Journal of Computational Neuroscience

, Volume 40, Issue 1, pp 27–50 | Cite as

Effects of polarization induced by non-weak electric fields on the excitability of elongated neurons with active dendrites

  • Robert I. Reznik
  • Ernest Barreto
  • Evelyn Sander
  • Paul So
Article

Abstract

An externally-applied electric field can polarize a neuron, especially a neuron with elongated dendrites, and thus modify its excitability. Here we use a computational model to examine, predict, and explain these effects. We use a two-compartment Pinsky-Rinzel model neuron polarized by an electric potential difference imposed between its compartments, and we apply an injected ramp current. We vary three model parameters: the magnitude of the applied potential difference, the extracellular potassium concentration, and the rate of current injection. A study of the Time-To-First-Spike (TTFS) as a function of polarization leads to the identification of three regions of polarization strength that have different effects. In the weak region, the TTFS increases linearly with polarization. In the intermediate region, the TTFS increases either sub- or super-linearly, depending on the current injection rate and the extracellular potassium concentration. In the strong region, the TTFS decreases. Our results in the weak and strong region are consistent with experimental observations, and in the intermediate region, we predict novel effects that depend on experimentally-accessible parameters. We find that active channels in the dendrite play a key role in these effects. Our qualitative results were found to be robust over a wide range of inter-compartment conductances and the ratio of somatic to dendritic membrane areas. In addition, we discuss preliminary results where synaptic inputs replace the ramp injection protocol. The insights and conclusions were found to extend from our polarized PR model to a polarized PR model with Ih dendritic currents. Finally, we discuss the degree to which our results may be generalized.

