Systems Science Seminar|
Analyzing the Cyton Model of Immune Regulation: A Mathematical Approach to Immunology
Vijay G. Subramanian
The Hamilton Institute, NUIM, IRELAND
Thursday, January 28, 2010|
4:00pm - 5:00pm
About the Event
A key step during an adaptive immune response is the proliferation of lymphocytes for five to twenty five cell divisions, followed by their stopping to divide and dying over a period of weeks. In this talk, starting with a brief primer on the adaptive immune response, we will present analysis of a cell-level stochastic model of lymphocyte population dynamics, called the Cyton Model. This was introduced by Hawkins et al. based on extensive flow-cytometry data. The model assumes stochastic values for division and survival times for each cell in a responding population. Experimental evidence indicates that the choice of times is drawn from a skewed distribution such as the lognormal, with the fate of individual cells being potentially highly variable. For this reason we calculate the higher moments of the model so that the expected variability can be determined. To do this we formulate a new analytic framework for the cyton model by introducing a generalization to the Bellman-Harris branching process. From the analysis we conclude that the immune response is robust and predictable despite the potential for great variability in the experience of each individual cell.
One drawback of flow-cytometry data is that individual cells cannot be tracked, so that it is not possible to investigate dependencies in the fate of cells within family trees. In the absence of this information, while the Cyton Model abandons the assumption of independence of lifetime and progeny number, it assumes that the fates of progeny are stochastically independent. However, new experimental observations of lymphocytes show that the fates of cells in the same family tree are not stochastically independent, e.g., Hawkins et al. Data from these experiments demonstrate that the death-or-division fates of cells in the same generation within a founding cell's family tree are strongly correlated, while there is little correlation between cells of distinct
generations and between cells in distinct family trees. We then investigate the impact of such correlations on the predicted expected variability of cell population size. Mathematically we conclude that while the introduction of correlation structure leaves the mean population size unchanged from the Cyton Model, the variance of the population size distribution is typically larger. Biologically, through comparison of model predictions for Cyton Model parameterizations determined by in vitro and in vivo experiments, we deduce that if collaterally consanguineous correlation extends beyond cousins, then the immune response is less predictable than would be concluded from the original Cyton Model.
Dr. Vijay G. Subramanian received the B.Tech. degree from IIT Madras,in 1993, the M.S. degree from the Indian Institute of Science, Bangalore, in 1995, and the Ph.D. degree from the University of Illinois at Urbana-Champaign, Urbana, in 1999. From 1999 to 2006, he was with the Networks Business, Motorola, Arlington Heights, IL where he worked on developing wireless scheduling algorithms deployed in many of Motorola's wireless data products. Since May 2006 he is a Research Fellow at the Hamilton Institute, NUIM, Ireland. His research interests include information theory, communication networks, queueing theory, mathematical immunology and applied probability.
Contact: ANN Pace
Sponsor: University of Michigan
Open to: Public