Abstract
Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, tumour spheroids more closely mimic the avascular tumour microenvironment where spatial differences in nutrient availability strongly influence growth. We show that spheroids initiated using significantly different numbers of cells grow to similar limiting sizes, suggesting that avascular tumours have a limiting structure; in agreement with untested predictions of classical mathematical models of tumour spheroids. We develop a novel mathematical and statistical framework to study the structure of tumour spheroids seeded from cells transduced with fluorescent cell cycle indicators, enabling us to discriminate between arrested and cycling cells and identify an arrested region. Our analysis shows that transient spheroid structure is independent of initial spheroid size, and the limiting structure can be independent of seeding density. Standard experimental protocols compare spheroid size as a function of time; however, our analysis suggests that comparing spheroid structure as a function of overall size produces results that are relatively insensitive to variability in spheroid size. Our experimental observations are made using two melanoma cell lines, but our modelling framework applies across a wide range of spheroid culture conditions and cell lines.
Highlights
Three-dimensional tumour spheroids provide an accessible and biologically realistic in vitro model of early avascular tumour growth [1, 2]
Reproducibility and uniformity in spheroid sizes is paramount [11,12,13], yet variability in the initial and final spheroid size is rarely accounted for, meaning subtle differences go undetected. We address this by developing a mathematical and statistical framework to study spheroid structure as a function of size, allowing us to ascertain whether initial spheroid size significantly affects growth dynamics
As we are primarily interested in spheroid structure and model validation, we focus our analysis on comparing the structure at different observation times and seeding densities rather than a more typical approach that calibrates the mathematical to all data simultaneously [25]
Summary
Three-dimensional tumour spheroids provide an accessible and biologically realistic in vitro model of early avascular tumour growth [1, 2]. Spheroids play a vital role in cancer therapy development, where the effect of a putative drug on spheroid growth is an indicator of efficacy [3,4,5,6,7,8,9,10] In this context, reproducibility and uniformity in spheroid sizes is paramount [11,12,13], yet variability in the initial and final spheroid size is rarely accounted for, meaning subtle differences go undetected. We observe that spheroids grow to a limiting size that is independent of the number of cells used to initiate the experiment (Fig. 1a–f), leading us to hypothesise that spheroids have a limiting structure [15] This behaviour is consistent with untested predictions of mathematical models of tumour progression [16,17,18,19,20,21,22,23,24,25] (Fig. 1g). We study the relationship between spheroid size and structure using a mathematical model that describes growth inhibition due to the spatial distribution of nutrients and metabolites
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