Estimating Mutation Rates from Clonal Tree Data (using modeling to understand the immune system) Steven H. Kleinstein Department of Computer Science Princeton University

The Immune System Protects the body from dangerous pathogens –viruses, bacteria, parasites Provides basis for vaccines (e.g., flu) Implicated in disease: –Autoimmune (Lupus, MS, Rheumatoid Arthritis) –Sepsis, Cancer Relatively new science, began with Jenner in 1796 Understanding will lead to better diagnostics and therapies

Why Model the Immune System? Immune response involves the collective and coordinated response of  cells and molecules Distributed throughout body –blood, lymph nodes, spleen, thymus, bone marrow, etc. Interactions involve feedback loops and non-linear dynamics Experiments often require artificial constructs High variability observed in experimental results Somatic Hypermutation: important component of response Experiments provide only a static window onto the real dynamics of immunity

Talk Outline Background Immunology 1.What are clonal trees? 2.What can we learn from them? 3.Method for estimating the hypermutation rate  Simulation Method  Analytical Method 4.Results on simulation and experimental data Summary, Conclusions and Open Problems

Germinal Center Effector Cells Overview of Humoral Immune Response Ag B B B B B Germinal Centers are the Site of Affinity Maturation (selection for cells with affinity-increasing mutations) Germinal Centers are the Site of Affinity Maturation (selection for cells with affinity-increasing mutations) B B Foreign Pathogen (Antigen) B B B

More about Germinal Centers Hundreds of germinal centers in spleen Composed of many cell types (B, T, FDC) Spatial structure that changes over time Driven by stochastic mutation process Observation involves sacrifice of animal While experiments have elucidated basic mechanisms, how these fit together is not well understood While experiments have elucidated basic mechanisms, how these fit together is not well understood

How do we learn about somatic hypermutation? 1.Inject mouse with antigen to provoke an immune response 2.Harvest spleen, cross-section and stain to identify proliferating cells B cells T cells 3.Microdissect groups of cells 4.Sequence DNA coding for B cell receptor

Experimental Microdissection Data How can we estimate the rate of mutation?

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

Clonal Tree Data from Micro-Dissection Clonal trees from sequence data based on pattern of shared mutations GermlineGGGATTCTC 1-C-----G G- 3A------GA 4A---C--GA Clonal tree ‘shapes’ reflect underlying dynamics 1(G  A) 9(C  A) (T  G) 2(G  C) 5(T  C) Germline

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 clonal trees with known mutation rate and number of divisions Compare:Rate of 0.2 division -1 for 14 divisions Rate of 0.4 division -1 for 7 divisions Use simulation to identify relevant shape measures

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 (Simulation Data)

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 (Kleinstein, Louzoun and Shlomchik, The Journal of Immunology, In Press) Also developed analytical method based on same underlying idea (Kleinstein, Louzoun and Shlomchik, The Journal of Immunology, In Press) 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 =

Simulation Method 12…d Tree 1 Tree 2 … Tree n # divisions (d) 12…d Tree 1 Tree 2 … Tree n # divisions (d) Equivalent, E(t,d) Observable, O(t,d) Used version of Golden Section Search to optimize mutation rate (  ) 2.Likelihood of experimentally observed tree t: 3.Likelihood of experimental dataset: 1.Run simulation many times to fill in equivalent and observable matrices Reasonable clone size? Same tree shape? For each mutation rate (  ) and lethal fraction ( )… t t

Validating the Simulation Method Use simulation to construct artificial data sets with limited number of trees/sequences reflecting currently available experimental data Method works even with limited number of clonal trees and sequences Results for simulation method Estimate of method precision (SD = division -1 )

Analytical Method Formulas to approximate tree shapes… Minimize error X(  ) over all experimentally observed trees (t) For each observed tree, choose number of divisions to minimize error Observed shapeCalculated shape The average number of mutations per sequence (M) The average number of sequences present at the root of the tree (R) Total number of sequences in nodes with repeated sequences (P)

Validating the Analytical Method Use simulation to construct artificial data sets with limited number of trees/sequences reflecting currently available experimental data Method works even with limited number of clonal trees and sequences

Experimental Data from Autoimmune Response Data set consists of 31 trees from 7 mice, average 6 sequences / tree 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 (William, Euler, Christensen, and Shlomchik. Science ) B cells (Idiotype + RF) T cells (CD3 + ) Single Micro-dissections

Stems Pruned to Reflect Local Expansion Closely related cells remain in close spatial proximity Mutation information retained in local branching structure Long stems may be artifact of local micro-dissection Initial Sequence Time Stem is removed New tree root Pick

Mutation Rate in an Autoimmune Response Estimated mutation rate is 0.7 x – 0.9 x base-pair -1 division -1 Consider range of values for lethal mutation frequency ( ) Likely value based on FWR R:S Ratios

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 0.9 x – 1.1 x base-pair -1 division -1 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

Summary for Estimating Mutation Rate  Mutation rate reflected in clonal tree ‘shapes’  Developed simulation and analytical methods  Synthetic datasets to estimate precision  Applied to autoimmune response & NP response  Most accurate mutation rate estimate to date  Future improvements with additional data

Noisy Optimization Can we adapt the number of runs at each parameter setting to the minimum required to determine which direction to look? How many runs should be used for each likelihood evaluation?

Bias in Simulation Method Can we remove the bias from the simulation method? No bias is present in the analytical method

Acknowledgements For more information: Yoram Louzoun (Bar-Ilan University) Mark Shlomchik (Yale University) (Kleinstein, Louzoun and Shlomchik, The Journal of Immunology, In Press)

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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

Acknowledgements For more information: Yoram Louzoun (Bar-Ilan University) Mark Shlomchik (Yale University) (Kleinstein, Louzoun and Shlomchik, The Journal of Immunology, In Press)