Quantifying the length and variance of the eukaryotic cell cycle phases by a stochastic model and dual nucleoside pulse labelling.
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To overcome this limitation, a redesigned experimental protocol is derived and validated in silico.The novelty is the timing of two consecutive pulses with distinct nucleosides that enables accurate and precise estimation of both the mean and the variance of the length of all phases.The proposed methodology to quantify the phase length distributions gives results potentially equivalent to those obtained with modern phase-specific biosensor-based fluorescent imaging.
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PubMed Central - PubMed
Affiliation: Instituto Gulbenkian de Ciência, Oeiras, Portugal; Department of Biology, Humboldt-Universität zu Berlin, Berlin Germany and Research Center ImmunoSciences, Charité - Universitätsmedizin Berlin, Berlin, Germany.
ABSTRACT
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A fundamental property of cell populations is their growth rate as well as the time needed for cell division and its variance. The eukaryotic cell cycle progresses in an ordered sequence through the phases G1, S, G2, and M, and is regulated by environmental cues and by intracellular checkpoints. Reflecting this regulatory complexity, the length of each phase varies considerably in different kinds of cells but also among genetically and morphologically indistinguishable cells. This article addresses the question of how to describe and quantify the mean and variance of the cell cycle phase lengths. A phase-resolved cell cycle model is introduced assuming that phase completion times are distributed as delayed exponential functions, capturing the observations that each realization of a cycle phase is variable in length and requires a minimal time. In this model, the total cell cycle length is distributed as a delayed hypoexponential function that closely reproduces empirical distributions. Analytic solutions are derived for the proportions of cells in each cycle phase in a population growing under balanced growth and under specific non-stationary conditions. These solutions are then adapted to describe conventional cell cycle kinetic assays based on pulse labelling with nucleoside analogs. The model fits well to data obtained with two distinct proliferating cell lines labelled with a single bromodeoxiuridine pulse. However, whereas mean lengths are precisely estimated for all phases, the respective variances remain uncertain. To overcome this limitation, a redesigned experimental protocol is derived and validated in silico. The novelty is the timing of two consecutive pulses with distinct nucleosides that enables accurate and precise estimation of both the mean and the variance of the length of all phases. The proposed methodology to quantify the phase length distributions gives results potentially equivalent to those obtained with modern phase-specific biosensor-based fluorescent imaging. Related in: MedlinePlus |
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Mentions: Crucially, as is a monotone increasing function of the spiral never crosses itself. For the imaginary part of vanishes as expected because and For this special case is obviously monotone decreasing with and restricted to the interval This means that the spiral can only ‘start’ in the interval between one and minus infinity. Taken together, this implies that if for and fixed the real part of is positive, then there exist a single ‘opportunity’ to cross the origin, while if negative there exists none. At the border where the real part is zero (Fig. 8 C), the corresponding value of is the only positive real root. Due to the monotonicity of any value of greater than the positive real root will result for in which does not admit for any solution. The different possible scenarios are exemplified in Fig. 8. |
View Article: PubMed Central - PubMed
Affiliation: Instituto Gulbenkian de Ciência, Oeiras, Portugal; Department of Biology, Humboldt-Universität zu Berlin, Berlin Germany and Research Center ImmunoSciences, Charité - Universitätsmedizin Berlin, Berlin, Germany.