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

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 G(1), S, G(2), 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

Multiscalar cellular automaton simulates in-vivo tumour-stroma patterns calibrated from in-vitro assay data

Background: The tumour stroma -or tumour microenvironment- is an important constituent of solid cancers and it is thought to be one of the main obstacles to quantitative translation of drug activity between the preclinical and clinical phases of drug development. The tumour-stroma relationship has been described as being both pro- and antitumour in multiple studies. However, the causality of this complex biological relationship between the tumour and stroma has not yet been explored in a quantitative manner in complex tumour morphologies.Methods: To understand how these stromal and microenvironmental factors contribute to tumour physiology and how oxygen distributes within them, we have developed a lattice-based multiscalar cellular automaton model. This model uses principles of cytokine and oxygen diffusion as well as cell motility and plasticity to describe tumour-stroma landscapes. Furthermore, to calibrate the model, we propose an innovative modelling platform to extract model parameters from multiple in-vitro assays. This platform provides a novel way to extract meta-data that can be used to complement in-vivo studies and can be further applied in other contexts.Results: Here we show the necessity of the tumour-stroma opposing relationship for the model simulations to successfully describe the in-vivo stromal patterns of the human lung cancer cell lines Calu3 and Calu6, as models of clinical and preclinical tumour-stromal topologies. This is especially relevant to drugs that target the tumour microenvironment, such as antiangiogenics, compounds targeting the hedgehog pathway or immune checkpoint inhibitors, and is potentially a key platform to understand the mechanistic drivers for these drugs.Conclusion: The tumour-stroma automaton model presented here enables the interpretation of complex in-vitro data and uses it to parametrise a model for in-vivo tumour-stromal relationships

A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies

Inferring average generation via division-linked labeling

For proliferating cells subject to both division and death, how can one estimate the average generation number of the living population without continuous observation or a division-diluting dye? In this paper we provide a method for cell systems such that at each division there is an unlikely, heritable one-way label change that has no impact other than to serve as a distinguishing marker. If the probability of label change per cell generation can be determined and the proportion of labeled cells at a given time point can be measured, we establish that the average generation number of living cells can be estimated. Crucially, the estimator does not depend on knowledge of the statistics of cell cycle, death rates or total cell numbers. We validate the estimator and illustrate its features through comparison with published data and physiologically parameterized stochastic simulations, using it to suggest new experimental designs

Synergising single-cell resolution and 4sU labelling boosts inference of transcriptional bursting

Despite the recent rise of RNA-seq datasets combining single-cell (sc) resolution with 4-thiouridine (4sU) labelling, analytical methods exploiting their power to dissect transcriptional bursting are lacking. Presented here is a mathematical model and Bayesian inference implementation to facilitate joint estimation and confidence quantification of the parameters governing transcriptional bursting dynamics on a genome-wide scale. It is demonstrated that, unlike conventional scRNA-seq, 4sU scRNA-seq resolves temporal parameters and furthermore boosts inference of dimensionless parameters via a synergy between single-cell resolution and 4sU labelling. Accounting for various sources of both biological and technical noise, the observed cell-specific transcript turnovers and abundances are naturally integrated, thus reducing the error across all parameters of interest; both dimensionless and temporal. Applying the method to published 4sU scRNA-seq data indicated that large bursts are required for genes with very high expression levels, such as mitochondrial genes. Linking with published ChIP-seq data uncovered otherwise obscured associations between different parameters and histone modifications, agreeing with but advancing upon previously reported results. Evidence is provided for a link between histone modifications and modulation of bursting dynamics through, for example, effects on transcript stability, with these effects being dependent upon the location of the modification throughout the gene. Algorithm performance was validated using simulated datasets with ground truth target parameter values, both with a detailed analysis at a single-gene scale and with a high level analysis at a genomewide scale

The kinetics, mechanisms, and consequences of HTLV-1 plus-strand expression in naturally-infected T-cell clones

HTLV-1 replication requires the expression of plus-strand-encoded transcriptional transactivator protein Tax. However, Tax protein, a surrogate for HTLV-1 plus-strand expression is seldom detected in freshly isolated infected blood. The kinetics and consequences of plus-strand expression remain poorly understood. I used two fluorescent protein-based Tax reporter systems to study the dynamics and consequences of plus-strand expression and the changes to the host gene expression during plus-strand expression in naturally HTLV-1-infected, non-malignant T-cell clones. Time-lapse live-cell imaging followed by single-cell analysis of two T-cell clones stably transduced with a short-lived enhanced green fluorescent protein Tax reporter system identified five patterns of Tax expression in both clones and the distribution of these patterns was different between the two clones. Mathematical modelling of the experimental data revealed that the mean duration of Tax expression differed between the two clones – 94 and 417 hours, respectively. Host cell transcriptome analysis during successive stages of plus-strand strand expression using a fluorescent timer protein-based Tax reporter system in naturally-infected T-cell clones identified dysregulation in the expression of genes related to multiple cellular processes, including cell cycle, DNA damage response, and apoptosis at the initiation of the plus-strand transcriptional burst. The plus-strand expression showed immediate but transient adverse effects, including reduced proliferation, increased apoptosis, upregulation of a DNA damage marker, and impaired cell cycle progression. In the longer term, the immediate negative consequences of Tax expression were offset by reduced apoptosis and increased proliferation as cells terminated plus-strand expression. Plus-strand expression was also associated with cell-to-cell adhesion and reduced motility. These findings show within and between clone variability in the patterns and duration of HTLV-1 plus-strand expression, changes to the host gene expression during successive stages of the plus-strand expression, and the balance between the beneficial and adverse effects on the host cell associated with the plus-strand expression.Open Acces