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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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Dual pulse protocol.A: Simplified schematic representations of the protocols corresponding to a conventional single pulse labelling with one nucleoside analog (e.g., BrdU) and a dual pulse labelling experiment with two different nucleoside analogs (e.g., BrdU together IdU or EdU). B: Artificial staining of single-pulse labelling data (for original data see Fig. 2), showing eight of the nine subpopulations that could potentially be identified with double-pulse labelling. Notice that the four population  and  that can be followed by the conventional protocol, have each been subdivided according to the cell cycle phases. The naming convention for the populations is as follows: the superscript ( = ‘labelled undivided’,  = ‘labelled divided’,  = ‘unlabelled’) indicates whether the population is labelled and whether it has divided since the time of the first pulse; the first and the second subscript () stand for the phase in which the population was at the time of the first and the second pulse respectively. Double subscripts are used only when necessary.
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pcbi-1003616-g004: Dual pulse protocol.A: Simplified schematic representations of the protocols corresponding to a conventional single pulse labelling with one nucleoside analog (e.g., BrdU) and a dual pulse labelling experiment with two different nucleoside analogs (e.g., BrdU together IdU or EdU). B: Artificial staining of single-pulse labelling data (for original data see Fig. 2), showing eight of the nine subpopulations that could potentially be identified with double-pulse labelling. Notice that the four population and that can be followed by the conventional protocol, have each been subdivided according to the cell cycle phases. The naming convention for the populations is as follows: the superscript ( = ‘labelled undivided’,  = ‘labelled divided’,  = ‘unlabelled’) indicates whether the population is labelled and whether it has divided since the time of the first pulse; the first and the second subscript () stand for the phase in which the population was at the time of the first and the second pulse respectively. Double subscripts are used only when necessary.

Mentions: In order to approach the conditions assumed in the thought experiment by avoiding the loss of information caused by the intermixing, we devised an extension of the current single pulse protocol, which places a second pulse immediately before measuring or fixing each sample (see Fig. 4, top). The second pulse is expected to expose the cells with a further nucleoside analog that can be distinguished from the first one by Depending on the cell cycle kinetics and the length of the measuring period, the additional pulse increases the number of classifiable populations from four up to nine distinct populations.


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)

Dual pulse protocol.A: Simplified schematic representations of the protocols corresponding to a conventional single pulse labelling with one nucleoside analog (e.g., BrdU) and a dual pulse labelling experiment with two different nucleoside analogs (e.g., BrdU together IdU or EdU). B: Artificial staining of single-pulse labelling data (for original data see Fig. 2), showing eight of the nine subpopulations that could potentially be identified with double-pulse labelling. Notice that the four population  and  that can be followed by the conventional protocol, have each been subdivided according to the cell cycle phases. The naming convention for the populations is as follows: the superscript ( = ‘labelled undivided’,  = ‘labelled divided’,  = ‘unlabelled’) indicates whether the population is labelled and whether it has divided since the time of the first pulse; the first and the second subscript () stand for the phase in which the population was at the time of the first and the second pulse respectively. Double subscripts are used only when necessary.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003616-g004: Dual pulse protocol.A: Simplified schematic representations of the protocols corresponding to a conventional single pulse labelling with one nucleoside analog (e.g., BrdU) and a dual pulse labelling experiment with two different nucleoside analogs (e.g., BrdU together IdU or EdU). B: Artificial staining of single-pulse labelling data (for original data see Fig. 2), showing eight of the nine subpopulations that could potentially be identified with double-pulse labelling. Notice that the four population and that can be followed by the conventional protocol, have each been subdivided according to the cell cycle phases. The naming convention for the populations is as follows: the superscript ( = ‘labelled undivided’,  = ‘labelled divided’,  = ‘unlabelled’) indicates whether the population is labelled and whether it has divided since the time of the first pulse; the first and the second subscript () stand for the phase in which the population was at the time of the first and the second pulse respectively. Double subscripts are used only when necessary.
Mentions: In order to approach the conditions assumed in the thought experiment by avoiding the loss of information caused by the intermixing, we devised an extension of the current single pulse protocol, which places a second pulse immediately before measuring or fixing each sample (see Fig. 4, top). The second pulse is expected to expose the cells with a further nucleoside analog that can be distinguished from the first one by Depending on the cell cycle kinetics and the length of the measuring period, the additional pulse increases the number of classifiable populations from four up to nine distinct populations.

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