Stochastic model for action potential simulation including ion shot noise

Abstract

Development of bioinspired devices for energy-efficient computing requires numerical models that can reproduce the global electrical behavior of neurons. We present herein a stochastic model based on the Monte Carlo technique that can reproduce the steady state and the action potential in neurons in terms of the probabilities for different ions to cross the cell membrane. Gating channels for sodium and potassium cations and leakage channels are taken into account following the Hodgkin–Huxley equations in a first stage. We then expand the model to include the time-dependent ion concentrations in the intra- and extracellular space and the related Nernst potentials, and the existence of ion pumps to equilibrate the steady-state currents. The model allows monitoring of the random passage of ions across a biological membrane, and thus includes the influence of ion shot noise. For small membrane areas, results evidence that, when considered alone, shot noise has a discernible effect on spiking in a wide range of excitation currents, not only by leading to the onset of spikes but also by inhibiting their appearance.

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References

  1. 1.

    Dennard, R.H., Gaesslen, F.H., Yu, H.-N., Rideovt, V.L., Bassous, E., Leblanc, A.: Design of ion-implanted MOSFET’s with very small physical dimensions. IEEE J. Solid-State Circuits SC–9, 256–268 (1974)

    Article  Google Scholar 

  2. 2.

    Eisenberg, B.: Ion channels as devices. J. Comput. Electron. 2, 245–249 (2003)

    Article  Google Scholar 

  3. 3.

    Shepherd, G.M. (ed.): Foundations of the Neuron Doctrine. Oxford Univ. Press, New York (1991)

  4. 4.

    Bear, M.F., Paradiso, M.A., Connors, B.W.: Neuroscience, Lippincott Willians & Wilkins, Philadelphia (2006). ISBN: 9780781760034

  5. 5.

    Ha, S.D., Ramanathan, S.: Adaptive oxide electronics: a review. J. Appl. Phys. 110, 071101(1-20) (2011)

    Google Scholar 

  6. 6.

    Kaneko, Y., Nishitani, Y., Ueda, M.: Ferroelectric artificial synapses for recognition of a multishaded image. IEEE Trans. Electron. Dev. 61, 2827–2833 (2014)

    Article  Google Scholar 

  7. 7.

    Pershin, Y.V., Di Ventra, M.: Experimental demonstration of associative memory with memristive neural networks. Neural Netw. 23, 881–886 (2010)

    Article  Google Scholar 

  8. 8.

    Prezioso, M., Merrikh-Bayat, F., Hoskins, B.D., Adam, G.C., Likharev, K.K., Strukov, D.B.: Training andoperation of an integrated neuromorphic network based on metal-oxide memristors. Nature 512, 61–64 (2015)

    Article  Google Scholar 

  9. 9.

    Romeo, A., Dimonte, A., Tarabella, G., D’Angelo, P., Erokhin, V., Iannotta, S.: A bio-inspired memory device based on interfacing Physarum polycephalum with an organic semiconductor. APL Mater. 3, 014909(1-6) (2015)

    Article  Google Scholar 

  10. 10.

    Chua, L.: Memristor, Hodgkin–Huxley and edge of chaos. IOP Nanotechnol. 24, 383001(1-14) (2013)

    Google Scholar 

  11. 11.

    Chein, W.R., Midtgaard, J., Shepherd, G.M.: Forward and backward propagation of dendritic impulses and their synaptic control in mitral cells. Science 278, 463–467 (1997)

    Article  Google Scholar 

  12. 12.

    Alle, H., Roth, A., Geiger, J.R.P.: Energy efficient action potentials in hippocampal mossy fibers. Science 325, 1405–1408 (2013)

    Article  Google Scholar 

  13. 13.

    Toghraee, R., Mashl, R.J., Lee, I.K., Jakobsson, E., Ravaioli, U.: Simulation of charge transport in ion channels and nanopores with anisotropic permittivity. J. Comput. Electron. 8, 98–109 (2009)

    Article  Google Scholar 

  14. 14.

    Van der Straaten, T.A., Kathawala, G., Trellakis, A., Eisengerg, R.S., Ravaioli, U.: BioMOCA—A Botzmann transport Monte Carlo model for ion channel simulation. Mol. Simul. 31, 151–171 (2005)

    Article  Google Scholar 

  15. 15.

    Hwang, H., Schatz, G.C., Ratner, M.A.: Kinetic lattice grand canonical Monte Carlo simulation for ion current calculations in a model ion channel system. J. Chem. Phys. 127, 024706(1-10) (2007)

    Google Scholar 

  16. 16.

    Corry, B., Hoyles, M., Allen, T.W., Walker, M., Kuyucak, S., Chung, S-Ho: Reservoir boundaries in brownian dynamics simulations of ion channels. Biophys. J. 82, 1975–1984 (2002)

    Article  Google Scholar 

  17. 17.

