1. Estimating the Mutation Rate from Clonal Tree Data Steven H. Kleinstein,Yoram Louzoun Princeton University Mark J. Shlomchik Yale University

2. Estimating the B Cell Mutation Rate Counting mutations is not sufficient, number of cell divisions at time of measurement is unknown Also, problems of mutation schedule and positive/negative selection Number of Cell Divisions Number of Mutations High Mutation Rate Low Mutation Rate Observed Number of Mutations

3. Clonal Tree Data from Micro-Dissection B cells T cells Micro-dissection Experiment Extra-follicular area in autoimmune mouse Clonal tree ‘shapes’ reflect underlying dynamics Clonal trees from sequence data based on pattern of shared mutations

4. Clonal Tree ‘Shape’ Reflects Underlying Dynamics BACD gctc BAD Initial Sequence a t a D t gct BA Investigate with computer simulation of B cell clonal expansion Simulate artificial clonal trees with known mutation rate and number of divisions Use distribution of shapes to estimate the mutation rate Compare:Rate of 0.2 division -1 for 14 divisions Rate of 0.4 division -1 for 7 divisions

5. Intermediate Vertices is Useful Measure Compare:Rate of 0.2 division -1 for 14 divisions Rate of 0.4 division -1 for 7 divisions Shape measures can supplement information from mutation counting

6. Method for Estimating Mutation Rate Find mutation rate that produces distribution of tree ‘shapes’ most equivalent to observed set of trees Assumes equivalent mutation rate in all trees, although number divisions may differ Also developed analytical method based on same underlying idea Experimental Observations Set of Observed Tree Shapes Mutation Rate Distribution of Tree Shapes Simulation of B cell expansion Number of mutations Intermediate vertices Sequences at root =

7. Experimental Data from Autoimmune Response Data consists of 28 picks from 7 mice,  200 sequences Data set particularly well-suited for estimating mutation rate Defined pick sizes provide upper-bound on clone size Small picks (< 50 cells) minimize positive selection Micro-dissection from extra-follicular areas in MRL/lpr AM14 heavy chain transgenic mice (Jacqueline William, Chad Euler, Sean Christensen and Mark J. Shlomchik) B cells (Idiotype + RF) T cells (CD3 + ) Single Micro-dissections

8. Stems Pruned to Reflect Local Expansion Closely related cells remain in close spatial proximity Data set consists of 31 trees, average 6 sequences / tree Long stems may be artifact of local micro-dissection Initial Sequence Time Mutation information retained in local branching structure Stem is removed New tree root Pick

9. Validating Methods with Limited Data Use simulation to construct artificial data sets with limited number of trees/sequences reflecting currently available experimental data Methods work even with limited number of clonal trees and sequences Results for simulation method Estimate of method precision (SD = 0.035 division -1 )

10. Mutation Rate in an Autoimmune Response Estimated mutation rate is 7 x 10 -4 – 9 x 10 -4 base-pair -1 division -1 Consider range of values for lethal mutation frequency Likely value based on FWR R:S Ratios

11. Mutation Rate in the Primary NP Response Data set consists of 23 trees, average 7 sequences / tree (Jacob et al., 1991), (Jacob and Kelsoe, 1992), (Jacob et al., 1993) and (Radmacher et al., 1998) Estimated mutation rate is greater than 3.7 x 10 -4 Data based on many large picks: Clone sizes may be very large In estimation, limited to: 10 3 in simulation estimate 10 4 in analytical estimate Positive selection clearly factor Still evaluating validity of methods for this NP data set

12. Summary & Conclusions  Mutation Rate Reflected in Clonal Tree ‘Shapes’  Developed Two Methods  Cross-Validated  Autoimmune Response  Data set well-suited for mutation rate estimation  Mutation Rate = 7 x 10 -4 – 9 x 10 -4 base-pair -1 division -1  Primary NP Response  Mutation Rate > 3.7 x 10 -4 base-pair -1 division -1  Future Improvements with Additional Data For more information: stevenk@cs.princeton.edu, www.cs.princeton.edu/~stevenk For more information: stevenk@cs.princeton.edu, www.cs.princeton.edu/~stevenk

13. Estimating the Mutation Rate from Clonal Tree Data B cell somatic hypermutation of is an important component of the immune response. However, despite its significance, precise estimates of the mutation rate do not currently exist. Micro-dissection studies of mutating B cell clones provide an opportunity to measure this rate more accurately than previously possible. Each micro-dissection provides a number of clonally related sequences which, through the analysis of shared mutations, can be genealogically related to each other. The ‘shape’ of these clonal trees is influenced by many processes including the hypermutation rate. We have developed two different methods to estimate the mutation rate based on these data. These method are applied to two sets of experimental data, one from an auto-immune response and one from the anti-hapten response to NP. In addition to comparing the results of the two procedures, we have investigated the effect on our estimate of assumptions such as the fraction of lethal mutations, and experimental decisions such as the micro-dissection pick size. Steven H. Kleinstein (stevenk@cs.princeton.edu) and Yoram Louzoun Princeton University Mark J. Shlomchik Yale University

14. Summary of Experimental Data A n Total number of cells used to generate the sequences U n Number of unique sequences used to create the tree T n The average number of mutations per sequence M n The number of unique mutations in the tree I N The number of intermediate nodes (with sampled sequences) R N The number of sampled sequences at the root of the tree Autoimmune Response Primary NP Response

15. Current Method Assumptions Common assumptions: –All trees have same underlying mutation rate –Mutation rate constant, associated with division Reasonable, but currently testing impact: –In each tree, all cells have same # divisions –No positive selection over time considered

16. Summary & Conclusions  Mutation Rate Reflected in Clonal Tree ‘Shapes’  Developed Two Methods  Cross-Validated  Autoimmune Response  Data set well-suited for mutation rate estimation  Mutation Rate = 7 x 10 -4 – 9 x 10 -4 base-pair -1 division -1  Primary NP Response  Mutation Rate > 3.7 x 10 -4 base-pair -1 division -1  Future Improvements with Additional Data For more information: stevenk@cs.princeton.edu, www.cs.princeton.edu/~stevenk For more information: stevenk@cs.princeton.edu, www.cs.princeton.edu/~stevenk