Circuit Models of the Passive Electrical Properties of Frog Skeletal Muscle Fibers

Abstract

The relation between the fine structure, electric field equations, and electric circuit models of skeletal muscle fibers is discussed. Experimental evidence illustrates the profound variation of potential with circumferential position, even at low frequencies (100 Hz). Since one-dimensional cable theory cannot account for such variation, three-dimensional cable theory must be used. Several circuit models of a sarcomere are presented and plots are made of the predicted phase angle between sinusoidal applied current and potential. The circuit models are described by equations involving normalized variables, since they affect the phase plot in a relatively simple way. A method is presented for estimating the values of the circuit elements and the standard deviation of the estimates. The reliability of the estimates is discussed. An objective measure of fit, Hamilton's R test, is used to test the significance of different fits to data. Finally, it is concluded that none of the proposed circuit models provides an adequate description of the observed variation of phase angle with circumferential location. It is not clear whether the source of disagreement is inadequate measurements or inadequate theory.'The flow of current in a cylindrical cell like a muscle fiber has often been analyzed by representing the cell as an equivalent circuit of resistors, capacitors, and wires (Bozler and Cole, 1935;Falk and Fatt, 1964;Eisenberg, 1967;Freygang et al., 1967;Schneider, 1970; see reviews by Jack et al., 1973;Peachey and Adrian, 1973). The adequacy of the circuit model can be tested by comparing, over a wide range of frequencies, the impedance predicted by the model with the impedance actually observed.he values of the circuit elements which give the best fit between the predicted impedance and that actually measured are interpreted as the intrinsic electrical properties of the corresponding structural elements of the muscle fiber.'I.'here are several ambiguities in this kind of circuit analysis besides the obvious ones produced by the limited range and accuracy of experimental

Ion conductances of the surface and transverse tubular membranes of skeletal muscle

“…2 led to a passive radial space constant of three fiber diameters and a membrane resistance of 1 kf~ 2 for both the surface and tubular membrane. These values are in good agreement with the previous analyses of the passive equivalent circuit of frog skeletal muscle (Falk & Fatt, 1964;Schneider, 1970;Valdiosera, Clausen & Eisenberg, 1974b). For the frequencyrange of the present measurements, the passive shell model has been shown to agree satisfactorily with the exact solution of the appropriate cable equations (Peachy & Adrian, 1973).…”

Transport-dependent alterations of membrane properties of mammalian colon measured using impedance analysis

“…It should be noted that the estimates of the parameter standard deviations are computed from a linearization of the model about the best-fit parameter set (see Hamilton, 1964). They do not reflect a true confidence interval for each parameter due to the nonlinear dependence of the impedance on each parameter (see Valdiosera, Clausen & Eisenberg, 1974 (R~,) of the crypt lumen becomes comparable to the apical membrane impedance ation estimate indicates that a parameter is poorly determined. For this reason, data were excluded from further analysis if any parameter had a standard deviation which exceeded the best-fit value for that parameter by more than 10%.…”

Membrane transport parameters in frog corneal epithelium measured using impedance analysis techniques

“…They do not reflect a true confidence interval for each parameter value due to the nonlinear dependence of the impedance on each parameter (see Valdiosera et al, 1974).…”