Unit membrane parameters of electrically syncytial tissues

Abstract

A change in the holding voltage, exposure to channel-blocking agents, and similar interventions will induce changes in the membrane properties of electrically syncytial tissues. The altered membrane characteristics will produce changes in the input resistance (RIN) and the phase angle (phi) of the complex admittance of the whole preparation. Exact geometry-independent formulas are derived that give the intervention-induced changes in the membrane capacitance and conductance in terms of the measured changes in RIN and phi. The formulas automatically account for the effects of extracellular resistance in tissues such as skeletal muscle fibers, cardiac Purkinje fibers, and small cardiac "aggregates." The size, shape, and resistance of the extracellular space may be arbitrary and need not be measured. The surface (invaginated) membranes, which face the bath (extracellular space), are assumed to be characterized by an RC circuit with specific capacity Cme (Cmi) and specific conductivity gme (gmi). It is assumed that the intracellular voltage gradient between the electrodes and the membranes is negligible or reliably calculable. The intervention is assumed to leave the geometry and resistivity of the extracellular space unchanged. Under these circumstances the intervention-induced changes in Cme, Cmi, gme, and gmi are determined exactly in terms of the corresponding changes in RIN and certain frequency domain integrals over phi. The technique is illustrated by synthetic data for RIN and phi generated by the "disk" model of a skeletal muscle fiber in which Cme and Cmi depend upon holding voltage. The corresponding voltage dependence of RIN and phi is successfully "inverted" to expose the underlying voltage dependence of Cme and Cmi. These computations suggest that the formulas for Cme and Cmi will be useful in realistic situations, since they are not too sensitive to experimental error in the data for RIN and phi. This method makes it possible to detect voltage-dependent capacity changes due to unit membrane processes (e.g., charge movement) as long as the intrinsic time constant of that process is very small (e.g., less than 1/30 ms). As a second example I consider a disk model that is exposed to increasing concentrations of a channel-blocking agent. The drug dependence of RIN and phi is used to calculate the drug dependence of the total membrane conductivity (the sum of gme and gmi, weighted by the areas of surface and invaginated membranes, respectively).