VIGRE2 Vertical Intergration of Research and Education Department of Mathematics, University of Utah

Yasmeen Hussain








Mentor: Aaron Fogelson
Major: Mathematics
Minor: Music

Summer 2007 project description:

I will work with Aaron Fogelson in the field of mathematical biology. This summer we propose to read papers related to control of the cell-cycle to learn about regulation of the cell cycle, learn how mathematical modeling has been applied to understanding this regulatory system, and gain experience in modeling and relating mathematical tools by reproducing the mathematical work in these papers. Our long-term goal is to develop original mathematical models of some aspects of cell biology and physiology.

Summer 2007 report

Fall 2007 project description:

Following our summer explorations into the properties of prototypical simple regulatory networks and their numerical implementation, especially in Matlab, I will work with Dr. Aaron Fogelson to look into more realistic and complex models of the cell cycle that have appeared in the literature. This will involve learning the relevant biology and more about the mathematics of the types of dynamical systems in these models. In addition, I will be looking more closely into "modeling process," that is, how to translate a written or pictorial description of a biological process into mathematics. The goal of this work is to gain sufficient experience to allow me to begin to think about formulating, manipulating, and studying new models of biochemical reaction networks.

Fall 2007 report

Spring 2008 project description:

Using Beltrami and Jest's paper "The role of membrane patch size and flow in regulating a proteolytic feedback threshold on a membrane: possible application in blood coagulation" as a starting point, I will work with Dr. Aaron Fogelson on learning how to, using MATLAB software, model and simulate spatially distributed biochemical reaction networks. While doing this, I will also learn about the biochemical and transport processes present in blood clotting. This will be accomplished by working through Dr. Fogelson's papers which present detailed models of blood clotting, constructed using both partial and ordinary differential equations. A goal of this work is to be able to extend these models, or simplified versions of these models, to include additional biological processes, including interactions of clotting mechanisms with innate immune response.

Spring 2008 final report

Summer 2008 project description:

I propose to continue my research with Professor Aaron Fogelson on models of blood coagulation. I am currently finishing the conversion of Fogelson's existing Fortran coagulation code to Matlab so that I can modify it. I will use this Matlab code to conduct additional parameter studies in computational experiments with the existing model equations. I will also extend the model to include some additional features of coagulation such as reactions involving factor XI and soluble tissue factors whose roles are currently the subjects of controversy in the clotting community and have not before been included in mathematical models of blood coagulation.

Fall 2009 project description:

This semester, I will be completing my work with Professor Fogelson. We now have a working model of coagulation with Factor XI included. We are in the process of conducting experiments on the model in order to test both its adherence to current biological knowledge and its adaptation to new challenges.

For example, one experiment considers the effect of Factor XI on coagulation at different levels of Tissue Factor. Another set of experiments is the modification of parameter values. Although some values were found in a comprehensive literature review, those values may have varying accuracy and other parameters were chosen by a process best known as the "educated guess." We are, therefore, making small changes to these values to see if they may affect the model's accuracy. Still another experiment is the addition of autoactivation parameters. Although autoactivation is listed by various papers as a source of activated FXI, there are no known parameters for its kinetics. In this experiment, we will be deriving our own parameters for autoactivation and observing their effect on the model.

The ultimate goal of this semester's work is a published paper detailing our work on the current model of hemostasis, especially with Factor V and Factor XI.