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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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Analysis of simulated dual pulse labelling data.A: Average kinetics of unlabelled (dashed line) and labelled cell cohorts (colored lines) were computed from Eq. 25, using ML parameter estimates from the U87 and the V79 data sets (U87:  V79:  units are hours). Support points and repeats were chosen according to the real experiments. Multinomial noise was added, mimicking the residuals found in the original data sets (see the Computational Methods section for more details). Finally, model solutions (lines) were fitted to the synthetic data sets (triangles). Best fit parameters (U87:  V79:  units are hours) B: ML parameter estimates from simulated data. All ML regions converge to point estimates (arrows). Squares indicate parameters used for generating the data (see A). C: Bayesian bi-variate 99%-credibility regions for the parameters  and  for each phase, based on the artificial data.
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pcbi-1003616-g005: Analysis of simulated dual pulse labelling data.A: Average kinetics of unlabelled (dashed line) and labelled cell cohorts (colored lines) were computed from Eq. 25, using ML parameter estimates from the U87 and the V79 data sets (U87: V79: units are hours). Support points and repeats were chosen according to the real experiments. Multinomial noise was added, mimicking the residuals found in the original data sets (see the Computational Methods section for more details). Finally, model solutions (lines) were fitted to the synthetic data sets (triangles). Best fit parameters (U87: V79: units are hours) B: ML parameter estimates from simulated data. All ML regions converge to point estimates (arrows). Squares indicate parameters used for generating the data (see A). C: Bayesian bi-variate 99%-credibility regions for the parameters and for each phase, based on the artificial data.

Mentions: To assess if the latter method would allow quantifying more accurately and precisely the parameters of the model, we generated in silico data mimicking the output of a hypothetical dual pulse experiment using Eq. 24 and Eq. 25 (see Fig. 5 A). We found that by employing the redesigned protocol with the same replicates and time points as in the corresponding data sets, we could reduce the regions corresponding to the ML up to point estimates (Fig. 5 B). Furthermore, the uncertainties due to noise became also significantly smaller (Fig. 5 C). Pooling this artificial data according to the output expected from a single pulse experiment, reproduced again the uncertainties seen in Fig. 3 C (not shown). Together this indicates that the redesigned dual pulse protocol provides parameter estimates with higher accuracy and precision. Real dual pulse labelling experiments will however be needed to confirm these theoretical predictions.


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)

Analysis of simulated dual pulse labelling data.A: Average kinetics of unlabelled (dashed line) and labelled cell cohorts (colored lines) were computed from Eq. 25, using ML parameter estimates from the U87 and the V79 data sets (U87:  V79:  units are hours). Support points and repeats were chosen according to the real experiments. Multinomial noise was added, mimicking the residuals found in the original data sets (see the Computational Methods section for more details). Finally, model solutions (lines) were fitted to the synthetic data sets (triangles). Best fit parameters (U87:  V79:  units are hours) B: ML parameter estimates from simulated data. All ML regions converge to point estimates (arrows). Squares indicate parameters used for generating the data (see A). C: Bayesian bi-variate 99%-credibility regions for the parameters  and  for each phase, based on the artificial data.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003616-g005: Analysis of simulated dual pulse labelling data.A: Average kinetics of unlabelled (dashed line) and labelled cell cohorts (colored lines) were computed from Eq. 25, using ML parameter estimates from the U87 and the V79 data sets (U87: V79: units are hours). Support points and repeats were chosen according to the real experiments. Multinomial noise was added, mimicking the residuals found in the original data sets (see the Computational Methods section for more details). Finally, model solutions (lines) were fitted to the synthetic data sets (triangles). Best fit parameters (U87: V79: units are hours) B: ML parameter estimates from simulated data. All ML regions converge to point estimates (arrows). Squares indicate parameters used for generating the data (see A). C: Bayesian bi-variate 99%-credibility regions for the parameters and for each phase, based on the artificial data.
Mentions: To assess if the latter method would allow quantifying more accurately and precisely the parameters of the model, we generated in silico data mimicking the output of a hypothetical dual pulse experiment using Eq. 24 and Eq. 25 (see Fig. 5 A). We found that by employing the redesigned protocol with the same replicates and time points as in the corresponding data sets, we could reduce the regions corresponding to the ML up to point estimates (Fig. 5 B). Furthermore, the uncertainties due to noise became also significantly smaller (Fig. 5 C). Pooling this artificial data according to the output expected from a single pulse experiment, reproduced again the uncertainties seen in Fig. 3 C (not shown). Together this indicates that the redesigned dual pulse protocol provides parameter estimates with higher accuracy and precision. Real dual pulse labelling experiments will however be needed to confirm these theoretical predictions.

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