Mathematical Modeling of Cancer Cell Lineages

Michelle ChenProfessor John Lowengrub, Ph.D.

August 2014

Chao Comprehensive Cancer Center, UCI

Scientific Background

Cell DivisionHallmarks of Cancer

Lineage Behavior in Absence of ControlFeedback, Radiation, and

Dedifferentiation

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

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Hallmarks of Cancer

Hanahan, Weinberg 2011 The Next Generation | Cell

Lineage Behavior

Lander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology

In absence of control

Lineage Behavior

Lander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology

In absence of control

Lineage Behavior

Derived Equations

Lander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology

In absence of control

Lineage Behavior

Derived Equations

Necessary Conditions for Establishing Steady State

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. differentiateLander, Gokoffski, Wan, Nie, Calof 2009 Cell Lineage | PLoS Biology

Youssefpour, Li, Lander, Lowengrub 2012 Multispecies Model | Journal of Theoretical Biology

Radiation

Diagnostic Imaging

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

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

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

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

HypothesisFeedback factors and

dedifferentiation play important roles in determining the optimal

radiotherapy strategy.

CompuCell3DComputational tool to study underlying

questions:Cell growth in response to feedback

Spatial organization of cellsEffects of radiation and growth factors

Acknowledgements

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