Determinism and variability of the morphogenesis pathways.

Along with a strict determinism of early embryogenesis in most living organisms, some of them exhibit variability of cell fates and developmental pathways. Here we discuss the phenomena of determinism and variability of developmental pathways, defining its dependence upon cell potency, cell sensitivity to the external signals and cell signaling. We propose a set of conjectures on the phenomenon of variability of developmental pathways, and denote a difference between a normal (local) variability, leading to an invariant final structure (e.g., embryo shape), and fundamental one, which is a switching between different developmental pathways, leading to different possible structures. For illustrating our conjectures, we analyzed early developmental stages of plant embryos with different levels of variability of morphogenesis pathways, and provide a set of computational experiments by Morphogenesis Software.

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

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.