How External Electrical Stimuli Can Act at Cellular Level in an in Vitro Culture: Mathematical Model and Experimental Analysis

Marina Flaibani and Nicola Elvassore. Department of Chemical Engeneering, University of Padova, via Marzolo, 9, Padova, 35131, Italy

Direct-current (DC) electric fields are present in all developing and regenerating animal tissues, yet their existence and potential impact on tissue repair and development are largely ignored. In vitro application of chronic electrical stimulation (ES) mimicking natural cell environment can be the starting point for a better understanding of in vivo cell behaviour. It appears that large ES can directly activate voltage-gated channels (VGCCs) by depolarizing the cell membrane and influence cell functionality, survival, differentiation, and proliferation. Moreover smaller and non-invasive ES may affect numerous molecular signalling events. The electrical stimulation of biological systems is generally subjected to a time-dependent applied voltages or currents. In the present work, we developed a model for rational understanding the physics of diffuse-charge dynamics and the influence of exogenous electric filed on cell culture in conductive medium. We considered a dilute electrolyte solution with 5 ions characterized by their concentrations, charges and diffusion coefficients. The electrolyte cell was limited by two parallel, planar electrodes. The bulk composition was described by dimensionless Nernst-Planck and Poisson equations. Hypothesis of “ideally polarizable” electrodes with no Faradaic processes were applied and the double layer theory was considered. The model is able to describe the transient changes in ionic distribution surrounding the cell membrane due to external ES. Our attention was focused in describing the difference in the double-layer composition and in the characteristic time scale phenomena due to different geometries and different chemico-physical properties of the culture chamber. Experimental analysis on neural and muscle cells with fast-response potential-sensitive probes helped to validate our mathematical model. Our model wants to be a versatile tools for a preliminary choice of electrical stimuli voltage, duration and frequency for each particular electrode-cell system.