Somatic evolution and cancer

1. Somatic evolution and cancer Natalia Komarova (University of California - Irvine)

2. Plan • Introduction: The concept of somatic evolution • Methodology: Stochastic processes on selection-mutation networks Two particular problems: • Stem cells, initiation of cancer and optimal tissue architecture (with L.Wang and P.Cheng) • Drug therapy and generation of resistance: neutral evolution inside a tumor (with D.Wodarz)

3. Darwinian evolution (of species) • Time-scale: hundreds of millions of years • Organisms reproduce and die in an environment with shared resources

4. Darwinian evolution (of species) • Time-scale: hundreds of millions of years • Organisms reproduce and die in an environment with shared resources • Inheritable germline mutations (variability) • Selection • (survival of the fittest)

5. Somatic evolution • Cells reproduce and die inside an organ of one organism • Time-scale: tens of years

6. Somatic evolution • Cells reproduce and die inside an organ of one organism • Time-scale: tens of years • Inheritable mutations in cells’ genomes (variability) • Selection • (survival of the fittest)

7. Cancer as somatic evolution • Cells in a multicellular organism have evolved to co-operate and perform their respective functions for the good of the whole organism

8. Cancer as somatic evolution • Cells in a multicellular organism have evolved to co-operate and perform their respective functions for the good of the whole organism • A mutant cell that “refuses” to co-operate may have a selective advantage

9. Cancer as somatic evolution • Cells in a multicellular organism have evolved to co-operate and perform their respective functions for the good of the whole organism • A mutant cell that “refuses” to co-operate may have a selective advantage • The offspring of such a cell may spread

10. Cancer as somatic evolution • Cells in a multicellular organism have evolved to co-operate and perform their respective functions for the good of the whole organism • A mutant cell that “refuses” to co-operate may have a selective advantage • The offspring of such a cell may spread • This is a beginning of cancer

11. Progression to cancer

12. Progression to cancer Constant population

13. Progression to cancer Advantageous mutant

14. Progression to cancer Clonal expansion

15. Progression to cancer Saturation

16. Progression to cancer Advantageous mutant

17. Progression to cancer Wave of clonal expansion

18. Genetic pathways to colon cancer (Bert Vogelstein) “Multi-stage carcinogenesis”

19. Methodology: modeling a colony of cells • Cells can divide, mutate and die

20. Methodology: modeling a colony of cells • Cells can divide, mutate and die • Mutations happen according to a “mutation-selection diagram”, e.g. u1 u4 u2 u3 (r3) (r4) (r2) (1) (r1)

21. Mutation-selection network u8 (r3) u8 (r2) (r6) u8 u5 (1) (r4) (r1) (r6) u2 u2 u5 u8 (r1) (r5) (r7)

22. Stochastic dynamics on a selection-mutation network

23. A birth-death process with mutations Selection-mutation diagram: Number of is i u (1) (r ) Number of is j=N-i Fitness = 1 Fitness = r >1

24. Evolutionary selection dynamics Fitness = 1 Fitness = r >1

25. Evolutionary selection dynamics Fitness = 1 Fitness = r >1

26. Evolutionary selection dynamics Fitness = 1 Fitness = r >1

27. Evolutionary selection dynamics Fitness = 1 Fitness = r >1

28. Evolutionary selection dynamics Fitness = 1 Fitness = r >1

29. Evolutionary selection dynamics Start from only one cell of the second type. Suppress further mutations. What is the chance that it will take over? Fitness = 1 Fitness = r >1

30. Evolutionary selection dynamics Start from only one cell of the second type. What is the chance that it will take over? If r=1 then = 1/N If r<1 then < 1/N If r>1 then > 1/N If r then = 1 Fitness = 1 Fitness = r >1

31. Evolutionary selection dynamics Start from zero cell of the second type. What is the expected time until the second type takes over? Fitness = 1 Fitness = r >1

32. Evolutionary selection dynamics Start from zero cell of the second type. What is the expected time until the second type takes over? In the case of rare mutations, we can show that Fitness = 1 Fitness = r >1

33. (a) (1) (r) What is the probability that by time ta mutant of has been created? Assume that and Two-hit process (Alfred Knudson 1971)

34. A two-step process

35. A two-step process

36. … … A two step process

37. (a) (1) (r) A two-step process Scenario 1: gets fixated first, and then a mutant of is created; Number of cells time

38. … Stochastic tunneling

39. (a) (1) (r) Two-hit process Scenario 2: A mutant of is created before reaches fixation Number of cells time

40. The coarse-grained description Long-lived states: x0 …“all green” x1 …“all blue” x2 …“at least one red”

41. Stochastic tunneling Neutral intermediate mutant Disadvantageous intermediate mutant Assume that and

42. Stem cells, initiation of cancer and optimal tissue architecture

43. Colon tissue architecture

44. Colon tissue architecture Crypts of a colon

45. Colon tissue architecture Crypts of a colon

46. Cancer of epithelial tissues Gut Cells in a crypt of a colon

47. Cancer of epithelial tissues Cells in a crypt of a colon Gut Stem cells replenish the tissue; asymmetric divisions

48. Cancer of epithelial tissues Cells in a crypt of a colon Gut Proliferating cells divide symmetrically and differentiate Stem cells replenish the tissue; asymmetric divisions

49. Cancer of epithelial tissues Cells in a crypt of a colon Gut Differentiated cells get shed off into the lumen Proliferating cells divide symmetrically and differentiate Stem cells replenish the tissue; asymmetric divisions

50. Finite branching process