Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion

Abstract

Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno-and phenotypic intratumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: (i) a glycolytic phenotype which produces acid that kills stromal cells and (ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: (i) rapidly (matrix-degraders dominate) or (ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.

Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion

“…We assume that the tumour grows logistically, with maximum growth rate ρ and carrying capacity K. Further, the ECM acts as a physical barrier that inhibits tumour cell movement, but not proliferation. Thus, following Gatenby & Gawlinski [2] and others [3,16,36], we define the diffusivity of tumour cells as a monotonically decreasing function of the ECM density to model the obstruction of movement by the ECM. The diffusivity of tumour cells in the absence of ECM is denoted by D N and the ECM density that inhibits all tumour cell movement is denoted by M Max .…”

“…A detailed description of the numerical methods employed is provided in electronic supplementary material, S2. Similarly to [16], we assume that the tumour has already spread to a position x = σ < L in the tissue and we impose initial conditions that satisfy, for M ∈…”

“…Experimental evidence has confirmed that such an interstitial gap can exist and, in this way, the model has led to novel and accurate predictions regarding tumour invasion. This is one of the reasons why this model and its variations have been widely investigated [3,[12][13][14][15][16].…”

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition

“…That being said, we have also neglected the role of non-tumour tissue, which acts as an additional competitor for space and resources in the tumour, and may help to control resistant subpopulations [18]. We, and others, have also investigated the important role of metabolism in regulating tumour progression, immune dynamics and treatment response [58][59][60]. The role of the tumour intrinsic metabolism versus the extrinsic tissue microenvironment metabolism has also not been considered here.…”

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

“…For instance, in their pioneering paper (Gatenby and Gawlinski 1996), Gatenby and Gawlinski used a reaction-diffusion system to explore how nonlinear interactions between cancer cells and abiotic components of the tumour microenvironment may shape tumour growth. The Gatenby-Gawlinski model has recently been extended in Strobl et al (2020), in order to take into account the presence of cells with different phenotypic characteristics within the tumour. Hybrid cellular automaton models have been employed to study the impact of hypoxia and acidity on tumour growth and invasion (Anderson et al 2006(Anderson et al , 2009Gatenby et al 2007;Hatzikirou et al 2012;Kim et al 2018;Robertson-Tessi et al 2015).…”