Abstract
In many human cancers, the rate of cell growth depends crucially on the size of the tumor cell population. Low, zero, or negative growth at low population densities is known as the Allee effect; this effect has been studied extensively in ecology, but so far lacks a good explanation in the cancer setting. Here, we formulate and analyze an individual-based model of cancer, in which cell division rates are increased by the local concentration of an autocrine growth factor produced by the cancer cells themselves. We show, analytically and by simulation, that autocrine signaling suffices to cause both strong and weak Allee effects. Whether low cell densities lead to negative (strong effect) or reduced (weak effect) growth rate depends directly on the ratio of cell death to proliferation, and indirectly on cellular dispersal. Our model is consistent with experimental observations from three patient-derived brain tumor cell lines grown at different densities. We propose that further studying and quantifying population-wide feedback, impacting cell growth, will be central for advancing our understanding of cancer dynamics and treatment, potentially exploiting Allee effects for therapy.
Highlights
A common feature of tumor growth is the production, by the cancer cells themselves, of hormones known as growth factors that increase the rate of cell division
We have developed a computational model that can explain the Allee effect in terms of growth factor signalling, and show by mathematical analysis of the model that the magnitude of the Allee effect depends on the ratio of cell death to proliferation, as well as the properties of the growth factor
Cells from the cell lines U3013MG, U3123MG and U3289MG obtained from the Human Glioma Cell Culture (HGCC) resource [28] were suspended in serum-free neural stem cell (NSC) medium, supplemented with B-27, N2, EGF, FGF and plated on 384 well plates (BD Falcon Optilux TC #353962) coated in laminin
Summary
Cancer growth is increasingly understood as an ecosystem, in which the different cellular components grow, and interact. In the 1970s, Bronk et al [6] showed that dependence on growth factors can give rise to a latent period preceding exponential growth This suggested that negative feedback at low population density can interfere with exponential tumor expansion. Recent methodological advances make it possible to quantify how interactions between distinct subclones within cell populations affect the growth dynamics of the tumor as a whole [10, 11]. These observations have motivated the formulation of mathematical models that aim to explain nonlinear deviations from exponential growth that occur in cancer cell populations
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