The steady-states of a multi-compartment, age–size distribution model of cell-growth

Begg, Ronald; Wall, David J. N.; Wake, G. C.

doi:10.1017/s0956792508007535

Cited by 5 publications

(7 citation statements)

References 23 publications

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“…Following the notation introduced in [54], we term the asymptotic solution of the model a phase stationary solution (PSS) to indicate that, in this regime, the cell fractions f 1 , f s and f 2 , and the distribution s(x, t) remain constant in time. This is similar to predictions from other models in the literature [8,10,13,21,54] in the context of unperturbed growth; this regime is usually referred to as balanced, or asynchronous, exponential growth [9,14]. As mentioned previously, we can write the solution to Eqs.…”

Section: Cell-cycle Progression In a Static Normoxic Environmentsupporting

confidence: 82%

A DNA-structured mathematical model of cell-cycle progression in cyclic hypoxia

Celora

Maini

Byrne

et al. 2021

Preprint

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New experimental data have shown how the periodic exposure of cells to low oxygen levels (i.e., cyclic hypoxia) impacts their progress through the cell-cycle. Cyclic hypoxia has been detected in tumours and linked to poor prognosis and treatment failure. While fluctuating oxygen environments can be reproduced in vitro, the range of oxygen cycles that can be tested is limited. By contrast, mathematical models can be used to predict the response to a wide range of cyclic dynamics. Accordingly, in this paper we develop a mechanistic model of the cell-cycle that can be combined with in vitro experiments, to better understand the link between cyclic hypoxia and cell-cycle dysregulation. A distinguishing feature of our model is the inclusion of impaired DNA synthesis and cell-cycle arrest due to periodic exposure to severely low oxygen levels. Our model decomposes the cell population into four compartments and a time-dependent delay accounts for the variability in the duration of the S phase which increases in severe hypoxia due to reduced rates of DNA synthesis. We calibrate our model against experimental data and show that it recapitulates the observed cell-cycle dynamics. We use the calibrated model to investigate the response of cells to oxygen cycles not yet tested experimentally. When the re-oxygenation phase is sufficiently long, our model predicts that cyclic hypoxia simply slows cell proliferation since cells spend more time in the S phase. On the contrary, cycles with short periods of re-oxygenation are predicted to lead to inhibition of proliferation, with cells arresting from the cell-cycle when they exit the S phase. While model predictions on short time scales (about a day) are fairly accurate (i.e, confidence intervals are small), the predictions become more uncertain over longer periods. Hence, we use our model to inform experimental design that can lead to improved model parameter estimates and validate model predictions.

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Section: Cell-cycle Progression In a Static Normoxic Environmentsupporting

confidence: 82%

A DNA-structured mathematical model of cell-cycle progression in cyclic hypoxia

Celora

Maini

Byrne

et al. 2021

Preprint

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“…where κ > 1. Since then, different variations and extensions of the original model have been studied and used to describe plant cells, diatoms ( [2], [4], [11], [8]) and also tumor growth [3] .…”

Section: Introductionmentioning

confidence: 99%

“…Under this assumption Hall and Wake proved that the steady-size mass distribution exists and satisfies the celebrated panto-graph functional-differential equation y ′ (x) = ay(κx) + by(x) (1) where κ > 1. Since then, different variations and extensions of the original model have been studied and used to describe plant cells, diatoms ( [2], [4], [11], [8]) and also tumor growth [3] .…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic approach to a cell growth model

Derfel¹,

Feng²,

Molchanov³

2019

Contemporary Mathematics

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We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in random proportion between two offsprings (mitosis). Using the technique of moment equations we study asymptotics of the the mass-space distribution of the particles. Mass distribution of the particles is the solution of the equation with linearly transformed argument: functional, functional-differential or integral. We derive several limit theorems describing the fluctuations of the density of the particles, first two moments of the total masses etc. Also, we consider the branching process in the presence of a random spatial motion (say, diffusion). Here we discuss the classical Fisher, Kolmogorov, Petrovski, Piskunov model and distribution of mass inside the propogation front.

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“…Analysis has been undertaken to determine the existence and stability of steady size/DNA distributions [22] which may occur under specific circumstances using an age structured model. Population balance models have been used not only on healthy, unperturbed cell lines but also to model the effects of various treatments to cancer cell populations [15] , [18] , [16] and [23] .…”

Section: Introductionmentioning

confidence: 99%

The Effect of the G1 - S transition Checkpoint on an Age Structured Cell Cycle Model

et al. 2014

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Knowledge of how a population of cancerous cells progress through the cell cycle is vital if the population is to be treated effectively, as treatment outcome is dependent on the phase distributions of the population. Estimates on the phase distribution may be obtained experimentally however the errors present in these estimates may effect treatment efficacy and planning. If mathematical models are to be used to make accurate, quantitative predictions concerning treatments, whose efficacy is phase dependent, knowledge of the phase distribution is crucial. In this paper it is shown that two different transition rates at the - checkpoint provide a good fit to a growth curve obtained experimentally. However, the different transition functions predict a different phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is effected by the phase distribution of the population this difference may be critical in treatment planning. Using an age-structured population balance approach the cell cycle is modelled with particular emphasis on the - checkpoint. By considering the probability of cells transitioning at the - checkpoint, different transition functions are obtained. A suitable finite difference scheme for the numerical simulation of the model is derived and shown to be stable. The model is then fitted using the different probability transition functions to experimental data and the effects of the different probability transition functions on the model's results are discussed.

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The steady-states of a multi-compartment, age–size distribution model of cell-growth

Cited by 5 publications

References 23 publications

A DNA-structured mathematical model of cell-cycle progression in cyclic hypoxia

A DNA-structured mathematical model of cell-cycle progression in cyclic hypoxia

Probabilistic approach to a cell growth model

The Effect of the G1 - S transition Checkpoint on an Age Structured Cell Cycle Model

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