Radiation-induced cell cycle perturbations: a computational tool validated with flow-cytometry data

Abstract

Cell cycle progression can be studied with computational models that allow to describe and predict its perturbation by agents as ionizing radiation or drugs. Such models can then be integrated in tools for pre-clinical/clinical use, e.g. to optimize kinetically-based administration protocols of radiation therapy and chemotherapy. We present a deterministic compartmental model, specifically reproducing how cells that survive radiation exposure are distributed in the cell cycle as a function of dose and time after exposure. Model compartments represent the four cell-cycle phases, as a function of DNA content and time. A system of differential equations, whose parameters represent transition rates, division rate and DNA synthesis rate, describes the temporal evolution. Initial model inputs are data from unexposed cells in exponential growth. Perturbation is implemented as an alteration of model parameters that allows to best reproduce cell-cycle profiles post-irradiation. The model is validated with dedicated in vitro measurements on human lung fibroblasts (IMR90). Cells were irradiated with 2 and 5 Gy with a Varian 6 MV Clinac at IRCCS Maugeri. Flow cytometry analysis was performed at the RadBioPhys Laboratory (University of Pavia), obtaining cell percentages in each of the four phases in all studied conditions up to 72 h post-irradiation. Cells show early [Formula: see text]-phase block (increasing in duration as dose increases) and later [Formula: see text]-phase accumulation. For each condition, we identified the best sets of model parameters that lead to a good agreement between model and experimental data, varying transition rates from [Formula: see text]- to S- and from [Formula: see text]- to M-phase. This work offers a proof-of-concept validation of the new computational tool, opening to its future development and, in perspective, to its integration in a wider framework for clinical use.

Figure 1

Cell growth curve. Number of unirradiated cells (pre-treatment condition) as a function of time and exponential fit of the data.

Figure 2

Flow-cytometry gating strategy. Gating hierarchy of a representative sample (sham 16 h). From left to right and from up to down: (a) in FSC-A versus SSC-A, identification of the cloud of cell-like events; (b) in FSC-A versus FSC-H, identification of singlets (single cell signals); (c) VL1-A histogram shows the cell-cycle profile; (d) in VL1-A versus BL1-A, three distinct groups (cells in ${\text{G}}_1$-phase, S-phase, and ${\text{G}}_2$/M-phases) are shown, and finally from the last gate in (e) we identify cells in M-phase in the VL1-A versus BL2-A plane.

Figure 3

Experimental cell-cycle distribution in sham and for irradiated samples. Percentages of cells in the four cell-cycle phases as a function of time respectively for: (a) the pre-treatment and the sham conditions, (b) the 2 Gy irradiated condition, and (c) the 5 Gy irradiated condition (data from Table 1). Percentages of cells in the M-phase are generally too low to be appreciated in the plot. Errors are reported as standard deviations at $1\sigma$.

Figure 4

Relative differences between the irradiated and the sham condition. 2 Gy versus sham (a), and 5 Gy versus sham (b), relative differences in the percentages of cells in each phase as a function of time (lines are a guide for the eye). Numerical data are reported in Table 2.

Figure 5

Model percentages of cells in each cell-cycle phase over time. Model percentages of cells in each phase with initial guess parameters by Steel (a), and with the optimized parameters (b). Dashed lines are the percentages of cells in each phase as measured experimentally (numerical values are given in the text); light coloured bands represent the experimental standard deviations at $1\sigma$ for the SDD condition.

Figure 6

Model perturbation for cell-cycle phases over time. Model perturbation for the 2 Gy condition (a), and for the 5 Gy condition (b). The model is in the unperturbed condition up to 10 h, cells are irradiated at t = 10 h. Errors are reported as standard deviations at $1\sigma$.