Keywords

Electric fields Excitability Hippocampus Pyramidal neurons 

References

  1. Barreto, E., & Cressman, J. (2011). Ion concentration dynamics as a mechanism for neuronal bursting. Journal of Biological Physics, 37(3), 361–373. doi:10.1007/s10867-010-9212-6.PubMedCentralCrossRefPubMedGoogle Scholar
  2. Berzhanskaya, J., Gorchetchnikov, A., & Schiff, S.J. (2007). Switching between gamma and theta: Dynamic network control using subthreshold electric fields. Neurocomputing, 70(10-12), 2091–2095. doi:10.1016/j.neucom.2006.10.124, http://www.sciencedirect.com/science/article/B6V10-4M9Y1V1-G/2/05a532a351f790864e8ff5511052b9c3, computational,neural circuitry.PubMedCentralCrossRefPubMedGoogle Scholar
  3. Bikson, M., & Rahman, A. (2013). Origins of specificity during tDCS: anatomical, activity-selective, and input-bias mechanisms. Frontiers in Human Neuroscience, 7, 688. doi:10.3389/fnhum.2013.00688.PubMedCentralCrossRefPubMedGoogle Scholar
  4. Bikson, M., Inoue, M., Akiyama, H., DJ, K., Fox, J., Miyakawa, H., & Jefferys, J. (2004). Effects of uniform extracellular dc electric fields on excitability in rat hippocampal slices in vitro. Journal of Physiology, 557(1), 175–190.PubMedCentralCrossRefPubMedGoogle Scholar
  5. Binder, D., Yao, X., Zador, Z., Sick, T., Verkman, A., & Manley, G. (2006). Increased seizure duration and slowed potassium kinetics in mice lacking aquaporin-4 water channels. GLIA, 53(6), 631–636. doi:10.1002/glia.20315.CrossRefPubMedGoogle Scholar
  6. Bose, A., & Booth, V. (2004). Bursting in 2-compartment neurons: A case study of the Pinsky-Rinzel model. Center for Applied Mathematics and Statistics.Google Scholar
  7. Cressman, J., John, R., Ullah, G., Ziburkus, J., Schiff, S., & Barreto, E. (2009). The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. Journal of Computational Neuroscience, 26(2), 159–170. doi:10.1007/s10827-008-0132-4.PubMedCentralCrossRefPubMedGoogle Scholar
  8. Cressman, J., Ullah, G., Ziburkus, J., Schiff, S., & Barreto, E. (2011). Erratum to: The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. Journal of Computational Neuroscience, 30(3), 781–781. doi:10.1007/s10827-011-0333-0.CrossRefGoogle Scholar
  9. Csicsvari, J., Jamieson, B., Wise, K., & Buzsaki, G. (2003). Mechanisms of gamma oscillations in the hippocampus of the behaving rat. Neuron, 37(2), 311–322. doi:10.1016/S0896-627302)01169-8.CrossRefPubMedGoogle Scholar
  10. Deans, J.K., Powell, A.D., & Jefferys, J.G.R. (2007). Sensitivity of coherent oscillations in rat hippocampus to ac electric fields. Journal Of Physiology-London, 583(2), 555–565. doi:10.1113/jphysiol.2007.137711.CrossRefGoogle Scholar
  11. Dietzel, I., Heinemann, U., & Lux, H. (1989). Relations between slow extracellular potential changes, glial potassium buffering, and electrolyte and cellular-volume changes during neuronal hyperactivity in cat brain. Glia, 2(1), 25–44. doi:10.1002/glia.440020104.CrossRefPubMedGoogle Scholar
  12. Dyhrfjeld-Johnsen, J., Morgan, R.J., & Soltesz, I. (2009). Double trouble? Potential for hyperexcitability following both channelopathic up- and downregulation of i(h) in epilepsy. Frontiers in neuroscience.Google Scholar
  13. Francis, J.T., Gluckman, B.J., & Schiff, S.J. (2003). Sensitivity of neurons to weak electric fields. The Journal of Neuroscience, 23(19), 7255–7261. http://www.jneurosci.org/cgi/reprint/23/19/7255.pdf.PubMedGoogle Scholar
  14. Gasparini, S., & DiFrancesco, D. (1999). Action of serotonin on the hyperpolarization-activated cation current (I-h) in rat CA1 hippocampal neurons. European Journal of Neuroscience.Google Scholar
  15. Ghai, R., Bikson, M., & Durand, D. (2000). Effects of applied electric fields on low-calcium epileptiform activity in the ca1 region of rat hippocampal slices. Journal Of Neurophysiology, 84(1), 274–280.PubMedGoogle Scholar
