Epithelial branching morphogenesis drives the development of organs such as the lung, salivary gland, kidney and the mammary gland. It involves cell proliferation, cell differentiation and cell migration. An elaborate network of chemical and mechanical signals between the epithelium and the surrounding mesenchymal tissues regulates the formation and growth of branching organs. Surprisingly, when cultured in isolation from mesenchymal tissues, many epithelial tissues retain the ability to exhibit branching morphogenesis even in the absence of proliferation. In this work, we propose a simple, experimentally plausible mechanism that can drive branching morphogenesis in the absence of proliferation and cross-talk with the surrounding mesenchymal tissue. The assumptions of our mathematical model derive from in vitro observations of the behaviour of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGF$\beta$1 inhibits the formation of cell protrusions, leading to curvature-dependent inhibition of sprouting. Our hybrid cellular Potts and partial-differential equation model correctly reproduces the experimentally observed tissue-geometry-dependent determination of the sites of branching, and it suffices for the formation of self-avoiding branching structures in the absence and also in the presence of cell proliferation.

This article is part of the theme issue ‘Multi-scale analysis and modelling of collective migration in biological systems’.

上皮分支形态发生驱动器官如肺、唾液腺、肾脏和乳腺的发育。它涉及细胞增殖、细胞分化和细胞迁移。上皮和周围间充质组织之间的化学和机械信号的复杂网络调节分支器官的形成和生长。令人惊讶的是，当与间充质组织分离培养时，许多上皮组织即使在没有增殖的情况下也能保持表现出分支形态发生的能力。在这项工作中，我们提出了一种简单的、实验上合理的机制，可以在没有增殖和与周围间充质组织串扰的情况下驱动分支形态发生。我们数学模型的假设来自体外对乳腺上皮细胞行为的观察。这些数据表明生长因子 TGF 的自分泌$\beta$1抑制细胞突起的形成，导致发芽的曲率依赖性抑制。我们的混合细胞 Potts 和偏微分方程模型正确地再现了实验观察到的组织几何依赖性确定的分支位点，并且足以在不存在和存在细胞增殖的情况下形成自回避分支结构.

本文是主题问题“生物系统中集体迁移的多尺度分析和建模”的一部分。