Mathematical Modeling Reveals the Factors Involved in the Phenomena of Cancer Stem Cells Stabilization

AbstractCancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, when isolated, CSCs return to their original proportion level as shown by various investigators. This phenomenon still remains to be explained.We suggest a mathematical model of cancer cell population dynamics, based on the main parameters of cell population dynamics, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and in non-CSCs. This model should help elucidating some important factors underlying the dynamics of the two populations, first of all, the phenomena of cancer stem cell population stabilization.Author SummaryCancer Stem Cells (CSC) present a subset of cancer cells which is thought to be responsible for tumor growth. That is why CSC are also named “tumor initiation cells”. Additionally, it was shown that CSC are resistant to chemo- and radio-therapies which suggests that these cells can be responsible for tumor relapses after these treatments. Experimental data in cancer cell lines have shown the intriguing phenomena of CSC population stability, which means that isolated CSC population rapidly stabilizes at its characteristic level (the relative proportion of CSC in a whole cancer population). We suggest a mathematical model of cancer cell population dynamics, based on experimentally measured dynamics of CSC population stabilization and including main parameters of cell population growth.We have computationally predicted probability of different scenarios of cancer cell behavior for each experimental case with measurable growth parameters. Moreover, we provide an analytical tool for elucidating important biochemical factors responsible for a particular dynamics of CSC population.The results may have important implications in therapeutic, because the destroying of a set of factors underlying CSC stability may help to avoid tumor relapses.

Download Full-text

Implications of a simple mathematical model to cancer cell population dynamics

Cell Proliferation ◽

10.1111/j.1365-2184.2006.00368.x ◽

2006 ◽

Vol 39 (1) ◽

pp. 15-28 ◽

Cited By ~ 17

Author(s):

A. L. Garner ◽

Y. Y. Lau ◽

D. W. Jordan ◽

M. D. Uhler ◽

R. M. Gilgenbach

Keyword(s):

Mathematical Model ◽

Population Dynamics ◽

Cancer Cell ◽

Cell Population ◽

Simple Mathematical Model ◽

Cell Population Dynamics ◽

Cancer Cell Population

Download Full-text

The CEA−/lo colorectal cancer cell population harbors cancer stem cells and metastatic cells

Oncotarget ◽

10.18632/oncotarget.13029 ◽

2016 ◽

Vol 7 (49) ◽

pp. 80700-80715 ◽

Cited By ~ 13

Author(s):

Chang Yan ◽

Yibing Hu ◽

Bo Zhang ◽

Lei Mu ◽

Kaiyu Huang ◽

...

Keyword(s):

Colorectal Cancer ◽

Stem Cells ◽

Cancer Stem Cells ◽

Cancer Cell ◽

Cell Population ◽

Colorectal Cancer Cell ◽

Metastatic Cells ◽

Cancer Cell Population

Download Full-text

Epithelial and mesenchymal prostate cancer cell population dynamics on a complex drug landscape

Convergent Science Physical Oncology ◽

10.1088/2057-1739/aa83bf ◽

2017 ◽

Vol 3 (4) ◽

pp. 045001 ◽

Cited By ~ 8

Author(s):

Ke-Chih Lin ◽

Gonzalo Torga ◽

Amy Wu ◽

Joshua D Rabinowitz ◽

Wesley J Murray ◽

...

Keyword(s):

Prostate Cancer ◽

Population Dynamics ◽

Cancer Cell ◽

Cell Population ◽

Prostate Cancer Cell ◽

Cell Population Dynamics ◽

Cancer Cell Population ◽

Complex Drug

Download Full-text

Identification of Cancer Cell Population Dynamics Leveraging the Effect of Pre-Treatment for Drug Schedule Design

2021 American Control Conference (ACC) ◽

10.23919/acc50511.2021.9482989 ◽

2021 ◽

Author(s):

Marius Wiggert ◽

Megan Turnidge ◽

Zoe Cohen ◽

Ellen M. Langer ◽

Rosalie C. Sears ◽

...

Keyword(s):

Population Dynamics ◽

Cancer Cell ◽

Cell Population ◽

Cell Population Dynamics ◽

Schedule Design ◽

Cancer Cell Population ◽

Pre Treatment

Download Full-text

Accounting for randomness in measurement and sampling in studying cancer cell population dynamics

IET Systems Biology ◽

10.1049/iet-syb.2013.0031 ◽

2014 ◽

Vol 8 (5) ◽

pp. 230-241

Author(s):

Siavash Ghavami ◽

Olaf Wolkenhauer ◽

Farshad Lahouti ◽

Mukhtar Ullah ◽

Michael Linnebacher

Keyword(s):

Population Dynamics ◽

Cancer Cell ◽

Cell Population ◽

Cell Population Dynamics ◽

Cancer Cell Population

Download Full-text

A Mathematical Model for Bone Cell Population Dynamics of Fracture Healing Considering the Effect of Energy Dissipation

10.1007/978-3-030-42707-8_3 ◽

2021 ◽

pp. 33-52

Author(s):

Mahziyar Darvishi ◽

Hooman Dadras ◽

Mohammad Mahmoodi Gahrouei ◽

Kiarash Tabesh ◽

Dmitry Timofeev

Keyword(s):

Mathematical Model ◽

Population Dynamics ◽

Energy Dissipation ◽

Fracture Healing ◽

Cell Population ◽

Bone Cell ◽

Cell Population Dynamics

Download Full-text

Colorectal cancer stem cells: Characterization and functional analysis

Journal of Clinical Oncology ◽

10.1200/jco.2009.27.15_suppl.4124 ◽

2009 ◽

Vol 27 (15_suppl) ◽

pp. 4124-4124

Author(s):

