2007 Summer Graduate Program
This year the program will focus on Systems Physiology. The program leaders are Jim Keener and Chiu-Yen Kao. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following two weeks are spent working on guided team projects and participating in a mini-conference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergraduates will also be considered.
The 2007 Summer Program dates are July 23 - August 10.
Lecturer: Jim Keener
Title: Mathematical Physiology
In these lectures Keener will give an introduction to mathematical models of cellular physiological processes, based on material found in Keener and Sneyd, Mathematical Physiology. Included will be discussion of enzyme kinetics and biochemical reaction networks, cellular transport processes (channels, transporters, ATPases), membrane excitability, calcium signaling, cell regulatory processes, bursting and secretion, cellular communication and coupling, and waves in continuous and discrete media. The lectures will assume familiarity with ordinary and partial differential equations, and some understanding of stochastic processes (Markov processes).
Computer labs: Chiu-Yen Kao
Week 1 |
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| Monday, July 23 | |||
| 9:00-10:00am | Jim Keener - PDF | ||
| 10:30-11:30am | Jim Keener - PDF | ||
| 2:00-4:00pm | Computer lab: Chiu-Yen Kao | ||
| Tuesday, July 24 | |||
| 9:00-10:00am | Jim Keener - PDF | ||
| 10:30-11:30am | Jim Keener - PDF | ||
| 2:00-4:00pm | Computer lab: Chiu-Yen Kao | Wednesday, July 25 | |
| 9:00-10:00am | Jim Keener - PDF | ||
| 10:30-11:30am | Jim Keener - PDF | ||
| 2:00-4:00pm | Computer lab: Chiu-Yen Kao | Thursday, July 26 | |
| 9:00-10:00am | Jim Keener - PDF | ||
| 10:30-11:30am | Jim Keener - PDF | ||
| 2:00-4:00pm | Computer lab: Chiu-Yen Kao | ||
| 4:00-5:15pm | Presentations of projects by project leaders | Friday, July 27 | |
| 9:00-10:00am | Jim Keener | ||
| 10:30-11:30am | Jim Keener | ||
| 2:00-4:30pm | Project assignments | ||
Teams work on projects: Monday, July 30 - Thursday, August 9
Team projects: Thursday, August 9 - Friday, August 10
Project 1: Collagen fiber formation in dermal wound healing
Project Leader: Richard Schugart
Presentation: PDF
Partcipants: Richard Gejji, Humberto Perez-Gonzalez, and Ying Wang
An adult dermal wound heals with the formation of scar tissue. An important factor in determining the quality of the healed tissue is the ratio between different kinds of collagen fibers. The project will develop a mathematical model of the scarred tissues, and compare it with healthy tissue. The model will involve a system of ODEs.
Project 2: Modelling the mechanical interactions between cells and biological gels
Project Leader: Ed Green
Partcipants: Genevieve Brown, Ozge Ozcakir, Hyejin Park, and Zeynep Teymeroglu
When grown in vitro, cells are frequently seeded into biological gels, such as collagen. The mechanical properties of the gel (such as stiffness, alignment of fibre in the microstructure, etc.) affect the architecture of the tissues formed by the cells. These cell-gel interactions are currently being investigated by a multidisciplinary team led by Dr Keith Gooch in the Department of Biomedical Engineering. In this project, we will investigate hypotheses for how cells can compact the surrounding gel, and how the fibrous gel microstructure may affect this process. Our models will be validated against experimental results from Dr Gooch's lab, and data from the literature.
Whilst it is up to the group to decide on their approach to the problem, it is suggested that previous experience of mathematical modelling using partial differential equations would be helpful, as would some knowledge of continuum mechanics (eg. fluid mechanics).
- Suggested reading:
- R. K. Sawhney and J. Howard,'Slow local movements of collagen fibres by fibroblasts drive the rapid global self-organisation of collagen gels', J. Cell Biology,2002,157 (6), p1083-1091.
- T. Korff and H. G. Augustin, 'Tensional forces in fibrillar extracellular matrices control directional capillary sprouting', J. Cell Sci., 1999,112, p3249-3258.
