Strategies for cancer stem cell elimination: Insights from mathematical modeling Vladimir Vainstein n , Oleg U. Kirnasovsky, Yuri Kogan, Zvia Agur Institute for Medical Biomathematics, 10 Te’ena str, P.O.B. 282, 60991 Bene Ataroth, Israel article info Article history: Received 9 March 2011 Received in revised form 29 September 2011 Accepted 15 December 2011 Available online 23 December 2011 Keywords: Cellular automata Cell differentiation Cancer therapy abstract The cancer stem cell (CSC) hypothesis states that only a small fraction of a malignant cell population is responsible for tumor growth and relapse. Understanding the relationships between CSC dynamics and cancer progression may contribute to improvements in cancer treatment. Analysis of a simple discrete mathematical model has suggested that homeostasis in developing tissues is governed by a ‘‘quorum sensing’’ control mechanism, in which stem cells differentiate or proliferate according to feedback they receive from neighboring cell populations. Further analysis of the same model has indicated that excessive stem cell proliferation leading to malignant transformation mainly results from altered sensitivity to such micro-environmental signals. Our aim in this work is to expand the analysis to the dynamics of established populations of cancer cells and to examine possible therapeutic avenues for eliminating CSCs. The proposed model considers two populations of cells: CSCs, which can divide indefinitely, and differentiated cancer cells, which do not divide and have a limited lifespan. We assume that total cell density has negative feedback on CSC proliferation and that high CSC density activates CSC differentiation. We show that neither stimulation of CSC differentiation nor inhibition of CSC proliferation alone is sufficient for complete CSC elimination and cancer cure, since each of these two therapies affects a different subpopulation of CSCs. However, a combination of these two strategies can substantially reduce the population sizes and densities of all types of cancer cells. Therefore, we propose that in clinical trials, CSC differentiation therapy should only be examined in combination with chemotherapy. Our conclusions are corroborated by clinical experience with differentiating agents in acute promyelocytic leukemia and neuroblastoma. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction The theory of cancer stem cells (CSCs) has drawn substantial attention from the scientific community in recent years (Sell, 2004; Zhou et al., 2009). According to this theory, cancer progres- sion is governed by CSCs, a subset of stem cell-like tumor cells that have the potential for unlimited replication and tumor initiation. The majority of tumor cells, in contrast, can undergo only a limited number of divisions and therefore cannot repopu- late a depleted tumor. Research findings are as yet inconclusive with regard to the universal applicability of the CSC theory (Quintana et al., 2008, for example, found evidence of a relatively large tumorigenic population among human melanoma cells, potentially challenging the CSC hypothesis for this type of cancer; see also Tomasson, 2009; Adams and Strasser, 2008; Kelly et al., 2007). Nonetheless, CSCs have been found to play crucial roles in the development and progression of leukemias and different solid tumors (le Viseur et al., 2008; Kavalerchik et al., 2008; Boman and Huang, 2008; Pohl et al., 2008; Kakarala and Wicha, 2008). The CSC paradigm holds meaningful ramifications for cancer therapy. As even a few CSCs might be sufficient to generate a tumor, one can intuitively conclude that an effective treatment must target the CSC population, ensuring that it dies out or at least does not manage to expand. Studies suggest that CSCs are relatively resistant to standard cytotoxic therapies (Cortes-Dericks et al., 2010). Therefore, there have been attempts to develop compounds that induce differentiation of CSCs in order to eliminate their ability to proliferate indefinitely, effectively exterminating cancer (Sanchez-Garcia et al., 2007; Spira and Carducci, 2003). Yet thus far, despite considerable research efforts and promising results in in vitro studies (see Spira and Carducci, 2003; Sell, 2004 for review), differentiation therapy has shown consistent clinical effectiveness for only one cancer indication: acute promyelocytic leukemia. Notably, in all clinical trials in which differentiating agents were administered as monotherapy, treatment either was of no efficacy at all (Trump et al., 1997; Culine et al., 1999; Adamson et al., 2007; Iida et al., 1999) or Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology 0022-5193/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2011.12.016 n Corresponding author. Tel.: þ972 39733075; fax: þ972 39733410. E-mail addresses: vladimir.dr@gmail.com, vladimir@imbm.org (V. Vainstein), oleg_kirnasovsky@mail.ru (O.U. Kirnasovsky), yuri@imbm.org (Y. Kogan), agur@imbm.org (Z. Agur). Journal of Theoretical Biology 298 (2012) 32–41