Different growth patterns of a cancer cell population as a function of its starting growth characteristics: analysis by mathematical modelling

Abstract

The growth kinetics of a cancer cell population as a function of the total number of cells and the proportion of proliferating and resting cells at the beginning of the growth has been analysed by a mathematical model. The model takes into account the processes of cell division, death and transition from proliferation to rest and backwards. It is shown that a single cell population growing under the same environmental conditions has an extremely broad spectrum of growth patterns. The whole multiplicity of possible growth patterns has been determined by the inherent cellular growth characteristics of the population, while the growth pattern actually realized of the variety of growth curves depends on the total number of cells and the proportion of proliferating and resting cells at the initial moment of growth. The model is shown to provide a good prediction of experimentally measured kinetics of regrowth of tumour cells subcultured after various times of the growth in unfed cultures, and the kinetics of tumour cell growth after severe hypoxia. The role of cell transitions between proliferating and resting stages in the problem of growth control is discussed.

Transforming growth factor-β1 signaling contributes to Caco-2 cell growth inhibition induced by 1,25(OH)2D3

“…It bears emphasis that, although the additional inhibition of Caco-2 cell growth, induced by the combination of TGF-␤1 and 1,25(OH) 2 D 3 in this study, or by butyrate (24, 42) is relatively modest, its impact on tumor progression may be considerable. Mathematical models of tumorigenesis have suggested, for example, that even limited decreases in their proliferative rates may ultimately result in significant inhibition of tumor growth (44,45).…”

Versal deformation and static bifurcation diagrams for the cancer cell population model

“…Solyanik [12]), and therefore subsequent treatment methods might lead to the complete annihilation of cancerous cells.…”

“…In their paper, Solyanik et al studied the resulting steady states and stability, assuming that the transition rate Q is zero ( [12]). …”

“…Their dynamics in time is described by the following differential equations introduced by Solyanik et al [12]:…”

“…The model is based on the dynamical system proposed by Solyanik et al ([12]), and estimates the behavior of the two types of cancer cell populations (proliferating and quiescent) based on approximately 10 measurements of the total cell population over one week [12]. Its main assumptions are as follows:…”