The role of negative conductances in neuronal subthreshold properties and synaptic integration

Abstract

Based on passive cable theory, an increase in membrane conductance produces a decrease in the membrane time constant and input resistance. Unlike the classical leak currents, voltage-dependent currents have a nonlinear behavior which can create regions of negative conductance, despite the increase in membrane conductance (permeability). This negative conductance opposes the effects of the passive membrane conductance on the membrane input resistance and time constant, increasing their values and thereby substantially affecting the amplitude and time course of postsynaptic potentials at the voltage range of the negative conductance. This paradoxical effect has been described for three types of voltage-dependent inward currents: persistent sodium currents, L- and T-type calcium currents and ligand-gated glutamatergic N-methyl-D-aspartate currents. In this review, we describe the impact of the creation of a negative conductance region by these currents on neuronal membrane properties and synaptic integration. We also discuss recent contributions of the quasi-active cable approximation, an extension of the passive cable theory that includes voltage-dependent currents, and its effects on neuronal subthreshold properties.

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References

  1. Agrawal N, Hamam BN, Magistretti J, Alonso A, Ragsdale DS (2001) Persistent sodium channel activity mediates subthreshold membrane potential oscillations and low-threshold spikes in rat entorhinal cortex layer V neurons. Neuroscience 102:53–64

    CAS  PubMed  Google Scholar 

  2. Andreasen M, Lambert JD (1999) Somatic amplification of distally generated subthreshold EPSPs in rat hippocampal pyramidal neurones. J Physiol 519:85–100

    CAS  PubMed  PubMed Central  Google Scholar 

  3. Boehlen A, Henneberger C, Heinemann U, Erchova I (2012) Contribution of near-threshold currents to intrinsic oscillatory activity in rat medial entorhinal cortex layer II stellate cells. J Neurophysiol 109:445–463

    PubMed  PubMed Central  Google Scholar 

  4. Branco T, Tozer A, Magnus CJ, Sugino K, Tanaka S, Lee AK, Wood JN, Sternson SM (2016) Near-perfect synaptic integration by Na v 1.7 in hypothalamic neurons regulates body weight. Cell 165:1749–1761

    CAS  PubMed  PubMed Central  Google Scholar 

  5. Buchanan JT, Moore LE, Hill R, Wallén P, Grillner S (1992) Synaptic potentials and transfer functions of lamprey spinal neurons. Biol Cybern 67:123–131

    CAS  PubMed  Google Scholar 

  6. Bui TV, Grande G, Rose PK (2008) Multiple modes of amplification of synaptic inhibition to motoneurons by persistent inward currents. J Neurophysiol 99:571–582

    PubMed  Google Scholar 

  7. Carter BC, Giessel AJ, Sabatini BL, Bean BP (2012) Transient sodium current at subthreshold voltages: activation by EPSP waveforms. Neuron 75:1081–1093

    CAS  PubMed  PubMed Central  Google Scholar 

  8. Ceballos C, Roque A, Leao R (2017) A negative slope conductance of the persistent sodium current prolongs subthreshold depolarizations. Biophys J. doi:10.1016/j.bpj.2017.06.047

  9. Connelly WM, Crunelli V, Errington AC (2016) Passive synaptic normalization and input synchrony-dependent amplification of cortical feedback in thalamocortical neuron dendrites. J Neurosci 36:3735–3754

    CAS  PubMed  PubMed Central  Google Scholar 

  10. Crunelli V, Mayer ML (1984) Mg 2+ dependence of membrane resistance increases evoked by NMDA in hippocampal neurones. Brain Res 311:392–396

    CAS  PubMed  Google Scholar 

  11. Curti S, Gomez L, Budelli R, Pereda AE (2008) Subthreshold sodium current underlies essential functional specializations at primary auditory afferents. J Neurophysiol 99:1683–1699

    PubMed  Google Scholar 

  12. Dagostin AA, Lovell PV, Hilscher MM, Mello CV, Leão RM (2015) Control of Phasic firing by a background leak current in avian forebrain auditory neurons. Front Cell Neurosci 9:471. doi:10.3389/fncel.2015.00471

    Article  PubMed  PubMed Central  Google Scholar 

  13. Deisz RA, Fortin G, Zieglgänsberger W (1991) Voltage dependence of excitatory postsynaptic potentials of rat neocortical neurons. J Neurophysiol 65:371–382

    CAS  PubMed  Google Scholar 

  14. Economo MN, Martínez JJ, White JA (2014) Membrane potential-dependent integration of synaptic inputs in entorhinal stellate neurons. Hippocampus 24:1493–1505