    Boda, D., Busath, D.D., Eisenberg, B., Henderson, D., Nonner, W.: Monte Carlo simulations of ion selectivity in a biological Na channel: charge-space competition. Phys. Chem. Chem. Phys. 4, 5154–5160 (2002)

    Article  Google Scholar 

  18. 18.

    Boda, D., Henderson, D., Busath, D.D.: Monte Carlo study of the selectivity of calcium channels: improved geometrical model. Mol. Phys. 1000, 2361–2368 (2002)

    Article  Google Scholar 

  19. 19.

    Valent, I., Neogrády, P., Schreiber, I., Marek, M.: Numerical solutions of the full set of the time-dependent Nernst-Planck and Poisson equations modeling electrodiffusion in a simple ion channel. J. Comput. Interdisciplin. Sci. 3, 65–76 (2012)

    Google Scholar 

  20. 20.

    Chung, S.-H., Kuyucak, S.: Recent advances in ion channel research. Biochim. Biophys. Acta 1565, 267–286 (2002)

  21. 21.

    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117(4), 500–544 (1952)

    Article  Google Scholar 

  22. 22.

    Hübel, N., Schöll, E., Dahlem, M.A.: Bistable dynamics underlying excitability of ion homeostasis in neuron models. PLOS Comput. Biol. 10(5), e1003551(1-15) (2014)

    Article  Google Scholar 

  23. 23.

    Faisal, A.A., Selen, L.P.J., Wolpert, D.M.: Noise in the nervous system. Nature Rev. 9, 292–303 (2008)

    Article  Google Scholar 

  24. 24.

    Schmidt, G., Goychuk, I., Hänggi, P.: Channel noise and synchronization in excitable membranes. Phys. A 325, 165–175 (2003)

    MathSciNet  Article  MATH  Google Scholar 

  25. 25.

    Adair, R.K.: Noise and stochastic resonance in voltage-gated ion channels. PNAS 100, 12099–12104 (2003)

    Article  Google Scholar 

  26. 26.

    Faisal, A.A., White, J.A., Laughlin, S.B.: Ion-channel noise places limits on the miniaturization of the brain’s wiring. Curr. Biol. 15, 1143–1149 (2005)

    Article  Google Scholar 

  27. 27.

    Läuger, P.: Shot noise in ion channels. Biochim. Biophys. Acta 413, 1–10 (1975)

    Article  Google Scholar 

  28. 28.

    Brunetti, R., Affinito, F., Jacoboni, C., Piccinini, E., Rudan, M.: Shot noise in single open ion channels: A computational approach based on atomistic simulations. J. Comput. Electron. 6, 391–394 (2007)

    Article  Google Scholar 

  29. 29.

    Schroeder, I., Hansen, U.-P.: Interference of shot noise of open-channel current with analysis of fast gating: patchers do not (yet) have to care. J. Membrane Biol. 229, 153–163 (2009)

    Article  Google Scholar 

  30. 30.

    Gillespie, D.T.: A general method for numerically simulating the stochastic time evolutions of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976)

    MathSciNet  Article  Google Scholar 

  31. 31.

    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)

    Article  Google Scholar 

  32. 32.

    Cannon, R.C., O’Donnel, C., Nolan, M.: Stochastic ion channel gating in dendritic neurons: morphology dependence and probabilistic synaptic activation of dendritic spikes. PLOS Comput. Biol. 6, e1000886(1-18) (2010)

    MathSciNet  Article  Google Scholar 

  33. 33.

    Huang, Y., Rüdiger, S., Shuai, J.: Accurate Langevin approaches to simulate Markovian channel dynamics. Phys. Biol. 12, 061001(1-22) (2015)

    Article  Google Scholar 

  34. 34.

    Wei, Y., Ullah, G., Steven, X., Schiff, J.: Unification of neuronal spikes, seizures, and spreading depression. J. Neurosci. 34(35), 11733–11743 (2014)

    Article  Google Scholar 

  35. 35.

    Kager, H., Wadman, W.J., Somjen, G.G.: Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J. Neurophysiol. 84, 495–512 (2000)

    Google Scholar 

  36. 36.

    Cressman, J.J., Ullah, G., Ziburkus, J., Schiff, S.J., Barreto, E.: The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. J. Comput. Neurosci. 26, 159–170 (2009)

    MathSciNet  Article  Google Scholar 

  37. 37.

    Barreto, E., Cressman, J.R.: Ion concentration dynamics as a mechanism for neural bursting. J. Biol. Phys. 37, 361–373 (2010)

    Article  Google Scholar 

  38. 38.

    Milo, R., Philips, R.: Cell Biology by the Numbers. Garland Science, New York (2015)

    Google Scholar 

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Correspondence to Beatriz G. Vasallo.

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Vasallo, B.G., Galán-Prado, F., Mateos, J. et al. Stochastic model for action potential simulation including ion shot noise. J Comput Electron 16, 419–430 (2017). https://doi.org/10.1007/s10825-017-0967-x

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Keywords

  • Monte Carlo technique
  • Action potential
  • Cell membranes
  • Ion shot noise