Mice and tumours
Female DBA/2 mice at the age of 8–12 weeks were obtained from the local breeding facility at the Institute of Immunology, Vilnius, Lithuania. SL2, a spontaneously arisen DBA/2 – derived lymphoma was maintained by weekly intraperitoneal passage in DBA/2 mice. Solid SL2 tumours for cell proliferation analysis were induced by subcutaneous injection of 107 SL2 cells on the chest of mice and analysed after 4 and 10 days.
Experimental research on animals has been conducted according to recommendations of the Lithuanian Ethics Committee for the Laboratory Animal Use.
Cell culture
Human acute T-cell leukaemia Jurkat cells were cultured in RPMI 1640 medium supplemented with 10% foetal bovine serum. The cultures were incubated at 37°C in a humidified atmosphere with 5% CO2.
BrdUrd labelling
The mice were injected i.p. with 1 ml of 2 mg/ml BrdUrd (5-bromo-2'-deoxyuridine, Sigma, St Louis, MO, USA) solution in physiological saline. The half-life of BrdUrd in rodent blood is only about 15 min. Therefore, a single i.p. injection acts as a pulse label [12]. At 10 h after BrdUrd injection the tumours were dissected and cut into slices of about 1 mm thickness. To avoid sampling errors, several slices were cut both from central and peripheral parts of a tumour. Tumour slices were fixed in 70% ethanol, and stored at +4°C for one or two days until staining.
For in vitro labelling of Jurkat cells, BrdUrd was dissolved in phosphate-buffered saline (PBS) and added to culture medium at a final concentration of 10 μM. After incubation for 30 min at 37°C, the cells were rinsed twice with RPMI 1640 medium and the cultures further incubated at 37°C. Samples for analysis were taken at 8, 10, 12 and 16 h after the BrdUrd pulse, the cells were washed with PBS and fixed in 70% ice-cold ethanol.
Flow cytometric staining and measurement
Slices of solid SL2 tumours were cut in fragments of about 1 mm3 and incubated in 0.4 mg/ml pepsin solution in 0.1 N HCl at 37°C with continuous agitation to produce a nuclear suspension. Isolation of nuclei was revealed by microscopic observation after 30 to 60 min of incubation. The nuclear suspension was filtered through a 48 μm nylon mesh. Nuclear suspensions of SL2 cells and suspensions of fixed Jurkat cells were washed and incubated in 2 N HCl for 30 min at room temperature for DNA denaturation. The acid solution was then neutralised with 0.1 M Na2B4O7 (pH 8.5) and the nuclear or cell suspensions were washed twice in PBS. Fifty μl of PBS containing 0.5% Tween 20 and 20 μl of FITC-conjugated mouse anti-BrdUrd monoclonal antibody (Becton Dickinson, Heidelberg, Germany) was added to the pellet containing 106 nuclei and incubated for 30 min at room temperature in the dark. After washing twice in PBS, 1 ml of a solution containing 5 mg/l propidium iodide (Sigma, St Louis, MO, USA) in PBS was added to the pellet and incubated for 30 min at 37°C in the dark.
The cellular DNA content and the amount of incorporated BrdUrd were simultaneously measured using a FACSort flow cytometer (Becton Dickinson, Heidelberg, Germany). Green fluorescent light emission (FITC = BrdUrd incorporation) was collected in the FL1 detector and red fluorescence (propidium iodide = DNA content) was collected in FL2 (for SL2 cells) or FL3 (for Jurkat cells) detector. Data from 15,000 nuclei per sample were acquired as dot plots of BrdUrd labelling vs. DNA content using LYSYS II software (Becton Dickinson, Heidelberg, Germany). Doublets were excluded by using the doublet discrimination mode. WinMDI version 2.8 software was used to analyse the acquired data.
Mathematical formulae for estimation of duration of cell cycle phases and GF in BrdUrd-labelled tumours
We propose that the total number of cells Sl labelled during the BrdUrd pulse can be estimated after any time interval shorter than the duration of the cell cycle as
where Slu – labelled undivided S cells, G2
lu – labelled undivided G2 cells, G1
ld – labelled divided G1 cells, and Sld – labelled divided S cells (1/2 is introduced to exclude cells produced after division). Theoretical DNA distributions of BrdUrd-labelled cells at different post-labelling times are graphically represented in Figure 1. The equation (1) is based on the assumption that labelled cell mortality or exit from the cell cycle during the period of measurement is negligible. If this is the case, the total number of cells labelled during the BrdUrd pulse remains constant throughout the cycle, provided that cells produced after division are excluded. Mitotic cells are not included in the analysis, since they lack the nuclear membrane and the cell membrane is disrupted by the nuclear isolation medium used for preparation for flow cytometric analysis [13]. Taking into account that the mitotic time is relatively short and the number of cells in mitosis can be regarded as negligible, the omission of mitotic cells may not have a considerable impact on estimation of the total number of BrdUrd-labelled cells.
