Skip to main content
Log in

On modelling the variability of interspike intervals during epileptic unit activity

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

In spite of the fact that the participation of well defined ionic particles in generating convulsive unit discharges is established, there is a gap between the data on ionic movements and on first-order statistics of firing patterns. Our aim was to tight this gap by studying the effectiveness of functionally separated electrical conductances of membrane during the generation of consecutive interspike interval histograms (IIHs) of unitary discharges. On account of the non-stationarity of the process curve fitting analysis which based on the simple modifications of the integrate-and-fire model has been implemented in the sequential interspike interval histogram procedure (SIIH). The experimental data were recorded from cat cortex treated with 3-Aminopyridine (3-Ap) by glass microelectrodes during nembutal anesthezia. Assuming the normal distribution of input parameters it is concluded, that the efficiency of the fluctuations of the active spike-generating conductance g g and the passive diffusional conductance g l may increase during the generation of the unimodal IIHs and the first mode of the bimodal IIHs. The simple conductance coupling g l =a·g g +b may participate in g l activation, moreover, the reciprocally coupled mechanism g g =c/g l may be driven by g l activation (a, b, c are the coupling constants). A temporal separation of processes governed by g g or g l respectively was observed. The timeindependent occurrences of the reciprocally coupled conductance processes may be involved in the unit activities represented by the prolonged IIHs and second modes of the bimodal IIHs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson, T.E., Rutledge, L.T.: Inhibition in penicillininduced epileptic foci. Electroencephalogr. Clin. Neurophys. 46, 498–509 (1979)

    Google Scholar 

  • Ayala, G.F., Spencer, W.A., Gumnit, R.J.: Penicillin as an epileptogenic agent: effect on an isolated synapse. Science 171, 915–917 (1971)

    Google Scholar 

  • Carnevale, N.T., Wachtel, H.: Two reciprocating current components underlying slow oscillations in Aplysia bursting neurons. Brain Res. Rev. 2, 45–68 (1980)

    Google Scholar 

  • Davenport, J., Schwindt, P.C., Crill, W.E.: Epileptogenic doses of penicillin do not reduce a monosynaptic GABA-mediated postsynaptic inhibition in the intact anaesthetized cat. Exp. Neurol. 65, 552–572 (1979)

    Google Scholar 

  • Davenport, J., Schwindt, P.C., Crill, W.E.: Presynaptic and long-lasting postsynaptic inhibition during penicillininduced spinal seizures. Neurology 28, 592–597 (1978)

    Google Scholar 

  • Dingleidine, R., Gjerstad, L.: Penicillin blocks hippocampal IPSPs, unmasking prolonged EPSPs. Brain Res. 168, 205–209 (1979)

    Google Scholar 

  • Eckert, R., Lux, H.D.: A voltage-sensitive persistent calcium conductance in neuronal somata of Helix. J. Physiol. (London) 254, 129–151 (1976)

    Google Scholar 

  • Futamachi, R.J., Prince, D.A.: Effects of penicillin on an excitatory synapse. Brain Res. 100, 589–597 (1975)

    Google Scholar 

  • Heinemann, U., Lux, H.D., Gutnick, M.J.: Extracellular free calcium and potassium during paroxysmal activity in the cerebral cortex of the cat. Exp. Brain Res. 27, 237–243 (1977)

    Google Scholar 

  • Heyer, C.B., Lux, H.D.: Control of the delayed outward potassium currents in bursting pace-maker neurones of the snail, Helix pomatia. J. Physiol. (London) 262, 349–382 (1976)

    Google Scholar 

  • Jankowska, E., Lundberg, A., Rudomin, P., Sykova, E.: Effects of 4-aminopyridine on transmission in excitatory and inhibitory synapses in the spinal cord. Brain Res. 136, 387–392 (1977)

    Google Scholar 

  • Kenyon, J.L., Gibbons, W.R.: 4-aminopyridine and the early outward current of sheep cardiac purkinje fibres. J. Gen. Physiol. 73, 139–157 (1979)

    Google Scholar 

  • Knight, B.W.: Dynamics of encoding in a population of neurons. J. Gen. Physiol. 59, 734–766 (1972)

