Differential Equations Seminar: undergraduate students
Sam Giannakoulias, Tess Sheets, Jamshaid Shahir
Monday, May 14, 2018 · 11:45 AM - 12:45 PM
Speaker: Sam Giannakoulias
Title: Modeling Adaptation in the Melanopsin Phototransduction Cascade
Abstract: The mammalian retina contains three photoreceptors: rods, cones, and intrinsically photosensitive retinal ganglion cells (IPRGC's). IPRGC's, unlike rods and cones, function primarily in non-image forming vision such as circadian photoentrainment and the pupillary light response. There are five subtypes of IPRGC's, all of which express melanopsin, a G-protein coupled receptor encoded by the OPN4 gene. Although little is known regarding the exact mechanism of the melanopsin phototransduction cascade, our previous work using data obtained from M1 IPRGC cells, alongside our mathematical simulations support that the receptor functions through a Gq pathway. The goal of this study is to investigate melanopsin adaptation in M1 IPRGC's from multi-flash experiments. Our approach towards modeling melanopsin adaptation was to model calcium dynamics on some of the rate functions in hypothesized pathway. The differential equations were numerically solved using MATLAB, and then the parameters were fit to wild type experimental data. Finally, parameter sensitivity analysis determined the parameters most affected by the calcium dynamics. In the future, we hope to use our adaptation model as a backbone for the investigation of the pathway found in other IPRGC subtypes. This is a joint work with Kathleen Hoffman, Hye-won Kang and Phyllis Robinson.
Speaker: Jamshaid Shahir
Title: Studying Cell Polarization Using a Stochastic Model
Abstract: Under chemical stimulation, motile eukaryotic cells polarize in response to external stimuli. This polarization involves the recruitment of various proteins from the Rho GTPase family to the plasma membrane, where they segregate to the front or back end of the cell. Previous studies have explained the mechanisms of cell polarization using a partial differential equation (PDE) model consisting of a single active/inactive protein pair with positive feedback. The polarization of the protein is maintained in the spatial domain after a transient time, a phenomenon called wave pinning, which is characterized by a halt of a propagating wave of protein activation. In this talk, I will introduce a continuous-time Markov chain model for wave pinning, simulated by the Gillespie's algorithm, and investigate how inherent noise affects the dynamics of cell polarization. In this model, spatial compartments are used to describe the diffusion of molecules in the domain. A traveling wave model of cell polarization is then simulated and compared to results from a PDE model under various cell volumes. As the cell volume increases, similar results to the PDE model and wave pinning behavior are observed. Finally, different values of the system parameters and their impact on the wave propagation in the model are examined.
This investigation was sponsored by NIH/NIGMS MARC U*STAR T34 12463 National Research Service Award to UMBC and is supported in part by the National Science Foundation (DMS-1620403).
Speaker: Theresa Sheets
Title: Modeling the Dynamic Interactions between the Autonomic Nervous System, the Cardiovascular System, and Behavioral Performance
Abstract: Many methods have been proposed to estimate physiologic measures of autonomic nervous system (ANS) activity. One of the more prevalent methods is heart rate variability (HRV). HRV has been shown to be a correlate of ANS activity and a surrogate to mental states like stress and anxiety. Despite success in many circumstances, HRV is limited in its ability to characterize ANS activity due to the non-specific and coarse treatment of the cardiovascular system. To address this gap, we model the baroreflex response using a set of coupled delay differential equations and compare predictions of ANS activity to traditional HRV measures. We use these equations to develop a time series estimate of sympathetic effect on heart rate, parasympathetic effect on heart rate, and sympathetic effect on arterial resistance. In this work, we examine data from sixteen participants who performe a cognitive depletion task for followed by a Stroop task with continuous heart rate and blood pressure monitoring. Features from the time series were related to accuracy and reaction time in the performance of the Stroop task. Results are presented in comparison to and ultimately combined with traditional measures of HRV to quantify the relationship between measures of autonomic control and behavior. This is a joint work with Kathleen Hoffman, Joshua Crone and Justin Brooks.