Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability

Abstract

Tumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used to understand cancer progression and develop cancer therapies, have been routinely performed for the past fifty years in constant external environments. Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases.

Formation and growth of co-culture tumour spheroids: new compartment-based mathematical models and experiments

“…The presence of FUCCI signals indicate living cells and a large central region that lacks FUCCI signals indicates a necrotic core (Fig 1G). We have previously shown that the seminal Greenspan mathematical model describes monoculture spheroid growth remarkably well [5, 6, 7, 21] (Fig 1E-H). Here, we quantitatively directly connect Greenspan’s model to co-culture spheroid data for the first time.…”

“…At later times proliferation at the periphery balances mass loss from the necrotic core resulting in a limiting spheroid structure [5, 6, 21]. To define R n ( t ) we consider oxygen mechanisms [7]. Oxygen, reported in terms of oxygen partial pressure p ( r, t ) [%], diffuses within the spheroid and is consumed by living cells at constant rate per unit volume of cells.…”

“…Spheroids also bridge the gap between two-dimensional in vitro experiments and three-dimensional in vivo experiments. Previously we have developed a framework to characterise the temporal evolution of monoculture spheroid size and structure [5, 6, 7]. Here, we focus on more complicated co-culture tumour spheroid experiments.…”

“…First, at early times each cell within the spheroid is able to proliferate and the spheroid grows exponentially. Second, at later times a necrotic core forms, thought to be due to lack of oxygen (Fig 1E,F) [7]. The spheroid then grows to a limiting size and structure where proliferation at the periphery is thought to balance loss from the necrotic core (Fig 1H) [5, 6, 7, 21].…”

“…Second, at later times a necrotic core forms, thought to be due to lack of oxygen (Fig 1E,F) [7]. The spheroid then grows to a limiting size and structure where proliferation at the periphery is thought to balance loss from the necrotic core (Fig 1H) [5, 6, 7, 21]. To visualise living and necrotic regions within each spheroid, we use fluorescent ubiquitination-based cell cycle indicator (FUCCI) transduced melanoma cell lines (Fig 1G) [23, 24].…”