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Quantifying the length and variance of the eukaryotic cell cycle phases by a stochastic model and dual nucleoside pulse labelling.

Weber TS, Jaehnert I, Schichor C, Or-Guil M, Carneiro J - PLoS Comput. Biol. (2014)

Bottom Line: 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.

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.

ABSTRACT
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.

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Stochastic cell cycle model.A: Scheme of the proposed cell cycle model with three phases  and  The dashed border between the  and the  phase indicates that the  and  phase are pooled into a single phase. The random time  a cell needs to complete the processes associated to each of the phases, follows a delayed exponential distribution with specific parameters  and  for each phase. B: Delayed-exponential completion time distribution density  with parameters  and C: Best fit of the complementary cumulative distribution  to the fraction of undivided cells after birth obtained by time lapse cinematography [5] of slow and fast dividing cell lines. D: Best fit of  defined by Eq. 4 (solid line) to inter-mitotic time distribution density measured by long-term video tracking of in vitro proliferating B-cells [10]. The data in C and D were read from the graphs in the original publications ([5] and [10] respectively).
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pcbi-1003616-g001: Stochastic cell cycle model.A: Scheme of the proposed cell cycle model with three phases and The dashed border between the and the phase indicates that the and phase are pooled into a single phase. The random time a cell needs to complete the processes associated to each of the phases, follows a delayed exponential distribution with specific parameters and for each phase. B: Delayed-exponential completion time distribution density with parameters and C: Best fit of the complementary cumulative distribution to the fraction of undivided cells after birth obtained by time lapse cinematography [5] of slow and fast dividing cell lines. D: Best fit of defined by Eq. 4 (solid line) to inter-mitotic time distribution density measured by long-term video tracking of in vitro proliferating B-cells [10]. The data in C and D were read from the graphs in the original publications ([5] and [10] respectively).

Mentions: The eukaryotic cell cycle is defined as an orderly sequence of three phases distinguished by cellular DNA content, termed and A dividing cell is supposed to proceed, under this minimalist view, from one phase to another in a fixed order, until reaching the end of phase. Here it completes cytokinesis generating two genetically identical daughter cells that are by definition in phase (Fig. 1 A). We assume that the completion time of any phase (i.e. the time lapse between the entry to and exit from that given phase) is a random variable which is distributed according to a delayed (or shifted) exponential density function (Fig. 1 B),


Quantifying the length and variance of the eukaryotic cell cycle phases by a stochastic model and dual nucleoside pulse labelling.

Weber TS, Jaehnert I, Schichor C, Or-Guil M, Carneiro J - PLoS Comput. Biol. (2014)

Stochastic cell cycle model.A: Scheme of the proposed cell cycle model with three phases  and  The dashed border between the  and the  phase indicates that the  and  phase are pooled into a single phase. The random time  a cell needs to complete the processes associated to each of the phases, follows a delayed exponential distribution with specific parameters  and  for each phase. B: Delayed-exponential completion time distribution density  with parameters  and C: Best fit of the complementary cumulative distribution  to the fraction of undivided cells after birth obtained by time lapse cinematography [5] of slow and fast dividing cell lines. D: Best fit of  defined by Eq. 4 (solid line) to inter-mitotic time distribution density measured by long-term video tracking of in vitro proliferating B-cells [10]. The data in C and D were read from the graphs in the original publications ([5] and [10] respectively).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4109856&req=5

pcbi-1003616-g001: Stochastic cell cycle model.A: Scheme of the proposed cell cycle model with three phases and The dashed border between the and the phase indicates that the and phase are pooled into a single phase. The random time a cell needs to complete the processes associated to each of the phases, follows a delayed exponential distribution with specific parameters and for each phase. B: Delayed-exponential completion time distribution density with parameters and C: Best fit of the complementary cumulative distribution to the fraction of undivided cells after birth obtained by time lapse cinematography [5] of slow and fast dividing cell lines. D: Best fit of defined by Eq. 4 (solid line) to inter-mitotic time distribution density measured by long-term video tracking of in vitro proliferating B-cells [10]. The data in C and D were read from the graphs in the original publications ([5] and [10] respectively).
Mentions: The eukaryotic cell cycle is defined as an orderly sequence of three phases distinguished by cellular DNA content, termed and A dividing cell is supposed to proceed, under this minimalist view, from one phase to another in a fixed order, until reaching the end of phase. Here it completes cytokinesis generating two genetically identical daughter cells that are by definition in phase (Fig. 1 A). We assume that the completion time of any phase (i.e. the time lapse between the entry to and exit from that given phase) is a random variable which is distributed according to a delayed (or shifted) exponential density function (Fig. 1 B),

Bottom Line: 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.

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.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus