1. Why are there so few key mutant clones? Why are there so few key mutant clones? The influence of stochastic selection and blocking on affinity maturation in the germinal center A small number of key somatic mutations lead to high-affinity binding in the anti-hapten immune responses to 2- phenyl-5-oxazolone (Ox) and (4-hydroxy-3-nitrophenyl)acetyl (NP). Current models of the germinal center hold that B cells carrying these key mutations are preferentially selected for expansion within the germinal centers. However, Radmacher et al. have shown that key mutants are observed in vivo significantly less frequently than expected by these well-known models. To account for this finding, they propose that selection is a stochastic process where key mutants may be overlooked by positive selection or recruited out of the germinal center. While acknowledging that a minimal amount of stochastic selection is probably unavoidable in the germinal center, we instead propose a structural explanation for the key mutant discrepancy. This model is based on the existence of a large number of blocking mutations whose presence can prevent the ability of key mutations to confer high affinity. Using mathematical modeling and computer simulation, we have studied the quantitative and qualitative effects that stochastic selection and blocking can have on the dynamics of the germinal center. Predicted effects have been compared with existing experimental data in order to understand the extent to which each mechanism contributes to the Ox and NP responses in vivo. Our results show that both models can reconcile the key mutant discrepancy. However, the blocking model accounts for other aspects of experimental data that are not predicted by the stochastic selection model. In particular, the blocking model is consistent with the observation that, compared with other clones, key mutants generally exhibit a higher number of mutations per sequence in the Ox response, but a lower number in the NP response. In addition to comparing these models with existing experimental data, we make a number of specific predictions that can be tested by future in vivo experiments to obtain further insights and validation. References: Radmacher, M. D., G. Kelsoe, and T. B. Kepler. 1998. Predicted and inferred waiting times for key mutations in the germinal centre reaction: Evidence for stochasticity in selection. Immunology and Cell Biology 76:373. Steven H. Kleinstein (stevenk@cs.princeton.edu) and Jaswinder Pal Singh, Princeton University

2. Key Mutations in Ox and NP Responses Frequency of key mutants followed in micro-dissection studies Small number of Key Mutations increase affinity  10-fold and are efficiently selected in germinal centers

3. Expected Rate of Key Mutant Production In the Ox response, theory predicts 8 key mutants per day! According to theory, in NP response… 2000Dividing B cells 2divisions per day 2daughter cells per division 10 -3 Mutation rate 0.34Micro-sequence specificity  0.20Transistion/transversion bias 0.54key mutants per day According to theory, in NP response… 2000Dividing B cells 2divisions per day 2daughter cells per division 10 -3 Mutation rate 0.34Micro-sequence specificity  0.20Transistion/transversion bias 0.54key mutants per day In the NP response, one key mutant is produced every other day

4. Theory and Experiment are Inconsistent How can we resolve this key mutant discrepancy? Experiments suggest that key mutant establishment is rare event… most germinal centers have no key mutants, all descended from single ancestor According to theory, rate of key mutant formation is high… most germinal centers have key mutants, descended from independent ancestors  Cells without key mutations Independent key mutant lineages

5. Although H  Q is over 2x more likely to occur at the DNA level, it is observed significantly less frequently than H  N. Partial Resolution of Key Mutant Discrepancy in Ox Hypothesis: H  Q requires second mutation Y  F for high affinity Germline…ATGCACTGGTACCAG…Low Affinity# Sequences Key Mutant (H  N)…ATGAACTGGTACCAG…High Affinity(54) Key Mutant (H  N)…ATGAACTGGTTCCAG…High Affinity(65) Key Mutant (H  Q)…ATGCAATGGTACCAG…Low Affinity(1) Key Mutant (H  Q)…ATGCAATGGTTCCAG…High Affinity(20) Helper Mutation Key Mutations

6. Computer Simulation Implementing Theory Follows the expansion and mutation of a B cell clone R FWRCDR SS STOP Other R LETHAL NEUTRALBLOCK STOP Other KEY NEUTRALBLOCK A Poisson distributed number of mutations occur with each division, the effect of each mutation is governed by the decision tree: B cells divide every 11-12 hours Key mutants divide every 7 hours Mutation begins day 5-7 and is associated with division Once GC capacity is reached, lower-affinity cells preferentially removed to maintain size Computer simulation is used to compare theory and experiment fBlock

7. Individual Germinal Center Behaviors Observed all-or-none distribution not predicted by model Ox Day 14-15NP Day 14-16 Key mutant discrepancy exemplified by observed all-or-none distribution of key mutants within individual germinal centers Experiments show many germinal centers have no key mutants, but those with key mutants are dominated by them

