Applied Mathematics Colloquium
Senior Thesis Presentations - Brewster, Ortega, Weideman
Friday, May 2, 2014 · 12 - 1 PM
Three Senior Honors Theses will be presented.
Title: The Influence of Stochastic Parameters on Calcium Waves in a Heart Cell
Presentation #2
Matthew Brewster
Abstract: Calcium is a critical component in many cellular functions. It
serves many important functions such as signal transduction, contraction
of muscles, enzyme function, and maintaining potential difference
across excitable membranes. In this study we examine calcium waves
in heart cells and how they diffuse. Calcium sparks are intracellular
release events which are important in converting electrical stimuli
into mechanical responses. We investigate the effects of a stochastic
spatially uniform flux density term as well as of a stochastic
spatially varying flux density term. We hypothesize that having a stochastic
flux density term is more physiologically accurate.
We use an array of statistical techniques as well as parallel
computing to facilitate the large number of simulation runs.
Title: A Mathematical Model of Melanopsin Phototransduction and Light Adaptation
Jessica Ortega
Abstract: Melanopsin is a recently discovered photopigment found in intrinsically photosensitive retinal ganglion cells (ipRGCs). It is involved in non-image forming vision, including circadian photoentrainment and the pupillary light reflex. It is also involved in light-related disorders, such as seasonal affective disorder. When light activates the photopigment, a phototransduction cascade commences, which produces an electrical signal that is sent to the brain. Light adaptation is the ability of the visual system to adjust its performance according to the ambient level of illumination. To describe melanopsin’s phototransduction and adaptation pathways, we developed a mathematical model by using the law of mass action to convert chemical equations describing the pathway to a series of differential equations that was solved with MATLAB. Model parameters of the activation and deactivation were determined by fitting the model results to experimental calcium imaging data collected from transfected human embryonic kidney cells expressing the melanopsin gene as well as electrophysiological data collected from ipRGCs. Mathematical simulations of the single flash produce results consistent with those seen in the experimental data.
This work was funded by NSF for Undergraduate Biology and Mathematics Research Training, NSF IOSO721608 to P.R.R., NEI R01Y019053 to P.R.R.
Presentation #3
Title: Morphogen Dynamics: The Diffusion of Signaling Molecules as Influenced by Ovarian Tissue
Ann Marie Weideman
Abstract: Morphogens are diffusible signaling molecules that influence embryonic cell identity through concentration differences. The formation of molecular gradients by diffusion and uptake allows for differentiation between otherwise homogenous cells located in spatial proximity. The dynamic effects of morphogens can be studied in the ovarian tissue of Drosophila melanogaster, where epithelial cells must be precisely determined to be either static or motile. The fates of the epithelial cells depend on their proximity to two signaling cells, the polar cells, and their secretion of a morphogen. However, we found that this cell fate determination does not always occur in the radially symmetric pattern expected. To elucidate this, we investigated the asymmetrical recruitment of border cells by modeling the secretion, diffusion, and binding of morphogens in an extracellular space delimited by an irregular landscape of juxtaposing cells. Computational experiments indicate that the asymmetric activation patterns observed can be explained by the relative position of extracellular gaps and the polar cells. We analyzed this further by relating in-vivo cases to two- and three-dimensional mathematical models in the anticipation that our work will provide a better understanding of cell fate decisions in animal development.
