A study of instability to electrical symmetry breaking in unicellular systems

Abstract

The formation of a transcellular electric potential by an initially homogeneous and symmetric unicellular system is treated as the result of a non-equilibrium transition of the homogeneous cellular state to a patterned state. A mathematical theory is set forth which incorporates effects due to ion binding by membraneous structures in the cell interior, nonlinearity in the membrane transport of ions and a membrane-localized, mobile ion transport mechanism. This is a general theory, applicable to any unicellular system, for which a stability criterion giving the response of the system to non-spherically symmetric perturbations can be calculated. The general theory is applied to a specific model of the Fucus egg cell system. The model is found to be unstable to non-spherically symmetric perturbations under experimental conditions which lead to the formation of a net transcellular electric field and accompanying ionic currents. This study shows that the Fucus phenomenon can be thought of as a self-organization event, the result of nonlinear, non-equilibrium processes occurring in the cell membrane.