Epithelial Tissue Growth Dynamics: Universal or Not?

Abstract

Universality of interfacial roughness in growing epithelial tissue has remained a controversial issue. Kardar-Parisi-Zhang (KPZ) and Molecular Beam Epitaxy (MBE) universality classes have been reported among other behaviors including total lack of universality. Here, we utilize a kinetic division model for deformable cells to investigate cell-colony scaling. With seemingly minor model changes, it can reproduce both KPZ-and MBE-like scaling in configurations that mimic the respective experiments. This result neutralizes the apparent scaling controversy. It can be speculated that this diversity in growth behavior is beneficial for efficient evolution and versatile growth dynamics.

Riemann surfaces for KPZ with periodic boundaries

“…The values of the exponents of the KPZ fixed point have been observed in experiments on growing colonies of bacteria [54] and cells [55,56], combustion fronts in paper [57][58][59], interface growth between turbulent phases in a liquid crystal [60][61][62][63], deposition at the edge of evaporating drops in colloidal suspensions [64,65], reaction fronts driven through a porous medium [66], see [67] for a detailed survey of those experiments. A common issue has been that the presence of strong enough quenched disorder in the medium may lead to a distinct universality class, where the noise in (1) depends on x and h(x , t ) rather than x and t .…”

KPZ fluctuations in finite volume

“…The values of the exponents of the KPZ fixed point have been observed in experiments on growing colonies of bacteria [54] and cells [55,56], combustion fronts in paper [57][58][59], interface growth between turbulent phases in a liquid crystal [60][61][62][63], deposition at the edge of evaporating drops in colloidal suspensions [64,65], reaction fronts driven through a porous medium [66], see [67] for a detailed survey of those experiments. A common issue has been that the presence of strong enough quenched disorder in the medium may lead to a distinct universality class, where the noise in (1) depends on x and h(x, t) rather than x and t. This was circumvented for combustion fronts by soaking the paper beforehand in a solution and for reaction fronts by driving the system with sufficient velocity through the porous medium.…”

Modeling growing confluent tissues using a lattice Boltzmann method: interface stability and fluctuations

“…Interface growth in biological systems has been studied experimentally [28,[40][41][42] and numerically [26,27,43,44] and, although KPZ scaling has been observed [26,28,43,44], there is some debate as to what the proper scaling is. Scaling in agreement with the molecular beam epitaxy universality class has also been reported [40,41], along with scaling inconsistent with either class [42,45].…”

“…As such, in recent years, numerous studies have sought to characterize the dynamics of the interface. This has been done by examining the stability of growing tissue fronts under different conditions [22][23][24][25] or by ascertaining the scaling behavior of the interface roughness to determine the universality class to which the growth process belongs [26][27][28][29][30][31]. Importantly, these studies led to conflicting results, leaving the question of the dynamics of growing tissue fronts and their stability unsettled.…”