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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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Effect of cell death and completion time distribution on parameter estimates.A: Comparison of analytical predictions (lines, Eq. 29) with simulated BrdU labelling experiment (squares). Cell death is assumed to occur exclusively during S phase with probability 0 (red) and 0.3 (blue) respectively. Only the  population is considered. Parameters:  units are hours. B: Difference between Eq. 29 (accounting for cell death) and Eq. 24 (neglecting cell death) at time  h (see dashed line in A), as a function of C: BrdU labelling experiments were simulated assuming gamma distributed phase completion times (red curve, graphs on left column) and cell death during S phase with probability  and  (green curve, graphs on left column). The effective completion time  (gray density plot, left column), the population growth (middle column) and the estimation of the mean and the standard deviation of  are shown for both cases. Approximate confidence intervals for the estimates are computed as 1.96 times the standard error. Even though  and the population growth are strongly influenced by the value of  both  and the estimates extracted from  are barely affected. The dashed lines in the middle column indicate the time of the first pulse, which was chosen such that the average population was similar in both scenarios. Parameters for gamma distributed completion time distribution of the three phases: shape:  scale:  delay:
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pcbi-1003616-g007: Effect of cell death and completion time distribution on parameter estimates.A: Comparison of analytical predictions (lines, Eq. 29) with simulated BrdU labelling experiment (squares). Cell death is assumed to occur exclusively during S phase with probability 0 (red) and 0.3 (blue) respectively. Only the population is considered. Parameters: units are hours. B: Difference between Eq. 29 (accounting for cell death) and Eq. 24 (neglecting cell death) at time h (see dashed line in A), as a function of C: BrdU labelling experiments were simulated assuming gamma distributed phase completion times (red curve, graphs on left column) and cell death during S phase with probability and (green curve, graphs on left column). The effective completion time (gray density plot, left column), the population growth (middle column) and the estimation of the mean and the standard deviation of are shown for both cases. Approximate confidence intervals for the estimates are computed as 1.96 times the standard error. Even though and the population growth are strongly influenced by the value of both and the estimates extracted from are barely affected. The dashed lines in the middle column indicate the time of the first pulse, which was chosen such that the average population was similar in both scenarios. Parameters for gamma distributed completion time distribution of the three phases: shape: scale: delay:

Mentions: where and represent the equivalents of and we had previously defined for the case of no cell loss. The former quantities, which now depend on are derived applying to Eq. 5 the same substitution as above. Expressions equivalent to Eq. 10 and Eq. 11 are obtained along the same lines. These become however rather lengthy and are therefore omitted here. Eq. 29 reproduces accurately in simulated BrdU pulse labelling experiments, if death occurs, as specified above (see Fig. 7 A for an example with and ). The differences between the analytical predictions for with 30% death and without death (denoted by ) are, for the parameter sets that we tested, relatively small, and vanish as expected, as tends to zero (see Fig. 7 B for computed at one specific time point ( h) for different values of ).


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)

Effect of cell death and completion time distribution on parameter estimates.A: Comparison of analytical predictions (lines, Eq. 29) with simulated BrdU labelling experiment (squares). Cell death is assumed to occur exclusively during S phase with probability 0 (red) and 0.3 (blue) respectively. Only the  population is considered. Parameters:  units are hours. B: Difference between Eq. 29 (accounting for cell death) and Eq. 24 (neglecting cell death) at time  h (see dashed line in A), as a function of C: BrdU labelling experiments were simulated assuming gamma distributed phase completion times (red curve, graphs on left column) and cell death during S phase with probability  and  (green curve, graphs on left column). The effective completion time  (gray density plot, left column), the population growth (middle column) and the estimation of the mean and the standard deviation of  are shown for both cases. Approximate confidence intervals for the estimates are computed as 1.96 times the standard error. Even though  and the population growth are strongly influenced by the value of  both  and the estimates extracted from  are barely affected. The dashed lines in the middle column indicate the time of the first pulse, which was chosen such that the average population was similar in both scenarios. Parameters for gamma distributed completion time distribution of the three phases: shape:  scale:  delay:
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003616-g007: Effect of cell death and completion time distribution on parameter estimates.A: Comparison of analytical predictions (lines, Eq. 29) with simulated BrdU labelling experiment (squares). Cell death is assumed to occur exclusively during S phase with probability 0 (red) and 0.3 (blue) respectively. Only the population is considered. Parameters: units are hours. B: Difference between Eq. 29 (accounting for cell death) and Eq. 24 (neglecting cell death) at time h (see dashed line in A), as a function of C: BrdU labelling experiments were simulated assuming gamma distributed phase completion times (red curve, graphs on left column) and cell death during S phase with probability and (green curve, graphs on left column). The effective completion time (gray density plot, left column), the population growth (middle column) and the estimation of the mean and the standard deviation of are shown for both cases. Approximate confidence intervals for the estimates are computed as 1.96 times the standard error. Even though and the population growth are strongly influenced by the value of both and the estimates extracted from are barely affected. The dashed lines in the middle column indicate the time of the first pulse, which was chosen such that the average population was similar in both scenarios. Parameters for gamma distributed completion time distribution of the three phases: shape: scale: delay:
Mentions: where and represent the equivalents of and we had previously defined for the case of no cell loss. The former quantities, which now depend on are derived applying to Eq. 5 the same substitution as above. Expressions equivalent to Eq. 10 and Eq. 11 are obtained along the same lines. These become however rather lengthy and are therefore omitted here. Eq. 29 reproduces accurately in simulated BrdU pulse labelling experiments, if death occurs, as specified above (see Fig. 7 A for an example with and ). The differences between the analytical predictions for with 30% death and without death (denoted by ) are, for the parameter sets that we tested, relatively small, and vanish as expected, as tends to zero (see Fig. 7 B for computed at one specific time point ( h) for different values of ).

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