Spencer Meryl A, Jabeen Zahera, Lubensky David K
Department of Physics, University of Michigan, 48103, Ann Arbor, MI, USA.
Eur Phys J E Soft Matter. 2017 Jan;40(1):2. doi: 10.1140/epje/i2017-11489-4. Epub 2017 Jan 17.
In computer simulations of dry foams and of epithelial tissues, vertex models are often used to describe the shape and motion of individual cells. Although these models have been widely adopted, relatively little is known about their basic theoretical properties. For example, while fourfold vertices in real foams are always unstable, it remains unclear whether a simplified vertex model description has the same behavior. Here, we study vertex stability and the dynamics of T1 topological transitions in vertex models. We show that, when all edges have the same tension, stationary fourfold vertices in these models do indeed always break up. In contrast, when tensions are allowed to depend on edge orientation, fourfold vertices can become stable, as is observed in some biological systems. More generally, our formulation of vertex stability leads to an improved treatment of T1 transitions in simulations and paves the way for studies of more biologically realistic models that couple topological transitions to the dynamics of regulatory proteins.
在干泡沫和上皮组织的计算机模拟中，顶点模型常被用于描述单个细胞的形状和运动。尽管这些模型已被广泛采用，但对其基本理论特性却知之甚少。例如，虽然真实泡沫中的四重顶点总是不稳定的，但尚不清楚简化的顶点模型描述是否具有相同的行为。在此，我们研究顶点模型中的顶点稳定性和T1拓扑转变动力学。我们表明，当所有边具有相同的张力时，这些模型中的静止四重顶点确实总是会分裂。相比之下，当允许张力取决于边的方向时，四重顶点可以变得稳定，正如在一些生物系统中所观察到的那样。更一般地说，我们对顶点稳定性的表述改进了模拟中对T1转变的处理，并为研究将拓扑转变与调节蛋白动力学相结合的更具生物学现实性的模型铺平了道路。
