Mathematical modeling reveals the factors involved in the phenomena of cancer stem cells stabilization

Abstract

Cancer 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, isolated CSCs rapidly regenerate the original population of stem and non-stem cells (non-CSCs) as shown by various investigators. This phenomenon still remains to be explained. We propose a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and non-CSCs sub-populations, and taking into account the stabilization phenomenon. The analysis of the model allows determination of time-varying corridors of probabilities for different cell fates, given the particular dynamics of cancer cells populations; and determination of a cell-cell communication factors influencing these time-varying probabilities of cell behavior (division, transition) scenarios. Though the results of the model have to be experimentally confirmed, we can anticipate the development of several fundamental and practical applications based on the theoretical results of the model.

Understanding the influence of substrate when growing tumorspheres

“…Yang, Plikus and Komarova used stochastic modeling to explore the relative importance of symmetric and asymmetric stem cell divisions, showing that tight homeostatic control is not necessarily associated with purely asymmetric divisions and that symmetric divisions can help to stabilize mouse paw epidermis lineage [ 14 ]. Recently, Bessonov and coworkers developed a model that allowed them to determine the influence of the population dynamics on the time-varying probabilities of different cell fates and the ascertainment of the cell-cell communication factors influencing these probabilities [ 15 ]. These authors suggest that a coordinated dynamical change of the cell behavior parameters occurs in response to a biochemical signal, which they describe as an underlying field.…”

An integrative model of cancer cell differentiation with immunotherapy*

“…Although we calculate a maximum value close to 10%, we will take an average of 5%. Most organs do not exceed 1% of Ss and only a few reach 5% [50,51] or 10% [52]. For this reason, we will use ρ PS = ρ PSmax 2 = 0.0295 day .…”

Evaluation of intracellular distribution of folate functionalized silica nanoparticles using fluorescence and hyperspectral enhanced dark field microscopy

“…It is well documented that cancer cells have a high turnover rate 13–16 as observed in pulmonary, 17 breast 18 or colorectal neoplasms. 19 Cancer cells have increased demands of metabolic precursors; 20 thus, the possibility of targeting cancer cells by “feeding” them with DDSs loaded with specific precursors, represents a strategy for an effective perturbation of their evolution.…”

“…8 These systems are designed considering a controlled drug release process, with rather low early degradation, 3 as well as a specific affinity for cancer cells. [9][10][11][12] It is well documented that cancer cells have a high turnover rate [13][14][15][16] as observed in pulmonary, 17 breast 18 or colorectal neoplasms. 19 Cancer cells have increased demands of metabolic precursors; 20 thus, the possibility of targeting cancer cells by "feeding" them with DDSs loaded with specific precursors, represents a strategy for an effective perturbation of their evolution.…”