1. Cell Cycle Control at the First Restriction Point and its Effect on Tissue Growth Joint work with Avner Friedman and Bei Hu (MBI, The Ohio State University and Notre Dame University) Chiu-Yen Kao 高 秋 燕

2. 2 Outline of the Talk 1.What is cell cycle? 2.Two restriction points (check points). 3.Mathematical Model: System of PDEs 4.Theorems 5.Numerical Demonstrations

3. 3 Cell Cycle http://herb4cancer.files.wordpress.com/2007/11/cell-cycle2.jpg

4. 4 Cell Cycle

5. 5 Mathematical Model: Equations

6. 6 Mathematical Model: Boundary Condition

7. 7 Control at the First Restriction Point

8. 8 Conservation of Total Density

9. 9 Radial Symmetric Velocity Oxygen Concentration

10. 10 Boundary Conditions & Initial Conditions The global existence and uniqueness for radially symmetric solutions is established by A. Friedman Remark: We assume the oxygen level is above the necrotic level and growth rate and death rate are independent of oxygen concentration.

11. 11 Check point Control : constant case

12. 12 Check point Control : constant case

13. 13 Check point Control : constant case

14. 14 Check point Control : constant case Idea: obtain a delay equation for Q

15. 15 Check point Control : constant case

16. 16 Check point Control : constant case

17. 17 Check point Control : constant case

18. 18 Check point Control : constant case Idea: lower bound & upper bound 00

19. 19 Check point Control : constant case Similarly,

20. 20 Numerical Simulation: Constant

21. 21 Numerical Simulation: Constant

22. 22 as Free Control

23. 23 as Free Control Idea: Mathematical Induction Thus

24. 24 Numerical Simulation: as Free Control

25. 25 The case of variable

26. 26 The case of variable

27. 27 Conclusion  A multiscale model with two time scales: the usual time,t, and the running time of cells in each phase of the cell cycle.  The growth or shrinkage of a tissue depends on a decision that individual cells make whether to proceed directly from the first restriction point to the S phase or whether to go first into quiescent state.  The radius can be controlled by. With suitable, the radius is bounded above and below for all time.  The model can be easily extended to two (or more) populations of cells. (ex. healthy cell and tumor cell)

28. 28 Selected References

29. 29 The End