Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation

Abstract

The paper provides a qualitative analysis of M.S. Vinogradova's nonlinear model for dynamics of the cell population system. This system describes the stem cells cultivation in vitro under resource constraints. The system consists of two populations, namely: population of normal cells and population of abnormal cells. Resource constraints are considered as linear dependences of mitosis parameters on the normalized densities of each population.One of the key parameters that effects on the realization of the system evolution scenarios is a parameter that determines a share of the normal cells, which pass, when dividing, into population of the abnormal cells. The paper analyses both the existence conditions of the rest points and the changes of the evolution scenarios of population system with changing abovementioned parameter and other system parameters held fixed. It is shown that there is a saddle-node bifurcation in the system; the bifurcation value of the parameter is found. The paper shows the interval of parameter values in which the favorable scenarios of population system evolution are implemented. It also presents results of mathematical modeling.DOI: 10.7463/mathm.0315.0811443

Keywords

• mathematical modeling
• stem cells
• population dynamics
• bifurcation
• development scenarios
• rest points