An age-and-cyclin-structured cell population model for healthy and tumoral tissues

Brikci, Fadia Bekkal; Clairambault, Jean; Ribba, Benjamin; Perthame, Benoı̂t

doi:10.1007/s00285-007-0147-x

Cited by 72 publications

(26 citation statements)

References 37 publications

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“…Given such a goal, the development of CFSE and flow cytometry proliferation assays makes structured population models a natural framework in which to work. Significant literature exists on the subject of structured population models [18, 50, 57], and they have been widely applied to populations of cells [1, 16, 17, 26, 27, 53]. …”

Section: Introductionmentioning

confidence: 99%

A new model for the estimation of cell proliferation dynamics using CFSE data

Banks

Sutton

Thompson

et al. 2011

Journal of Immunological Methods

100

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CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and division-linked changes in cell behavior. Recently [13, 43, 45], a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter γ used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.

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Section: Introductionmentioning

confidence: 99%

A new model for the estimation of cell proliferation dynamics using CFSE data

Banks

Sutton

Thompson

et al. 2011

Journal of Immunological Methods

100

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“…One of the most famous transport models is the McKendrick equation for the cell division cycle [182], in which the structure variable is age in the cell cycle, on which the focus is thus set to represent the relevant heterogeneity in the cell population. This modelling frame has been used in many other settings (e.g., [4,21,95,30,201]), to represent cell population growth by progression in the cell cycle in a population of cells, tumour or healthy, but never thus far, to our knowledge, to study evolution towards drug resistance.…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

Chisholm

Lorenzi

Clairambault

2016

Biochimica et Biophysica Acta (BBA) - General Subjects

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BACKGROUND. Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. SCOPE OF REVIEW.We focus on intra-tumour heterogeneity, namely betweencell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies.MAJOR CONCLUSIONS. Plasticity in cancer cells, i.e., partial reversal to a stemlike status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies.GENERAL SIGNIFICANCE. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics.

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“…Such an approach was followed, for example, by Csikász-Nagy et al [9] and by Gérard & Goldbeter [10], who studied the dynamics of a five-variable model that can be seen as a skeleton version of their much more detailed model for the Cdk network [6]. In an alternative approach, not focusing on the biochemical intricacies of intracellular dynamics, cell populations of various ages are described by continuous, partial differential equations [11].…”

Section: Introductionmentioning

confidence: 99%

An automaton model for the cell cycle

et al. 2010

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We consider an automaton model that progresses spontaneously through the four successive phases of the cell cycle: G1, S (DNA replication), G2 and M (mitosis). Each phase is characterized by a mean duration t and a variability V. As soon as the prescribed duration of a given phase has passed, the transition to the next phase of the cell cycle occurs. The time at which the transition takes place varies in a random manner according to a distribution of durations of the cell cycle phases. Upon completion of the M phase, the cell divides into two cells, which immediately enter a new cycle in G1. The duration of each phase is reinitialized for the two newborn cells. At each time step in any phase of the cycle, the cell has a certain probability to be marked for exiting the cycle and dying at the nearest G1/S or G2/M transition. To allow for homeostasis, which corresponds to maintenance of the total cell number, we assume that cell death counterbalances cell replication at mitosis. In studying the dynamics of this automaton model, we examine the effect of factors such as the mean durations of the cell cycle phases and their variability, the type of distribution of the durations, the number of cells, the regulation of the cell population size and the independence of steady-state proportions of cells in each phase with respect to initial conditions. We apply the stochastic automaton model for the cell cycle to the progressive desynchronization of cell populations and to their entrainment by the circadian clock. A simple deterministic model leads to the same steady-state proportions of cells in the four phases of the cell cycle.

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An age-and-cyclin-structured cell population model for healthy and tumoral tissues

Cited by 72 publications

References 37 publications

A new model for the estimation of cell proliferation dynamics using CFSE data

A new model for the estimation of cell proliferation dynamics using CFSE data

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

An automaton model for the cell cycle

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