    PubMed  PubMed Central  Google Scholar 

  15. Enyedi P, Czirják G (2010) Molecular background of leak K+ currents: two-pore domain potassium channels. Physiol Rev 90:559–605

    CAS  PubMed  Google Scholar 

  16. Farries MA, Kita H, Wilson CJ (2010) Dynamic spike threshold and zero membrane slope conductance shape the response of subthalamic neurons to cortical input. J Neurosci 30:13180–13191

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Fernandez FR, Malerba P, White JA (2015) Non-linear membrane properties in entorhinal cortical stellate cells reduce modulation of input-output responses by voltage fluctuations. PLoS Comput Biol 11:e1004188. doi:10.1371/journal.pcbi.1004188

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  18. Finkelstein A, Mauro A (2011) Physical principles and formalisms of electrical excitability. In: Kandel ER (ed) Comprehensive physiology. American Physiological Society, Bethesda, pp 161–213

    Google Scholar 

  19. Fricker D, Miles R (2000) EPSP amplification and the precision of spike timing in hippocampal neurons. Neuron 28:559–569

    CAS  PubMed  Google Scholar 

  20. Ghaffari BV, Kouhnavard M, Aihara T, Kitajima T (2015) Mathematical modeling of subthreshold resonant properties in pyloric dilator neurons. Biomed Res Int 2015:21

    Google Scholar 

  21. Ghigliazza RM, Holmes P (2004) Minimal models of bursting neurons: how multiple currents, conductances, and timescales affect bifurcation diagrams. SIAM J App Dyn Syst 3:636–670

    Google Scholar 

  22. Gillessen T, Alzheimer C (1997) Amplification of EPSPs by low Ni2+- and amiloride-sensitive Ca2+ channels in apical dendrites of rat CA1 pyramidal neurons. J Neurophysiol 77:1639–1643

    CAS  PubMed  Google Scholar 

  23. Goldberg JA, Deister CA, Wilson CJ (2007) Response properties and synchronization of rhythmically firing dendritic neurons. J Neurophysiol 97:208–219

    PubMed  Google Scholar 

  24. González-Burgos G, Barrionuevo G (2001) Voltage-gated sodium channels shape subthreshold EPSPs in layer 5 pyramidal neurons from rat prefrontal cortex. J Neurophysiol 86:1671–1684

    PubMed  Google Scholar 

  25. Gutfreund Y, Segev I (1995) Subthreshold oscillations and resonant frequency in guinea-pig cortical neurons: physiology and modelling. J Physiol 483:621–640

    CAS  PubMed  PubMed Central  Google Scholar 

  26. Hardie JB, Pearce RA (2006) Active and passive membrane properties and intrinsic kinetics shape synaptic inhibition in hippocampal CA1 pyramidal neurons. J Neurosci 26:8559–8569

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Hirsch JA, Gilbert CD (1991) Synaptic physiology of horizontal connections in the cat's visual cortex. J Neurosci 11:1800–1809

    CAS  PubMed  PubMed Central  Google Scholar 

  28. Hirsch JA, Oertel D (1988) Intrinsic properties of neurones in the dorsal cochlear nucleus of mice, in vitro. J Physiol 396:535–548

    CAS  PubMed  PubMed Central  Google Scholar 

  29. Hoffman DA, Magee JC, Colbert CM, Johnston D (1997) K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Nature 387:869–875

    CAS  PubMed  Google Scholar 

  30. Hu H, Vervaeke K, Storm JF (2002) Two forms of electrical resonance at theta frequencies, generated by M-current, h-current and persistent Na+ current in rat hippocampal pyramidal cells. J Physiol 545:783–805

    CAS  PubMed  PubMed Central  Google Scholar 

  31. Hutcheon B, Yarom Y (2000) Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci 23:216–222

    CAS  PubMed  Google Scholar 

  32. Hutcheon B, Miura RM, Puil E (1996a) Models of subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76:698–714

    CAS  PubMed  Google Scholar 

  33. Hutcheon B, Miura RM, Puil E (1996b) Subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76:683–697

    CAS  PubMed  Google Scholar 

  34. Izhikevich EM (2007) Dynamical systems in neuroscience. MIT Press, Cambridge

    Google Scholar 

  35. Jackson WF (2016) Boosting the signal: endothelial inward rectifier K+ channels. Microcirculation 24(3):e12319. doi:10.1111/micc.12319

  36. Jacobson GA, Diba K, Yaron-Jakoubovitch A, Oz Y, Koch C, Segev I, Yarom Y (2005) Subthreshold voltage noise of rat neocortical pyramidal neurones. J Physiol 564:145–160

