Resting Phase, Cell Cycle

The present modeling approach is based on the dynamics of stem cell populations stratified with respect to cell differentiation. Cell differentiation is defined through the variable α∈[0,1] with α = 0 for pure stem cells and α = 1 for fully differentiated cells. The model assumes cell differentiation to be subject to random changes defined by the conditional probability density function (cpdf) for given α and the randomization rate R(α) quantifying the number of random events per time (Equations (2) and (3)). The cpdf is assumed to be Gaussian centered at α with standard deviation (noise amplitude) σ(α). It is renormalized to unity for each α to account for the truncation to the interval [0,1]. The noise amplitude is specified as a sum of piecewise linear or quadratic functions q_i(α) = u₀+u₁(α−α_iq)+u₂(α−α_iq)² localized by tanh-type radial basis functions with b_i(α) = 1/2 tanh[(r_i−α+α_ib)/s_i]+1/2 tanh[(r_i+α−α_ib)/s_i], in which α_iq and α_ib denote the offset of the polynomial and the radial base, respectively, whereas r_i specifies the characteristic radius, and s_i the transfer width of the base. Cells are assumed to proliferate according to the growth rate r(α) and the time-dependent apoptosis rate a(t) = a₁t irrespective of generation. The two-dimensional rate equation for the average number of cells is numerically solved by the explicit Euler Forward Method on a 2D-grid of discrete differentiation values α_i, i = 1,…,n_a, and generation-specific cell cycle phases k = 1,…,n_p according to in which n_c denotes the number of cell cycle phases per generation, ρ(k) = 2 if k≡1(mod n_c) to account for cell doubling and ρ(k) = 1 otherwise. Furthermore, ϕ(k) = 0 if k = n_p and ϕ(k) = 1 otherwise. It is understood that M(a_i, k−1) = 0 for k = 1. The cell cycle terms in the second row of Equation (4) implement the continuous cell cycle model of León et al. [50] (link) without G₀ phase arrest. The number of cells in generation l is calculated by summing over its cell cycle phases . The dynamics of the marginal relative frequencies associated with cell differentiation can easily be derived from .
Truncation of the cpdf to the unit interval generally results in non-symmetric scattering and thus in a non-vanishing drift term A(α) as defined for the Fokker-Planck equation [47] . This term mimics a deterministic dynamic component corresponding to f(α) in the Langevin equation (1). The results of the present study were checked against either using the numerically determined non-zero A(α) or setting A(α) = 0 in the equilibrated distributions. We found no notable difference except for the S1 to D1 transition shown in Figure 3, for which, however, also the Fokker-Planck approximation to the master equation breaks down.

To obtain A549 and U87 cells in different cell cycle, cells were treated with a serum-free culture medium for 48 h (G0/G1 phase), 2 mm thymidine (S phase) or 200 ng/mL nocodazole (G2/M phase) for 16 h at 37 °C in a humidified 5% CO₂ atmosphere41 (link)42 (link)43 44 (link). To assess the cell cycle distribution, all the cells above were collected and fixed in 70% ethanol overnight. After removal of ethanol, samples were washed three times with PBS, and then incubated with RNase A for 30 min. Next, samples were stained with PI and evaluated by a flow cytometer (Cytomics^TM FC 500, Beckman Coulter, Miami, FL, USA).

A total of 10⁴ cells were treated with 91 and 182 μΜ for the T98 cell line, and 98 and 196 μΜ for the U87 cell line of linearol. Untreated cells were used as negative control having less than 1% of DMSO. At least three independent experiments were performed, and all samples were run in triplicates. Cells were treated with linearol at its IC50 and 2IC50 values. Flow cytometric analysis was performed 72 h post-treatment with linearol. For the DNA cell cycle, cells were treated with trypsin, centrifuged, washed with PBS twice and then incubated with PI (Propidium Iodide) working solution (50 µg/mL PI, 20 mg/mL RNase A, and 0.1% Triton X-100, Sigma-Aldrich, St. Louis, MO, USA) for 15 min at 37 °C in the dark. With the use of a flow cytometer (Omnicyt Flow Cytometer, Cytognos, Athens, Greece), the PI fluorescence of 10⁴ individual nuclei was determined. Then, the fractions of cells in G0/G1, S, G2/M and sub-G0/G1 phase were analyzed.

