Farhadifar Reza, Röper Jens-Christian, Aigouy Benoit, Eaton Suzanne, Jülicher Frank
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Curr Biol. 2007 Dec 18;17(24):2095-104. doi: 10.1016/j.cub.2007.11.049.
Epithelial junctional networks assume packing geometries characterized by different cell shapes, neighbor number distributions and areas. The development of specific packing geometries is tightly controlled; in the Drosophila wing epithelium, cells convert from an irregular to a hexagonal array shortly before hair formation. Packing geometry is determined by developmental mechanisms that likely control the biophysical properties of cells and their interactions.
To understand how physical cellular properties and proliferation determine cell-packing geometries, we use a vertex model for the epithelial junctional network in which cell packing geometries correspond to stable and stationary network configurations. The model takes into account cell elasticity and junctional forces arising from cortical contractility and adhesion. By numerically simulating proliferation, we generate different network morphologies that depend on physical parameters. These networks differ in polygon class distribution, cell area variation, and the rate of T1 and T2 transitions during growth. Comparing theoretical results to observed cell morphologies reveals regions of parameter space where calculated network morphologies match observed ones. We independently estimate parameter values by quantifying network deformations caused by laser ablating individual cell boundaries.
The vertex model accounts qualitatively and quantitatively for the observed packing geometry in the wing disc and its response to perturbation by laser ablation. Epithelial packing geometry is a consequence of both physical cellular properties and the disordering influence of proliferation. The occurrence of T2 transitions during network growth suggests that elimination of cells from the proliferating disc epithelium may be the result of junctional force balances.
上皮连接网络呈现出以不同细胞形状、邻居数量分布和面积为特征的堆积几何结构。特定堆积几何结构的发育受到严格控制；在果蝇翅上皮中，细胞在刚要形成刚毛之前从不规则排列转变为六边形阵列。堆积几何结构由可能控制细胞生物物理特性及其相互作用的发育机制决定。
为了理解物理细胞特性和增殖如何决定细胞堆积几何结构，我们使用上皮连接网络的顶点模型，其中细胞堆积几何结构对应于稳定和静止的网络构型。该模型考虑了细胞弹性以及由皮层收缩性和粘附产生的连接力。通过对增殖进行数值模拟，我们生成了依赖于物理参数的不同网络形态。这些网络在多边形类别分布、细胞面积变化以及生长过程中T1和T2转变的速率方面存在差异。将理论结果与观察到的细胞形态进行比较，揭示了参数空间中计算出的网络形态与观察到的形态相匹配的区域。我们通过量化激光消融单个细胞边界引起的网络变形来独立估计参数值。
顶点模型在定性和定量上解释了翅芽中观察到的堆积几何结构及其对激光消融扰动的响应。上皮堆积几何结构是物理细胞特性和增殖的无序影响共同作用的结果。网络生长过程中T2转变的发生表明，从增殖的翅芽上皮中消除细胞可能是连接力平衡的结果。
