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Abstract
We study the flow of electrical currents in spherical cells with a non-conducting core, so that current flow is restricted to a thin shell below the cell’s membrane. Examples of such cells are fat storing cells (adipocytes). We derive the relation between current and voltage in the passive regime and examine the conditions under which the cell is electro-tonically compact. We compare our results to the well-studied case of electrical current flow in cylinder structures, such as neurons, described by the cable equation. In contrast to the cable, we find that for the sphere geometry (1) the voltage profile across the cell depends critically on the electrode geometry, and (2) the charging and discharging can be much faster than the membrane time constant; however, (3) voltage clamp experiments will incur similar distortion as in the cable case. We discuss the relevance for adipocyte function and experimental electro-physiology.
Highlights
Many biological cells rely on electrical signals for intracellular and intercellular communication; this includes neurons and other cell types, such as cardiac, muscle, and endocrine cells
The cable equation describes the spatiotemporal dynamics of the voltage along the cable in response to intracellular current injection along the cylinder
The cable equation is important for interpretation of experimental procedures, for instance to understand the fidelity of voltage clamp recordings
Summary
Many biological cells rely on electrical signals for intracellular and intercellular communication; this includes neurons and other cell types, such as cardiac, muscle, and endocrine cells. Currents can only run in the thin spherical cytoplasmic shell between inner cell membrane and the fat (Fig. 1) Given this unique morphology, it is not clear how charges from localized ion fluxes spread across the cell (Fedorenko et al 2020). Accurate patch clamp recordings require the cell to be electro-tonically compact (Armstrong and Gilly 1992; Fedorenko et al 2020), but the conditions for this are not known for the sphere geometry. To answer such questions, we derive here the equivalent of the cable equation for spherical geometries and analyze its properties. The charging curve for sphere geometries is not known
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