Quantifying the length and variance of the eukaryotic cell cycle phases by a stochastic model and dual nucleoside pulse labelling

PLoS Comput Biol. 2014 Jul 24;10(7):e1003616. doi: 10.1371/journal.pcbi.1003616. eCollection 2014 Jul.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Cell Cycle / physiology*
  • Cell Death
  • Cell Proliferation
  • Cytological Techniques
  • Eukaryotic Cells / cytology*
  • Eukaryotic Cells / physiology*
  • Kinetics
  • Models, Biological*
  • Nucleosides / metabolism*
  • Stochastic Processes

Substances

  • Nucleosides

Grants and funding

This work was supported by Fundação para a Ciência e a Tecnologia (Portugal) through fellowship SFRH/BD/64913/2009 to TSW and grant PTDC/EEACRO/104658/2008 to JC, by the German Ministry of Education and Research (BMBF) within the SYSTHER-INREMOS consortium, Grant Nos. 0315005B to MOG and TSW, and by the German Krebshilfe 108787 to CS. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.