Dot plots of BrdUrd labelling vs. DNA content were used to gate BrdUrd-positive cells (Figure 2A). The gate settings were adjusted on the control profiles, so as reproducibly to distinguish BrdUrd-positive fluorescence. G1
ld, Sld, Slu and G2
lu compartments in each DNA histogram of BrdUrd-positive cells were determined manually and numbers of cells in each of these compartments were obtained using statistics option of WinMDI 2.8 software (Figure 2B). These cell numbers were used in the equations of the proposed method. Instead of cell numbers, cell percentages over the total number of cells measured per sample can also be used.
The proposed method requires that considerable proportions of cells be found in Slu and Sld compartments. Slu and Sld compartments can be distinguished in the DNA histogram of BrdUrd-positive cells, provided that the time interval t after the BrdUrd pulse is shorter than the duration of the S phase, but sufficient for the labelled cells to re-enter a new S phase, i.e. if
+
< t < TS (
,
and TS are durations of G2, G1 and S phases of the cell cycle, respectively). Sld compartment was separated from Slu compartment by the channel corresponding to the lowest number of events (Figure 2C).
The number of labelled cells traversing S phase per unit time can be estimated as
The number of labelled cells traversing G2 phase, mitosis, G1 phase and re-entering S phase per unit time can be estimated as
The labelled cells begin to enter G1 phase after time
and the number of cells traversing G1 phase and re-entering S phase per unit time can be estimated as
The labelled cells begin to re-enter S phase after time
+
and the number of cells re-entering S phase per unit time can be estimated as
Estimation of durations of cell cycle phases in the proposed method is based on the assumption that the number of labelled cells traversing the cell cycle per unit time is constant. One of the models illustrating this assumption is the rectangular age distribution of proliferating cells described by Steel [14]. In this case, ν1 = ν2 = ν3 = ν4 and
The equation (1) and sequentially the equalities of the equation (6) can be used to determine TS,
and
:
GF can be estimated using the classical formula reported by Steel [14]:
where LI is the labelling index of the whole population and LIP is the labelling index of proliferating cells. If the number of labelled cells traversing the cell cycle per unit time is constant, we have
where TC is the duration of the cell cycle (TC =
+ TS +
). The LI can be calculated by the formula proposed by Johansson et al. [13]:
where nt is the total number of BrdUrd-positive and BrdUrd-negative cells measured per sample, G2 is the total number of G2 phase cells and G2
ul is the number of unlabelled G2 cells. In the proposed method, t < TS and G2
ul is negligible. Thus, the total number of G2 phase cells is approximately equal to G2
lu.
Formulae for estimation of durations of cell cycle phases based on a decreasing exponential cell age distribution hypothesis are presented in the Additional file 1.
RM approach
In addition to using the proposed formulae, TS values were estimated also using the classical RM method [1], here referred to as RM (linear), and the more recently proposed RM method, based on a cubic fit to the RM [6], here referred to as RM (cubic). The latter method also allows calculation of
. Using the RM (linear) method, the relative mean DNA content RM(t) of the moving cohort of BrdUrd-labelled cells in relation to that of G1 and G2 cells, was calculated using the formula
where
and
are the mean DNA content of cells in G1 and G2 phases, respectively, FLU is the mean DNA content of labelled undivided cells (Slu and G2
lu) and t is post-labelling time. TS was calculated from the equation
Using the RM (cubic) method, TS was calculated from the equation
In this equation, ν is defined as
where flu(t) and fld(t) are fractions of labelled undivided and labelled divided cells, respectively, at post-labelling time t. In our case, flu(t) is the fraction of Slu and G2
lu cells, and fld(t) – the fraction of G1
ld and Sld cells, respectively, in the total number of cells nt measured per sample.
An assumed exponential growth rate c was estimated as
where
was calculated from the equation
= t + ln(1 - fld(t)/2)/c (19)
Statistics
Pearson's correlation coefficient was used to determine the correlation between the TS or
values obtained using the proposed method and the RM approach. Differences between the GF values at day 4 and day 10 were analysed by the Wilcoxon rank sums test.