Stochastic Components of the Immune System Response

Assistant Professor Dejan Milutinovic, AMS Department
Friday, November 20, 2009, 2:00 pm, Interdisciplinary Sciences Building, room 231
Hosted by Physics Department
Applied Mathematics & Statistics

Abstract

Mathematical modeling of immunological data is a powerful tool
for understanding the immune system dynamics. The immune response is the
result of a large amount of interactions among individual cells. Therefore,
there exists a structural similarity of immune response models to the mass
action law model of chemical reactions. Consequently, deterministic ordinary
differential equation models are widely used in attempts to understand
experimental data trends and estimate relevant biological parameters.
Discrepancies between models and data are usually attributed either to
measurement errors, or biological parameter variations, while a small
number of data points appears to be a limiting factor for a more detailed
analysis. In the first part of my talk, I use LCMV viral infection data
providing evidence that data variations are most likely the result of
intrinsic immune system stochasticity, the so-called process noise. In the
second part of the talk, I will introduce a model of a T-cell down-regulation.
The cell is considered to be an automaton and the cell state is described by
discrete and continuous variables; therefore, the state is a hybrid and
the model is the so-called hybrid automaton. Utilizing the probability
density function evolution of the cell model hybrid state reveals details
of individual cell dynamics and overcomes limitations due to a small number
of observed time points. These results lead to the conclusion that progress in
immunology and biology in general depends not only on the development of novel
mathematical models of biological phenomena, but also on models of instrumentations
involved in experiments.