Long-Wavelength Interface Fluctuations Between Different Cell Populations are Suppressed by Friction

The study of interfaces between different cell populations or between cells and their environment is of great importance due to its relevance to various biological processes, such as compartmentalization during embryonic development and interfacial instability during cancer metastasis. A common theoretical framework to understand these phenomena is treating different cell populations as immiscible fluids with interfaces controlled by effective surface tensions arising from the interactions between the cells. Capillary Wave Theory (CWT) is usually the theoretical basis for these studies. However, special features in cellular systems such as complex cell-cell interactions and non-equilibrium can result in non-regular interface phenomena different from the predictions of regular CWT. In these cellular systems, another general feature is the high dissipation due to friction between cells and their environment. In this study, we use vertex model to simulate the interface between two groups of deformable cells moving under Brownian Dynamics and show that the interface fluctuation spectrum for these friction-dominated systems is qualitatively different from the prediction of CWT, with fluctuations in the long-wavelength regime being suppressed. These results greatly change our understanding of interfacial phenomena in overdamped systems and point out better ways to estimate surface tension.