Statistical mechanics of cell aggregates: explaining the phase transition and paradoxical piezoelectric behavior of soft biological tissues

Abstract

Piezoelectricity in biological soft tissues is a controversial issue with differing opinions. While there is compelling experimental evidence to suggest a piezoelectric-like response in tissues such as the aortic wall (among others), there are equally compelling experiments that argue against this notion. In addition, the lack of a polar structure in the underlying components of most soft biological tissues supports the latter. In this paper, we address the collective behavior of cells within a two-dimensional cell aggregate from the viewpoint of statistical mechanics. Our starting point is the simplest form of energy for cell behavior that only includes known observable facts e.g., the electrical Maxwell stress or electrostriction, resting potential across cell membranes, elasticity, and we explicitly exclude any possibility of electromechanical coupling reminiscent of piezoelectricity at the cellular level. We coarse-grain our cellular aggregate to obtain its emergent mechanical, physical, and electromechanical properties. Our findings indicate that the fluctuation of cellular strain (E) plays a similar role as the absolute temperature in a conventional atomistic-level statistical model. The coarse-grained effective free energy reveals several intriguing features of the collective behavior of cell aggregates, such as solid–fluid phase transitions and a distinct piezoelectric-like coupling, even though it is completely absent at the microscale. Closed-form formulas are obtained for key electromechanical properties, including stiffness, effective resting potential, critical E²-temperature (or fluctuation) for solid–fluid phase transitions, and apparent piezoelectric coupling in terms of fluctuation and electric potential regulated by active cellular processes.