Nemati Hossein, de Graaf J
Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
Soft Matter. 2024 Oct 30;20(42):8337-8352. doi: 10.1039/d4sm00445k.
The cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular cellular Potts model.
细胞Potts模型，也称为Glazier-Graner-Hogeweg模型，是一种基于晶格的方法，通过该方法可以对单个细胞水平的生物组织进行数值研究。传统上，二维系统假设为方形或六边形的底层晶格结构，已知这会在模型组织的结构和动力学中引入伪影。也就是说，在规则晶格上，细胞可以呈现由底层晶格对称性决定的形状。在这里，我们开发了该方法的一个变体，可应用于广泛的（非）规则晶格。我们表明，在源自类流体构型的不规则晶格上，可以消除两种类型的伪影。我们进一步报告了单分散融合细胞中存在的类流体无序相和类固体六边形有序相之间的转变，该转变是其表面张力的函数。这种转变显示出一级相变的特征，并且不同于通常在顶点模型和主动Voronoi模型中报道的玻璃化/堵塞转变。我们通过分析在我们的状态空间中发现的形状参数分布来强调这一点。我们的分析为未来使用（非）规则细胞Potts模型研究上皮组织提供了有用的参考。
