Differential Equations Seminar

Senior theses presentations

Location

Mathematics/Psychology : 401

Date & Time

May 2, 2016, 11:00 am12:00 pm

Description

Speaker: Gloria Diederich

Tttle:
 Bifurcation Analysis of a Computational Model of a Neuron in Thalamic Reticular Nucleus

Abstract: Sleep spindles are the hall-mark of oscillations observed in TRN. A Hodgkin and Huxley based computational model of TRN neurons was derived by Destexhe et al. 1994 and we aim to better understand how  the properties of TRN neurons  using techniques from dynamical systems such as bifurcation analysis. We first updated the parameters from Destexhe et al to be consistent with recent experimental data. The behavior of the cell changes from oscillations to steady state as the membrane potential varies. The goal of my thesis is understand the bifurcation diagram  as the membrane potential varies. The resulting diagram indicates a homoclinic bifurcation leading to two stable states: an equilibrium and a periodic orbit. 


Speaker: Adam Byerly

Tttle:
 A Mathematical Model of Melanopsin Short and Long Term Light Adaptation

Abstract: G protein-coupled receptors (GPCRs) are a protein family of receptors that respond to stimuli outside of a cell, and trigger an intracellular response. Within this family lies a subset of receptors, known as Opsins, which are responsible for the conversion of light into a biological signal. Melanopsin is one such Opsin that is found in intrinsically photosensitive retinal ganglion cells (ipRGCs) and has been shown to affect circadian photoentrainment and pupillary constriction. While the full phototransduction pathway of melanopsin remains unelucidated, we suggest that melanopsin is internalized after activation by light and deactivation by β-arrestin. We additionally suggest that internalization accounts for the long term adaptation of Melanopsin, but also that a calcium-feedback mechanism is involved in short term adaptation. To test this hypothesis, we synthesized GFP-tagged melanopsin constructs in a mammalian expression vector, PMT3, through cassette mutagenesis and expressed these constructs in Human Embryonic Kidney (HEK) cells. We then assayed the localization of melanopsin within the cell using confocal microscopy. Preliminary results from confocal imaging confirms internalization of the melanopsin constructs  in HEK cells. Similar constructs were used in a serial calcium imaging assay. This phenomenon is modelled by a series of stoichiometric equations based on the underlying biological processes that are converted to ordinary differential equations (ODEs).