International Science Index


All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model


Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

[1] A. Hodgkin and A. Huxley, "A quantitative description of membrane current and its application toconduction and excitation in nerve," The Journal of Physiology, vol. 117, no. 4, pp. 500-544, 1952.
[2] E. D. Adrian, "The all-or-none principle in nerve," The Journal of physiology, vol. 47, no. 6, pp. 460-474, 1914.
[3] S. Winkler, "Comparative mathematical modelling of groundwater pollution (Doctoral dissertation)," 2014.
[4] J. R. Schwarz and G. Eikhof, "Na currents and action potentials in rat myelinated nerve fibers at 20 and 37 C," European Journal of Physiology, vol. 409, p. 569–577, 1987.
[5] S. Y. Chiu, J. M. Ritchie, R. B. Rogart and D. Stagg, "A quantitative description of membrane currents in rabbit myelinated nerve," Journal of Physiology, vol. 292, p. 149–166, 1979.
[6] J. M. González-Miranda, "Nonlinear oscillations in a muscle pacemaker cell model", Communications in Nonlinear Science and Numerical Simulation, vol. 43, p. 330-340, 2017