8. Mutation Dynamics in Ox and NP Responses In NP response, key mutants are less mutated then other cells Ox response data from: (Ziegner et al., 1994) and (Camacho, 1998) NP response data from: (Jacob et al., 1991), (Jacob and Kelsoe, 1992), (Jacob et al., 1993) and (Radmacher et al., 1998) OxNP Clones with key mutations  Clones without key mutations

9. Mechanisms to Resolve Key Mutant Discrepancy Stochastic Selection (Suggested by: Radmacher et al. (1998). Immunology and Cell Biology 76, 373-381) Key mutants “lost” due to probabilistic nature of selection and emigration Blocking Many mutations can block ability of key mutations to confer high affinity Methodology 1.Use computer simulation to estimate value of critical parameter providing best-fit with experimental data on fraction of cells with key mutations within individual germinal centers 2.Determine if resulting dynamics resolves the key mutant discrepancy 3.If no, rule out mechanism 4.If yes, compare predicted dynamics with other experimental data (e.g., mutation dynamics) Computer simulation used to investigate mechanisms

10. The Stochastic Selection Mechanism Lowering the probability of recycling has two effects: Lineage extinctions may explain many GC with no key mutant clones, but clonal dominance in remaining GC difficult to explain due to slower take-over Lowering the probability of recycling has two effects: Lineage extinctions may explain many GC with no key mutant clones, but clonal dominance in remaining GC difficult to explain due to slower take-over Key mutants “lost” due to probabilistic nature of selection & emigration 2n2n 2n2n Divide Apoptosis Exit GC Bind Antigen Find T help 1 1 Lethal Mutations Stochastic Selection All selection mechanisms lumped together and modeled as single critical parameter: probability of recycling (r)

11. Individual GC Behaviors with Stochastic Selection Compare simulation and experiment at maximum likelihood probability of recycling Stochastic selection can resolve the key mutant discrepancy Ox r = 0.800 NP r = 0.875 Simulation predicts single dominant founder for both responses, and…

12. Mutation Dynamics with Stochastic Selection Presence or absence of stochastic selection does not influence mutation dynamics, offers no explanation for observed pattern among key mutants in NP response —Cells without key mutations Predicted distribution of key mutants Experimentally observed key mutants OxNP Model parameters chosen to reproduce mutation pattern in cells without key mutations

13. The Blocking Mechanism Proposes that many mutations block ability of key mutations to confer high affinity Blocking has same dual effect as stochastic selection, in addition: lowers rate of mutation accumulation among key mutant clones Blocking has same dual effect as stochastic selection, in addition: lowers rate of mutation accumulation among key mutant clones Increased Blocking Ox NP —— Key Mutants ------ Other Cells Days post-immunization Number of Mutations Critical parameter is the frequency of blocking mutations

14. Individual GC Behaviors with Blocking Compare simulation and experiment at maximum likelihood frequency of blocking mutations Blocking resolves key mutant discrepancy, and… Ox fBlock = 0.75 NP fBlock = 0.35 Simulation predicts single dominant founder for both responses, and…

15. Mutation Dynamics with Blocking Presence of blocking mutations lowers effective mutation rate among key mutants only, explains mutation dynamics in both responses —Cells without key mutations Predicted distribution of key mutants Experimentally observed key mutants OxNP Model parameters chosen to reproduce mutation pattern in cells without key mutations

16. Requirement for Blocking Mechanism Prediction: blocking mutations follow distribution of contact residues Blocking can occur in both chains, but only one chain observed in experiments Why does blocking have greater impact on mutation dynamics in NP response when frequency of blocking mutations is higher in Ox response? In NP, blocking mutations may be concentrated in the observed heavy chain, and thus can have disproportionate impact on observed mutation accumulation Ox Sequence data from light chain 50% contact residues in light chain NP Sequence data from heavy chain 80% contact residues in heavy chain

17. Making Verifiable Predictions NP Blocking model predicts key mutants have lower Replacement:Silent ratio NP High variability due to limited number of sequences collected, more experimental data is required to verify prediction High variability due to limited number of sequences collected, more experimental data is required to verify prediction …but, if few sequences are sampled (as in current experiments) Clones with key mutations

18. Summary and Conclusions  Observations Key Mutant Discrepancy: Many key mutants predicted by theory, but not observed in experiments Mutation Dynamics: Key mutant clones more mutated than other cells in Ox, but less mutated in NP  Can One Mechanism Explain Both Observations?  Stochastic Selection Mechanism  NO  No explanation for mutation dynamics in NP  Blocking Mechanism  YES  Explains key mutant discrepancy & mutation dynamics Made many verifiable predictions for further insight and validation