Journal of Comparative Physiology A

, Volume 196, Issue 9, pp 613–628 | Cite as

Calcium-dependent control of temporal processing in an auditory interneuron: a computational analysis

  • Abhilash Ponnath
  • Hamilton E. FarrisEmail author
Original Paper


Sensitivity to acoustic amplitude modulation in crickets differs between species and depends on carrier frequency (e.g., calling song vs. bat-ultrasound bands). Using computational tools, we explore how Ca2+-dependent mechanisms underlying selective attention can contribute to such differences in amplitude modulation sensitivity. For omega neuron 1 (ON1), selective attention is mediated by Ca2+-dependent feedback: [Ca2+]internal increases with excitation, activating a Ca2+-dependent after-hyperpolarizing current. We propose that Ca2+ removal rate and the size of the after-hyperpolarizing current can determine ON1’s temporal modulation transfer function (TMTF). This is tested using a conductance-based simulation calibrated to responses in vivo. The model shows that parameter values that simulate responses to single pulses are sufficient in simulating responses to modulated stimuli: no special modulation-sensitive mechanisms are necessary, as high and low-pass portions of the TMTF are due to Ca2+-dependent spike frequency adaptation and post-synaptic potential depression, respectively. Furthermore, variance in the two biophysical parameters is sufficient to produce TMTFs of varying bandwidth, shifting amplitude modulation sensitivity like that in different species and in response to different carrier frequencies. Thus, the hypothesis that the size of after-hyperpolarizing current and the rate of Ca2+ removal can affect amplitude modulation sensitivity is computationally validated.


Adaptation Temporal processing Roex filter Evolution Temperature 





Equivalent rectangular bandwidth




Omega neuron 1


Postsynaptic potential


Spike frequency peak


Signal-to-noise ratio


Fast adaptation time constant


Temporal modulation transfer function


Time constant for Ca2+ removal


Slow adaptation time constant



Two anonymous reviewers as well as C. Canavier, S. Selvakumar, S. Achuthan and W. Gordon provided useful comments on the project and/or manuscript. N. Bazan generously provided equipment and software. No animals were used for this computational project. The study was funded in part by the NIH Grant # P20RR016816 to N. Bazan.


