ON THE EXISTENCE OF A G_o‐PHASE IN THE CELL CYCLE

Abstract

The model is based on the assumption that the cell cycle contains a Go‐phase which cells leave randomly with a constant probability per unit time, γ. After leaving the Go‐phase, the cells enter the C‐phase which ends with cell division. The C‐phase and its constituent phases, the‘true’G1‐phase, the S‐phase, the G2‐phase and mitosis are assumed to have constant durations of T, T1Ts, T2 and Tm, respectively. For renewal tissue it is assumed that the probability per unit time of being lost from the population is a constant for all cells irrespective of their position in the cycle. The labelled mitosis curve and labelling index for continuous labelling are derived in terms of γ, T, and Ts. The model generates labelled mitosis curves which damp quickly and reach a constant value of twice the initial labelling index, if the mean duration of the Go‐phase is sufficiently long. It is shown that the predicted labelled mitosis and continuous labelling curves agree reasonably well with the experimental curves for the hamster cheek pouch if T has a value of about 60 hr. Data are presented for the rat dorsal epidermis which support the assumption that there is a constant probability per unit time of a cell being released from the Go‐phase.

Tumor cell kinetics using two labels and flow cytometry

“…Incubation was carried out for 45 min at room temperature in the dark. After washing, the preparation was then resuspended in 10 pgiml propidium iodide (PI; Sigma) in PBS and incubated with 5 pg/ml of RNase (Sigma) for 20 min at 37°C before carrying out flow cytometry.…”

“…The initial labeling index in this tumor system declined as tumor volume increased, but the lines all extrapolated back to similar points on the time axis. As can be shown from Equation 10, with LIl/Br set equal to zero, this intercept approximates -Ts, the length of S phase. A mean value of 11.8 5 0.5 h was obtained for T, in this fashion, similar to the mean value of 10.9 5 1.7 h obtained concurrently in the same tumors by the relative movement method, using only the BrdUrd (longest) time point (Table 1).…”

Periodic oscillations in leukopoiesis models with two delays

“…Since (12) reduces to (9) when τ 2 = 0, under assumption (H 1 ) the steady state (Q * , W * ) is locally asymptotically stable when τ 2 = 0 (see Proposition 3.1). Consequently, with assumption (H 1 ), when τ 2 increases, the stability of the steady state can only be lost if pure imaginary roots appear.…”

“…Consequently, with assumption (H 1 ), when τ 2 increases, the stability of the steady state can only be lost if pure imaginary roots appear. Hence we look for purely imaginary roots λ = ±iω, ω ∈ R, of (12).…”

“…In 1978, Mackey [26] proposed a mathematical model of hematopoietic stem cells dynamics inspired by the works of Lajtha [24] and Burns and Tannock [12]. Formed by a system of two nonlinear delay differential equations, where the delay describes the average cell cycle duration, this model stressed the influence of some factors (such as the apoptotic rate, the introduction rate, the cell cycle duration) playing an important role in the appearance of periodic solutions.…”