Radial percolation reveals that Cancer Stem Cells are trapped in the core of colonies

Abstract

Using geometrical arguments, it is shown that Cancer Stem Cells (CSCs) must be confined inside solid tumors under natural conditions. Aided by an agent-based model and percolation theory, the probability of a CSC being positioned at the border of a colony is estimated. This probability is estimated as a function of the CSC self-renewal probabilityps; i.e., the chance that a CSC remains undifferentiated after mitosis. In the most common situations ps is low, and most CSCs produce differentiated cells at a very low rate. Theresults presented here show that CSCs form a small core in the center of a cancer cell colony; they become quiescent due to the lack of space to proliferate, which stabilizestheir population size. This result provides a simple explanation for the CSC niche size, dispensing with the need for quorum sensing or other proposed signaling mechanisms. Italso supports the hypothesis that metastases are likely to start at the very beginning of tumor development.

Assessing the distribution of cancer stem cells in tumorspheres

“…Its CSC fraction is 64%, larger than the 54% of the previous case, a result almost trivial that agrees with our most used modeling hypotheses: the growing rate can only be measured for the bulk of the cells 13 , thus, the outcome of the mitosis of a CSC is given just by a probability rather than a specific growth rate for each cell phenotype. Moreover, while we expect the quantitative results reported in Barberis, 2021 8 to be significantly different for three dimensions, the qualitative ones are likely to remain the same. The CSCs would form paths and be heterogeneously distributed, forming "patches" at the border (surface) of the spheroids after approximately one week.…”

“…Here, we measured both, the total amount of cells in each spheroid and the respective CSC fraction, information that will lead to improving the accuracy of mathematical models such as the ones summarized in 12 . Furthermore, we estimate that the growth rate is around r =1.1 cell/day, which allows us to establish and set the temporal scale of simulations as those in 8 . Of note, this value is in agreement with the one obtained by fitting experimental data with mathematical modeling 13 and encourages us to extend to three dimensions our mathematical and computational models.…”

Assessing the distribution of cancer stem cells in tumorspheres

“…Indeed, mathematical methods previously developed by us allowed to estimate the expected fraction of CSCs for tumorspheres in different culture conditions 7 – 9 and the effect of specific therapies on their development 10 among other theoretical results 11 – 14 . In particular, we computationally simulated the growth of a colony of cells in two dimensions using an Agent-Based Model (ABM) that mimics basic features of CSCs proliferation to form a spheroid 15 . The simulated spheroid grows from a single CSC and the cells can undergo mitosis at a fixed rate (the Population Doubling Time or PDT).…”

“…This last situation may describe most experimental conditions used for culturing tumorspheres 3 , 16 – 19 and agrees with our previous mathematical models 7 – 9 . Inspired by these simulations, in the present work we generate tumorspheres from MCF-7 cells and analyze them by confocal microscopy to obtain a method of image processing that fits biological data with already developed mathematical models for the distribution of CSCs in tumorspheres 15 . We chose tumorspheres as a simplified 3D tumor model since they are cellular structures generated from a variety of tumors from epithelial tissues, such as breast, lung, prostate, or colorectal cancer 20 .…”

Effects of a Differentiating Therapy on Cancer-Stem-Cell-Driven Tumors

“…The growing recognition of the importance of understanding the processes underpinning CSC-fueled tumor growth has led to the formulation of a number of mathematical models [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. These models offer insights into growth and differentiation rates, cell population fractions, lateral inhibition, and chemo-and radio-therapy effects, to cite a few processes.…”