  1. Art JJ, Wu YC, Fettiplace R (1995) The calcium-activated potassium channels of turtle hair-cells. J Gen Physiol 105:49–72CrossRefPubMedGoogle Scholar
  2. Baden T, Hedwig B (2007) Neurite-specific Ca2+ dynamics underlying sound processing in an auditory interneurone. Dev Neurobiol 67:68–80CrossRefPubMedGoogle Scholar
  3. Benda J, Hennig RM (2008) Spike-frequency adaptation generates intensity invariance in a primary auditory interneuron. J Comput Neurosci 24:113–136CrossRefPubMedGoogle Scholar
  4. Benda J, Herz AVM (2003) A universal model for spike-frequency adaptation. Neural Comput 15:2523–2564CrossRefPubMedGoogle Scholar
  5. Benda J, Bethge M, Hennig M, Pawelzik K, Herz AVM (2001) Spike-frequency adaptation: phenomenological model and experimental tests. Neurocomputing 38:105–110CrossRefGoogle Scholar
  6. Benda J, Longtin A, Maler L (2005) Spike-frequency adaptation separates transient communication signals from background oscillations. J Neurosci 25:2312–2321CrossRefPubMedGoogle Scholar
  7. Bennet-Clark HC (1989) Songs and the physics of sound production. In: Huber F, Moore TE, Loher W (eds) Cricket behavior and neurobiology. Cornell University Press, Ithaca, pp 227–261Google Scholar
  8. Bentley DR, Hoy RR (1972) Genetic-control of neuronal network generating cricket (TeleogryllusGryllus) song patterns. Anim Behav 20:478–492CrossRefPubMedGoogle Scholar
  9. Bond CT, Maylie J, Adelman JP (2005) SK channels in excitability, pacemaking and synaptic integration. Curr Opin Neurobiol 15:305–311CrossRefPubMedGoogle Scholar
  10. Burrell BD, Crisp KM (2008) Serotonergic modulation of afterhyperpolarization in a neuron that contributes to learning in the leech. J Neurophysiol 99:605–616CrossRefPubMedGoogle Scholar
  11. Bush SL, Schul J (2006) Pulse-rate recognition in an insect: evidence of a role for oscillatory neurons. J Comp Physiol A 192:113–121CrossRefGoogle Scholar
  12. Chen QH, Toney GM (2009) Excitability of paraventricular nucleus neurones that project to the rostral ventrolateral medulla is regulated by small-conductance Ca2+-activated K+ channels. J Physiol 587:4235–4247CrossRefPubMedGoogle Scholar
  13. Dean I, Harper NS, McAlpine D (2005) Neural population coding of sound level adapts to stimulus statistics. Nat Neurosci 8:1684–1689CrossRefPubMedGoogle Scholar
  14. Dean I, Robinson BL, Harper NS, McAlpine D (2008) Rapid neural adaptation to sound level statistics. J Neurosci 28:6430–6438CrossRefPubMedGoogle Scholar
  15. Doherty JA (1985a) Temperature coupling and trade-off phenomena in the acoustic communication-system of the cricket, Gryllus bimaculatus de Geer (Gryllidae). J Exp Biol 114:17–35Google Scholar
  16. Doherty JA (1985b) Trade-off phenomena in calling song recognition and phonotaxis in the cricket, Gryllus bimaculatus (Orthoptera, Gryllidae). J Comp Physiol A 156:787–801CrossRefGoogle Scholar
  17. Egelhaaf M, Borst A (1995) Calcium accumulation in visual interneurons of the fly—stimulus dependence and relationship to membrane-potential. J Neurophysiol 73:2540–2552PubMedGoogle Scholar
  18. Engel J, Schultens HA, Schild D (1999) Small conductance potassium channels cause an activity-dependent spike frequency adaptation and make the transfer function of neurons logarithmic. Biophys J 76:1310–1319CrossRefPubMedGoogle Scholar
  19. Esch H, Huber F, Wohlers DW (1980) Primary auditory neurons in crickets—physiology and central projections. J Comp Physiol 137:27–38CrossRefGoogle Scholar
  20. Faber ES, Sah P (2007) Functions of SK channels in central neurons. Clin Exp Pharmacol Physiol 34:1077–1083CrossRefPubMedGoogle Scholar
  21. Fan G-X, Liu QH (2004) Fast Fourier transform for discontinuous functions. IEEE Trans Antennas Propag 52:461–465CrossRefGoogle Scholar
