Abstract
Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret co-culture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan’s seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan’s seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.
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Code and Data Availability
Key computer code used to generate computational results and datasets generated and analysed during this study are summarised in the electronic supplementary material and are available on a GitHub repository (https://github.com/ryanmurphy42/Murphy2022CoCulture).
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Acknowledgements
We thank Associate Professor Rick Sturm, Frazer Institute (University of Queensland) for providing the fibroblasts. We thank John Blake for guidance using IncuCyte. This research was carried out at the Translational Research Institute (TRI), Woolloongabba, QLD. TRI is supported by a grant from the Australian Government. We thank the staff in the microscopy core facility at TRI for their technical support. We thank Professor Atsushi Miyawaki, RIKEN, Wako-city, Japan, for providing the FUCCI constructs, and Professor Meenhard Herlyn, The Wistar Institute, Philadelphia, PA, for providing the cell lines. We thank the four reviewers for their helpful comments.
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MJS and NKH are supported by the Australian Research Council (DP200100177).
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All authors conceived and designed the study. RJM performed the mathematical and statistical modelling, and drafted the article. GG performed all experimental work. All authors provided comments and approved the final version of the manuscript. NKH and MJS contributed equally.
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Murphy, R.J., Gunasingh, G., Haass, N.K. et al. Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments. Bull Math Biol 86, 8 (2024). https://doi.org/10.1007/s11538-023-01229-1
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DOI: https://doi.org/10.1007/s11538-023-01229-1