    CAS  PubMed  PubMed Central  Google Scholar 

  37. Johnston D, Wu SMS (1994) Foundations of cellular neurophysiology. MIT press, Cambridge, pp 39–53

    Google Scholar 

  38. Káli S, Zemankovics R (2012) The effect of dendritic voltage-gated conductances on the neuronal impedance: a quantitative model. J Comput Neurosci 33:257–284

    PubMed  Google Scholar 

  39. Klink R, Alonso A (1993) Ionic mechanisms for the subthreshold oscillations and differential electroresponsiveness of medial entorhinal cortex layer II neurons. J Neurophysiol 70:144–157

    CAS  PubMed  Google Scholar 

  40. Klink R, Alonso A (1997) Ionic mechanisms of muscarinic depolarization in entorhinal cortex layer II neurons. J Neurophysiol 77:1829–1843

    CAS  PubMed  Google Scholar 

  41. Koch C (1984) Cable theory in neurons with active, linearized membranes. Biol Cybern 50:15–33

    CAS  PubMed  Google Scholar 

  42. Koch C (1998) Biophysics of computation: information processing in single neurons. Oxford University Press, New York, pp 381–400

    Google Scholar 

  43. Leao RM, Li S, Doiron B, Tzounopoulos T (2012) Diverse levels of an inwardly rectifying potassium conductance generate heterogeneous neuronal behavior in a population of dorsal cochlear nucleus pyramidal neurons. J Neurophysiol 107:3008–3019

    CAS  PubMed  PubMed Central  Google Scholar 

  44. Lipowsky R, Gillessen T, Alzheimer C (1996) Dendritic Na+ channels amplify EPSPs in hippocampal CA1 pyramidal cells. J Neurophysiol 76:2181–2191

    CAS  PubMed  Google Scholar 

  45. Liu S, Shipley MT (2008) Intrinsic conductances actively shape excitatory and inhibitory postsynaptic responses in olfactory bulb external tufted cells. J Neurosci 28:10311–10322

    CAS  PubMed  PubMed Central  Google Scholar 

  46. MacDonald JF, Porietis AV, Wojtowicz JM (1982) L-aspartic acid induces a region of negative slope conductance in the current-voltage relationship of cultured spinal cord neurons. Brain Res 237:248–253

    CAS  PubMed  Google Scholar 

  47. Magee JC (1998) Dendritic hyperpolarization-activated currents modify the integrative properties of hippocampal CA1 pyramidal neurons. J Neurosci 18:7613–7624

    CAS  PubMed  PubMed Central  Google Scholar 

  48. Manuel M, Meunier C, Donnet M, Zytnicki D (2007) Resonant or not, two amplification modes of proprioceptive inputs by persistent inward currents in spinal motoneurons. J Neurosci 27:12977–12988

    CAS  PubMed  PubMed Central  Google Scholar 

  49. Mathews PJ, Jercog PE, Rinzel J, Scott LL, Golding NL (2010) Control of submillisecond synaptic timing in binaural coincidence detectors by Kv1 channels. Nat Neurosci 13:601–609

    CAS  PubMed  PubMed Central  Google Scholar 

  50. Matsumoto-Makidono Y, Nakayama H, Yamasaki M, Miyazaki T, Kobayashi K, Watanabe M, Kano M, Sakimura K, Hashimoto K (2016) Ionic basis for membrane potential resonance in neurons of the inferior olive. Cell Rep 16:994–1004

    CAS  PubMed  Google Scholar 

  51. Moore LE, Buchanan JT, Murphey CR (1995) Localization and interaction of N-methyl-D-aspartate and non-N-methyl-D-aspartate receptors of lamprey spinal neurons. Biophys J 68:96–103

  52. Moore LE, Buchanan JT, Murphey CR (1994) Anomalous increase in membrane impedance of neurons during NMDA activation. In: Eeckman FH (ed) Computation in neurons and neural systems. Kluwer Academic, Boston, pp 9–14

    Google Scholar 

  53. Moore LE, Chub N, Tabak J, O’Donovan M (1999) NMDA-induced dendritic oscillations during a soma voltage clamp of chick spinal neurons. J Neurosci 19:8271–8280

    CAS  PubMed  PubMed Central  Google Scholar 

  54. Pape HC, Driesang RB (1998) Ionic mechanisms of intrinsic oscillations in neurons of the basolateral amygdaloid complex. J Neurophysiol 79:217–226

    CAS  PubMed  Google Scholar 

  55. Porres CP, Meyer EM, Grothe B, Felmy F (2011) NMDA currents modulate the synaptic input–output functions of neurons in the dorsal nucleus of the lateral lemniscus in mongolian gerbils. J Neurosci 31:4511–4523

