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Logistic Proliferation of Cells in Scratch Assays is Delayed

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Abstract

Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell monolayer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction–diffusion models have been calibrated to data from scratch assays. These models typically include a logistic source term to describe carrying capacity-limited proliferation; however, the choice of using a logistic source term is often made without examining whether it is valid. Here we study the proliferation of PC-3 prostate cancer cells in a scratch assay. All experimental results for the scratch assay are compared with equivalent results from a proliferation assay where the cell monolayer is not scratched. Visual inspection of the time evolution of the cell density away from the location of the scratch reveals a series of sigmoid curves that could be naively calibrated to the solution of the logistic growth model. However, careful analysis of the per capita growth rate as a function of density reveals several key differences between the proliferation of cells in scratch and proliferation assays. Our findings suggest that the logistic growth model is valid for the entire duration of the proliferation assay. On the other hand, guided by data, we suggest that there are two phases of proliferation in a scratch assay; at short time, we have a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. These two phases are observed across a large number of experiments performed at different initial cell densities. Overall our study shows that simply calibrating the solution of a continuum model to a scratch assay might produce misleading parameter estimates, and this issue can be resolved by making a distinction between the disturbance and growth phases. Repeating our procedure for other scratch assays will provide insight into the roles of the disturbance and growth phases for different cell lines and scratch assays performed on different substrates.

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Acknowledgements

This work is supported by the Australian Research Council (DP140100249, FT130100148), and we appreciate the helpful comments from the two referees.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia

    Wang Jin, Esha T. Shah, Catherine J. Penington, Scott W. McCue & Matthew J. Simpson

  2. Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK

    Philip K. Maini

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  1. Wang Jin
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  2. Esha T. Shah
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  3. Catherine J. Penington
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  4. Scott W. McCue
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  5. Philip K. Maini
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  6. Matthew J. Simpson
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Correspondence to Matthew J. Simpson.

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Jin, W., Shah, E.T., Penington, C.J. et al. Logistic Proliferation of Cells in Scratch Assays is Delayed. Bull Math Biol 79, 1028–1050 (2017). https://doi.org/10.1007/s11538-017-0267-4

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  • DOI: https://doi.org/10.1007/s11538-017-0267-4

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