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.
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Selected References
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- Adrian R. H., Chandler W. K., Hodgkin A. L. The kinetics of mechanical activation in frog muscle. J Physiol. 1969 Sep;204(1):207–230. doi: 10.1113/jphysiol.1969.sp008909. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Adrian R. H., Costantin L. L., Peachey L. D. Radial spread of contraction in frog muscle fibres. J Physiol. 1969 Sep;204(1):231–257. doi: 10.1113/jphysiol.1969.sp008910. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Costantin L. L. The role of sodium current in the radial spread of contraction in frog muscle fibers. J Gen Physiol. 1970 Jun;55(6):703–715. doi: 10.1085/jgp.55.6.703. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Eisenberg R. S., Engel E. The spatial variation of membrane potential near a small source of current in a spherical cell. J Gen Physiol. 1970 Jun;55(6):736–757. doi: 10.1085/jgp.55.6.736. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Eisenberg R. S., Gage P. W. Ionic conductances of the surface and transverse tubular membranes of frog sartorius fibers. J Gen Physiol. 1969 Mar;53(3):279–297. doi: 10.1085/jgp.53.3.279. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Eisenberg R. S. The equivalent circuit of single crab muscle fibers as determined by impedance measurements with intracellular electrodes. J Gen Physiol. 1967 Jul;50(6):1785–1806. doi: 10.1085/jgp.50.6.1785. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Eisenberg R. S., Vaughan P. C., Howell J. N. A theoretical analysis of the capacitance of muscle fibers using a distributed model of the tubular system. J Gen Physiol. 1972 Mar;59(3):360–373. doi: 10.1085/jgp.59.3.360. [DOI] [PMC free article] [PubMed] [Google Scholar]
- FALK G., FATT P. LINEAR ELECTRICAL PROPERTIES OF STRIATED MUSCLE FIBRES OBSERVED WITH INTRACELLULAR ELECTRODES. Proc R Soc Lond B Biol Sci. 1964 Apr 14;160:69–123. doi: 10.1098/rspb.1964.0030. [DOI] [PubMed] [Google Scholar]
- Franzini-Armstrong C. Studies of the triad. II. Penetration of tracers into the junctional gap. J Cell Biol. 1971 Apr;49(1):196–203. doi: 10.1083/jcb.49.1.196. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Freygang W. H., Jr, Rapoport S. I., Peachey L. D. Some relations between changes in the linear electrical properties of striated muscle fibers and changes in ultrastructure. J Gen Physiol. 1967 Nov;50(10):2437–2458. doi: 10.1085/jgp.50.10.2437. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Freygang W. H., Trautwein W. The structural implications of the linear electrical properties of cardiac Purkinje strands. J Gen Physiol. 1970 Apr;55(4):524–547. doi: 10.1085/jgp.55.4.524. [DOI] [PMC free article] [PubMed] [Google Scholar]
- González-Serratos H. Inward spread of activation in vertebrate muscle fibres. J Physiol. 1971 Feb;212(3):777–799. doi: 10.1113/jphysiol.1971.sp009356. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hodgkin A. L., Nakajima S. Analysis of the membrane capacity in frog muscle. J Physiol. 1972 Feb;221(1):121–136. doi: 10.1113/jphysiol.1972.sp009743. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hodgkin A. L., Nakajima S. The effect of diameter on the electrical constants of frog skeletal muscle fibres. J Physiol. 1972 Feb;221(1):105–120. doi: 10.1113/jphysiol.1972.sp009742. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Peachey L. D. The sarcoplasmic reticulum and transverse tubules of the frog's sartorius. J Cell Biol. 1965 Jun;25(3 Suppl):209–231. doi: 10.1083/jcb.25.3.209. [DOI] [PubMed] [Google Scholar]
- Peskoff A., Eisenberg R. S. Interpretation of some microelectrode measurements of electrical properties of cells. Annu Rev Biophys Bioeng. 1973;2:65–79. doi: 10.1146/annurev.bb.02.060173.000433. [DOI] [PubMed] [Google Scholar]
- Schneider M. F. Linear electrical properties of the transverse tubules and surface membrane of skeletal muscle fibers. J Gen Physiol. 1970 Nov;56(5):640–671. doi: 10.1085/jgp.56.5.640. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Valdiosera R., Clausen C., Eisenberg R. S. Impedance of frog skeletal muscle fibers in various solutions. J Gen Physiol. 1974 Apr;63(4):460–491. doi: 10.1085/jgp.63.4.460. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Valdiosera R., Clausen C., Eisenberg R. S. Measurement of the impedance of frog skeletal muscle fibers. Biophys J. 1974 Apr;14(4):295–315. doi: 10.1016/S0006-3495(74)85917-5. [DOI] [PMC free article] [PubMed] [Google Scholar]