  16. Gluckman, B.J., Neel, E.J., Netoff, T.I., Ditto, W.L., Spano, M.L., & Schiff, S.J. (1996). Electric field suppression of epileptiform activity in hippocampal slices. Journal of Neurophysiology, 76(6), 4202–4205. http://jn.physiology.org/cgi/content/abstract/76/6/4202, http://jn.physiology.org/cgi/reprint/76/6/4202.pdf.PubMedGoogle Scholar
  17. Gluckman, B.J., So, P., Netoff, T.I., Spano, M.L., & Schiff, S.J. (1998). Stochastic resonance in mammalian neuronal networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, 8(3), 588–598. doi:10.1063/1.166340, http://link.aip.org/link/?CHA/8/588/1.CrossRefGoogle Scholar
  18. Gluckman, B.J., Nguyen, H., Weinstein, S.L., & Schiff, S.J. (2001). Adaptive electric field control of epileptic seizures. Journal of Neuroscience, 21(2), 590–600. http://www.jneurosci.org/cgi/reprint/21/2/590.pdf.PubMedGoogle Scholar
  19. Golding, T.K.Y.K.W.S.N., & Mickus, N.L. (2005). Factors mediating powerful voltage attenuation along ca1 pyramidal neuron dendrites. Journal of Physiology-London.Google Scholar
  20. Han, C.L., Hu, W., Stead, M., Zhang, T., Zhang, J.G., Worrell, G.A., & Meng, F.G. (2014). Electrical stimulation of hippocampus for the treatment of refractory temporal lobe epilepsy. Brain Research Bulletin, 109(0), 13–21. doi:10.1016/j.brainresbull.2014.08.007, http://www.sciencedirect.com/science/article/pii/S0361923014001336.CrossRefPubMedGoogle Scholar
  21. Holt, G.R., & Koch, C. (1999). Electrical interactions via the extracellular potential near cell bodies. Journal of Computational Neuroscience, 6(2), 169–184. http://www.springerlink.com.mutex.gmu.edu/content/u262m146864wu008/fulltext.pdf.CrossRefPubMedGoogle Scholar
  22. Janigro, D. (2006). Brain water and ion fluxes: a hard-to-die hypothesis to explain seizure. Epilepsy Currents.Google Scholar
  23. Lippert, A., & Booth, V. (2009). Understanding effects on excitability of simulated I (h) modulation in simple neuronal models. Biological Cybernetics.Google Scholar
  24. McNamara, J. (1994). Cellular and molecular basis of epilepsy. The Journal of Neuroscience, 14(6), 3413–3425. http://www.jneurosci.org, http://www.jneurosci.org/cgi/reprint/14/6/3413.pdf.PubMedGoogle Scholar
  25. Mikkelsen, R., Andreasen, M., & Nedergaard, S. (2013). Suppression of epileptiform activity by a single short-duration electric field in rat hippocampus in vitro. Journal of Neurophysiology, 109(11), 2720–2731. doi:10.1152/jn.00887.2012.CrossRefPubMedGoogle Scholar
  26. Miranda, P.C., Lomarev, M., & Hallett, M. (2006). Modeling the current distribution during transcranial direct current stimulation. Clinical Neurophysiology, 117(7), 1623–1629. doi:10.1016/j.clinph.2006.04.009, http://www.sciencedirect.com/science/article/pii/S1388245706001726.CrossRefPubMedGoogle Scholar
  27. Moody, W.J., Futamachi, K.J., & Prince, D.A. (1974). Extracellular potassium activity during epileptogenesis. Experimental Neurology, 42(2), 248–263. doi:10.1016/0014-488674)90023-5, http://www.sciencedirect.com/science/article/B6WFG-4BJW0K8-S5/2/5a1576e44b031b336a2de8069c9f4a03.CrossRefPubMedGoogle Scholar
  28. Park, E.H., So, P., Barreto, E., Gluckman, B., & Schiff, S. (2003). Electric field modulation of synchronization in neuronal networks. Neurocomputing, 52–54, 169–175. http://www.sciencedirect.com/science/article/B6V10-47T2GNT-K/2/5e5a42a4855dfd83da36607af3a75b8e.CrossRefGoogle Scholar
  29. Park, E.H., Barreto, E., Gluckman, B.J., Schiff, S.J., & So, P. (2005). A model of the effects of applied electric fields on neuronal synchronization. Journal of Computational Neuroscience, 19, 53–70. http://www.springerlink.com/content/w1681302gth46592.PubMedCentralCrossRefPubMedGoogle Scholar
  30. Pinsky, P.F., & Rinzel, J. (1994). Intrinsic and network rhythmogenesis in a reduced traub model for ca3 neurons. Journal of Computational Neuroscience, 1(1–2), 39–60.CrossRefPubMedGoogle Scholar
  31. Pucihar, G., Miklavcic, D., & Kotnik, T. (2009). A time-dependent numerical model of transmembrane voltage inducement and electroporation of irregularly shaped cells. IEEE Transactions on Biomedical Engineering, 56(5), 1491–1501. doi:10.1109/TBME.2009.2014244.CrossRefPubMedGoogle Scholar
