Math Model for Cancer Micro Env Model

A micro-environmental mode of carcinogenesis

Xu Zhou

Max Planck Institute for Complex Physics

SEMINAR "Principles of cancer development“, November 10, 2008

What causes Cancer? – cellular view

• Once it was taken as infectious disease

• Genetic disease of multi-cellular organism- Oncogenes - tumor suppressor genes

• Evolution vs. de-evolution

What microenvironment is important?

• Clone is cell reprogramming by changing microenvironment

• Normal breast epithelium cells => cancer cell by ECM-degrading enzyme

• Tumour microenvironment’s roles in in tumor development, start in 1960’s, now revived

“The tumour microenvironment—Introduction”, Seminars in Cancer Biology , 12, 2, 87-155, (2002)

What causes Cancer? – Environmental view

• Tumour microenvironment in driving tumorigenesis depend on somatic genetic alterations?

• Tumour microenvironment is independent from cancer cell gene mutation

“Tumour microenvironment: No changes necessary”, Nature Reviews Cancer 8, 324 – 325, (2008)

Cancer develops with the change of its microenvironment

• Cell with oncogene turning on => extra growth => still benign

• Balance with ECM structures destroyed => Cancer

• Cancer stem cells, epithelial-mesenchymal transition, increased angiogenesis and unrestrained cell growth may result from deregulation of tissue microenvironment

Hypothesis of micro-environment selection model

1) There is no cancer programming

2) cancer gene mutation under selection pressure of microenvironment

Waddinton’s epigenetic landscape

A warm-up: predator-prey model

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Cancer Evolution model (I)

• A kinetic model with parameters Start

• Xi – number of different phenotypes

• Ki – need to contact with base

memberane

Cancer Evolution model (II)

• Cancer evolution

- proliferation away from base

membrane

- invasive

• Evolution dynamics change, leads to

different phenotypes

Evolution barriers vs. Cancer mutations

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Tumorigenesis vs. Dynamic system evolutions

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The good of the Model• A mathematical framework to

explain why phenotypes appear in certain pattern

• Parameters to associate hallmark of cancer mutations

• Cure cancer by re-engineering its microenvironment

What’s bad in the model• This is not new derived from this

model

• Each phenotype change is triggered by changing those parameters manually.

• i.e. I know what’s happening, then I put it into the model

Conclusions• Cancer is caused by genetic mutations

and environmental selections

• Cancer development can be modeled as evolution dynamic system, each phenotype corresponds to a certain evolution advantage in the micro-environment

• Cure cancer by re-engineering its microenvironment

Some key questions about cancer

• Multi-cellular disease

• Sth wrong with coordination of cells

• Of old age