# DE Seminars: Fall 2009

#### Monday September 14

Title |
A reaction/diffusion system with a very fast reaction |

Speaker |
Thomas Seidman Department of Mathematics and Statistics UMBC |

**Abstract:**

A variety of settings involve reaction/diffusion systems in a thin film or membrane, e.g., in the `film’ surrounding an individual bubble in a bubble reactor. With suitable scaling, most reactions are negligible but it remains necessary to consider some few fast rections.

Here, we consider a model problem involving a compound reaction [2A+B–>*], consisting of an extremely fast reaction [A+B–>C] (producing the intermediate compound C) coupled with a somewhat slower reaction [A+C–>*]. We are interested in what happens in the limit as this fast reaction rate goes to infinity. For the steady state problem in one space dimension, it has been known that the solution goes to a well-defined limit and we now see how that result can be obtained in the time-dependent context in n spatial dimensions.

[This is joint work with A.Muntean (Eindhoven).]

#### Monday September 28

Title |
Modeling the regulation and control of free radicals and uncoupling proteins in pancreatic beta-cell mitochondria |

Speaker |
Will Heyett National Institutes of Health |

**Abstract:**

Pancreatic beta-cells sense the ambient blood-glucose concentration and secrete insulin to signal other tissues to take up glucose. Mitochondria play a key role in this response as they metabolize nutrients to produce ATP and reactive oxygen species (ROS), both of which are involved in insulin secretion signaling. I will present a mathematical model of beta-cell mitochondrial respiration, ATP synthesis, and ROS production and control in response to glucose and fatty acid stimulation. The model is based on data available in the literature and previously developed models. It is consistent with a number of experimental observations reported in the literature. Most notably, it captures the nonlinear rise in the proton leak rate at high membrane potential and the increase in this leak due to uncoupling protein (UCP) activation by ROS. The functional forms used to model ROS production and UCP regulation yield insight into these mechanisms, as many details have not yet been unraveled in the experimental literature. We will examine the short- and long-term effects of UCP activation inhibition and changes in the mitochondrial density on mitochondrial responses to glucose. I will show results that support the hypothesis that long-term fatty acid exposure may inhibit glucose-stimulated insulin secretion, and suggest that increasing mitochondrial density while decreasing UCP activity may be an effective way to increase glucose-stimulated insulin secretion while decreasing oxidative stress. I will also discuss how the model may also be useful in a clinical setting, such as to predict the insulin secretion rate and quantify beta-cell function from the glucose and fatty acid profiles of an individual.

#### Monday October 5

Title |
Efficient Simulation of Reaction-Diffusion with a Fast Reaction in the Asymptotic Limit using COMSOL Multiphysics |

Speaker |
Aaron Churchill Department of Mathematics and Statistics |

**Abstract:**

We study a reaction-diffusion system where one reaction is much faster than the other reaction. As the rate of this fast reaction increases, the width of the reaction interface becomes much smaller, so numerical simulation of the system becomes more difficult and costly. Thus we are interested in the asymptotic limit as the large rate goes to infinity. In the limit, we can define an equivalent model with better numerical characteristics. This equivalence is demonstrated first by analytic definition and second by direct simulation using COMSOL Multiphysics. Efficiency and accuracy are also compared for several reaction rates and the symptotic limit to demonstrate the equivalence of the two component model to the three species model in the asymptotic limit.

[This is collaborative work between Aaron Churchill, Guan Wang, Dr. Matthias K. Gobbert, and Dr. Thomas I. Seidman ).]

#### Monday October 12

Title |
Mathematical Reductions of Intracellular Signaling in a Pancreatic Beta Cell |

Speaker |
Brad Peercy Department of Mathematics and Statistics UMBC |

**Abstract:**

In response to food, pancreatic beta cells secrete the protein, insulin. To accomplish this there are electrical and biochemical cascades within the cell, which have both short term and long term effects. We focus on the biochemistry and, specifically, on the reaction of Protein Kinase A and its diffusion into the nucleus as a long term effect of the signaling cascade. However, to account for experimentally observed delays we propose a rapid buffer at the nuclear membrane. Furthermore, the effective diffusion due to this rapid buffer is proposed to be the slowest interaction in the system. We non-dimensionalize and using a small parameter we further reduce the system and predict a novel, biophysically relevant mechanism for nuclear translocation of Protein Kinase A.

#### Monday October 19

Title |
Autoantigenicity or pathogenicity? What is the difference anyways? |

Speaker |
Anmar Khadra NIH |

**Abstract:**

Recent experimental evidence suggests that antigenic stability facilitates antigen shuttling from target tissue to dendritic cells (DCs), enabling cross-priming of naive T cells. On the other hand, antigenic stability affects the efficiency of peptide-MHC (p-MHC) complex formation, altering a target cell’s susceptibility to killing by the resulting cytotoxic T-lymphocytes (CTLs). Using a mathematical model, we show how antigenic stability and p-MHC production efficiency interplay in autoantigenicity and pathogenic potential of target cell proteins in autoimmune disease. We consider protein allocated to both rapidly degraded versus stable functional pools (fractions f),contributing, with relative efficiency η, to p-MHC presentation on a target cell, as well as to cross-presentation on a DC; we analyze the combined effect of these parameters. Our results suggest that autoantigenicity and pathogenicity (ability to elicit T cell activation vs. target cell lysis) are not equivalent, and that pathogenicity peaks at low to moderate levels of autoantigenicity.

#### Monday November 9

Title |
Math buzz |

Speaker |
Thomas Seidman Department of Mathematics and Statistics UMBC |

**Abstract:**

We view `buzz’ as a characteristic aspect of communication/interaction involving novelty and a Matthew effect for the topic and the implication of affective subtexts for the population.

While buzz has always been present, there has been little effort to model its dynamics; in any case, these have been profoundly changed in recent years by the advent of modern telecommunications. In this talk we make some attempt at developing a model (comparable to epidemiological models) for the spread/diffusion of buzz as it may relate to some particular topic. Thus, this involves modeling both a population space and a topic space, preferably as continua, as well as the dynamics.

This remains very much work-in-progress and I am looking forward to suggestive comments.

#### Monday December 7

Title |
Fast Solvers for Models of Fluid Flow with Spectral Elements |

Speaker |
P. Aaron Lott National Institute of Standards and Technology |

**Abstract:**

Numerical simulation of fluid dynamics allows for improved prediction and design of natural and engineered systems such as those involving air, water and blood. Due to variations in inertial and viscous forces, such systems routinely involve dynamics that occur on disparate length and time scales. In order to numerically simulate these dynamics, intricate mathematical modeling and computational methods are required.

Numerical solvers used in fluid simulations have traditionally been based on fast Poisson solvers. Recent advances in solution techniques for convection-diffusion systems based on multigrid and domain decomposition strategies have enabled the development of new and efficient techniques for simulating fluid systems. We will introduce a new technique for solving convection-diffusion systems based on a spectral element discretization and discuss how this can be used as a primary component of a block preconditioning strategy for solving steady incompressible fluid flow problems. Our technique is centered on domain decomposition which uses fast diagonalization to efficiently compute dense subdomain interiors.