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Differential Equations Seminar

Samantha Furman, Laurel Mazur and Janita Patwardhan, UMBC

Monday, May 1, 2017
11:00 AM - 12:00 PM
Mathematics/Psychology : 401
Speaker: Samantha Furman
Title: Skeletal Muscle Atrophy:  Extending and Fitting a Mathematical Model
Abstract: Skeletal muscle atrophy occurs when there is a higher concentration of the transcription factor Forkhead box protein O1 (Foxo-1) inside the nucleus of a skeletal muscle cell than in the cytoplasm. Within a skeletal muscle cell, only dephosphorylated Foxo-1 can enter the nucleus, while only phosphorylated Foxo-1 can exit the nucleus. External stimuli such as insulin and leptomycin can activate a series of events in the cytoplasm, starting with the activation of protein kinase B (Akt) and ending with the phosphorylation of Foxo-1. Modeling the effects of these external stimuli can provide insight into how the skeletal muscle cell functions and how muscle degrades. The original model of this system was a time-dependent function with fixed parameters for the rates of phosphorylation and dephosphorylation as well as for insulin concentration. Our goal was to build on this study by shifting the fixed values of external stimuli to dynamic values and transform our time-dependent model into a dynamic model dependent on external stimuli concentration as well as time. We connected a previous model of insulin-like growth factor 1 (IGF-1) activation of Akt to our model of Akt phosphorylation of Foxo-1 in order to quantify the impact of IGF-1 on the nuclear-cytoplasmic ratio of Foxo-1. Differential equations, non-dimensional analysis, parameter optimization, and simulation conducted with MATLAB and other dynamical systems softwares were used in this study. We were able to create a functioning model that models the effects of IGF-1 on the nuclear-cytoplasmic ratio of Foxo-1. This research is a good foundation for future studies that may model other external stimuli nuclear translocation systems based on similar mathematical analyses.

Speaker: Laurel Mazur
Title: Assessing De Novo Bank Performance Using Statistical Techniques
Abstract: Newly established banks, so-called de novo banks, face different pressures when compared to their more established peers. This study attempts to look at de novo bank performance using to statistical techniques – a multinomial logit model and a Heckman selection model. Expanding on a paper written by DeYoung (2003) we will look at the determinants of various exit outcomes for de novo banks in the years leading up to the most recent financial crisis. Then, following the methodology of Balla, Prescott and Walter (2016), we will investigate the determinants of losses to the FDIC as a result of bank failure in two distinct periods – 1986-1992 and 2006-2013. Prior to the introduction of the models, detailed literature reviews on de novo banks and bank failures are provided to enhance the understanding of the institutional aspects of this study. We find that the de novo bank failure rate is significantly influenced by regional economic conditions, asset quality and the composition of the loan portfolio. We also find that an accounting variable, Interest Receivable, significantly affects both the failure rate and the losses to the FDIC as a result of failure. Regarding exit outcomes, we find similar effects of some variables across all exit outcomes though most have differing effects for one or more outcome. One particular variable of interest is the Capital Ratio, a commonly used indicator of bank resiliency and health, higher values of which appear to have a counterintuitive effect on de novo banks.

Speaker: Janita Patwardhan
Title: Analyzing a Mathematical Model of cAMP-PKA Dynamics in Pancreatic β−Cells 
Diabetes is characterized by high levels of glucose in the blood. Insulin, which helps to lower the blood glucose levels, is secreted in a pulsatile manner by pancreatic beta cells. To better understand the dynamics of insulin secretion, we studied a model of a key regulatory pathway in the process, the cyclic adenosine monophosphate (cAMP)-protein kinase A (PKA) signaling pathway. In order to examine the pulsatile nature of insulin secretion, we used phase space and bifurcation analysis to investigate the mechanism that causes oscillatory behavior in the model. Looking at various subsystems, we determined that higher levels of dynamic PKA from increased levels of dynamic cAMP lead to oscillations in the full model.