Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1999 Mar;76(3):1310–1319. doi: 10.1016/S0006-3495(99)77293-0

Small conductance potassium channels cause an activity-dependent spike frequency adaptation and make the transfer function of neurons logarithmic.

J Engel 1, H A Schultens 1, D Schild 1
PMCID: PMC1300110  PMID: 10049314

Abstract

We made a computational model of a single neuron to study the effect of the small conductance (SK) Ca2+-dependent K+ channel on spike frequency adaptation. The model neuron comprised a Na+ conductance, a Ca2+ conductance, and two Ca2+-independent K+ conductances, as well as a small and a large (BK) Ca2+-activated K+ conductance, a Ca2+ pump, and mechanisms for Ca2+ buffering and diffusion. Sustained current injection that simulated synaptic input resulted in a train of action potentials (APs) which in the absence of the SK conductance showed very little adaptation with time. The transfer function of the neuron was nearly linear, i.e., both asymptotic spike rate as well as the intracellular free Ca2+ concentration ([Ca2+]i) were approximately linear functions of the input current. Adding an SK conductance with a steep nonlinear dependence on [Ca2+]i (. Pflügers Arch. 422:223-232; Köhler, Hirschberg, Bond, Kinzie, Marrion, Maylie, and Adelman. 1996. Science. 273:1709-1714) caused a marked time-dependent spike frequency adaptation and changed the transfer function of the neuron from linear to logarithmic. Moreover, the input range the neuron responded to with regular spiking increased by a factor of 2.2. These results can be explained by a shunt of the cell resistance caused by the activation of the SK conductance. It might turn out that the logarithmic relationships between the stimuli of some modalities (e.g., sound or light) and the perception of the stimulus intensity (Fechner's law) have a cellular basis in the involvement of SK conductances in the processing of these stimuli.

