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

Stability analysis. as a function of  for fixed values of  For  (green circle) the real part of Q takes, depending on  a value in the interval  The values for x are increasing from A-D, while  and  remain unchanged. For relatively low values of  (A-B) the real part  is positive for  After one or several turns, i.e by increasing  the spiral can potentially cross the origin only once (empty circle). In A the spiral misses the origin, while in B the spiral crosses the origin after one turn. Crossing of the origin means that the corresponding complex number  is a root of Q. In C the spiral starts at the origin. This represents the only real positive root of Q. For initially negative values of  (D) the spiral can never cross the origin because the distance to the center point (gray circle) is already in the beginning for  larger than the distance between the latter and the origin. By increasing y this distance will even grow further according to Eq. 33.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003616-g008: Stability analysis. as a function of for fixed values of For (green circle) the real part of Q takes, depending on a value in the interval The values for x are increasing from A-D, while and remain unchanged. For relatively low values of (A-B) the real part is positive for After one or several turns, i.e by increasing the spiral can potentially cross the origin only once (empty circle). In A the spiral misses the origin, while in B the spiral crosses the origin after one turn. Crossing of the origin means that the corresponding complex number is a root of Q. In C the spiral starts at the origin. This represents the only real positive root of Q. For initially negative values of (D) the spiral can never cross the origin because the distance to the center point (gray circle) is already in the beginning for larger than the distance between the latter and the origin. By increasing y this distance will even grow further according to Eq. 33.

Mentions: Crucially, as is a monotone increasing function of the spiral never crosses itself. For the imaginary part of vanishes as expected because and For this special case is obviously monotone decreasing with and restricted to the interval This means that the spiral can only ‘start’ in the interval between one and minus infinity. Taken together, this implies that if for and fixed the real part of is positive, then there exist a single ‘opportunity’ to cross the origin, while if negative there exists none. At the border where the real part is zero (Fig. 8 C), the corresponding value of is the only positive real root. Due to the monotonicity of any value of greater than the positive real root will result for in which does not admit for any solution. The different possible scenarios are exemplified in Fig. 8.


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)

Stability analysis. as a function of  for fixed values of  For  (green circle) the real part of Q takes, depending on  a value in the interval  The values for x are increasing from A-D, while  and  remain unchanged. For relatively low values of  (A-B) the real part  is positive for  After one or several turns, i.e by increasing  the spiral can potentially cross the origin only once (empty circle). In A the spiral misses the origin, while in B the spiral crosses the origin after one turn. Crossing of the origin means that the corresponding complex number  is a root of Q. In C the spiral starts at the origin. This represents the only real positive root of Q. For initially negative values of  (D) the spiral can never cross the origin because the distance to the center point (gray circle) is already in the beginning for  larger than the distance between the latter and the origin. By increasing y this distance will even grow further according to Eq. 33.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003616-g008: Stability analysis. as a function of for fixed values of For (green circle) the real part of Q takes, depending on a value in the interval The values for x are increasing from A-D, while and remain unchanged. For relatively low values of (A-B) the real part is positive for After one or several turns, i.e by increasing the spiral can potentially cross the origin only once (empty circle). In A the spiral misses the origin, while in B the spiral crosses the origin after one turn. Crossing of the origin means that the corresponding complex number is a root of Q. In C the spiral starts at the origin. This represents the only real positive root of Q. For initially negative values of (D) the spiral can never cross the origin because the distance to the center point (gray circle) is already in the beginning for larger than the distance between the latter and the origin. By increasing y this distance will even grow further according to Eq. 33.
Mentions: Crucially, as is a monotone increasing function of the spiral never crosses itself. For the imaginary part of vanishes as expected because and For this special case is obviously monotone decreasing with and restricted to the interval This means that the spiral can only ‘start’ in the interval between one and minus infinity. Taken together, this implies that if for and fixed the real part of is positive, then there exist a single ‘opportunity’ to cross the origin, while if negative there exists none. At the border where the real part is zero (Fig. 8 C), the corresponding value of is the only positive real root. Due to the monotonicity of any value of greater than the positive real root will result for in which does not admit for any solution. The different possible scenarios are exemplified in Fig. 8.

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