    Google Scholar 

  • Kostyuk, P.G., Kulikov, M.A., Pyatigorsky, B.Ya., Vasilenko, D.A.: Analysis of background impulse activity of pyramidal tract neurons in cat. Nejrofiziologija 4, 3–11 (1972) (in russian)

    Google Scholar 

  • Levine, M.W., Shefner, J.M.: A model for the variability of interspike intervals during sustained firing of a retinal neuron. Biophys. J. 19, 241–252 (1977)

    Google Scholar 

  • Levithan, H., Segundo, J.P., Moore, G.P., Perkel, D.H.: Statistical analysis of membrane potential fluctuations. Biophys. J. 8, 1256–1274 (1968)

    Google Scholar 

  • Lew, L.V., Ferreira, H.G.: Calcium transport and the properties of a calcium-activated potassium channel in red cell membranes. In: Current Topics in Membranes and Transport. Vol. 10, pp 217–277. Bronner, F., Kleinzeller, A. (eds.). New York: Academic Press 1978

    Google Scholar 

  • Llinás, R., Walton, K., Bohr, V.: Synaptic transmission in squid giant synapse after potassium conductance blockadge with external 3- and 4-aminopyridine. Biophys. J. 16, 83–86 (1976)

    Google Scholar 

  • Lundh, H., Thesleff, S.: The mode of action of 4-aminopyridine and quanidin on transmitter release from motor nerve terminals. Europ. J. Pharmacol. 42, 411–422 (1977)

    Google Scholar 

  • Lux, H.D.: The kinetics of extracellular potassium: relation to epileptogenesis. Epilepsia 15, 375–393 (1974)

    Google Scholar 

  • Matsumoto, H., Ayala, G.F., Gumnit, R.J.: Neuronal behavior and triggering mechanism in cortical epileptic focus. J. Neurophysiol. 32, 688–703 (1969)

    Google Scholar 

  • Meyer, H., Prince, D.A.: Convulsant action of penicillin: effects on inhibitory mechanisms. Brain Res. 53, 477–482 (1973)

    Google Scholar 

  • Moody, W.J., Jr., Futamachi, K.J., Prince, D.A.: Extracellular potassium activity during epileptogenesis. Exp. Neurol. 42, 248–263 (1974)

    Google Scholar 

  • Nicholson, C., Steinberg, R., Stöckle, H., Ten Bruggencate, G.: Calcium decrease associated with aminopyridine-induced potassium increase in cat cerebellum. Neurosci. Lett. 3, 315–319 (1976a)

    Google Scholar 

  • Nicholson, C., Ten Bruggencate, G., Senekowitch, R.: Large potassium signals and slow potentials evoked during aminopyridine or barium superfusion in cat cerebellum. Brain Res. 113, 606–610 (1976b)

    Google Scholar 

  • Partridge, L.D., Thompson, S.H., Smith, S.J., Connor, J.A.: Currentvoltage relationships of repetitively firing neurons. Brain Res. 164, 69–79 (1979)

    Google Scholar 

  • Parzen, E.: On estimation of a probability density function and mode. Ann. Math. Stat. 33, 1065–1076 (1962)

    Google Scholar 

  • Pernier, J., Gerin, P.: Temporal patterns analysis of spontaneous unit activity in the neocortex. Biol. Cybern. 18, 123–136 (1975)

    Google Scholar 

  • Pongrácz, F., Pongrácz, G., Szente, M.: Microcomputer method for the analysis of spontaneous bursting activity of units in epileptic cat cortex. Electroencephalogr. Clin. Neurophysiol. 49, 195–199 (1980)

    Google Scholar 

  • Pongrácz, F., Szente, M.: Simulation of the ionic mechanisms of molluscan neurons under pentylenetetrazol-induced effects. Acta Phys. Sci. Hung. 53, 327–336 (1979)

    Google Scholar 

  • Pongrácz, F., Szente, M.: Microcomputer-aided point-process analysis of epileptic unit activity. In: Lectures of Int. Symp. on Math. and Comp. Methods in Physiol., Budapest, 1980 (in press)

