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

Chaffey, Gary; Lloyd, David J. B.; Skeldon, Anne C.; Kirkby, N.F.

doi:10.1371/journal.pone.0083477

Cited by 9 publications

(8 citation statements)

References 25 publications

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“…In all our simulations we observed that the derivative of the transition age is always smaller than one (Results not shown). To avoid restricting the parameter regime, age-structured models with multiple compartments for the cell-cycle phases [6,10] can be considered.…”

Section: Discussionmentioning

confidence: 99%

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays

et al. 2019

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Scratch assays are in-vitro methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. Typically, scratch assays are modelled by reaction diffusion equations depicting cell migration by Fickian diffusion and modelling proliferation by a logistic term. In a recent paper (Jin, W. et al. Bull Math Biol (2017)), the authors observed experimentally that during the early stage of the recolonisation process, there is a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. The authors did not identify the precise mechanism that causes the disturbance phase but showed that ignoring it can lead to incorrect parameter estimates. The aim of this work is to show that a non-linear age-structured population model can account for the two phases of proliferation in scratch assays. The model consists of an age-structured cell cycle model of a cell population, coupled with an ordinary differential equation describing the resource concentration dynamics in the substrate. The model assumes a resource-dependent cell cycle threshold age, above which cells are able to proliferate. By studying the dynamics of the full system in terms of the subpopulations of cells that can proliferate and the ones that can not, we are able to find conditions under which the model captures the two-phase behaviour. Through numerical simulations we are able

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Section: Discussionmentioning

confidence: 99%

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays

et al. 2019

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“…A recent study of different transition rate functions in cell-cycle PBMs has indicated that the particular function used had little impact on the ability of the model to fit the experimental data [27]. We assumed a normal cumulative distribution function for the transition probabilities G(C E ) and G(C B ) (see §1 in the electronic supplementary material).…”

Section: Development Of a Multi-stage Population Balance Model Based On Cyclin Concentrationmentioning

confidence: 99%

A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity

Fuentes-Garí

Misener

García-Münzer

et al. 2015

J. R. Soc. Interface.

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Acute myeloid leukaemia is characterized by marked inter-and intra-patient heterogeneity, the identification of which is critical for the design of personalized treatments. Heterogeneity of leukaemic cells is determined by mutations which ultimately affect the cell cycle. We have developed and validated a biologically relevant, mathematical model of the cell cycle based on unique cell-cycle signatures, defined by duration of cell-cycle phases and cyclin profiles as determined by flow cytometry, for three leukaemia cell lines. The model was discretized for the different phases in their respective progress variables (cyclins and DNA), resulting in a set of time-dependent ordinary differential equations. Cell-cycle phase distribution and cyclin concentration profiles were validated against population chase experiments. Heterogeneity was simulated in culture by combining the three cell lines in a blinded experimental set-up. Based on individual kinetics, the model was capable of identifying and quantifying cellular heterogeneity. When supplying the initial conditions only, the model predicted future cell population dynamics and estimated the previous heterogeneous composition of cells. Identification of heterogeneous leukaemia clones at diagnosis and post-treatment using such a mathematical platform has the potential to predict multiple future outcomes in response to induction and consolidation chemotherapy as well as relapse kinetics.

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“…In this case, model parameters are activation and degradation rates of regulatory proteins and their concentration. Alternatively, the model can include expressions for the percentage of cells that are found to be in a given cell-cycle phase, thus providing a “population overview” 7 , 8 . Model parameters are then transition probabilities between different phases.…”

Section: Introductionmentioning

confidence: 99%

Radiation-induced cell cycle perturbations: a computational tool validated with flow-cytometry data

Lonati

Barbieri

Guardamagna

et al. 2021

Sci Rep

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Cell cycle progression can be studied with computational models that allow to describe and predict its perturbation by agents as ionizing radiation or drugs. Such models can then be integrated in tools for pre-clinical/clinical use, e.g. to optimize kinetically-based administration protocols of radiation therapy and chemotherapy. We present a deterministic compartmental model, specifically reproducing how cells that survive radiation exposure are distributed in the cell cycle as a function of dose and time after exposure. Model compartments represent the four cell-cycle phases, as a function of DNA content and time. A system of differential equations, whose parameters represent transition rates, division rate and DNA synthesis rate, describes the temporal evolution. Initial model inputs are data from unexposed cells in exponential growth. Perturbation is implemented as an alteration of model parameters that allows to best reproduce cell-cycle profiles post-irradiation. The model is validated with dedicated in vitro measurements on human lung fibroblasts (IMR90). Cells were irradiated with 2 and 5 Gy with a Varian 6 MV Clinac at IRCCS Maugeri. Flow cytometry analysis was performed at the RadBioPhys Laboratory (University of Pavia), obtaining cell percentages in each of the four phases in all studied conditions up to 72 h post-irradiation. Cells show early $${\text{G}}_{2}$$ G 2 -phase block (increasing in duration as dose increases) and later $${\text{G}}_{1}$$ G 1 -phase accumulation. For each condition, we identified the best sets of model parameters that lead to a good agreement between model and experimental data, varying transition rates from $${\text{G}}_{1}$$ G 1 - to S- and from $${\text{G}}_{2}$$ G 2 - to M-phase. This work offers a proof-of-concept validation of the new computational tool, opening to its future development and, in perspective, to its integration in a wider framework for clinical use.

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

Cited by 9 publications

References 25 publications

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays

A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity

Radiation-induced cell cycle perturbations: a computational tool validated with flow-cytometry data

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