An approach to electrical modeling of single and multiple cells

Abstract

Previous theoretical approaches to understanding effects of electric fields on cells have used partial differential equations such as Laplace's equation and cell models with simple shapes. Here we describe a transport lattice method illustrated by a didactic multicellular system model with irregular shapes. Each elementary membrane region includes local models for passive membrane resistance and capacitance, nonlinear active sources of the resting potential, and a hysteretic model of electroporation. Field amplification through current or voltage concentration changes with frequency, exhibiting significant spatial heterogeneity until the microwave range is reached, where cellular structure becomes almost ''electrically invisible.'' In the time domain, membrane electroporation exhibits significant heterogeneity but occurs mostly at invaginations and cell layers with tight junctions. Such results involve emergent behavior and emphasize the importance of using multicellular models for understanding tissue-level electric field effects in higher organisms. E lectric field effects in biological systems are of long-standing scientific interest. Endogenous fields are important in development (1) and wound healing (2). Small external fields from dc to ϾϷ1 GHz are of interest with respect to sensory systems, medical applications, and possible human health hazards (3-12). Larger pulsed fields are involved in stimulation of excitable cells (13,14) and electroporation and heating of tissue in vivo (15)(16)(17)(18)(19) and cells in vitro (20)(21)(22)(23) or ex vivo (24).Biological cells contain highly conductive aqueous electrolytes separated by thin, low-conductivity membranes populated with electrically active macromolecules. As a result, multicellular systems are extremely heterogeneous with respect to their passive electrical properties (local resistance and capacitance) and both passive and active interaction mechanisms (ion pumps, voltage-gated channels, and electroporatable membrane regions). This heterogeneity creates a basic complication: an applied field, E ជ app , leads to a response field, E ជ res , that differs spatially and temporally from E ជ app within the biological system. Here E ជ app is the field that would exist if the biological system were replaced by a purely conductive medium.Many of these interactions have biological relevance. Fields guide ionic currents (1, 2) and cause Joule heating. At cell membranes fields drive conformational changes in macromolecules, particularly ion channels (7,13,14) and membrane-associated enzymes (6, 25), and cause electroporation (15-19, 26, 27) and the related events of electro-insertion (24) and electrofusion (22,26,27). Several of these interactions can take place simultaneously, although often one interaction dominates. Importantly, these interactions depend on the local electric field, not the average applied field usually reported in experimental studies or predicted by tissue-level simulations. Accordingly, it is important to create and solve increasingly realisti...

Stimulation of Capacitative Calcium Entry in HL-60 Cells by Nanosecond Pulsed Electric Fields

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Single cell dielectric spectroscopy

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