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

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 <i>e.g.</i>, 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 (<b>E</b>) 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 <b>E</b>²-temperature (or fluctuation) for solid-fluid phase transitions, and apparent piezoelectric coupling in terms of fluctuation and electric potential regulated by active cellular processes.