    CAS  PubMed  PubMed Central  Google Scholar 

  56. Prescott SA, De Koninck Y (2005) Integration time in a subset of spinal lamina I neurons is lengthened by sodium and calcium currents acting synergistically to prolong subthreshold depolarization. J Neurosci 25:4743–4754

    CAS  PubMed  PubMed Central  Google Scholar 

  57. Putzier I, Kullmann PH, Horn JP, Levitan ES (2009) Cav1. 3 channel voltage dependence, not Ca2+ selectivity, drives pacemaker activity and amplifies bursts in nigral dopamine neurons. J Neurosci 29:15414–15419

    CAS  PubMed  PubMed Central  Google Scholar 

  58. Remme MW, Rinzel J (2011) Role of active dendritic conductances in subthreshold input integration. J Comput Neurosci 31:13–30

    PubMed  Google Scholar 

  59. Richardson MJ, Brunel N, Hakim V (2003) From subthreshold to firing-rate resonance. J Neurophysiol 89:2538–2554

    PubMed  Google Scholar 

  60. Ries CR, Puil E (1999) Ionic mechanism of isoflurane’s actions on thalamocortical neurons. J Neurophysiol 81:1802–1809

    CAS  PubMed  Google Scholar 

  61. Rosenkranz JA, Johnston D (2007) State-dependent modulation of amygdala inputs by dopamine-induced enhancement of sodium currents in layer V entorhinal cortex. J Neurosci 27:7054–7069

    CAS  PubMed  PubMed Central  Google Scholar 

  62. Rotaru DC, Lewis DA, Gonzalez-Burgos G (2007) Dopamine D1 receptor activation regulates sodium channel-dependent EPSP amplification in rat prefrontal cortex pyramidal neurons. J Physiol 581:981–1000

    CAS  PubMed  PubMed Central  Google Scholar 

  63. Rotstein HG (2015) Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents. J Comput Neurosci 38:325–354

    PubMed  Google Scholar 

  64. Rotstein HG (2016) The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales. J Comput Neurosci 42:133–166

    PubMed  Google Scholar 

  65. Rotstein HG, Nadim F (2014) Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. J Comput Neurosci 37:9–28

    PubMed  Google Scholar 

  66. Sabah NH, Leibovic KN (1969) Subthreshold oscillatory responses of the Hodgkin–Huxley cable model for the squid giant axon. Biophys J 9:1206–1222

  67. Saint Mleux B, Moore LE (2000) Active Dendritic membrane properties of Xenopus larval spinal neurons analyzed with a whole cell soma voltage clamp. J Neurophysiol 83:1381–1393

  68. Schwindt PC, Crill WE (1995) Amplification of synaptic current by persistent sodium conductance in apical dendrite of neocortical neurons. J Neurophysiol 74:2220–2224

    CAS  PubMed  Google Scholar 

  69. Scott LL, Mathews PJ, Golding NL (2010) Perisomatic voltage-gated sodium channels actively maintain linear synaptic integration in principal neurons of the medial superior olive. J Neurosci 30:2039–2050

    CAS  PubMed  PubMed Central  Google Scholar 

  70. Smith PD, Brett SE, Luykenaar KD, Sandow SL, Marrelli SP, Vigmond EJ, Welsh DG (2008) KIR channels function as electrical amplifiers in rat vascular smooth muscle. J Physiol 586:1147–1160

    CAS  PubMed  Google Scholar 

  71. Stafstrom CE, Schwindt PC, Crill WE (1982) Negative slope conductance due to a persistent subthreshold sodium current in cat neocortical neurons in vitro. Brain Res 236:221–226

    CAS  PubMed  Google Scholar 

  72. Stafstrom CE, Schwindt PC, Chubb MC, Crill WE (1985) Properties of persistent sodium conductance and calcium conductance of layer V neurons from cat sensorimotor cortex in vitro. J Neurophysiol 53:153–170

    CAS  PubMed  Google Scholar 

  73. Stuart G (1999) Voltage–activated sodium channels amplify inhibition in neocortical pyramidal neurons. Nat Neurosci 2:144–150

    CAS  PubMed  Google Scholar 

  74. Stuart G, Sakmann B (1995) Amplification of EPSPs by axosomatic sodium channels in neocortical pyramidal neurons. Neuron 15:1065–1076

    CAS  PubMed  Google Scholar 

  75. Sun H, An S, Luhmann HJ, Kilb W (2014) Resonance properties of GABAergic interneurons in immature GAD67-GFP mouse neocortex. Brain Res 1548:1–11

