Simulation methods for spatiotemporal models of biochemical signaling networks

WANDA STRYCHALSKI: Simulation Methods for Spatiotemporal Models of Biochemical Signaling Networks (Under the direction of David Adalsteinsson and Timothy C. Elston) Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through a signaling network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells in a differential algebraic formulation to handle the complex boundary dynamics encountered in biological systems. The method is second order in space and time. Several models of signaling systems are simulated in realistic cell morphologies obtained from live cell images. We then examine the effects of geometry on signal transduction. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we present a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion equation. We then show that shape