A van der Waals-like Transition Between Normal and Cancerous Phases in Cell Populations Dynamics of Colorectal Cancer.

Based on a deterministic continuous model of cell populations dynamics in the colonic crypt and in colorectal cancer, we propose four combinations of feedback mechanisms in the differentiations from stem cells (SCs) to transit cells (TCs) and then to differentiated cells (DCs), the four combinations include the double linear (LL), the linear and saturating (LS), the saturating and linear (SL), and the double saturating (SS) feedbacks, respectively. The relative fluctuations of the population of SCs, TCs, and DCs around equilibrium states with four feedback mechanisms are studied by using the Langevin method. With the increasing of net growth rate of TCs, it is found that the Fano factors of TCs and DCs go to a peak in a transient phase, and then increase again to infinity in the cases of LS and SS feedbacks. The "up-down-up" characteristic on the Fano factor (like the van der Waals loop) demonstrates that there exists a transient phase between the normal and cancerous phases, our novel findings suggest that the mathematical model with LS or SS feedback might be better to elucidate the dynamics of a normal and abnormal (cancerous) phases.