estimating the mutation rate from clonal tree data steven h. kleinstein,yoram louzoun princeton...
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Estimating the Mutation RateEstimating the Mutation Ratefrom Clonal Tree Datafrom Clonal Tree Data
Steven H. Kleinstein,Yoram LouzounPrinceton University
Mark J. ShlomchikYale University
Estimating the B Cell Mutation RateCounting mutations is not sufficient,
number of cell divisions at time of measurement is unknown
Also, problems of mutation schedule and positive/negative selection Also, problems of mutation schedule and positive/negative selection
Number of Cell Divisions
Num
ber
of M
utat
ions
High Mutation Rate
Low Mutation Rate
Observed Number of Mutations
Clonal Tree Data from Micro-Dissection
B cells T cells
Micro-dissection ExperimentExtra-follicular area in autoimmune mouse
Clonal tree ‘shapes’ reflect underlying dynamicsClonal tree ‘shapes’ reflect underlying dynamics
Clonal trees from sequence data based on pattern of shared mutations
Clonal Tree ‘Shape’ Reflects Underlying Dynamics
BA C D
g ct c
BA D
Initial Sequence
a t
Initial Sequence
a
D
t
g ct
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 rateUse distribution of shapes to estimate the mutation rate
Compare: Rate of 0.2 division-1 for 14 divisionsRate of 0.4 division-1 for 7 divisions
0
1
2
3
4
5
6
7
8
9
10
11
EDGES
VERTICIE
S
NODES
LEAVES
LEAF C
ELLS
INTERM
IDIA
TE VERTIC
ES
INTRM
EDIATE C
ELLS
REPEAT NODES
REPEAT CELL
S
INTERM
EDIATE N
ODES
INTERM
EDIATE N
ODE CELL
S
GERMLI
NE
UNIQUE M
UTATIO
NS
TOTAL M
UTATIO
NS
ROOT CELL
S
ANY ROOT
Ave
rag
e N
um
ber
Intermediate Vertices is Useful Measure Compare: Rate of 0.2 division-1 for 14 divisions
Rate of 0.4 division-1 for 7 divisions
0.2
0.4
0.6
0.8
1
1.2
1.4
1.5 1.7 1.9 2.1 2.3 2.5
Total Mutations Per Sequence
Inte
rmed
iate
Ver
ticie
s
Shape measures can supplement information from mutation countingShape measures can supplement information from mutation counting
Method for Estimating Mutation RateFind mutation rate that produces distribution of tree
‘shapes’ most equivalent to observed set of trees
1.E-39
1.E-37
1.E-35
1.E-33
1.E-31
1.E-29
1.E-27
1.E-25
0.10 0.20 0.30 0.40 0.50
Mutation Rate (per division)
Like
lihoo
d
Assumes equivalent mutation rate in all trees, although number divisions may differ
Also developed analytical method based on same underlying ideaAlso developed analytical method based on same underlying idea
ExperimentalObservations
Set of ObservedTree Shapes
Mutation Rate
Distribution ofTree Shapes
Simulation ofB cell expansion
Number of mutationsIntermediate vertices
Sequences at root
=
Experimental Data from Autoimmune Response
Data consists of 28 picks from 7 mice, 200 sequencesData 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+)
SingleMicro-dissections
Stems Pruned to Reflect Local Expansion
Closely related cells remain in close spatial proximity
Data set consists of 31 trees, average 6 sequences / treeData set consists of 31 trees, average 6 sequences / tree
Long stems may be artifact of local micro-dissection
Initial Sequence
Tim
e
Mutation information retained in local branching structure
Stem is removed
New tree root
Pick
Validating Methods with Limited DataUse simulation to construct artificial data sets with limited number of trees/sequences reflecting currently available experimental data
y = 1.2073x
R2 = 0.9149
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Actual Mutation Rate (per division)
Pre
dict
ed M
utat
ion
Rat
e (p
er d
ivis
ion)
Methods work even with limited number of clonal trees and sequences
Methods work even with limited number of clonal trees and sequences
Results for simulation method
Estimate of method precision(SD = 0.035 division-1)
Mutation Rate in an Autoimmune Response
Estimated mutation rate is 7 x 10-4 – 9 x 10-4 base-pair-1 division-1Estimated mutation rate is 7 x 10-4 – 9 x 10-4 base-pair-1 division-1
