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 intra-tumour 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.

中文翻译：

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混合搭配：表型共存是癌症侵袭的关键促进因素


侵袭健康组织是恶性肿瘤的一个明显特征。传统上，入侵被认为是由细胞驱动的，这些细胞已经获得了克服身体所采用的一系列生物和物理防御所需的所有必要特征。然而，鉴于越来越多的证据表明肿瘤内基因和表型异质性，另一种假设出现了：侵袭是否是由具有不同特征的细胞集合驱动的，这些细胞共同促进了侵袭过程？在本文中，我们使用数学模型来评估该假设在酸介导的入侵背景下的可行性。我们假设肿瘤扩张受到抑制生长的基质和阻止癌细胞运动的细胞外基质（ECM）的阻碍。此外，我们假设有两种类型的癌细胞：(i) 糖酵解表型，产生杀死基质细胞的酸；(ii) 基质降解表型，局部重塑 ECM。我们扩展了 Gatenby-Gawlinski 反应扩散模型，导出了五个耦合反应扩散方程组来描述由此产生的入侵过程。我们描述了空间均匀稳态的特征，并在一个空间维度上进行了模拟研究，以确定当我们改变两种表型之间的竞争强度时肿瘤如何发展。我们发现，当两种细胞类型能够稳定共存时，总体肿瘤生长最为广泛，因为这使得细胞能够局部混合并从特征组合中获益最多。相反，当物种间竞争超过物种内竞争时，种群在空间上分离并且入侵被阻止：（i）快速（基质降解者占主导地位）或（ii）缓慢（产酸者占主导地位）。 总的来说，我们的工作表明，异质肿瘤细胞群之间的空间和生态关系是决定它们合作能力的关键因素。具体来说，我们预测不同表型稳定共存的肿瘤比表型在空间上分离的肿瘤更具侵袭性。