The prediction of electrostatic forces (EFs) between biological cells still poses challenges of great scientific importance, e.g., cell recognition, electroporation (EP), and mechanosensing. Frequency-domain finite element simulations explore a variety of cell configurations in the range of parameters typical for eukaryotic cells. Here, by applying an electric field to a pair of layered concentric shells, a prototypical model of a biological cell, we provide numerical evidence that the instantaneous EF changes from repulsion to attraction as the drive frequency of the electric field is varied. We identify crossover frequencies and discuss their dependence as a function of field frequency, conductivity of the extracellular medium, and symmetry of the configuration of cells. We present findings which suggest that the spectrum of EFs depends sensitively on the configuration of cells. We discuss the signatures of the collective behavior of systems with many cells in the spectrum of the EF and highlight a few of the observational consequences that this behavior implies. By looking at different cell configurations, we are able to show that the repulsion-to-attraction transition phenomenon is largely associated with an asymmetric electrostatic screening at very small separation between cells. These findings pave the way for the experimental observation of the electromagnetic properties of efficient and simple models of biological tissues.

• Received 25 June 2015
• Revised 8 September 2015

DOI:https://doi.org/10.1103/PhysRevE.92.042717