- A. Tosin and D. Ambrosi and L. Preziosi,'Mechanics and chemotaxis in the morphogenesis of vascular networks', Bull. Math. Biol., 2006, 68(7), p1819-1836.
Project 3: TB Vaccine Strategies
Project Leader: Barbara Szomolay
Partcipants: Sungwoo Ahn, Aaron Brown, and Robert McDougal
Tuberculosis is a major health problem causing more than 2 million deaths annually. The current vaccine, BCG is the most widely used vaccine in the world, but it provides only partial protection against the disease (estimates of protection range from 0-80%) and in particular in the high endemic regions BCG has failed to control TB. Therefore, a new vaccine is needed that can prevent new cases of tuberculosis, estimated at 8-10 million a year. One approach to increase the efficacy of BCG could be to add genes from M. tuberculosis encoding proteins (ESAT-6, Ag85A, and Ag85B) known to mediate protection as subunit vaccines. It has been shown that a vaccination with a fusion protein consisting of Ag85B and ESAT-6 promoted strong immune response, which was highly protective against TB in the mouse and non-human primate models. We aim to model these two vaccine strategies mathematically via a set of ordinary differential equations and to compare the results with real data.
J. Dietrich, C.V. Lundberg, and P. Andersen, TB vaccine strategies - What is needed to solve a complex problem?, Tuberculosis, Vol. 86, 2006.
Project 4: Creating and Analyzing a Modular Model of Apoptosis
Project Leaders: Baltazar Aguda and Chiu-Yen Kao
Presentation: PDF
Partcipants: Semik Ghosh, Heather Harrington, Ken Ho, and K.C. Tung
Apoptosis, or programmed cell death, is triggered either by extrinsic factors (e.g. certain cytokines that dock on cell membrane receptors) or intrinsic factors (e.g. cytochrome c released from mitochondria due to intracellular stress). Both types of death factors induce the activation of caspases -- proteolytic enzymes that chew up proteins. The aims of this project are: (1) to integrate the extrinsic and intrinsic pathways of apoptosis into a comprehensive network model, and (2) to develop a computer program to solve the dynamical equations of the model and explore the regions of parameter space where all-or-none decisions of cell death are taken, and, if possible, determine analytic expressions involving a set of key parameters that controls cell death decision.
[Reference: Legewie E, et al. (2006) PLoS Computational Biology 2(9): e120., and Refs.(103)-(105) cited at the end of this paper.]
Project 5: Mathematics, Cell metabolism and Public Health
Project Leader: Paula Grajdeanu
Presentation: PDF
Partcipants: Han Han, James Sharpnack, and David Tello
The purpose of the project is to use mathematics to study some aspects of cell metabolism, in particular the methionine metabolism.
The methionine cycle is important for the regulation of homocysteine, an important risk factor for heart disease, and for the control of DNA methylation. Both hyper- and hypomethylation have been proposed as crucial steps in chains of events that turn normal cells into cancerous cells.
A mathematical model will be developed based on standard biochemical kinetics. The model consists of four differential equations that can be solved to give the time course of the concentrations of the four main substrates in the cycle under various circumstances. We shall conduct computational "experiments" that give understanding of the regulatory behavior of the methionine cycle under normal conditions and the behavior in the presence of genetic variation and dietary dificiencies.
Project 6: Modeling the control of solid tumor growth by cytotoxic T-lymphocytes
Project Leader: Anastasios Matzavinos
Presentation: PPT
Partcipants: Sayanti Banerjee, Badal Joshi, Haiyan Tian, and Xueying Wang
This project focuses on tumor immunology and, in particular, the dynamics of the interaction of cytotoxic T-lymphocytes (a special type of white blood cell) with specific types of tumor cells. The aim of the project is to develop predictive mathematical models describing the attack of tumor cells by lymphocytes in a small, multicellular tumor, without necrosis and at some stage prior to tumor-induced angiogenesis. Attention will be focused upon the well-documented phenomenon of cancer dormancy and the m echanisms by which tumors escape immune defenses.
