Flow cytometric analysis of the cell cycle: Mathematical modeling and biological interpretation

Abstract

Estimation of the repartition of asynchronous cells in the cell cycle can be explained by two hypotheses:

• - the cells are supposed to be distributed into three groups: cells with a 2c DNA content (G0/1 phase), cells with a 4c DNA content (G2+M phase) and cells with a DNA content ranging from 2c to 4c (S phase);

• - there is a linear relationship between the amount of fluorescence emitted by the fluorescent probe which reveals the DNA and the DNA content.

According to these hypotheses, the cell cycle can be represented by the following equation:

All the solutions for this equation are approximations. Non parametric methods (or graphical methods: rectangle, peak reflect) only use one or two phase(s) of the cell cycle, the remaining phase(s) being estimated by exclusion. In parametric methods (Dean & Jett, Baisch II, Fried), the DNA_T(x) distribution is supposed to be known and is composed of two gaussians (representative of G0/1 and G2+M) and a P(x,y) function representative of S phase. Despite the generality, these models are not applicable to all sample types, particularly heterogeneous cell populations with various DNA content. In addition, the cell cycle is dependent on several regulation points (transition from quiescence to proliferation, DNA synthesis initiation, mitosis induction) and biological perturbations can also lead to cytokinesis perturbations.

Before the emergence of flow cytometry, the current view of cell cycle resided in the assessment of cell proliferation (increase in cell number) or the kinetic of molecules incorporation (DNA precursors). The widespread development of flow cytometry has revealed the concept of cell cycle distribution and this snapshot distribution required methods to analyze this new information; this aspect led to the notion of cell cycle Mathematical Modeling.