Tumor Migration Analysis. Mohammed El-Kebir

Transcription

1 Tumor Migration Analysis Mohammed El-Kebir

2 samples Mutation Matrix mutations Standard hylogenetic Techniques Sample Tree A Cellular History of Metastatic Cancer * mutation unobserved clones migration *homoplasy Tumor hylogenetic Techniques Sequencing and Mutation Calling time Clone Tree primary metastasis metastasis Migration History mutation Cell Division and Mutation History Cell Migration History inferred extant clones

3 Cell Division/Mutation and Migration are Separate rocesses (1) Cell division and mutation (2) Cell migration Cascading Seeding??? arallel Seeding Leaf-labeled Clone Tree T 3

4 Cell Division/Mutation and Migration are Separate rocesses Migration Graph G Vertex Labeling l Leaf-labeled Clone Tree T μ(t, l) = 8 migrations Given T and l, migrations are bichromatic edges in T, or edges in G 4

5 Cell Division/Mutation and Migration are Separate rocesses Migration Graph G G Vertex Labeling l l Leaf-labeled Clone Tree T μ(t, l) = 8 migrations Given T and l, migrations are bichromatic edges in T, or edges in G T μ(t, l ) = 4 migrations Goal: Given T, find vertex labeling l with minimum number of migrations 5

6 Minimum Migration Analysis in Ovarian Cancer Mcherson et al. (2016). Divergent modes of clonal spread and intraperitoneal mixing in high-grade serous ovarian cancer. Nature Genetics. Instance of the maximum parsimony small phylogeny problem Can be solved in polynomial time [Fitch, 1971; Sankoff, 1975] migrations A D emtum Right Fallopian Tube Right Ovary Appendix m = 7 anatomical sites Small Bowel Left Fallopian Tube Left Ovary F H B A6 A5 A4 A3 A2 A1 E1 D1 G1 F1 I1 H2 H1 C1 B5 B4 B3 B2 B1 6

7 Outline Cell division and mutation Cell migration Tumor hylogeny Estimation Tumor Migration Analysis [El-Kebir et al., RECOMB 2016]; [El-Kebir*, Satas* et al., Cell Systems 2016] [El-Kebir et al., Nature Genetics 2018] Biological roblem Assumptions Computational roblem Reconstructing migration history of a metastatic cancer Migrations are rare Migrations are independent Approach Dynamic programming (Sankoff/Fitch algorithm) arsimonious Migration History: Given T, find vertex labeling l with minimum number of migrations 7

8 Are there multiple vertex labelings with migrations? Mcherson et al. (2016). Divergent modes of clonal spread and intraperitoneal mixing in high-grade serous ovarian cancer. Nature Genetics. A emtum Right Fallopian Tube Right Ovary Appendix m = 7 anatomical sites Small Bowel Left Fallopian Tube Left Ovary D F H B A6 A5 A4 A3 A2 A1 E1 D1 G1 F1 I1 H2 H1 C1 B5 B4 B3 B2 B1 8

9 Minimum Migration History is Not Unique Enumerate all minimum-migration vertex labelings in the backtracestep Appendix Left Fallopian Tube Left Ovary Right Fallopian Tube Right Ovary Small Bowel entum 9

10 Comigrations: Simultaneous Migrations of Multiple Clones Multiple tumor cells migrate simultaneously through the blood stream [Cheung et al., 2016] Second objective: number γ of comigrations is the number of multi-edges in migration graph G γ = 10 Not necessarily true in the case of directed cycles Clone Tree T A Migration Graph G A6 A5 A4 A3 A2 A1 E1 D D1 G1 F F1 I1 H H2 H1 C1 B5 B B4 B3 B2 B1 Appendix Left Fallopian Tube Left Ovary Right Fallopian Tube Right Ovary Small Bowel entum 10

11 Comigrations: Simultaneous Migrations of Multiple Clones Multiple tumor cells migrate simultaneously through the blood stream [Cheung et al., 2016] Second objective: number γ of comigrations is the number of multi-edges in migration graph G γ = 10 γ = 11 Not necessarily true in the case of directed cycles γ = 7 Appendix Left Fallopian Tube Left Ovary Right Fallopian Tube Right Ovary Small Bowel entum γ = 11 γ = 7 11

12 Tradeoff between Migrations and Comigrations Minimum number γ* of comigrations is m 1 (where m is #anatomical sites) comigrations γ γ min Non-binary single-source seeding (SS) Non-binary multi-source seeding (MS) Non-binary reseeding (R) Reported migrations µ A μ = 14 migrations γ* = 6 comigrations D F Appendix Left Fallopian Tube Left Ovary Right Fallopian Tube Right Ovary Small Bowel entum H B A6 A5 A4 A3 A2 A1 E1 D1 G1 F1 I1 H2 H1 C1 B5 B4 B3 B2 B1 12

13 min = µ (D) Tradeoff between Migrations, Comigrations and Migration attern monoclonal (m) polyclonal (p) single-source seeding (S) tree multi-tree multi-tree multi-source 1 2 single-source multi-source seeding (S) seeding (M) migrations µ monoclonal (m) polyclonal (p) µmin seeding (M) directed acyclic graph directed acyclic directed acyclic multi-graph multi-graph (A) (A) reseeding (R) directed graph directed graph directed directed multi-graph multi-graph comigration n m 1 comigration number m 1 µ = µ = min min µmin µmin m 1 migration number µ (B) m 1 migration number µ 13

14 arsimonious Migration History roblem MH roblem arsimonious Migration History Clone Tree T Allowed patterns {S, M, R} polyclonal single source seeding (ps) µ =4 =2 arsimonious Migration History roblem: Given a clone tree! and a set " of allowed migration patterns, find a vertex labeling l with the minimum migration number $ (!) and subsequently the smallest comigration number ()(!).