  22. Farris HE, Hoy RR (2002) Two-tone suppression in the cricket, Eunemobius carolinus (Gryllidae, Nemobiinae). J Acoust Soc Am 111:1475–1485CrossRefPubMedGoogle Scholar
  23. Farris HE, Mason AC, Hoy RR (2004) Identified auditory neurons in the cricket Gryllus rubens: temporal processing in calling song sensitive units. Hear Res 193:121–133CrossRefPubMedGoogle Scholar
  24. Farris HE, Wells GB, Ricci AJ (2006) Steady-state adaptation of mechanotransduction modulates the resting potential of auditory hair cells, providing an assay for endolymph [Ca2+]. J Neurosci 26:12526–12536CrossRefPubMedGoogle Scholar
  25. Faulkes Z, Pollack GS (2001) Mechanisms of frequency-specific responses of omega neuron 1 in crickets (Teleogryllus oceanicus): a polysynaptic pathway for song? J Exp Biol 204:1295–1305PubMedGoogle Scholar
  26. Fortune ES, Rose GJ (1997) Passive and active membrane properties contribute to the temporal filtering properties of midbrain neurons in vivo. J Neurosci 17:3815–3825PubMedGoogle Scholar
  27. Fortune ES, Rose GJ (2001) Short-term synaptic plasticity as a temporal filter. Trends Neurosci 24:381–385CrossRefPubMedGoogle Scholar
  28. French AS (1986) The role of calcium in the rapid adaptation of an insect mechanoreceptor. J Neurosci 6:2322–2326PubMedGoogle Scholar
  29. Frisina RD (2001) Subcortical neural coding mechanisms for auditory temporal processing. Hear Res 158:1–27CrossRefPubMedGoogle Scholar
  30. Getting PA (1974) Modification of neuron properties by electrotonic synapses. I. Input resistance, time constant, and integration. J Neurophysiol 37:846–857PubMedGoogle Scholar
  31. Gollisch T, Herz AVM (2004) Input-driven components of spike-frequency adaptation can be unmasked in vivo. J Neurosci 24:7435–7444CrossRefPubMedGoogle Scholar
  32. Harris DM, Dallos P (1979) Forward masking of auditory nerve fiber responses. J Neurophysiol 42:1083–1107PubMedGoogle Scholar
  33. Hartmann WH (1998) Signals, sound, and sensation. AIP Press, New YorkGoogle Scholar
  34. Hennig RM (1988) Ascending auditory interneurons in the cricket Teleogryllus commodus (Walker)—comparative physiology and direct connections with afferents. J Comp Physiol A 163:135–143CrossRefPubMedGoogle Scholar
  35. Hennig RM (2003) Acoustic feature extraction by cross-correlation in crickets? J Comp Physiol A 189:589–598CrossRefGoogle Scholar
  36. Hennig RM, Weber T (1997) Filtering of temporal parameters of the calling song by cricket females of two closely related species: a behavioral analysis. J Comp Physiol A 180:621–630CrossRefGoogle Scholar
  37. Hildebrandt KJ, Benda J, Hennig RM (2009) The origin of adaptation in the auditory pathway of locusts is specific to cell type and function. J Neurosci 29:2626–2636CrossRefPubMedGoogle Scholar
  38. Hille B (1992) Ionic conductances of excitable membranes. Sinaurer Associates Inc., SunderlandGoogle Scholar
  39. Hirschberg B, Maylie J, Adelman JP, Marrion NV (1999) Gating properties of single SK channels in hippocampal CA1 pyramidal neurons. Biophys J 77:1905–1913CrossRefPubMedGoogle Scholar
  40. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117:500–544Google Scholar
  41. Horowitz P, Hill W (1989) The art of electronics. Cambridge University Press, CambridgeGoogle Scholar
  42. Horseman G, Huber F (1994) Sound localization in crickets.1. contralateral inhibition of an ascending auditory interneuron (An1) in the cricket Gryllus bimaculatus. J Comp Physiol A 175:389–398CrossRefGoogle Scholar
  43. Hoy RR (1974) Genetic-control of acoustic behavior in crickets. Am Zool 14:1067–1080Google Scholar
  44. Hoy RR, Paul RC (1973) Genetic-control of song specificity in crickets. Science 180:82–83CrossRefPubMedGoogle Scholar
  45. Hoy RR, Hahn J, Paul RC (1977) Hybrid cricket auditory-behavior—evidence for genetic coupling in animal communication. Science 195:82–84CrossRefPubMedGoogle Scholar