    CAS  PubMed  Google Scholar 

  76. Thomson AM, Girdlestone D, West DC (1988) Voltage-dependent currents prolong single-axon postsynaptic potentials in layer III pyramidal neurons in rat neocortical slices. J Neurophysiol 60:1896–1907

    CAS  PubMed  Google Scholar 

  77. Urban NN, Henze DA, Barrionuevo G (1998) Amplification of perforant-path EPSPs in CA3 pyramidal cells by LVA calcium and sodium channels. J Neurophysiol 80:1558–1561

    CAS  PubMed  Google Scholar 

  78. Vervaeke K, Hu H, Graham LJ, Storm JF (2006) Contrasting effects of the persistent Na+ current on neuronal excitability and spike timing. Neuron 49:257–270

    CAS  PubMed  Google Scholar 

  79. Wessel R, Kristan WB, Kleinfeld D (1999) Supralinear summation of synaptic inputs by an invertebrate neuron: dendritic gain is mediated by an “inward rectifier” K+ current. J Neurosci 19:5875–5888

    CAS  PubMed  PubMed Central  Google Scholar 

  80. Williams SR, Stuart GJ (2003) Voltage-and site-dependent control of the somatic impact of dendritic IPSPs. J Neurosci 23:7358–7367

    CAS  PubMed  PubMed Central  Google Scholar 

  81. Wilson CJ (2005) The mechanism of intrinsic amplification of hyperpolarizations and spontaneous bursting in striatal cholinergic interneurons. Neuron 45:575–585

    CAS  PubMed  Google Scholar 

  82. Wu N, Enomoto A, Tanaka S, Hsiao CF, Nykamp DQ, Izhikevich E, Chandler SH (2005) Persistent sodium currents in mesencephalic v neurons participate in burst generation and control of membrane excitability. J Neurophysiol 93:2710–2722

    CAS  PubMed  Google Scholar 

  83. Wu N, Hsiao CF, Chandler SH (2001) Membrane resonance and subthreshold membrane oscillations in mesencephalic V neurons: participants in burst generation. J Neurosci 21:3729–3739

    CAS  PubMed  PubMed Central  Google Scholar 

  84. Yamada-Hanff J, Bean BP (2015) Activation of Ih and TTX-sensitive sodium current at subthreshold voltages during CA1 pyramidal neuron firing. J Neurophysiol 114:2376–2389

    CAS  PubMed  PubMed Central  Google Scholar 

  85. Yamashita T, Isa T (2004) Enhancement of excitatory postsynaptic potentials by preceding application of acetylcholine in mesencephalic dopamine neurons. Neurosci Res 49:91–100

    CAS  PubMed  Google Scholar 

  86. Yang RH, Wang WT, Chen JY, Xie RG, Hu SJ (2009) Gabapentin selectively reduces persistent sodium current in injured type-a dorsal root ganglion neurons. Pain 143:48–55

    CAS  PubMed  Google Scholar 

  87. Yaron-Jakoubovitch A, Jacobson GA, Koch C, Segev I, Yarom Y (2008) A paradoxical isopotentiality: a spatially uniform noise spectrum in neocortical pyramidal cells. Front Cell Neurosci 2:1–9. doi:10.3389/neuro.03.003.2008

  88. Yoshii K, Moore LE, Christensen BN (1988) Effect of subthreshold voltage-dependent conductances on the transfer function of branched excitable cells and the conduction of synaptic potentials. J Neurophysiol 59:706–716

    CAS  PubMed  Google Scholar 

  89. Zsiros V, Hestrin S (2005) Background synaptic conductance and precision of EPSP-spike coupling at pyramidal cells. J Neurophysiol 93:3248–3256

    PubMed  Google Scholar 

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Acknowledgments

This work was supported by FAPESP (2016/01607-4) and CNPq (470745/2012-6) grants to RML, and FAPESP (2013/07699-0) and CNPq (306251/2014-0) grants to ACR. CCC is a PhD scholarship recipient from CAPES.

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Correspondence to Antonio C. Roque or Ricardo M. Leão.

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This article is part of a Special Issue on ‘Latin America’ edited by Pietro Ciancaglini and Rosangela Itri

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Ceballos, C.C., Roque, A.C. & Leão, R.M. The role of negative conductances in neuronal subthreshold properties and synaptic integration. Biophys Rev 9, 827–834 (2017). https://doi.org/10.1007/s12551-017-0300-8

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Keywords

  • Passive cable theory
  • Voltage-dependent inward currents
  • Neuronal membrane
  • Synaptic integration
  • Neuronal subthreshold properties