Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect.
The exact mechanisms of spontaneous tumor remission or complete response to treatment are phenomena in oncology that are not completely understood. We use a concept from ecology, the Allee effect, to help explain tumor extinction in a model of tumor growth that incorporates feedback regulation of stem cell dynamics, which occurs in many tumor types where certain signaling molecules, such as Wnts, are upregulated. Due to feedback and the Allee effect, a tumor may become extinct spontaneously or after therapy even when the entire tumor has not been eradicated by the end of therapy. We quantify the Allee effect using an 'Allee index' that approximates the area of the basin of attraction for tumor extinction. We show that effectiveness of combination therapy in cancer treatment may occur due to the increased probability that the system will be in the Allee region after combination treatment versus monotherapy. We identify therapies that can attenuate stem cell self-renewal, alter the Allee region and increase its size. We also show that decreased response of tumor cells to growth inhibitors can reduce the size of the Allee region and increase stem cell densities, which may help to explain why this phenomenon is a hallmark of cancer.
Department of Mathematics, University of California, Irvine, Irvine, CA, USA. konstorum@uchc.edu.|Center for Complex Biological Systems, University of California, Irvine, Irvine, CA, USA. konstorum@uchc.edu.|Center for Quantitative Medicine, University of Connecticut Health Center, Farmington, CT, USA. konstorum@uchc.edu.
Anna
http://orcid.org/0000-0003-4024-2058
A
Konstorum
Centre for Mathematical Biology, University of Alberta, Edmonton, AB, Canada.
Thomas
T
Hillen
Department of Mathematics, University of California, Irvine, Irvine, CA, USA. lowengrb@math.uci.edu.|Center for Complex Biological Systems, University of California, Irvine, Irvine, CA, USA. lowengrb@math.uci.edu.|Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA. lowengrb@math.uci.edu.
John
J
Lowengrub
D049109:Cell Proliferation; D000066673:Cell Self Renewal; D025461:Feedback, Physiological; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009365:Neoplasm Regression, Spontaneous / Q000473:pathology / Q000503:physiopathology; D009369:Neoplasms / Q000473:pathology / Q000503:physiopathology / Q000628:therapy; D014411:Neoplastic Stem Cells / Q000473:pathology* / Q000502:physiology*; D015398:Signal Transduction
Allee effect; Cancer stem cell; Stable Manifold Theorem; Tumor extinction