15 samples Mutation Matrix mutations Standard hylogenetic Techniques Sample Tree A Cellular History of Metastatic Cancer * mutation unobserved clones migration *homoplasy Tumor hylogenetic Techniques Sequencing and Mutation Calling time Clone Tree primary metastasis metastasis Migration Graph mutation Cell Division and Mutation History Cell Migration History Label ancestral vertices by anatomical sites migration inferred extant clones Resolve clone tree ambiguities?

16 Resolving Clone Tree Ambiguities arsimonious Migration History (MH): Given a clone tree! and a set " of allowed migration patterns, find a vertex labeling l with the minimum migration number $ (!) and subsequently the smallest comigration number ()(!). polytomy Clone Tree T MH Allowed patterns {S, M, R} MH-TR polyclonal single source seeding (ps) resolved polytomy µ =4 =2 arsimonious Migration History with Tree Refinement (MH-TR): Given a clone tree! and a set " of allowed migration patterns, find a refinement! of! and vertex labeling l of! with the minimum migration number $ (! ), and subsequently smallest comigration number ^) (! ). monoclonal single source seeding (ms) µ =2 =2 17

17 olytomy Resolution in Ovarian Cancer (A) 9 8 Ovarian Cancer 7 [Mcherson et al.] anatomical sites m =7 Resolved polyclonal single-source seeding (ps) Unresolved polyclonal single-source seeding (ps) Reported (B) RUt Mcherson et al. ps (µ, ) = (11, 6) (C) MACHINA (MH) ps (D) MACHINA (MH) ps (µ, ) = (12, 6) (µ, ) = (13, 6) comigrations γ γ min RUt (E) RUt (B) (F) (G) (C) (D) Rv Bwl Brn Bm (E) MACHINA (MH-TR) ps RUt Rv Bwl Brn Bm (F) MACHINA (MH-TR) ps RUt Rv Bwl Brn Bm (G) MACHINA (MH-TR) ps (µ, ) = (11, 6) (µ, ) = (11, 6) (µ, ) = (11, 6) RUt RUt RUt migrations µ Rv Bwl Brn Bm Rv Bwl Brn Bm Rv Bwl Brn Bm 18

18 { { Resolving Clone Tree Ambiguities arsimonious Migration History with Tree Refinement (MH-TI): Given a set! of allowed migration patterns and mutation frequency confidence intervals (# $ = & $ ',), # * = [& * ',) ]), find a frequency matrix # ^ = [^& ',) ], a clone tree /, and a vertex labeling l of / such that: (1) ^& ',) [& $ ',), & * ',) ]; (2) ^# satisfies the sum condition for /; and (3) vertex labeling l of / has minimum migration number 4 (/) and subsequently smallest comigration number 67(/). F F + = = { ˆF 3 5 = { M2 T 0 MH-TI roblem arsimonious Migration History with Tree Inference U resolved polytomy B µ =2 =2 monoclonal single source seeding (ms) 19

19 Applying MACHINA to Metastatic Breast Cancer comigration number min µmin Hoadley et al. Tumor Evolution in Two atients with Basal-like Breast Cancer: A Retrospective Genomics Study of Multiple Metastases. LOS Med, 13(12) 2016 Resolved monoclonal single-source seeding (ms) olyclonal single-source seeding (ps) Monoclonal multi-source seeding (mm) olyclonal multi-source seeding (pm) Reported (B) (Supp.) (A) (Supp.) migration number µ (B) -2% -0.8% liver 51.6% Reported 0% 1.4% -0.64% rib kidney breast (µ, ) = (12, 6) 1 (µ, )=(5, 5) 1 1.6% 2.28% -2.2% 1.6% lung brain % -0.06% 60% 5% % 2.2% % -0.02% 34.4% 42.6% % 29.8% polyclonal multi-source seeding (pm) (C) 44% % 51% monoclonal single-source seeding (ms) 55% % 72% 3.6% Inferred 2 4 resolved polytomy 7 resolved polytomy 10 28% 39% breast lung rib liver kidney brain 20

20 samples Mutation Matrix mutations Standard hylogenetic Techniques Sample Tree A Cellular History of Metastatic Cancer * mutation unobserved clones migration *homoplasy Tumor hylogenetic Techniques Sequencing and Mutation Calling time Clone Tree primary metastasis metastasis Migration Graph mutation Cell Division and Mutation History Cell Migration History Label ancestral vertices by anatomical sites migration inferred extant clones Resolve clone tree ambiguities

21 Conclusions Cell division and mutation Cell migration Tumor hylogeny Estimation [El-Kebir*, Oesper* et al., ISMB 2015/Bioinformatics] [El-Kebir et al., RECOMB 2016]; [El-Kebir*, Satas* et al., Cell Systems 2016] Tumor Migration Analysis [El-Kebir et al., Nature Genetics 2018] recise mathematical models are needed to describe the evolutionary process in cancer: Do not try to solve everything at once; it is OK to simplify and gradually add complexity Understanding combinatorial structure leads to a better understanding of the problem at hand This leads to better and efficient algorithms 22