Limits...
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.

Show MeSH

Related in: MedlinePlus

Robustness of parameter estimates to empirical phase duration distributions that are not delayed exponential functions.A-B: Least-squares fitting of histograms predicted from a hypoexponential distribution with two decay and one delay parameter  to measurements of phase durations using fluorescent biosensors [35]. The number of cells that were tracked in the original study was around 15 cells. C: Best fit of the cell cycle model with delayed exponential completion time distribution densities to synthetic data generated from a model with hypoexponential completion time distribution densities for the  and  phase with parameters as in A and B. D: Recovery of the initial distribution densities (solid lines) using the delayed exponential model (dashed line). Both the average and the variability in the  phase completion time distribution (original average: 10.70 h, estimated average: 10.88 h; original std: 2.03 h, estimated std: 1.99 h) were estimated accurately. The data shown in A-B was read from the graphs in the original publication ([35]).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4109856&req=5

pcbi-1003616-g006: Robustness of parameter estimates to empirical phase duration distributions that are not delayed exponential functions.A-B: Least-squares fitting of histograms predicted from a hypoexponential distribution with two decay and one delay parameter to measurements of phase durations using fluorescent biosensors [35]. The number of cells that were tracked in the original study was around 15 cells. C: Best fit of the cell cycle model with delayed exponential completion time distribution densities to synthetic data generated from a model with hypoexponential completion time distribution densities for the and phase with parameters as in A and B. D: Recovery of the initial distribution densities (solid lines) using the delayed exponential model (dashed line). Both the average and the variability in the phase completion time distribution (original average: 10.70 h, estimated average: 10.88 h; original std: 2.03 h, estimated std: 1.99 h) were estimated accurately. The data shown in A-B was read from the graphs in the original publication ([35]).

Mentions: Empirical measurements [35] indicate that the cycle phase time for the S phase is distributed closer to a delayed hypoexponential or a delayed gamma distribution (see below) rather than the caricatural delayed exponential. Therefore, an important question which arises is how much do the estimates of the average and standard deviation in phase durations obtained with this simple model depend on the true underlying distribution? While many different scenarios could be tested we opted to fit a delayed hypoexponential density with two decay and one delay parameter to direct in vitro measurements of and phase durations employing fluorescent biosensors (Fig. 6 A-B, [35]). Using the obtained best-fit estimates, we then performed in silico dual-pulse labelling experiments, in which the phase durations were drawn in the case of the and phase from delayed hypoexponential density functions (Fig. 6 C). Finally we fitted the simple model, i.e., Eq. 24 and Eq. 25, which is based on delayed exponential distributions, to this data, to see if we could recover the original averages and standard deviations despite using the ‘wrong’ caricatural model. Both summary statistics (i.e., mean, standard deviation) of phase durations could successfully be re-estimated (Fig. 6 D). Although generalizing this finding lies out of the scope of this article, it suggests that even if the true underlying distribution is not a delayed-exponential function, important quantities like the average and standard deviation of the phase durations may still be estimated with the simple model developed herein. It also indicates that BrdU labelling experiments with a realistic number of samples are unlikely to have the power to discriminate between delayed exponential and more complex density distributions.


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)

Robustness of parameter estimates to empirical phase duration distributions that are not delayed exponential functions.A-B: Least-squares fitting of histograms predicted from a hypoexponential distribution with two decay and one delay parameter  to measurements of phase durations using fluorescent biosensors [35]. The number of cells that were tracked in the original study was around 15 cells. C: Best fit of the cell cycle model with delayed exponential completion time distribution densities to synthetic data generated from a model with hypoexponential completion time distribution densities for the  and  phase with parameters as in A and B. D: Recovery of the initial distribution densities (solid lines) using the delayed exponential model (dashed line). Both the average and the variability in the  phase completion time distribution (original average: 10.70 h, estimated average: 10.88 h; original std: 2.03 h, estimated std: 1.99 h) were estimated accurately. The data shown in A-B was read from the graphs in the original publication ([35]).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003616-g006: Robustness of parameter estimates to empirical phase duration distributions that are not delayed exponential functions.A-B: Least-squares fitting of histograms predicted from a hypoexponential distribution with two decay and one delay parameter to measurements of phase durations using fluorescent biosensors [35]. The number of cells that were tracked in the original study was around 15 cells. C: Best fit of the cell cycle model with delayed exponential completion time distribution densities to synthetic data generated from a model with hypoexponential completion time distribution densities for the and phase with parameters as in A and B. D: Recovery of the initial distribution densities (solid lines) using the delayed exponential model (dashed line). Both the average and the variability in the phase completion time distribution (original average: 10.70 h, estimated average: 10.88 h; original std: 2.03 h, estimated std: 1.99 h) were estimated accurately. The data shown in A-B was read from the graphs in the original publication ([35]).
Mentions: Empirical measurements [35] indicate that the cycle phase time for the S phase is distributed closer to a delayed hypoexponential or a delayed gamma distribution (see below) rather than the caricatural delayed exponential. Therefore, an important question which arises is how much do the estimates of the average and standard deviation in phase durations obtained with this simple model depend on the true underlying distribution? While many different scenarios could be tested we opted to fit a delayed hypoexponential density with two decay and one delay parameter to direct in vitro measurements of and phase durations employing fluorescent biosensors (Fig. 6 A-B, [35]). Using the obtained best-fit estimates, we then performed in silico dual-pulse labelling experiments, in which the phase durations were drawn in the case of the and phase from delayed hypoexponential density functions (Fig. 6 C). Finally we fitted the simple model, i.e., Eq. 24 and Eq. 25, which is based on delayed exponential distributions, to this data, to see if we could recover the original averages and standard deviations despite using the ‘wrong’ caricatural model. Both summary statistics (i.e., mean, standard deviation) of phase durations could successfully be re-estimated (Fig. 6 D). Although generalizing this finding lies out of the scope of this article, it suggests that even if the true underlying distribution is not a delayed-exponential function, important quantities like the average and standard deviation of the phase durations may still be estimated with the simple model developed herein. It also indicates that BrdU labelling experiments with a realistic number of samples are unlikely to have the power to discriminate between delayed exponential and more complex density distributions.

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