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Cell Cycle Control at the First Restriction Point and its Effect on Tissue Growth

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. Outline of the Talk. What is cell cycle? Two restriction points (check points).

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Cell Cycle Control at the First Restriction Point and its Effect on Tissue Growth

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

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

  4. Cell Cycle

  5. Mathematical Model: Equations

  6. Mathematical Model: Boundary Condition

  7. Control at the First Restriction Point

  8. Conservation of Total Density

  9. Radial Symmetric Velocity Oxygen Concentration

  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. Check point Control : constant case

  12. Check point Control : constant case

  13. Check point Control : constant case

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

  15. Check point Control : constant case

  16. Check point Control : constant case

  17. Check point Control : constant case

  18. Check point Control : constant case Idea: lower bound & upper bound 0 0

  19. Check point Control : constant case Similarly,

  20. Numerical Simulation: Constant

  21. Numerical Simulation: Constant

  22. as Free Control

  23. as Free Control Idea: Mathematical Induction Thus

  24. Numerical Simulation: as Free Control

  25. The case of variable

  26. The case of variable

  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. Selected References

  29. The End Thank you for your attention!! Questions??

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