The Equivalent Circuit of Single Crab Muscle Fibers As Determined by Impedance Measurements with Intracellular Electrodes

The input impedance of muscle fibers of the crab was determined with microelectrodes over the frequency range 1 cps to 10 kc/sec. Care was taken to analyze, reduce, and correct for capacitive artifact. One dimensional cable theory was used to determine the properties of the equivalent circuit of the membrane admittance, and the errors introduced by the neglect of the three dimensional spread of current are discussed. In seven fibers the equivalent circuit of an element of the membrane admittance must contain a DC path and two capacitances, each in series with a resistance. In two fibers, the element of membrane admittance could be described by one capacitance in parallel with a resistance. In several fibers there was evidence for a third very large capacitance. The values of the elements of the equivalent circuit depend on which of several equivalent circuits is chosen. The circuit (with a minimum number of elements) that was considered most reasonably consistent with the anatomy of the fiber has two branches in parallel: one branch having a resistance R(e) in series with a capacitance C(e); the other branch having a resistance R(b) in series with a parallel combination of a resistance R(m) and a capacitance C(m). The average circuit values (seven fibers) for this model, treating the fiber as a cylinder of sarcolemma without infoldings or tubular invaginations, are R(e) = 21 ohm cm(2); C(e) = 47 µf/cm(2); R(b) = 10.2 ohm cm(2); R(m) = 173 ohm cm(2); C(m) = 9.0 µf/cm(2). The relation of this equivalent circuit and another with a nonminimum number of circuit elements to the fine structure of crab muscle is discussed. In the above equivalent circuit R(m) and C(m) are attributed to the sarcolemma; R(e) and C(e), to the sarcotubular system; and R(b), to the amorphous material found around crab fibers. Estimates of actual surface area of the sarcolemma and sarcotubular system permit the average circuit values to be expressed in terms of unit membrane area. The values so expressed are consistent with the dielectric properties of predominantly lipid membranes.