1. Mathematical Modeling of Cancer Cell Lineages Michelle Chen Professor John Lowengrub, Ph.D. August 2014 Chao Comprehensive Cancer Center, UCI

2. Scientific Background Cell Division Hallmarks of Cancer Lineage Behavior in Absence of Control Feedback, Radiation, and Dedifferentiation

3. Cell Division  Symmetric Division: stem cell produces two stem cells  Asymmetric Division: stem cell produces one stem cell + one differentiating cell  Symmetric Differentiation: stem cell produces two differentiated cells Nature Reviews | Molecular Cell Biology qrs

4. Hallmarks of Cancer Hanahan, Weinberg 2011 The Next Generation | Cell

5. Lineage Behavior Lander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology  In absence of control

6. Lineage Behavior Lander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology  In absence of control

7. Lineage Behavior  Derived Equations  Lander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology  In absence of control

8. Lineage Behavior  Derived Equations   Necessary Conditions for Establishing Steady State 

9. Feedback  Terminally differentiated cells release proteins that feedback upon less differentiated cells in lineage  Act to promote differentiation and decrease rates of proliferation  Stem cells release short-range factor promoting self- renewal, long-range inhibitor of this factor  Integral-feedback mechanism implemented is key to successful control  Lower probability that progenitor cells replicate vs. differentiate Lander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology Youssefpour, Li, Lander, Lowengrub 2012 Multispecies Model | Journal of Theoretical Biology

10. Radiation Diagnostic Imaging

11. Radiation  Effects of radiation on the growth and differentiation of cells in lineage  Linear-Quadratic Model to represent such growth  Mechanistic and biologically based  Practical number of parameters  Predictable fractionation dependencies for cell killing  Well-documented predictive properties for dose effects  Well-validated theoretically and experimentally up to 10 Gy Brenner 2008 Linear Quadratic Model | National Institute of Health

12. Radiation  Effects of radiation on the growth and differentiation of cells in lineage  Linear-Quadratic Model to represent such growth  Probability of survival:   After n doses of radiation:  Douglas, Fowler 1976 Multiple Small Doses of X Rays | National Institute of Health

13. Dedifferentiation  Conversion of differentiated cells back into stem or less differentiated cells  Pajonk investigated breast cancer cells  Induce reprogramming through radiation treatment  Rate of dedifferentiation increases with radiation dose Lagadec, Vlashi, Donna, Dekmezian, Pajonk 2012 Radiation-Induced Reprogramming | Stem Cells

14. Underlying Questions  How are cells from the lineage spatially organized, and how does this organization depend on the feedback from growth factors?  If patients are given a dose of radiation, what is the optimal dose for cancer cell treatment?  Cell death and cell differentiation influences feedback, causing nonlinear interaction  Cells not being killed experience changing conditions due to feedback factors

15. Hypothesis Feedback factors and dedifferentiation play important roles in determining the optimal radiotherapy strategy.

16. CompuCell3D Computational tool to study underlying questions: Cell growth in response to feedback Spatial organization of cells Effects of radiation and growth factors

17. Acknowledgements Professor John Lowengrub, Ph.D. University of California, Irvine