Stochastic Stage-structured Modeling of the Adaptive Immune System Dennis L. Chao 1, Miles P. Davenport 2, Stephanie Forrest 1, and Alan S. Perelson 3 Department of Computer Science University of New Mexico Department of Pathology University of New South Wales Theoretical Biology and Biophysics Los Alamos National Laboratory 123 IEEE Computer Society Bioinformatics Conference Stanford, California August 11-14, 2003

2 Introduction ● Understand the body's response to disease. ● Explore new treatments for disease. Studying the immune system is important to: Modeling as an approach to studying the immune system: ● To run experiments difficult to perform in real life. ● To make observations impossible to make in the real world. ● To create variations of the system.

3 Immunological models ● Biological ● Mathematical ● Computer Three approaches to immunological modeling:

4 Computer modeling ● Usually individual-based modeling. ● Build a system based on description of components (cells). ● One can directly incorporate experimental findings on cell behavior into computer models. ● The process of building a model highlights gaps and inconsistencies in our knowledge. ● But individual-based modeling is computationally expensive...

5 Stochastic stage-structured modeling ● The life cycle of a cell is divided into stages. ● All cells in a given stage are assumed to be identical. ● We need only to keep track of the number of cells in each stage. ● Discrete time steps are used. ● Transitions between stages are stochastic.

6 Characteristics of our modeling approach ● Discrete populations ● Stochasticity ● Computationally efficient ● Computational cost is proportional to the number of stages (100s), not the number of cells (10 8 ). Computational efficiency Level of detail captured Individual-based models Stochastic stage-structured models Mathematical models

7 Cytotoxic T cells (CTLs) ● Clearing viral infections ● Immune system response to cancer ● Tissue graft rejection ● Some autoimmune disorders Cytotoxic T cells play an important role in: A CTL killing an influenza-infected cell

8 The CTL response to virus ● Virus reaches high levels on first exposure. ● The immune response eliminates the infection. ● Immunological memory provides protective immunity in subsequent infections by the same virus. ● Secondary response to infection is larger and faster. ● Response is specific to the pathogen.

9 Individual cell behavior ● Our model requires the specification of the behavior of individual T cells. ● We would like the aggregate behavior of a population of T cells to generate an realistic immune response. ● Therefore, our model must match experiments at 2 scales: ● Cellular behavior (studies of small populations of cells) ● Immune response (studies of the immune response of organisms)

10 Model T cell behavior ● When naïve cells are stimulated by pathogens, they become effector cells. ● Effector cells proliferate and eliminate infected cells. ● Some effector cells become memory cells, which will respond more quickly than naïve cells.

11 The programmed response ● Removing the pathogen does not affect the T cell response. ● T cells seem to have a “programmed response.” ● T cells must have state. Mercado et al., Early Programming of T cell populations responding to bacterial infection. J Immunol 165 (12),

12 Primary and secondary responses (simulated) ● Secondary response is larger and faster than the primary. ● Virus is rapidly cleared by the secondary response. ● Secondary exposure “boosts” immunological memory.

13 Programmed response (simulated) ● Eliminating antigen does not stop the immune response. ● T cells must have state for this result. ● This phenomenon is not typically captured by mathematical models, which are stateless.

14 Future experiments ● Vaccination strategies ● Prime-boost vaccinations ● Low vs. high dose vaccinations ● Effect of a mutating pathogen ● Evolution of pathogens ● Development of “escape” mutants

15 The program ● A tool for immunologists and students. ● Written in Java for portability. ● Source code will be released. ● Work in progress – no user interface or documentation yet. ● Contact me ( ) if you are interested.

16 Summary ● The model incorporates a significant amount of experimental data into a coherent framework. ● Results agree with experiments. ● The program will be available as a tool for immunological experiments.

17 Thank you!