Full Text

The Full Text of this article is available as a PDF (145.2 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Armstrong C. M. Voltage-dependent ion channels and their gating. Physiol Rev. 1992 Oct;72(4 Suppl):S5–13. doi: 10.1152/physrev.1992.72.suppl_4.S5. [DOI] [PubMed] [Google Scholar]
  2. Avoli M., Olivier A. Electrophysiological properties and synaptic responses in the deep layers of the human epileptogenic neocortex in vitro. J Neurophysiol. 1989 Mar;61(3):589–606. doi: 10.1152/jn.1989.61.3.589. [DOI] [PubMed] [Google Scholar]
  3. Bal T., McCormick D. A. Mechanisms of oscillatory activity in guinea-pig nucleus reticularis thalami in vitro: a mammalian pacemaker. J Physiol. 1993 Aug;468:669–691. doi: 10.1113/jphysiol.1993.sp019794. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Barrett J. N., Magleby K. L., Pallotta B. S. Properties of single calcium-activated potassium channels in cultured rat muscle. J Physiol. 1982 Oct;331:211–230. doi: 10.1113/jphysiol.1982.sp014370. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Blatz A. L., Magleby K. L. Single apamin-blocked Ca-activated K+ channels of small conductance in cultured rat skeletal muscle. Nature. 1986 Oct 23;323(6090):718–720. doi: 10.1038/323718a0. [DOI] [PubMed] [Google Scholar]
  6. Connors B. W., Malenka R. C., Silva L. R. Two inhibitory postsynaptic potentials, and GABAA and GABAB receptor-mediated responses in neocortex of rat and cat. J Physiol. 1988 Dec;406:443–468. doi: 10.1113/jphysiol.1988.sp017390. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. De Schutter E., Bower J. M. An active membrane model of the cerebellar Purkinje cell. I. Simulation of current clamps in slice. J Neurophysiol. 1994 Jan;71(1):375–400. doi: 10.1152/jn.1994.71.1.375. [DOI] [PubMed] [Google Scholar]
  8. Destexhe A., Contreras D., Sejnowski T. J., Steriade M. A model of spindle rhythmicity in the isolated thalamic reticular nucleus. J Neurophysiol. 1994 Aug;72(2):803–818. doi: 10.1152/jn.1994.72.2.803. [DOI] [PubMed] [Google Scholar]
  9. Engel J., Rabba J., Schild D. A transient, RCK4-like K+ current in cultured Xenopus olfactory bulb neurons. Pflugers Arch. 1996 Sep;432(5):845–852. doi: 10.1007/s004240050207. [DOI] [PubMed] [Google Scholar]
  10. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. HODGKIN A. L., KEYNES R. D. Movements of labelled calcium in squid giant axons. J Physiol. 1957 Sep 30;138(2):253–281. doi: 10.1113/jphysiol.1957.sp005850. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Helmchen F., Imoto K., Sakmann B. Ca2+ buffering and action potential-evoked Ca2+ signaling in dendrites of pyramidal neurons. Biophys J. 1996 Feb;70(2):1069–1081. doi: 10.1016/S0006-3495(96)79653-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Koike H., Mano N., Okada Y., Oshima T. Repetitive impulses generated in fast and slow pyramidal tract cells by intracellularly applied current steps. Exp Brain Res. 1970;11(3):263–281. doi: 10.1007/BF01474386. [DOI] [PubMed] [Google Scholar]
  14. Köhler M., Hirschberg B., Bond C. T., Kinzie J. M., Marrion N. V., Maylie J., Adelman J. P. Small-conductance, calcium-activated potassium channels from mammalian brain. Science. 1996 Sep 20;273(5282):1709–1714. doi: 10.1126/science.273.5282.1709. [DOI] [PubMed] [Google Scholar]
  15. Lancaster B., Nicoll R. A. Properties of two calcium-activated hyperpolarizations in rat hippocampal neurones. J Physiol. 1987 Aug;389:187–203. doi: 10.1113/jphysiol.1987.sp016653. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Lanthorn T., Storm J., Andersen P. Current-to-frequency transduction in CA1 hippocampal pyramidal cells: slow prepotentials dominate the primary range firing. Exp Brain Res. 1984;53(2):431–443. doi: 10.1007/BF00238173. [DOI] [PubMed] [Google Scholar]
  17. Leinders T., Vijverberg H. P. Ca2+ dependence of small Ca(2+)-activated K+ channels in cultured N1E-115 mouse neuroblastoma cells. Pflugers Arch. 1992 Dec;422(3):223–232. doi: 10.1007/BF00376206. [DOI] [PubMed] [Google Scholar]
  18. Madison D. V., Nicoll R. A. Control of the repetitive discharge of rat CA 1 pyramidal neurones in vitro. J Physiol. 1984 Sep;354:319–331. doi: 10.1113/jphysiol.1984.sp015378. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Mason A., Larkman A. Correlations between morphology and electrophysiology of pyramidal neurons in slices of rat visual cortex. II. Electrophysiology. J Neurosci. 1990 May;10(5):1415–1428. doi: 10.1523/JNEUROSCI.10-05-01415.1990. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. McManus O. B., Magleby K. L. Kinetic states and modes of single large-conductance calcium-activated potassium channels in cultured rat skeletal muscle. J Physiol. 1988 Aug;402:79–120. doi: 10.1113/jphysiol.1988.sp017195. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Neher E., Augustine G. J. Calcium gradients and buffers in bovine chromaffin cells. J Physiol. 1992 May;450:273–301. doi: 10.1113/jphysiol.1992.sp019127. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Pedarzani P., Storm J. F. Dopamine modulates the slow Ca(2+)-activated K+ current IAHP via cyclic AMP-dependent protein kinase in hippocampal neurons. J Neurophysiol. 1995 Dec;74(6):2749–2753. doi: 10.1152/jn.1995.74.6.2749. [DOI] [PubMed] [Google Scholar]
  23. Roche E., Prentki M. Calcium regulation of immediate-early response genes. Cell Calcium. 1994 Oct;16(4):331–338. doi: 10.1016/0143-4160(94)90097-3. [DOI] [PubMed] [Google Scholar]
  24. Schild D. Whole-cell currents in olfactory receptor cells of Xenopus laevis. Exp Brain Res. 1989;78(2):223–232. doi: 10.1007/BF00228894. [DOI] [PubMed] [Google Scholar]
  25. Tucker T. R., Fettiplace R. Monitoring calcium in turtle hair cells with a calcium-activated potassium channel. J Physiol. 1996 Aug 1;494(Pt 3):613–626. doi: 10.1113/jphysiol.1996.sp021519. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Wang X. J. Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J Neurophysiol. 1998 Mar;79(3):1549–1566. doi: 10.1152/jn.1998.79.3.1549. [DOI] [PubMed] [Google Scholar]
  27. Wang X. Y., McKenzie J. S., Kemm R. E. Whole-cell K+ currents in identified olfactory bulb output neurones of rats. J Physiol. 1996 Jan 1;490(Pt 1):63–77. doi: 10.1113/jphysiol.1996.sp021127. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Zhou F. M., Hablitz J. J. Layer I neurons of rat neocortex. I. Action potential and repetitive firing properties. J Neurophysiol. 1996 Aug;76(2):651–667. doi: 10.1152/jn.1996.76.2.651. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES