1. Toward Quantitative Simulation of Germinal Center Dynamics Toward Quantitative Simulation of Germinal Center Dynamics Biological and Modeling Insights from Experimental Validation Department of Computer Science, Princeton University Steven Kleinstein Steven Kleinstein stevenk@cs.princeton.edu J.P. Singh J.P. Singh jps@cs.princeton.edu

2. DUICMI 2000 Talk Outline Germinal center model during typical immune response How to simulate the specific response to oxazolone Experimental validation: average dynamics - individual dynamics Why the model fails and how to fix it Preliminary results using extended model

3. DUICMI 2000 The Oprea-Perelson Model (Liu et al. Immunity 1996 4: 241) Includes mechanism underlying affinity maturation Oprea, M., and A. Perelson. 1997. J. Immunol. 158:5155. Affinity-Dependent Selection Proliferate & Diversify Dark-Zone Centroblasts Light-Zone Centrocytes Memory Death

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

5. DUICMI 2000 Simulated Germinal Center Dynamics Seed GrowMature

6. DUICMI 2000 Does model apply to specific system? Compare dynamics with data from oxazolone response General Parameters Response Specific Affinity & Mutation: Germline k on & k off Transition Probabilities Affinity Factor Half-life Migration Rates Physical Capacity

7. DUICMI 2000 Experimental Validation Step #1 (Berek, Berger and Apel, 1991) The dynamics of splenic germinal center B cells Among cells with canonical receptor, Key Mutation is highly selected

8. DUICMI 2000 Searching Parameter Space Two selection pressures: Rescue from apoptosis Competition for antigen Two selection pressures: Rescue from apoptosis Competition for antigen NOTE: Lower R 2 is better fit

9. DUICMI 2000 Agreement (under realistic assumptions) But, this is not the whole story...

10. DUICMI 2000 Experimental Validation Step #2 The dynamics within individual germinal centers (Ziegner, Steinhauser and Berek, 1994) Single Founder Single Founder

11. DUICMI 2000 Experimental Validation Step #2 Statistical model for NP response showing all-or-none property (Radmacher, Kelsoe and Kepler, 1998) The dynamics within individual germinal centers

12. DUICMI 2000 A New Implementation is Needed Differential equations implicitly model average-case dynamics and have no notion of individual cells Create new discrete/stochastic simulation of the Oprea-Perelson model Follows individual cells Predicts distribution of behaviors

13. DUICMI 2000 Model Differs From Experiment Model predicts  6 founding cells Model predicts  6 founding cells

14. DUICMI 2000 The Root of the Problem Too many high-affinity clones, too soon Additional mechanisms for “overlooking” potential founders have been proposed (Radmacher, Kelsoe and Kepler, 1998)

15. DUICMI 2000 Implementing Rare Selection Decrease the probability of recycling Affinity-Dependent Selection Proliferate & Diversify Dark-Zone Centroblasts Light-Zone Centrocytes Memory Death

16. DUICMI 2000 The Effect of Rare Selection

17. DUICMI 2000 A Fundamental Problem Selection is on the critical path to clonal dominance Affinity-Dependent Selection Affinity-Independent Proliferation Dark-Zone Centroblasts Light-Zone Centrocytes Memory Death

18. DUICMI 2000 Fixing the Oprea-Perelson Model Selected cells have a faster effective division rate Affinity-Dependent Selection Selection-Dependent Proliferation Dark-Zone Centroblasts Light-Zone Centrocytes Memory Death

19. DUICMI 2000 Preliminary Agreement with Experiment Model predicts  1 founding cell Model predicts  1 founding cell

20. DUICMI 2000  Oprea-Perelson model (applied to oxazolone) Predicts average GC dynamics Fails to predict individual GC behavior  Different mechanisms are required for: Selection of high-affinity founder Clonal dominance  Extended Oprea-Perelson model works - so far Summary & Conclusions

21. DUICMI 2000  Quantitative analysis of extended model Develop optimization algorithms  Incorporate additional validation constraints Size, Mutation, Clonal Trees, etc.  Incorporate additional biological constraints Spatial aspects, biased mutation, etc.  Apply model to other experimental systems Future Work