Analysis and modeling of cells, cell behavior, and helical biological molecules - Benoit, Steven Richard, author; Putkaradze, Vakhtang, advisor; Shipman, Patrick, committee member; Estep, Don, committee member; Marconi, Mario, committee member; Tobet, Stuart, committee member (Colorado State University. Libraries, 2011)
Mathematical models of biological systems have evolved over time and through the introduction and growth of computer simulation and analysis. Models have increased in sophistication and power through the combination of multi-scale approaches, molecular and granular dynamics simulations, and advances in parallelization and processing speed. However, current cell models cannot accurately predict behaviors at the whole-cell scale, nor can molecular models predict accurately the complex shape assumed by large biological molecules including proteins, although significant progress is being made toward this goal. The present work introduces new models in three domains within biological systems modeling. We first discuss a phenomenological model of observed cell motions in developing tissue that characterizes cells according to a best-fit generalized diffusion model and combines this data with Voronoi diagrams to effectively visualize patterns of cell behavior in tissue. Next, we present a series of component models for cells and cell structure that support simulations involving tens to hundreds of cells in a way that captures behaviors ignored by existing models, including pseudopod formation, membrane mechanics, cytoskeletal polymerization / depolymerization, and chemical signal transduction. The resulting models exhibit many of the behaviors of real-world cells including polarization and chemotaxis. Finally, we present a method for analysis of biological molecules that form helical conformations that includes long-range electrostatic interactions as well as short-range interactions to prevent self-intersections. We consider the stability of molecules with repeating monomers that include off-axis charge concentrations and derive energy landscapes to identify stable conformations, then analyze helical stability using geometric methods.
Keywords: cell models; helical molecules