Interfaces in tissues are ubiquitous, both between tissue and environment as well as between populations of different cell types. The propagation of an interface can be driven mechanically. % e.g. by a difference in the respective homeostatic stress of the different cell types. Computer simulations of growing tissues are employed to study the stability of the interface between two tissues on a substrate. From a mechanical perspective, the dynamics and stability of this system is controlled mainly by four parameters of the respective tissues: (i) the homeostatic stress (ii) cell motility (iii) tissue viscosity and (iv) substrate friction. For propagation driven by a difference in homeostatic stress, the interface is stable for tissue-specific substrate friction even for very large differences of homeostatic stress; however, it becomes unstable above a critical stress difference when the tissue with the larger homeostatic stress has a higher viscosity. A small difference in directed bulk motility between the two tissues suffices to result in propagation with a stable interface, even for otherwise identical tissues. Larger differences in motility force, however, result in a finite-wavelength instability of the interface. Interestingly, the instability is apparently bound by nonlinear effects and the amplitude of the interface undulations only grows to a finite value in time.

中文翻译：

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生长组织中界面的不稳定性和指法

组织中的界面无处不在，无论是在组织和环境之间，还是在不同细胞类型的群体之间。可以机械地驱动界面的传播。％例如通过不同细胞类型的各自稳态压力的差异。生长组织的计算机模拟被用来研究基质上两种组织之间界面的稳定性。从机械角度来看，该系统的动力学和稳定性主要由各个组织的四个参数控制：（i）稳态应力（ii）细胞运动（iii）组织粘度和（iv）基质摩擦。对于由稳态应力差异驱动的传播，即使对于非常大的稳态应力差异，界面对于组织特异性基底摩擦也是稳定的；然而，当具有较大稳态应力的组织具有较高粘度时，它在临界应力差以上变得不稳定。两种组织之间定向体积运动的微小差异足以导致具有稳定界面的传播，即使对于其他相同的组织也是如此。然而，运动力的较大差异会导致界面的有限波长不稳定性。有趣的是，不稳定性显然受到非线性效应的约束，界面起伏的幅度只随时间增长到一个有限值。然而，运动力的较大差异会导致界面的有限波长不稳定性。有趣的是，不稳定性显然受到非线性效应的约束，界面起伏的幅度只随时间增长到一个有限值。然而，运动力的较大差异会导致界面的有限波长不稳定性。有趣的是，不稳定性显然受到非线性效应的约束，界面起伏的幅度只随时间增长到一个有限值。