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Mathematical model of tumour spheroid experiments with real-time cell cycle imaging

View ORCID ProfileWang Jin, Loredana Spoerri, Nikolas K. Haass, View ORCID ProfileMatthew J. Simpson
doi: https://doi.org/10.1101/2020.12.06.413856
Wang Jin
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland 4001, Australia
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Loredana Spoerri
2The University of Queensland, The University of Queensland, Diamantina Institute, Translational Research Institute, Brisbane, Australia
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Nikolas K. Haass
2The University of Queensland, The University of Queensland, Diamantina Institute, Translational Research Institute, Brisbane, Australia
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Matthew J. Simpson
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland 4001, Australia
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  • For correspondence: matthew.simpson@qut.edu.au
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Abstract

Three-dimensional (3D) in vitro tumour spheroid experiments are an important tool for studying cancer progression and potential drug therapies. Standard experiments involve growing and imaging spheroids to explore how different experimental conditions lead to different rates of spheroid growth. These kinds of experiments, however, do not reveal any information about the spatial distribution of the cell cycle within the expanding spheroid. Since 2008, a new experimental technology called fluorescent ubiquitination-based cell cycle indicator (FUCCI), has enabled real time in situ visualisation of the cell cycle progression. FUCCI labelling involves cells in G1 phase of the cell cycle fluorescing red, and cells in the S/G2/M phase of the cell cycle fluorescing green. Experimental observations of 3D tumour spheroids with FUCCI labelling reveal significant intratumoural structure, as the cell cycle status can vary with location. Although many mathematical models of tumour spheroid growth have been developed, none of the existing mathematical models are designed to interpret experimental observations with FUCCI labelling. In this work we extend the mathematical framework originally proposed by Ward and King (1997) to develop a new mathematical model of FUCCI-labelled tumour spheroid growth. The mathematical model treats the spheroid as being composed of three subpopulations: (i) living cells in G1 phase that fluoresce red; (ii) living cells in S/G2/M phase that fluoresce green; and, (iii) dead cells that do not fluoresce. We assume that the rates at which cells pass through different phases of the cell cycle, and the rate of cell death, depend upon the local oxygen concentration in the spheroid. Parameterising the new mathematical model using experimental measurements of cell cycle transition times, we show that the model can capture important experimental observations that cannot be addressed using previous mathematical models. Further, we show that the mathematical model can be used to quantitatively mimic the action of anti-mitotic drugs applied to the spheroid. All software required to solve the nonlinear moving boundary problem associated with the new mathematical model are available on GitHub.

Competing Interest Statement

The authors have declared no competing interest.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-ND 4.0 International license.
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Posted December 07, 2020.
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Mathematical model of tumour spheroid experiments with real-time cell cycle imaging
Wang Jin, Loredana Spoerri, Nikolas K. Haass, Matthew J. Simpson
bioRxiv 2020.12.06.413856; doi: https://doi.org/10.1101/2020.12.06.413856
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Mathematical model of tumour spheroid experiments with real-time cell cycle imaging
Wang Jin, Loredana Spoerri, Nikolas K. Haass, Matthew J. Simpson
bioRxiv 2020.12.06.413856; doi: https://doi.org/10.1101/2020.12.06.413856

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