1. Simulating the Immune System Martin Weigert Department of Molecular Biology Steven Kleinstein, Erich Schmidt, Tim Hilton, J.P. Singh Department of Computer Science Philip E. Seiden IBM Research and Department of Molecular Biology

2. IA 2000 Program in Integrated Computer and Application Sciences PICASso C S PPPL Astro Geo BIO Engg. GFDL Genomics Finance Foster interdisciplinary research & train a new breed of researcher

3. IA 2000 Why simulate the immune system?  Understand the big (system-level) picture  Compared to lab experiments simulations are cheap, easy and quick!  Make difficult or impossible measurements  Help focus experiments  Test “wild” theories in the privacy of your office

4. IA 2000 How to simulate the immune system?  Ordinary (or Partial) Differential Equations  Generalized Cellular Automata  Statistical model, etc... Ab 2 Ab 3 Ab n Ab 1 Ag 2 Ag 3 Ag m Ag 1

5. IA 2000 (Takahashi et al. J. Exp. Med., 187:885 1998) Example: Modeling Affinity Maturation B B Ag B B

6. IA 2000 Germinal Center: Germinal Center: The site of affinity maturation Immunity 1996 4: 241–250 Germinal Center http://www.chemistry.ucsc.edu/ Mouse Spleen

7. IA 2000 Developing a mathematical model Many parameters are based on experimental measurements Light-Zone B cell Affinity Ag XiXi CiCi B cell - Antigen Complex BiBi Dark-Zone B cell flow bind unbind

8. IA 2000 Oprea-Perelson Model Equations Oprea, M., and A. Perelson. 1997. J. Immunol. 158:5155. A complex model that includes many details

9. IA 2000 Simulated Germinal Center Dynamics

10. IA 2000 Extending the state-of-the-art... Shortcomings of current models  Typical Response  Qualitative validation  Average-case dynamics  Mechanism of selection is implicit Contributions of our work  Specific Response  Quantitative validation  Average & Distribution  Mechanism of selection is explicit

11. IA 2000 Validating model with data from the oxazolone response (Berek, Berger and Apel, 1991)

12. IA 2000 Dynamics of Individual Germinal Centers In addition, response tends to be all-or-none (Ziegner, Steinhauser and Berek, 1994) Single Founder Single Founder

13. IA 2000 Pitfalls of Differential Equations Implicitly model average-case dynamics and have no notion of individual cells Develop discrete/stochastic implementation of the model Follows individual cells Predicts distribution of behaviors

14. IA 2000 Run simulation 500 times to simulate a spleen’s worth of germinal centers Making a discrete/stochastic simulation  Fixed-increment time advance framework  Assume Poisson processes  Use 1-e -   t to calculate event probability  Random numbers determine occurrence Use CS-MPI cluster to run this embarrassingly parallel program

15. IA 2000 Conclusions of Simulation Study The standard model cannot explain dynamics within individual germinal centers Propose extension to standard model Various assumptions necessary for agreement  Suggest Experiments

16. IA 2000 Visualization Using the Display Wall How does clonal tree ‘shape’ reflect the underlying dynamics of the germinal center

17. IA 2000 Using Clonal Trees to Measure Selection Pressure (Hilton, Singh and Kleinstein, 2000)

18. IA 2000 IMMSIM A cellular-automata based model of the complete immune response

19. IA 2000 For more information check out www.cs.princeton.edu/immsim For more information check out www.cs.princeton.edu/immsim