  • Sanderson, A.C., Kobler, B.: Sequential interval histogram analysis of non-stationary neuronal spike trains. Biol. Cybern. 22, 61–71 (1976)

    Google Scholar 

  • Schwartzkroin, P.A., Slawsky, M.: Probable calcium spikes in hippocampal neurons. Brain Res. 135, 157–161 (1977)

    Google Scholar 

  • Schwindt, P., Crill, W.: Role of a persistent inward current in motoneuron bursting during spinal seizures. J. Neurophysiol. 43, 1296–1318 (1980)

    Google Scholar 

  • Spencer, A.W., Kandel, E.R.: Synaptic inhibition of seizures. In: Basic mechanisms of the epilepsies. pp. 575–603. Jasper, H.H., Ward, Jr.A.A., Pope, A. (eds.). Boston: Little Brown 1969

    Google Scholar 

  • Sypert, G.W., Ward, A.A., Jr.: Changes in extracellular potassium activity during neocortical propagated seizures. Exp. Neurol. 45, 19–41 (1974)

    Google Scholar 

  • Szente, M., Pongrácz, F.: Aminopyridine-induced seizure activity. Electroencephalogr. Clin. Neurophys. 46, 605–608 (1979a)

    Google Scholar 

  • Szente, M., Pongrácz, F.: Aminopyridine-induced scizure activity in the primary and mirror foci of the cat's cerebral cortex. In: Abstracts of 11th Epilepsy Int. Symp., p. 21, Firenze, 1979b

  • Traub, R.D., Llinás, R.: Hippocampal pyramidal cells: significance of dendritic ionic conductances for neuronal function and epileptogenesis. J. Neurophysiol. 42, 476–496 (1979)

    Google Scholar 

  • Van Duijn, H., Schwartzkroin, P.A., Prince, D.A.: Action of penicillin on inhibitory processes in the cat's cortex. Brain Res. 53, 470–476 (1973)

    Google Scholar 

  • Verveen, A.A., De Felice, L.J.: Membrane noise. In: Progress in Biophysics and Molecular Biology. Vol. 28, pp. 189–265. Butler, J.A.V., Noble, D. (eds.). Oxford: Pergamon Press 1974

    Google Scholar 

  • Verveen, A.A., Derksen, H.E.: Fluctuation phenomena in nerve membrane. Proc. IEEE 56, 906–916 (1968)

    Google Scholar 

  • Whisler, J.W., Johnston, D.: Epileptogenesis: a model for the involvement of slow membrane events and extracellular potassium. J. Theor. Biol. 75, 271–288 (1978)

    Google Scholar 

  • Williamson, T.L., Crill, W.E.: The effects of pentylenetetrazol on molluscan neurons. I. Intracellular recording and stimulation. Brain Res. 116, 217–229 (1976a)

    Google Scholar 

  • Williamson, T.L., Crill, W.E.: The effects of pentylenetetrazol on molluscan neurons. II. Voltage-clamp studies. Brain Res. 116, 231–249 (1976b)

    Google Scholar 

  • Wong, R.K.S., Prince, D.A.: Participation of calcium spikes during intrinsic burst firing in hippocampal neurons. Brain Res. 159, 385–390 (1978)

    Google Scholar 

  • Wong, R.K.S., Prince, D.A., Basbaum, A.I.: Intradendritic recordings from hippocampal neurons. Proc. Nat. Acad. Sci. (Wash.) 76, 986–990 (1979)

    Google Scholar 

  • Yagi, K., Yukiko, S.: Recurrent inhibition and facilitation: demonstration in the tubero-infundibular system and effects of strychnine and picrotoxin. Brain Res. 84, 155–159 (1975)

    Google Scholar 

  • Yeh, J.Z., Oxford, G.S., Wu, C.H., Narahashi, T.: Interactions of aminopyridines with potassium channels of squid axon membranes. Biophys. J. 16, 77–81 (1976)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pongrácz, F., Szente, M. On modelling the variability of interspike intervals during epileptic unit activity. Biol. Cybern. 41, 165–177 (1981). https://doi.org/10.1007/BF00340318

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00340318

Keywords

Navigation