  32. Radman, T., Su, Y., An, J.H., Parra, L.C., & Bikson, M. (2007). Spike timing amplifies the effect of electric fields on neurons: Implication for endogenous field effects. The Journal of Neuroscience, 27, 3030–3036.CrossRefPubMedGoogle Scholar
  33. Radman, T., Ramos, R.L., Brumberg, J.C., & Bikson, M. (2009). Role of cortical cell type and morphology in subthreshold and suprathreshold uniform electric field stimulation in vitro. Brain Stimulation, 2, 215–228. experimental and Theoretic polarization of neuron.PubMedCentralCrossRefPubMedGoogle Scholar
  34. Reato, D., Rahman, A., Bikson, M., & Parra, L.C. (2010). Low-intensity electrical stimulation affects network dynamics by modulating population rate and spike timing. The Journal of Neuroscience, 30(45), 15,067–15,079. doi:10.1523/JNEUROSCI.2059-10.2010, http://www.jneurosci.org/cgi/content/abstract/30/45/15067.CrossRefGoogle Scholar
  35. Richardson, K.A., Gluckman, B.J., Weinstein, S.L., Glosch, C.E., Moon, J.B., Gwinn, R.P., Gale, K., & Schiff, S.J. (2003). In vivo modulation of hippocampal epileptiform activity with radial electric fields. Epilepsia Series 4, 44(6), 768–777. http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=10130960&site=ehost-live.
  36. Richardson, K.A., Schiff, S.J., & Gluckman, B.J. (2005). Control of traveling waves in the mammalian cortex. Physical Review Letters, 94(2), 028,103. doi:10.1103/PhysRevLett.94.028103, http://prola.aps.org.mutex.gmu.edu/abstract/PRL/v94/i2/e028103.CrossRefGoogle Scholar
  37. Sunderam, S., Chernyy, N., Peixoto, N., Mason, J.P., Weinstein, S.L., Schiff, S.J., & Gluckman, B.J. (2009). Seizure entrainment with polarizing low-frequency electric fields in a chronic animal epilepsy model. Journal of Neural Engineering, 6(4). doi:10.1088/1741-2560/6/4/046009. In vivo very low freq to modulate excitability in tetanically induced epileptic rats.
  38. Tranchina, D., & Nicholson, C. (1986). A model for the polarization of neurons by extrinsically applied electric fields. Biophysical Journal, 50, 1139–1156.PubMedCentralCrossRefPubMedGoogle Scholar
  39. Traub, R.D., & Milesm, R. (1991). Neuronal Networks of the Hippocampus. Cambridge.Google Scholar
  40. Traub, R., Dudek, F., Snow, R., & Knowles, W. (1985a). Computer simulations indicate that electrical field effects contribute to the shape of the epileptiform field potential. Neuroscience, 15(4), 947–958.CrossRefPubMedGoogle Scholar
  41. Traub, R., Dudek, F., Taylor, C.P., & Knowles, W.D. (1985b). Simulation of hippocampal afterdischarges synchronized by electrical interactions. Neuroscience, 14, 1033–1038.CrossRefPubMedGoogle Scholar
  42. Traub, R.D., Wong, R.K., Miles, R., & Michelson, H. (1991). A model of a ca3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. Journal of Neurophysiology, 66(2), 635–650. http://jn.physiology.org/cgi/content/abstract/66/2/635. http://jn.physiology.org/cgi/reprint/66/2/635.pdf.PubMedGoogle Scholar
  43. Vigmond, E., Velazquez, J.L.P., Valiante, T.A., Bardakjian, B.L., & Carlen, P.L. (1997). Mechanisms of electrical coupling between pyramidal cells. Journal of Neurophysiology, 78, 3107–3116.PubMedGoogle Scholar
  44. Weiss, S.A., & Faber, D.S. (2010). Field effects in the cns play functional roles. Frontiers In Neural Circuits, 4. doi:10.3389/fncir.2010.00015.
  45. Yi, G.S., Wang, J., Wei, X.L., Tsang, K.M., Chan, W.L., Deng, B., & Han, C.X. (2014). Exploring how extracellular electric field modulates neuron activity through dynamical analysis of a two-compartment neuron model. Journal of Computational Neuroscience, 36(3), 383–399. doi:10.1007/s10827-013-0479-z.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Robert I. Reznik
    • 1
  • Ernest Barreto
    • 1
  • Evelyn Sander
    • 2
  • Paul So
    • 1
  1. 1.School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfaxUSA
  2. 2.Department of Mathematical SciencesGeorge Mason UniversityFairfaxUSA

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