Abstract
Propagation of the action potential is a complex process, and the relationships among the various factors involved in conduction have not been clear. We use three mathematical models of uniform conduction in a cable to clarify some of these relationships. One model is newly derived here, and two have been previously derived by Hunter et al. (1975, Prog. Biophys. Mol. Biol., 30:99-144). These models were able to simulate individual experimental action potential upstrokes previously obtained (Walton and Fozzard, 1983, Biophys. J., 44:1-8). The models were then utilized to provide relationships between measures of conduction. Among these were that maximal upstroke velocity (Vmax) is directly proportional to peak inward ionic current normalized by capacitance that is filled during the upstroke (I/Cf), and that conduction velocity was directly related to the square root of either Vmax or I/Cf. These relationships were shown to be model independent and to predict the experimental results, thus providing validated quantitative relationships that were not discernible through use of experimental data alone. The concept of safety factor was considered and a parameter was proposed that may be related to safety factor.
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Selected References
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- Cooley J. W., Dodge F. A., Jr Digital computer solutions for excitation and propagation of the nerve impulse. Biophys J. 1966 Sep;6(5):583–599. doi: 10.1016/S0006-3495(66)86679-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Easton D. M. Exponentiated exponential model (Gompertz kinetics) of Na+ and K+ conductance changes in squid giant axon. Biophys J. 1978 Apr;22(1):15–28. doi: 10.1016/S0006-3495(78)85467-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Goldstein S. S., Rall W. Changes of action potential shape and velocity for changing core conductor geometry. Biophys J. 1974 Oct;14(10):731–757. doi: 10.1016/S0006-3495(74)85947-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
- HUXLEY A. F. Ion movements during nerve activity. Ann N Y Acad Sci. 1959 Aug 28;81:221–246. doi: 10.1111/j.1749-6632.1959.tb49311.x. [DOI] [PubMed] [Google Scholar]
- Hunter P. J., McNaughton P. A., Noble D. Analytical models of propagation in excitable cells. Prog Biophys Mol Biol. 1975;30(2-3):99–144. doi: 10.1016/0079-6107(76)90007-9. [DOI] [PubMed] [Google Scholar]
- JENERICK H. AN ANALYSIS OF THE STRIATED MUSCLE FIBER ACTION CURRENT. Biophys J. 1964 Mar;4:77–91. doi: 10.1016/s0006-3495(64)86770-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Khodorov B. I., Timin E. N. Nerve impulse propagation along nonuniform fibres. Prog Biophys Mol Biol. 1975;30(2-3):145–184. doi: 10.1016/0079-6107(76)90008-0. [DOI] [PubMed] [Google Scholar]
- Levin D. N., Fozzard H. A. A cleft model for cardiac Purkinje strands. Biophys J. 1981 Mar;33(3):383–408. doi: 10.1016/S0006-3495(81)84902-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Matsumoto G., Tasaki I. A study of conduction velocity in nonmyelinated nerve fibers. Biophys J. 1977 Oct;20(1):1–13. doi: 10.1016/S0006-3495(77)85532-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
- TASAKI I., HAGIWARA S. Capacity of muscle fiber membrane. Am J Physiol. 1957 Mar;188(3):423–429. doi: 10.1152/ajplegacy.1957.188.3.423. [DOI] [PubMed] [Google Scholar]
- Walton M. K., Fozzard H. A. Experimental study of the conducted action potential in cardiac Purkinje strands. Biophys J. 1983 Oct;44(1):1–8. doi: 10.1016/S0006-3495(83)84272-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Winsor C. P. The Gompertz Curve as a Growth Curve. Proc Natl Acad Sci U S A. 1932 Jan;18(1):1–8. doi: 10.1073/pnas.18.1.1. [DOI] [PMC free article] [PubMed] [Google Scholar]