Research Article

Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics

T. Stiehl and A. Marciniak-Czochra ^c1

Interdisciplinary Center for Scientific Computing (IWR) Institute of Applied Mathematics and BIOQUANT University of Heidelberg, Im Neuenheimer Feld 267 D - 69120 Heidelberg, Germany

Abstract

The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts. Using linear stability analysis we derive conditions necessary and sufficient for expansion of malignant cell clones, based on fundamental cellular properties. This approach reveals different scenarios of cancer initiation and provides qualitative hints to possible treatment strategies.

(Online publication January 25 2012)

Key Words:

• multi-compartmental models;
• stem cell differentiation;
• environmental signaling;
• leukemia;
• cancer stem cells;
• leukemic stem cells;
• linear stability analysis

Mathematics Subject Classification:

• 34D20;
• 34D35;
• 92D25;
• 92C50;
• 92C37

Correspondence:

^c1 Corresponding author. E-mail: anna.marciniak@iwr.uni-heidelberg.de