Mathematical Model of Heterogeneous Cancer Growth with an Autocrine Signalling Pathway

Overview

Journal Cell Prolif

Date 2012 Jul 13

PMID 22783948

Citations 2

Authors

G-M Hu

C-Y Lee

Y-Y Chen

N-N Pang

W J Tzeng

Affiliations

Soon will be listed here.

Abstract

Objectives: Cancer is a complex biological occurrence which is difficult to describe clearly and explain its growth development. As such, novel concepts, such as of heterogeneity and signalling pathways, grow exponentially and many mathematical models accommodating the latest knowledge have been proposed. Here, we present a simple mathematical model that exhibits many characteristics of experimental data, using prostate carcinoma cell spheroids under treatment.

Materials And Methods: We have modelled cancer as a two-subpopulation system, with one subpopulation representing a cancer stem cell state, and the other a normal cancer cell state. As a first approximation, these follow a logistical growth model with self and competing capacities, but they can transform into each other by using an autocrine signalling pathway.

Results And Conclusion: By analysing regulation behaviour of each of the system parameters, we show that the model exhibits many characteristics of actual cancer growth curves. Features reproduced in this model include delayed phase of evolving cancer under 17AAG treatment, and bi-stable behaviour under treatment by irradiation. In addition, our interpretation of the system parameters corresponds well with known facts involving 17AAG treatment. This model may thus provide insight into some of the mechanisms behind cancer.

Citing Articles

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References

Ganguly R, Puri I . Mathematical model for the cancer stem cell hypothesis. Cell Prolif. 2006; 39(1):3-14. PMC: 6495990. DOI: 10.1111/j.1365-2184.2006.00369.x. View

Swierniak A, Kimmel M, Smieja J . Mathematical modeling as a tool for planning anticancer therapy. Eur J Pharmacol. 2009; 625(1-3):108-21. PMC: 2813310. DOI: 10.1016/j.ejphar.2009.08.041. View

Bajzer Z, Vuk-Pavlovic S . Modeling positive regulatory feedbacks in cell-cell interactions. Biosystems. 2005; 80(1):1-10. DOI: 10.1016/j.biosystems.2004.09.025. View

Garner A, Lau Y, Jordan D, Uhler M, Gilgenbach R . Implications of a simple mathematical model to cancer cell population dynamics. Cell Prolif. 2006; 39(1):15-28. PMC: 6495727. DOI: 10.1111/j.1365-2184.2006.00368.x. View

Gupta P, Chaffer C, Weinberg R . Cancer stem cells: mirage or reality?. Nat Med. 2009; 15(9):1010-2. DOI: 10.1038/nm0909-1010. View

Reya T, Morrison S, Clarke M, Weissman I . Stem cells, cancer, and cancer stem cells. Nature. 2001; 414(6859):105-11. DOI: 10.1038/35102167. View

Enmon R, Yang W, Ballangrud A, Solit D, Heller G, Rosen N . Combination treatment with 17-N-allylamino-17-demethoxy geldanamycin and acute irradiation produces supra-additive growth suppression in human prostate carcinoma spheroids. Cancer Res. 2003; 63(23):8393-9. View

Ghosh S, Elankumaran S, Puri I . Mathematical model of the role of intercellular signalling in intercellular cooperation during tumorigenesis. Cell Prolif. 2011; 44(2):192-203. PMC: 6496144. DOI: 10.1111/j.1365-2184.2011.00739.x. View

Usmani S, Bona R, Li Z . 17 AAG for HSP90 inhibition in cancer--from bench to bedside. Curr Mol Med. 2009; 9(5):654-64. DOI: 10.2174/156652409788488757. View

10.

Tanaka G, Hirata Y, Goldenberg S, Bruchovsky N, Aihara K . Mathematical modelling of prostate cancer growth and its application to hormone therapy. Philos Trans A Math Phys Eng Sci. 2010; 368(1930):5029-44. DOI: 10.1098/rsta.2010.0221. View

11.

Grivennikov S, Karin M . Autocrine IL-6 signaling: a key event in tumorigenesis?. Cancer Cell. 2008; 13(1):7-9. DOI: 10.1016/j.ccr.2007.12.020. View

12.

Wolkenhauer O, Auffray C, Baltrusch S, Bluthgen N, Byrne H, Cascante M . Systems biologists seek fuller integration of systems biology approaches in new cancer research programs. Cancer Res. 2009; 70(1):12-3. PMC: 2802734. DOI: 10.1158/0008-5472.CAN-09-2676. View

13.

Ganguly R, Puri I . Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis. Cell Prolif. 2007; 40(3):338-54. PMC: 6496895. DOI: 10.1111/j.1365-2184.2007.00434.x. View

14.

Chang H, Hemberg M, Barahona M, Ingber D, Huang S . Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature. 2008; 453(7194):544-7. PMC: 5546414. DOI: 10.1038/nature06965. View

15.

Leder K, Holland E, Michor F . The therapeutic implications of plasticity of the cancer stem cell phenotype. PLoS One. 2010; 5(12):e14366. PMC: 3003707. DOI: 10.1371/journal.pone.0014366. View