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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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Model based parameter estimation.A: Best fit of the model predictions (lines) to experimentally determined cell fractions after BrdU pulse labelling (dots). U87: In vitro cultured U87 human glioblastoma cancer cell line (three replicates). V79: In vitro cultured V79 Chinese hamster cells (single replicate) (courtesy G. Wilson). Best fit parameter values used to compute model predictions (U87:  V79:  units are hours). B: Approximate ML regions for the parameters  and  associated to each phase (gray:  red:  green: ). C: Bayesian bi-variate 99%-credibility regions for the parameters  and  for each phase. Arrows indicate point estimates and the dashed lines delineate the information that could have been gained in our thought experiment under noise-free conditions from two support points, one at  and a second at . The U87 data set was generated as described in the Experimental Methods section. The V79 data set was a kind gift of G. Wilson.
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pcbi-1003616-g003: Model based parameter estimation.A: Best fit of the model predictions (lines) to experimentally determined cell fractions after BrdU pulse labelling (dots). U87: In vitro cultured U87 human glioblastoma cancer cell line (three replicates). V79: In vitro cultured V79 Chinese hamster cells (single replicate) (courtesy G. Wilson). Best fit parameter values used to compute model predictions (U87: V79: units are hours). B: Approximate ML regions for the parameters and associated to each phase (gray: red: green: ). C: Bayesian bi-variate 99%-credibility regions for the parameters and for each phase. Arrows indicate point estimates and the dashed lines delineate the information that could have been gained in our thought experiment under noise-free conditions from two support points, one at and a second at . The U87 data set was generated as described in the Experimental Methods section. The V79 data set was a kind gift of G. Wilson.

Mentions: As a preliminary test we minimized the residual sum of squares i.e., least-squares fitting, of adequate mixtures of Eq. 24 and Eq. 25 to extracted frequencies at different time points after the pulse. We found that, for properly chosen parameter values, both data sets were reasonably well approximated by the model predictions (Fig. 3 A).


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)

Model based parameter estimation.A: Best fit of the model predictions (lines) to experimentally determined cell fractions after BrdU pulse labelling (dots). U87: In vitro cultured U87 human glioblastoma cancer cell line (three replicates). V79: In vitro cultured V79 Chinese hamster cells (single replicate) (courtesy G. Wilson). Best fit parameter values used to compute model predictions (U87:  V79:  units are hours). B: Approximate ML regions for the parameters  and  associated to each phase (gray:  red:  green: ). C: Bayesian bi-variate 99%-credibility regions for the parameters  and  for each phase. Arrows indicate point estimates and the dashed lines delineate the information that could have been gained in our thought experiment under noise-free conditions from two support points, one at  and a second at . The U87 data set was generated as described in the Experimental Methods section. The V79 data set was a kind gift of G. Wilson.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003616-g003: Model based parameter estimation.A: Best fit of the model predictions (lines) to experimentally determined cell fractions after BrdU pulse labelling (dots). U87: In vitro cultured U87 human glioblastoma cancer cell line (three replicates). V79: In vitro cultured V79 Chinese hamster cells (single replicate) (courtesy G. Wilson). Best fit parameter values used to compute model predictions (U87: V79: units are hours). B: Approximate ML regions for the parameters and associated to each phase (gray: red: green: ). C: Bayesian bi-variate 99%-credibility regions for the parameters and for each phase. Arrows indicate point estimates and the dashed lines delineate the information that could have been gained in our thought experiment under noise-free conditions from two support points, one at and a second at . The U87 data set was generated as described in the Experimental Methods section. The V79 data set was a kind gift of G. Wilson.
Mentions: As a preliminary test we minimized the residual sum of squares i.e., least-squares fitting, of adequate mixtures of Eq. 24 and Eq. 25 to extracted frequencies at different time points after the pulse. We found that, for properly chosen parameter values, both data sets were reasonably well approximated by the model predictions (Fig. 3 A).

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