UC San Diego

Molecular dynamics simulations can be used to probe a wide range of biologically relevant problems. One such problem is the mechanism of allostery. Allosteric regulation in biological systems is of considerable interest given the vast number of proteins that exhibit such behavior. Designing a consistent framework for allostery that can be rapidly quantified could pave the way for synthetic catalysts, allosteric inhibitors, and a more general understanding of protein function. To this end, this work explores some of the conventional uses of dynamical network analysis as applied to a model of allostery and shows that dynamical networks are highly dependent on what constituents of a protein are correlated. The work goes onto to show that the commonly used alpha-carbon of an amino acid, although a nexus joining the backbone and side -chain, is an inferior handle to use for correlated motions and does not model side-chain interactions as well as the center of mass of an amino acid. The alpha-carbon is shown to be highly correlated to the amino acid's backbone center of mass. Other node choices are explored within the framework of dynamical network analysis and signaling pathways are calculated between the two stereospecific receptor sites known to exhibit allostery in HisH-HisF Thermotoga Maritima. Further work expands around the optimal signaling pathway within HisH-HisF to include sub-optimal pathways. The Weighted Implementation of Suboptimal Paths (WISP) is developed as an efficient algorithm and tool for generating a statistical distribution of pathways between residues known to play in allostery. For HisH-HisF the degeneracy, or number of times an amino acid participates in a signaling pathway, shifts between the allosterically active and allosterically inactive forms (holo-state and apo-state respectively). Furthermore, all of the paths are tighter and exhibit more correlation for the allosterically active state. This shows evidence of a loss of entropy along the signaling pathways when the effector molecule, PRFAR, is bound. Lastly, a general approach to solving evolution equations for probability densities is described using interacting trajectory ensembles. This is done by deriving the general equations of motion for the trajectories in the kinematic space (e.g., configuration or phase space). The time rate of change of the trajectory members depends on both external forces and on the probability density itself. The dependence the trajectory has on the probability density lead to interactions between the ensemble members and a loss of each members independence. The result is illustrated by a number of numerical examples