POB cells were seeded at a density of 1 × 10⁵/well in a 24-well plate (n = 3) and cultured for 24 h. Vibrations (3, 30, and 300 Hz) were then applied once for 30 min to the experimental groups. After 24 h, cells in both the experimental and control groups were stained using the Cell-Clock Cell Cycle Assay Kit (Biocolor, Carrickfergus, UK). The cells stained in three colors (yellow, green, and dark blue) were magnified 100-fold upon microscopic imaging. Imaging analysis software ImageJ (NIH, Bethesda, MD, USA) was used to acquire pixel data for each color tone, and cell count proportions were determined for each cell cycle stage based on the proportions of each color tone out of the total pixel values (yellow: G0/G1 stage, green: S/G2 initial stage, dark blue: G2 late stage/M stage).

For metaphase analysis, after irradiation Cal 51 cells were allowed to grow in a complete medium at 37 ℃ and 5% CO₂. Cells were fixed at 16 h after exposure, proceeded by a 1 h colcemid treatment (50 ng/ml) for metaphase accumulation, and stained with 3% Giemsa.
After exposure to proton beams and ⁶⁰Co γ-rays the blood samples (resting PBL at G₀ cell cycle stage) were diluted in 4.5 ml of RPMI medium supplemented by 20% fetal calf serum, 2 mM L-glutamine, 100 U/ml penicillin, 100 μg/ml streptomycin and 1.5% phytohaemagglutinin (PHA), incubated at 37° C and 5% CO₂, fixed at 48 h after PHA stimulation, proceeded by a 3 h colcemid treatment (200 ng/ml) for metaphase accumulation, and stained with 3% Giemsa. Typically, 100–300 metaphases were analyzed for every data point. Chromosomal aberrations were classified according to Savage (1976). All aberrations of the chromosome and chromatid types visible without karyotyping were recorded. The chromosome-type aberrations comprise paired fragments, dicentrics, centric and acentric rings (the latter also includes double minutes) and translocations visible without karyotyping. The chromatid-type aberrations include the chromatid-type breaks and chromatid-type exchanges. The gaps were not scored as aberrations.
For the PCC analysis, PBL were isolated from the blood by gradient centrifugation using BD Vacutainer^® CPT^™ (Becton, Dickinson and Co., USA) and cultured in the same RPMI medium 48 h prior to irradiation. Exponentially growing lymphocytes and Cal 51 cells were allowed to repair for various times after irradiation (0–12 h) and then were forced to condense chromatin prematurely by addition of 50 nM calyculin A (Sigma) immediately after irradiation and left for 1 h in 37° C. Then, the cells were treated with 0.075 M KCl for 10–15 min at 37 ℃ and fixed with methanol:glacial acetic acid (3:1). Cells were dropped onto a clean wet slide, airdried and stained with 3% Giemsa. Typically, 100–200 G₂-phase cells were analyzed for every data point. The scoring and recording criteria followed those given in IAEA Manual (2011 ). The damage was classified as chromatid breaks, isochromatid breaks (excess figures) and chromatid exchanges (Kowalska et al. 2020 (link)). The yield of isochromatid breaks was measured from the excess number of chromosomes (> 46 figures) observed (IAEA 2011 ). In G₂-phase of the cell cycle, the isochromatid break occurs when two breaks are formed on the opposite sister chromatids in a close proximity. Since one isochromatid break results from the breakage of both chromatid threads, one isochromatid break was scored as two chromatid breaks. Exchanges were also scored as two breaks. For further details, see (Kowalska et al. 2020 (link)).