Analysis of radiation-induced changes to human melanoma cultures using a mathematical model

Abstract

Objectives: Tumour cells respond to ionizing radiation by cycle arrest, cell death or repair and possible regrowth. We have developed a dynamic mathematical model of the cell cycle to incorporate transition probabilities for entry into DNA replication and mitosis. In this study, we used the model to analyse effects of radiation on cultures of five human melanoma cell lines.

Materials and methods: Cell lines were irradiated (9 Gy) prior to further culture and harvesting at multiple points up to 96 h later. Cells were fixed, stained with propidium iodide and analysed for G(1)-, S- and G(2)/M-phase cells by flow cytometry. Data for all time points were fitted to a mathematical model. To provide unique solutions, cultures were grown in the presence and absence of the mitotic poison paclitaxel, added to prevent cell division.

Results: The model demonstrated that irradiation at 9 Gy induced G(2)-phase arrest in all lines for at least 96 h. Two cell lines with wild-type p53 status additionally exhibited G(1)-phase arrest with recovery over 15 h, as well as evidence of cell loss. Resumption of cycling of surviving cells, as indicated by increases in G(1)/S and G(2)/M-phase transitions, was broadly comparable with results of clonogenic assays.

Conclusions: The results, combined with existing data from clonogenic survival assays, support the hypothesis that a dominant effect of radiation in these melanoma lines is the induction of long-term cell cycle arrest.

Figure 1

Model of the effect of radiation on the cell division cycle incorporating transitions for entry from G ₁ ‐phase to S‐phase and from G ₂ ‐phase to mitosis . The model also has terms for S‐ and M‐phase duration, as well as terms for cell loss.

Figure 2

Flow cytometry profiles of the NZM3 cell line. Dashed line indicates experimental data, while the solid line indicates fit of the mathematical model. Dotted peaks to the left of the profile for NZM3 cells (approximately 0.1 and 0.2 times the G₁‐phase DNA content) originate from DNA of chicken erythrocytes, which was added as an internal standard.

Figure 3

Values for the (r_G1S) and r_G2M cell cycle transitions (using the model outlined in Fig. 1 ) as a function of time after irradiation for each of the cell lines.

Figure 4

Flow cytometry profiles for the NZM4 cell line. Dashed line indicates experimental data and solid line indicates fit of the mathematical model. Other details are as in Fig. 2.

Figure 5

Flow cytometry profiles for the NZM5 cell line. Dashed line indicates experimental data and solid line indicates fit of the mathematical model. Other details are as in Fig. 2.

Figure 6

Flow cytometry profiles for the NZM6 cell line. Dashed line indicates experimental data and solid line indicates fit of the mathematical model. Other details are as in Fig. 2.

Figure 7

Flow cytometry profiles for the NZM13 cell line. Dashed line indicates experimental data and solid line indicates fit of the mathematical model. Other details are as in Fig. 2.