Autocrine signaling explains the emergence of Allee effects in cancer cell populations

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 of brain tumor cells 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.

Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework

“…Similarly, whether cancer 2022 The Author(s) Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited. spreads to a different body part from a primary tumour site depends on the survival of small numbers of tumour cells growing successfully in new locations [7,8]. A classical continuum model for studying the survival of biological populations is the strong Allee effect model, based on an ordinary differential equation (ODE),…”

“…For example, predicting whether a species released into a wild area will survive is crucial in protecting endangered animals [6]. Similarly, whether cancer spreads to a different body part from a primary tumour site depends on the survival of small numbers of tumour cells growing successfully in new locations [7,8]. A classical continuum model for studying the survival of biological populations is the strong Allee effect model, based on an ordinary differential equation (ODE), dCfalse(tfalse)dt=λCfalse(tfalse)(1−C(t)K)(C(t)A−1),where Cfalse(tfalse)≥0 is the population density at time t≥0, λ>0 is the intrinsic growth rate, K>0 is the carrying capacity density and 0<A<K is the Allee threshold density [9–15].…”

“…The strong Allee effect model belongs to a broader class of population models, called bistable population dynamics models, and the key feature of these models is that they involve three equilibrium points: and are stable equilibrium points, and , where is unstable. There are many ODE models of this kind, not just the classical cubic form in ( 1.1 ) [ 8 , 16 – 18 ].…”