T. Yeung ◽

J. Wilding ◽

W. Bodmer

Keyword(s):

Colorectal Cancer ◽

Stem Cells ◽

Stem Cell ◽

Cancer Stem Cells ◽

Cancer Cells ◽

Cell Lines ◽

Cancer Cell ◽

Tumour Growth ◽

Colorectal Cancer Cell Lines ◽

Colorectal Cancer Stem Cells

4124 Background: Cancer stem cells are defined as cells within a tumour that are able to self-renew and differentiate into all cell lineages within that tumour. With our extensive panel of colorectal cell lines, our aims are: 1) To characterise and isolate cancer stem cells based on stem cell markers, morphological appearances and the ability to form multiple lineages; 2) To understand how cancer stem cells drive tumour growth and progression. Methods: 1) Fluorescent Activated Cell Sorting (FACS); 2) In vitro soft agar clonogenic and Matrigel differentiation assays; 3) In vivo tumourigenic NOD/SCID mice assay; 4) Confocal immunofluorescence imaging. Results: 1) A subpopulation of cells can differentiate into crypt-like megacolonies, retaining the ability to self-renew and differentiate. SW1222 cell line forms heterogeneous colonies when single cells are plated in Matrigel. Megacolonies can both self-renew and form terminally differentiated small colonies, whereas small colonies cannot form megacolonies. Megacolonies develop crypt-like structures and increase their expression of differentiation markers (CDX-1, CK-20) over time. Experiments are currently under way to confirm that cells from megacolonies are able to initiate tumours in NOD/SCID mice. Some cell lines retain the ability to differentiate into both neuroendocrine and epithelial lineages. 2) CD44+CD24+ enriches for the cancer stem cell population. Colorectal cancer cell lines HCT116, HT29, LS180, LS174T and SW1222 express both CD44 and CD24. The CD44+CD24+ subpopulation is the most clonogenic. In SW1222, CD44+CD24+ cells enrich for megacolonies and can reform all four CD44/CD24 subpopulations. 3) Hypoxia reduces differentiation, increases stem-like phenotype and enhances clonogenicity. Hypoxia increases the proportion of undifferentiated colorectal cancer cells when plated on Matrigel and increases clonogenicity. Conclusions: 1) Colorectal cancer cell lines contain subpopulations of cells that have the ability to self-renew, differentiate and drive tumour growth, and may be characterised by their cell surface markers and colony morphology. 2) CD44+CD24+ can be used as markers for colorectal cancer stem cells. 3) Hypoxia increases the stem-like phenotype of cancer cells, reduces differentiation and increases clonogenicity. No significant financial relationships to disclose.

Download Full-text

Finsler-type estimators for the cancer cell population dynamics

Publications de l Institut Mathematique ◽

10.2298/pim140602004b ◽

2015 ◽

Vol 98 (112) ◽

pp. 53-69

Author(s):

Vladimir Balan ◽

Jelena Stojanov

Keyword(s):

Dynamical System ◽

Population Growth ◽

Cancer Cell ◽

Cell Population ◽

Biological Models ◽

Cell Population Dynamics ◽

Finsler Structure ◽

Cell Population Growth ◽

Cancer Cell Population ◽

The Difference

We introduce a Finslerian model related to the classical Garner dynamical system, which models the cancer cell population growth. The Finsler structure is determined by the energy of the deformation field-the difference of the fields, which describe the reduced and the proper biological models. It is shown that a certain locally-Minkowski anisotropic Randers structure, obtained by means of statistical fitting, is able to provide a Zermelo-type drift of the overall cancer cell population growth, which occurs due to significant changes within the cancerous process. The geometric background, the applicative advantages and perspective openings of the constructed geometric structure are discussed.

Download Full-text

A Novel Fluorescent Dye Invades Mitochondria to Selectively Kill Cancer Stem Cells via Increased ROS Production

Bioinorganic Chemistry and Applications ◽

10.1155/2021/4763944 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Bei-Bei Zhang ◽

Jun-gang Liu ◽

Xian-Yu Bai ◽

Yuan-Jiao Huang ◽

Ning Xu ◽

...

Keyword(s):

Stem Cells ◽

Cell Proliferation ◽

Cancer Stem Cells ◽

Cancer Cells ◽

Cancer Cell ◽

Cancer Diagnosis ◽

Drug Exposure ◽

Fluorescent Dye ◽

Cancer Cell Proliferation ◽

Ros Production

Development of multiple agents has a significant impact on the cancer diagnosis and therapy. Several fluorescent dyes including near-infrared (NIR) fluorescent agents have been already well studied in the field of photodynamic therapy (PDT). In the present study, we reported a novel fluorescent dye could obviously inhibit cancer cell proliferation with slight toxic effects on the biological organism. Furthermore, it displayed selective staining on cancer cells, particularly on cancer stem cells (CSCs), rather than normal cells. Mechanically, this dye preferred to invading mitochondria of cancer cells and inducing overwhelming reactive oxygen species (ROS) production. The in vivo experiments further demonstrated that this dye could image cancer cells and even CSCs in a short-time intratumor injection manner using a zebrafish model and subsequently inhibit cancer cell proliferation after a relatively long-time drug exposure. Taken together, the future development of this agent will promise to make an essential contribution to the cancer diagnosis and therapeutics.

Download Full-text