Toward Quantitative Simulation of Germinal Center Dynamics Steven Kleinstein Dept. of Computer Science Princeton University J.P. Singh J.P. Singh Dept. of Computer Science Princeton University With continual guidance from: Martin Weigert Dept. of Molecular Biology Princeton University Philip E. Seiden IBM Research Center, Dept. of Molecular Biology

Affinity Maturation (Takahashi et al. J. Exp. Med., 187: ) B cells with affinity-increasing mutations are selected for binding to antigen

The Germinal Center Physical site of B cell hypermutation and selection Spleen Germinal Center Immunity : 241–250

Experimental studies have elucidated the basic molecular mechanisms underlying the germinal center reaction. (e.g., hypermutation, FDC binding, Apoptosis) However, it is still not well understood how these mechanisms fit together. How does the germinal center work?

Shortcomings of Current Models Common Models  Prototypical Response  Qualitative validation  Average-case dynamics  Mechanism of selection is implicit Our Goal  Specific Response  Quantitative validation  Average & Distribution  Mechanism of selection is explicit

Talk Outline Background Germinal center model during prototypical immune response How to simulate the specific response to oxazolone Experimental validation: average dynamics & individual dynamics Summary & Conclusions

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

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

Simulated Germinal Center Dynamics

Does model apply to specific system? Compare dynamics with data from oxazolone response General Parameters Response Specific Germline Affinity Effect of mutation Half-life Migration Rates Physical Capacity Key Mutations are highly selected in germinal center

Experimental Validation Step #1 (Berek, Berger and Apel, 1991) The average dynamics of germinal centers

Experimental Validation Step #2 The dynamics within individual germinal centers (Ziegner, Steinhauser and Berek, 1994) Single Founder (all-or-none) Single Founder (all-or-none)

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

Model Differs From Experiment Model predicts  7 founding cells per germinal center

Limiting the Number of Founders Affinity-Dependent Selection Proliferate & Diversify Decreased Generation (e.g., lower mutation rate) Decreased Selection (e.g. lower probability of recycling) Memory Death Many hypothesis can be tested by changing parameter values

Affinity Maturation  Founders Average Number of Founders R2R2

Parameter changes alone cannot bring simulation into strict agreement with data on average and individual dynamics simultaneously Two possibilities... Data not correctly interpreted Changes to model are necessary Two possibilities... Data not correctly interpreted Changes to model are necessary

Is Problem Data Interpretation? The Case for Multiple Founders Can be tested by collecting more data, or stronger statistical tests

Can Extending the Model Help? Affinity-Dependent Selection Proliferate & Diversify Memory Death Allow selected cells an advantage, independent of affinity Motivation: processes which reduce number of founders restrict the growth rate of the actual founder

Extended Models Produce Agreement Single founder predicted Extensions can be tested by experiment

 Applied Oprea-Perelson to Oxazolone Allows prediction of specific experiments  Quantitative Validation Predicts average GC dynamics Fails to predict individual GC behavior  Analysis  Two Possibilities Experimental data is not correctly interpreted –Too limited, need to collect more –Develop stronger statistical tests Extensions to OP model are necessary Summary & Conclusions