A Computational Investigation of the Role of Ion Gradients in Signal Generation in Neurons

  • Seyed Ali Sadegh ZadehEmail author
  • Chandra Kambhampati
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 858)


Sodium (Na+) and potassium (K+) are two physiologically essential electrolytes whose concentrations play important role in nerve impulses, and disorders affecting the nervous system. In this paper, using computational modelling, the response of a neuron is investigated for different concentrations Sodium and Potassium ions, and the resultant ion gradients. These include the combination of imbalances in both sodium and potassium. It is shown that the responses to various concentrations are in line with current clinical thinking. The levels of the ions determine the characteristics of the response, namely, the resting potential, the magnitude of the spikes, and the inter-spike interval. The results and the ability to represent changes in ion concentrations and the gradients across membranes will help in developing models for more complex networks of neurons.


Physiological model Bio-signals analysis and interpretation Modeling and identification 


  1. 1.
    Melnik, R.: Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts, 1st edn. Wiley, Hoboken (2015)CrossRefGoogle Scholar
  2. 2.
    Mazur, J.: Mathematical Models and the Experimental Analysis of Behavior. Exp Anal Behav 85(2), 275–291 (2006)CrossRefGoogle Scholar
  3. 3.
    Winkler, S.: Comparative mathematical modelling of groundwater pollution (Doctoral dissertation) (2014)Google Scholar
  4. 4.
    Kemmetmüller, W.: Mathematical Modeling and Nonlinear Control of Electrohydraulic and Electrorheological Systems, 1st edn. Shaker Aachen, Herzogenrath (2008)Google Scholar
  5. 5.
    Kugi, A.: Non-linear Control Based on Physical Models: Electrical, Mechanical and Hydraulic Systems (Lecture Notes in Control and Information Sciences), 1st edn. Springer, London (2001)zbMATHGoogle Scholar
  6. 6.
    Bacak, B., Segaran, J., Molkov, Y.: Modeling the effects of extracellular potassium on bursting properties in pre-Bötzinger complex neurons. J. Comput. Neurosci. 40(2), 231–245 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hodgkin, A., Huxley, A.: Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. Physiol 116, 49–472 (1952)Google Scholar
  8. 8.
    Jensen, M., et al.: Mechanism of voltage gating in potassium channels. Science 336(6078), 229–233 (2012)CrossRefGoogle Scholar
  9. 9.
    Schneidman, E., Freedman, B., Segev, I.: Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput. 10(7), 1679–1703 (1998)CrossRefGoogle Scholar
  10. 10.
    Izhikevich, E.: Simple model of spiking neurons. IEEE Trans. Neural Networks 14(6), 1569–1572 (2003)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kang, Q., Huang, B., Zhou, M.: Dynamic behavior of artificial hodgkin-huxley neuron model subject to additive noise. IEEE Transactions on Cybernetics 46(9), 2083–2093 (2016)CrossRefGoogle Scholar
  12. 12.
    LuWang, M., J.-L., Wen, J., Dong, X.-W.: Implementation of Hodgkin-Huxley neuron model in FPGAs. In: 2016 Asia-Pacific International Symposium on Electromagnetic Compatibility, APEMC (2016)Google Scholar
  13. 13.
    Mahmud, M., Vassanelli, S.: Differential modulation of excitatory and inhibitory neurons during periodic stimulation. Front. Neurosci. (2016)Google Scholar
  14. 14.
    Brette, R., et al.: Simulation of networks of spiking neurons: a review of tools and strategies. J. Comput. Neurosci. 23(3), 349–398 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Nygren, A., et al.: Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. Circ. Res. 82(1), 63–81 (1998)CrossRefGoogle Scholar
  16. 16.
    Waxman, S.: Sodium channels, the electrogenisome and the electrogenistat: lessons and questions from the clinic. J. Physiol. 590, 2601–2612 (2012)CrossRefGoogle Scholar
  17. 17.
    Frohlich, F., Jezernik, S.: Feedback control of Hodgkin-Huxleynerve cell dynamics. Control Eng. Pract. 13, 1195–1206 (2005)CrossRefGoogle Scholar
  18. 18.
    Chappell, M., Payne, S.: The Action Potential. Physiol. Eng. 13, 33–41 (2016)CrossRefGoogle Scholar
  19. 19.
    Rossetto, M.: A note on the falsification of the ionic theory of hair cell transduction. Commun. Integr. Biol. 9(2) (2016)CrossRefGoogle Scholar
  20. 20.
    Dormand, J., Prince, P.: A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6(1), 19–26 (1980)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Sarangdhar, M., Kambhampati, C.: Spiking Neurons: Is Coincidence-Factor Enough for Comparing Responses with Fluctuating Membrane Voltage?. World Congress on Engineering, London (2008)Google Scholar
  22. 22.
    Sarangdhar, M., Kambhampati, C.: Quantification of similarity using amplitudes and firing times of a Hodgkin-Huxley neural response. Electr. Eng. Appl. Comput. 90, 687–698 (2011)CrossRefGoogle Scholar
  23. 23.
    Ha, Y., Jeong, J., Kim, Y., Churchill, D.: Sodium and Potassium relating to parkinson’s disease and traumatic brain injury. Alkali Metal Ions Role Life 16, 585–601 (2016)CrossRefGoogle Scholar
  24. 24.
    Walkowska, A., et al.: Effects of high and low sodium diet on blood pressure and heart rate in mice lacking the functional Grainyhead-like 1 gene. Physiol. Res. (2016)Google Scholar
  25. 25.
    Gijsbersa, L., Mölenberg, F., Bakker, S., Geleijnsea, J.: Potassium supplementation and heart rate: a meta-analysis of randomized controlled trials. Nutr. Metabol. Cardiovasc. Dis. 26(8), 674–682 (2016)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of HullHullUK

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