1. 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 {dlchao,forrest}@cs.unm.edu Department of Pathology University of New South Wales m.davenport@unsw.edu.au Theoretical Biology and Biophysics Los Alamos National Laboratory asp@t10.lanl.gov 123 IEEE Computer Society Bioinformatics Conference Stanford, California August 11-14, 2003

2. 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. 3 Immunological models ● Biological ● Mathematical ● Computer Three approaches to immunological modeling:

4. 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. 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. 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. 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. 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. 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. 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. 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), 6833-9. 2000.

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. 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. 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. 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 ( dlchao@cs.unm.edu ) if you are interested.

16. 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. 17 Thank you! http://www.cs.unm.edu/~dlchao dlchao@cs.unm.edu