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The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible cell plasticity among cancer cells has received much attention very recently. Here we present a generalized multi-phenotypic cancer model by integrating cell plasticity with the conventional hierarchical structure of cancer cells. We prove that under very weak assumption, the nonlinear dynamics of multi-phenotypic proportions in our model has only one stable steady state and no stable limit cycle. This result theoretically explains the phenotypic equilibrium phenomena reported in various cancer cell lines. Furthermore, according to the transient analysis of our model, it is found that cancer cell plasticity plays an essential role in maintaining the phenotypic diversity in cancer especially during the transient dynamics. Two biological examples with experimental data show that the phenotypic
The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and model selec
The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still question able if the phenotypic
Following antigen stimulation, the net outcomes of a T cell response are shaped by integrated signals from both positive co-stimulatory and negative regulatory molecules. Recently, the blockade of negative regulatory molecules (i.e. immune checkpoint
Studying the development of malignant tumours, it is important to know and predict the proportions of different cell types in tissue samples. Knowing the expected temporal evolution of the proportion of normal tissue cells, compared to stem-like and
The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisati