Quantifying the Length and Variance of the Eukaryotic Cell Cycle Phases by a Stochastic Model and Dual Nucleoside Pulse Labelling

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 and 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.

Genome-wide analysis of replication timing by next-generation sequencing with E/L Repli-seq

“…In human cells, this process typically lasts 8–10 hours 1 . Different regions of the genome replicate at different times during S phase, following a defined replication timing (RT) program 2–8 .…”

Evidence that the cell cycle is a series of uncoupled, memoryless phases

“…These apparently stochastic differences in cell-cycle durations were originally attributed exclusively to the G1 phase 13 . However, more recent studies in multiple cell types have revealed that S and G2 also contribute significant variability to total cell cycle duration 3,14,15 . Collectively, these studies have revealed that differences in cell cycle durations are an inherent property of individual cells and raise the fundamental question of how these durations are determined.Over the past 50 years, multiple models have been put forth to explain the differences in cell cycle phase durations among individual cells.…”

Aggregated spatio-temporal division patterns emerge from reoccurring divisions of neural stem cells

“…To infer cell cycle kinetics from our data we implemented a non-spatial model of dividing NSCs with 5 parameters: the minimal cell cycle length d cc and minimal S-phase length d sp , their variability β cc and β sp parametrizing a lag-exponential (Weber et al, 2014) distribution, and the re-division probability p re-div (see Supplementary Figure 5A). From this model we simulate dividing NSCs and a BrdU-EdU-labelling experiment (Supplementary Figure 5B) and evaluate the percentage of re-dividing cells and DLS.…”

“…32h+9h is however not able to explain a plateauing of reviding NSCs for ∆t ≥ 24h. Instead of constant cell cycle and S-phase length, we thus assume them to be distributed as delayed exponential distributions (Weber et al, 2014) ,…”