochloride + water (at 0.3 molal and 0.6 molal). Our simulations reproduce the Kirkwood-Buff integrals, which guarantees that the KBFF provides an adequate balance of solute-solvent, solute-solute, and solvent-solvent interactions. Additionally, we show that the KBFF does not sacrifice reproduction of other solution properties in order to achieve this improved description of intermolecular interactions. We present these results as validating evidence for the future use of the KBFF in simulations of peptides and small proteins.

Doctor of Philosophy / Department of Chemistry / Paul E. Smith / The impact of computer simulations has become quite significant especially with the development of supercomputers during the last couple of decades. They are used in a wide range of purposes such as exploring experimentally inaccessible phenomena and providing an alternative when experiments are expensive, dangerous, time consuming, difficult and controversial. In terms of applications in biological systems molecular modeling techniques can be used in rational drug design, predicting structures of proteins and circumstances where the atomic level descriptions provided by them are valuable for the understanding of the systems of interest. Hence, the potential of computer simulations of biomolecular systems is undeniable. Irrespective of the promising uses of computer simulations, it cannot be guaranteed that the results will be realistic. The precision of a molecular simulation depends on the degree of sampling achieved during the simulation while the accuracy of the results depends on the satisfactory description of intramolecular and intermolecular interactions in the system, i.e. the force field. Recently, we have been developing a force field for molecular dynamics simulations of biological systems based on the Kirkwood Buff (KB) theory of solutions, not only with an emphasis on the accurate description of intermolecular interactions, but also by reproducing several physical properties such as partial molar volume, compressibility and composition dependent chemical potential derivatives to match with respective experimental values. In this approach simulation results in terms of KB integrals can be directly compared with experimental data through a KB analysis of the solution properties and therefore it provides a simple and clear method to test the capability of the KB derived force field. Initially, we have provided a rigorous framework for the analysis of experimental and simulation data concerning open and closed multicomponent systems using the KB theory of solutions. The results are illustrated using computer simulations for various concentrations of the solutes Gly, Gly₂ and Gly₃ in both open and closed systems, and in the absence or presence of NaCl as a cosolvent. Then, we have attempted to quantify the interactions between amino acids in aqueous solutions using the KB theory of solutions. The results are illustrated using computer simulations for various concentrations of the twenty zwitterionic amino acids at ambient temperature and pressure. Next, several amino acids were also studied at higher temperatures and pressures and the results are discussed in terms of the preferential (solute over solvent) interactions between the amino acids. Finally, we have described our most recent efforts towards a complete force field for peptides and proteins. The results are illustrated using molecular dynamics simulations of several tripeptides, selected peptides and selected globular proteins at ambient temperature and pressure followed by replica exchange molecular dynamics simulations of a few selected peptides.

Doctor of Philosophy / Department of Chemistry / Paul E. Smith / Kirkwood Buff (KB) theory is one of the most important theories of solutions. The theory can relate integrals over radial (pair) distribution functions (rdfs) in the grand canonical ensemble to common thermodynamic properties. An inversion of the KB theory has been proposed by Ben-Naim and this has led to the wide spread popularity of KB theory. The idea of the KB inversion procedure is to calculate KB integrals from available thermodynamic properties. The KB theory can be used to validate the force field (ff) parameters used in molecular dynamics simulations. We have tested a series of small molecule ff parameters using KB theory that consists of both atom centered partial atomic charges and extra charge sites. The results indicate that using extra charge sites, derived from QM calculations, does not necessarily provide a more accurate representation of condensed phase properties. A further study aimed at an ongoing project of deriving new biomolecular ff parameters based on KB theory, has developed ff parameters for esters in order to represent the ester conjugation of the phospholipid molecule. The models were further tested against experimental properties. Preferential solvation (PS) is an important concept of solution mixtures that can be described using KB theory. The difference between local composition and bulk composition in solution mixtures leads to the concept of PS. A generalized explanation based on local mole fractions was derived by Ben-Naim using KB theory. However, the original expressions have been modified over years. Here, we propose a new approach based on local volume fractions to explore PS in binary and ternary solution mixtures. Experimental and simulation data were used to examine different approaches to PS. A relationship between the rdf and the triplet distribution function can be obtained using the Kirkwood Superposition Approximation (KSA). A combination of Fluctuation Solution Theory and experimental rdfs are used to examine the KSA at a series of state points for pure water. The accuracy of several other approximate relationships between the pair and triplet correlation functions was also investigated and are in good agreement for regions of the phase diagram where the compressibility is small.

Doctor of Philosophy / Department of Chemistry / Paul E. Smith / In the study of biological systems, 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. Recently, 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, recent results concerning the formulation and evaluation of preferential interactions in biological systems in terms of KB integrals are presented. In particular, experimental and simulated preferential interactions of a cosolvent with a biomolecule in the presence of water are described. Second, a force field for the computer simulation of aqueous solutions of amides is presented. The force field is designed to reproduce the experimentally observed density and KB integrals for N-methylacetamide (NMA), allowing for an accurate description of the NMA activity. Other properties such as the translational diffusion constant and heat of mixing are also well reproduced. The force field is then extended to include N,N'-dimethylacetamide and acetamide with good success. The models presented here provide a basis for an accurate force field for peptides and proteins. Comparison between the developed KB force fields (KBFF) and existing force fields is performed for amide and glycine and proves that the KBFF approach is competitive. Also, explicit expressions are developed for the chemical potential derivatives, partial molar volumes, and isothermal compressibility of solution mixtures involving four components at finite concentrations using the KB theory of solutions. A general recursion relationship is also provided which can be used to generate the chemical potential derivatives for higher component solutions. Finally, a pairwise preferential interaction model (PPIM), described by KB integrals is developed to quantify and characterize the interactions between functional groups observed in peptides.

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.

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