Evolution and cancer: A mathematical biology approach

Agur et al. 2010 Edited by Professor Marek Kimmel

Cancer is, in some sense, a condensed-time laboratory of evolution. Dedifferentiated cells form colonies that survive in a hostile environment, and they evolve new metabolic circuits and aggression and resistance mechanisms. They also can muster cooperation of fibroblasts and lymphocytes, and attract blood vessels. Modeling of these phenomena, well underway, will also help understand basic mechanisms of life.

Taken together, the articles in this thematic series illustrate the substantial progress that occurred over the past decade. Qualitative and quantitative understanding of cancer is a necessary condition for engineering approaches to fight it. The latter are still scarce.

A sequel to this series was published in 2016.

Evolution and cancer: a mathematical biology approach

Authors: Marek Kimmel

Citation: Biology Direct 2010 5:29

Content type: Editorial Published on: 20 April 2010
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A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease

Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease.

Authors: Bruce P Ayati, Claire M Edwards, Glenn F Webb and John P Wikswo

Citation: Biology Direct 2010 5:28

Content type: Research Published on: 20 April 2010
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Oscillatory dynamics in a model of vascular tumour growth - implications for chemotherapy

Investigations of solid tumours suggest that vessel occlusion may occur when increased pressure from the tumour mass is exerted on the vessel walls. Since immature vessels are frequently found in tumours and m...

Authors: IJ Stamper, MR Owen, PK Maini and HM Byrne

Citation: Biology Direct 2010 5:27

Content type: Research Published on: 20 April 2010
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A new stochastic and state space model of human colon cancer incorporating multiple pathways

Studies by molecular biologists and geneticists have shown that tumors of human colon cancer are developed from colon stem cells through two mechanisms: The chromosomal instability and the micro-satellite inst...

Authors: Wai Y Tan and Xiao W Yan

Citation: Biology Direct 2010 5:26

Content type: Research Published on: 20 April 2010
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A theoretical quantitative model for evolution of cancer chemotherapy resistance

Disseminated cancer remains a nearly uniformly fatal disease. While a number of effective chemotherapies are available, tumors inevitably evolve resistance to these drugs ultimately resulting in treatment fail...

Authors: Ariosto S Silva and Robert A Gatenby

Citation: Biology Direct 2010 5:25

Content type: Research Published on: 20 April 2010
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The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model

Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond...

Authors: Steffen E Eikenberry, John D Nagy and Yang Kuang

Citation: Biology Direct 2010 5:24

Content type: Research Published on: 20 April 2010
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Tumor morphological evolution: directed migration and gain and loss of the self-metastatic phenotype

Aside from the stepwise genetic alterations known to underlie cancer cell creation, the microenvironment is known to profoundly influence subsequent tumor development, morphology and metastasis. Invasive clust...

Authors: Heiko Enderling, Lynn Hlatky and Philip Hahnfeldt

Citation: Biology Direct 2010 5:23

Content type: Research Published on: 20 April 2010
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Episodic, transient systemic acidosis delays evolution of the malignant phenotype: Possible mechanism for cancer prevention by increased physical activity

The transition from premalignant to invasive tumour growth is a prolonged multistep process governed by phenotypic adaptation to changing microenvironmental selection pressures. Cancer prevention strategies ar...

Authors: Kieran Smallbone, Philip K Maini and Robert A Gatenby

Citation: Biology Direct 2010 5:22

Content type: Research Published on: 20 April 2010
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Selection in spatial stochastic models of cancer: Migration as a key modulator of fitness

We study the selection dynamics in a heterogeneous spatial colony of cells. We use two spatial generalizations of the Moran process, which include cell divisions, death and migration. In the first model, migra...

Authors: Craig J Thalhauser, John S Lowengrub, Dwayne Stupack and Natalia L Komarova

Citation: Biology Direct 2010 5:21

Content type: Research Published on: 20 April 2010
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Disruption of a Quorum Sensing mechanism triggers tumorigenesis: a simple discrete model corroborated by experiments in mammary cancer stem cells

The balance between self-renewal and differentiation of stem cells is expected to be tightly controlled in order to maintain tissue homeostasis throughout life, also in the face of environmental hazards. Theor...

Authors: Zvia Agur, Yuri Kogan, Liora Levi, Hannah Harrison, Rebecca Lamb, Oleg U Kirnasovsky and Robert B Clarke

Citation: Biology Direct 2010 5:20

Content type: Research Published on: 20 April 2010
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Cancer models, genomic instability and somatic cellular Darwinian evolution

The biology of cancer is critically reviewed and evidence adduced that its development can be modelled as a somatic cellular Darwinian evolutionary process. The evidence for involvement of genomic instability ...

Authors: Mark P Little

Citation: Biology Direct 2010 5:19

Content type: Review Published on: 20 April 2010
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