Computational statistical mechanics of protein function

Molecular dynamics (MD) provides an atomically detailed description of the dynamics of a system of atoms. It is a useful tool to understand how protein function arises from the dynamics of the atoms of the protein and of its environment. When the MD model is accurate, analyzing a MD trajectory unveils features of the proteins that are not available from a single snapshot or a static structure. When the sampling of the accessible configurations is accurate, we can employ statistical mechanics (SM) to connect the trajectory generated by MD to experimentally measurable kinetic and thermodynamic quantities that are related to function. In this dissertation I describe three applications of MD and SM in the field of biochemistry. First, I discuss the theory of alchemical methods to compute free energy differences. In these methods a fragment of a system is computationally modified by removing its interactions with the environment and creating the interactions of the environment with the new species. This theory provides a numerical scheme to efficiently compute protein-ligand affinity, solvation free energies, and the effect of mutations on protein structure. I investigated the theory and stability of the numerical algorithm. The second research topic that I discuss considers a model of the dynamics of a set of coarse variables. The dynamics in coarse space is modeled by the Smoluchowski equation. To employ this description it is necessary to have the correct potential of mean force and diffusion tensor in the space of coarse variables. I describe a new method that I developed to extract the diffusion tensor from a MD simulation. Finally, I employed MD simulations to explain at a microscopic level the stereospecificity of the enzyme ketoreductase. To do so, I ran multiple simulations of the enzyme bound with the correct ligand and its enantiomer in a reactive configuration. The simulations showed that the enzyme retained the correct stereoisomer closer to the reactive configuration, and highlighted which interactions are responsible for the specificity. These weak physical interactions enhance binding with the correct ligand even prior to the steps of chemical modification.