Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the new discrete model and continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than an intrinsic proliferative advantage. We advise when the continuum model is beneficial and demonstrate why naively adding source/sink terms to a continuum model without considering the underlying discrete model may lead to incorrect results.

中文翻译：

---

异质上皮组织中的机械细胞竞争

机械细胞竞争在组织发育、癌症侵袭和组织老化过程中很重要。异质性在实际应用中起着关键作用，因为癌细胞可能具有与正常细胞不同的细胞硬度和不同的增殖率。为了研究这种现象，我们提出了一种异质上皮组织动力学的一维机械模型，其中包括细胞长度依赖性增殖和死亡机制。增殖和死亡被随机纳入离散模型，并在我们推导出的相应连续模型中作为源/汇项出现。使用新的离散模型和连续统描述，我们探索了多种应用，包括经历增殖和死亡的同质组织的进化，以及在异质环境中的竞争，癌组织与相邻的正常组织竞争空间。该框架使我们能够假设新机制，以解释癌细胞通过机械差异而不是内在增殖优势胜过健康细胞的能力。我们建议连续模型何时有益，并说明为什么天真地将源/汇项添加到连续模型而不考虑潜在的离散模型可能会导致不正确的结果。