5.0E-04
6.0E-04
7.0E-04
8.0E-04
9.0E-04
1.0E-03
1.1E-03
0 0.1 0.2 0.3 0.4 0.5 0.6
Fraction of FWR Replacement Mutations Lethal ()
Est
imat
ed M
utat
ion
Rat
e
Simulation Estimate
Analytical Estimate
Consider range of values for lethal mutation frequency
Likely value based on FWR R:S Ratios
Mutation Rate in the Primary NP ResponseData 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 10-4Estimated mutation rate is greater than 3.7 x 10-4
1.0E-04
3.0E-04
5.0E-04
7.0E-04
9.0E-04
1.1E-03
1.3E-03
0 0.1 0.2 0.3 0.4 0.5 0.6
Fraction of FWR Replacement Mutations Lethal ()
Est
imat
ed M
utat
ion
Rat
e Simulation Estimate
Analytical EstimateData based on many large picks:
Clone sizes may be very largeIn estimation, limited to:103 in simulation estimate104 in analytical estimate
Positive selection clearly factor
Still evaluating validity of methods for this NP data set
Summary & Conclusions
Mutation Rate Reflected in Clonal Tree ‘Shapes’Developed Two Methods Cross-ValidatedAutoimmune Response
Data set well-suited for mutation rate estimationMutation Rate = 7 x 10-4 – 9 x 10-4 base-pair-1 division-1
Primary NP ResponseMutation Rate > 3.7 x 10-4 base-pair-1 division-1
Future Improvements with Additional Data
For more information:
[email protected], www.cs.princeton.edu/~stevenk
For more information:
[email protected], www.cs.princeton.edu/~stevenk
Estimating the Mutation RateEstimating the Mutation Ratefrom Clonal Tree Datafrom 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 ([email protected]) and Yoram LouzounPrinceton University
Mark J. ShlomchikYale University
Summary of Experimental DataAn Total number of cells used to generate the sequences
Un Number of unique sequences used to create the tree
Tn The average number of mutations per sequence
Mn The number of unique mutations in the tree
IN The number of intermediate nodes (with sampled sequences)
RN The number of sampled sequences at the root of the tree
Autoimmune Response Primary NP ResponseMouse Pick/Tree An Un Tn Mn In Rn 2205 5a2,3 30 7 1.38 11 0 2 2205 5a5 20 6 1.00 7 0 2 2205 5f1,2.K 100 2 0.17 1 0 5 2205 5f1,2.L 100 1 0.00 0 0 5 2205 5f1,2.M 100 1 0.00 0 0 2 2540 11f,g 85 6 2.17 7 2 0 2540 11g1 30 2 1.20 3 0 0 4270 10j1 10 1 0.00 0 0 6 4270 10j2 20 3 1.83 6 1 0 5281 14c1 30 3 6.00 3 1 0 5281 14a1,3 20 3 0.18 2 0 9 5281 14c2 10 3 2.00 4 1 2 7976 16b3.A 15 3 2.17 6 1 0 7976 16b3.B 15 2 1 0 1 7976 16c1 50 1 0.00 0 0 5 7976 16c2.A 20 3 0.29 2 0 5 7976 16c2.B 20 1 0.00 0 0 7 7976 16d1 20 3 0.25 2 0 6 7976 16d2 20 2 0.14 1 0 6 7976 16c3.A 10 2 0.75 1 0 1 7976 16c3.B 10 1 0.00 0 0 1 7983 17a4.A 10 2 0.33 2 0 3 7983 17a4.B 10 2 0.25 1 0 2 7983 17a4.C 10 1 0.00 0 0 1 7983 17a5.A 50 6 3.25 15 1 1 7983 17a5.B 50 1 0.00 0 0 1 4641 12a2,b1 17 3 2 1 2 4641 12c1 10 1 0.00 0 0 6 4641 12c2 6 2 0.14 1 0 6 4641 12d2 50 4 2.80 9 1 1 4641 12e1,2 20 2 0.09 1 0 10
Germinal Center Day An Un Mn In Rn 61AM40 8 ? 7 11 1 1 61AM41.A 8 ? 5 7 1 0 61AM41.B 8 ? 3 3 1 0 61AM14 8 ? 6 10 0 7 61AM16 8 ? 11 20 1 2 61AB08 10 ? 2 1 0 1 B12 10 ? 3 3 0 1 B17.A 10 ? 2 1 0 2 B17.B 10 ? 3 2 0 1 B17.C 10 ? 2 4 0 0 L1AB01 10 ? 2 1 0 8 L1AB02 10 ? 2 1 0 9 L1AB03 10 ? 2 1 0 1 L1AD01.A 14 ? 5 11 1 4 L1AD01.B 14 ? 2 1 0 1 L1AD02 14 ? 7 9 3 3 L1AD03 14 ? 4 9 2 0 L1AD05 14 ? 7 10 4 0 61AD01 14 ? 7 9 3 1 61AD02 14 ? 10 51 4 0 61AA02 16 ? 5 7 1 0 GC8 16 ? 10 23 6 0 GC24 16 ? 14 38 6 0
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
Summary & Conclusions
Mutation Rate Reflected in Clonal Tree ‘Shapes’Developed Two Methods Cross-ValidatedAutoimmune Response
Data set well-suited for mutation rate estimationMutation Rate = 7 x 10-4 – 9 x 10-4 base-pair-1 division-1
Primary NP ResponseMutation Rate > 3.7 x 10-4 base-pair-1 division-1
Future Improvements with Additional Data
For more information:
[email protected], www.cs.princeton.edu/~stevenk
For more information:
[email protected], www.cs.princeton.edu/~stevenk