  46. Huguenard JR, McCormack TJ (1994) Electrophysiology of the neuron. Oxford University Press, New YorkGoogle Scholar
  47. Imaizumi K, Pollack GS (2005) Central projections of auditory receptor neurons of crickets. J Comp Neurol 493:439–447CrossRefPubMedGoogle Scholar
  48. Janiszewski J, Otto D (1989) Responses and song pattern copying of omega-type I-neurons in the cricket, Gryllus bimaculatus, at different prothoracic temperatures. J Comp Physiol A 164:443–450CrossRefGoogle Scholar
  49. Kang SH, Carl A, McHugh JM, Goff HR, Kenyon JL (2008) Roles of mitochondria and temperature in the control of intracellular calcium in adult rat sensory neurons. Cell Calcium 43:388–404CrossRefPubMedGoogle Scholar
  50. Katz PS, Harris-Warrick RM (1999) The evolution of neuronal circuits underlying species-specific behavior. Curr Opin Neurobiol 9:628–633CrossRefPubMedGoogle Scholar
  51. Lee JCF, Callaway JC, Foehring RC (2005) Effects of temperature on calcium transients and Ca2+-dependent afterhyperpolarizations in neocortical pyramidal neurons. J Neurophysiol 93:2012–2020CrossRefPubMedGoogle Scholar
  52. Leinders T, Vijverberg HP (1992) Ca2+ dependence of small Ca(2 +)-activated K+ channels in cultured N1E–115 mouse neuroblastoma cells. Pflugers Arch 422:223–232CrossRefPubMedGoogle Scholar
  53. Machne X, Orozco R (1970) Electrical properties of axons of Callinectes sapidus. Am J Physiol 219:1147–1153PubMedGoogle Scholar
  54. Marsat G, Pollack GS (2004) Differential temporal coding of rhythmically diverse acoustic signals by a single interneuron. J Neurophysiol 92:939–948CrossRefPubMedGoogle Scholar
  55. Marsat G, Pollack GS (2005) Effect of the temporal pattern of contralateral inhibition on sound localization cues. J Neurosci 25:6137–6144CrossRefPubMedGoogle Scholar
  56. McCormack TJ (2003) Comparison of K+-channel genes within the genomes of Anopheles gambiae and Drosophila melanogaster. Genome Biol 4:R58CrossRefPubMedGoogle Scholar
  57. McCormick DA, Huguenard JR (1992) A model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol 68:1384–1400PubMedGoogle Scholar
  58. Moore BC, Glasberg BR, Plack CJ, Biswas AK (1988) The shape of the ear’s temporal window. J Acoust Soc Am 83:1102–1116CrossRefPubMedGoogle Scholar
  59. Mutoh H, Yoshino M (2004) L-type Ca2+ channel and Ca2+-permeable nonselective cation channel as a Ca2+ conducting pathway in myocytes isolated from the cricket lateral oviduct. J Comp Physiol B 174:21–28CrossRefPubMedGoogle Scholar
  60. Nabatiyan A, Poulet JF, de Polavieja GG, Hedwig B (2003) Temporal pattern recognition based on instantaneous spike rate coding in a simple auditory system. J Neurophysiol 90:2484–2493CrossRefPubMedGoogle Scholar
  61. Nolting A, Ferraro T, D’hoedt D, Stocker M (2007) An amino acid outside the pore region influences apamin sensitivity in small conductance Ca2+-activated K+ channels. J Biol Chem 282:3478–3486CrossRefPubMedGoogle Scholar
  62. Numata T, Yoshino M (2005) Characterization of single L-type Ca2+ channels in myocytes isolated from the cricket lateral oviduct. J Comp Physiol B 175:257–263CrossRefPubMedGoogle Scholar
  63. Patterson RD, Nimmo-Smith I, Weber DL, Milroy R (1982) The deterioration of hearing with age: frequency selectivity, the critical ratio, the audiogram, and speech threshold. J Acoust Soc Am 72:1788–1803CrossRefPubMedGoogle Scholar
  64. Pedarzani P, Mosbacher J, Rivard A, Cingolani LA, Oliver D, Stocker M, Adelman JP, Fakler B (2001) Control of electrical activity in central neurons by modulating the gating of small conductance Ca2+-activated K+ channels. J Biol Chem 276:9762–9769CrossRefPubMedGoogle Scholar
  65. Pedarzani P, McCutcheon JE, Rogge G, Jensen BS, Christophersen P, Hougaard C, Strobaek D, Stocker M (2005) Specific enhancement of SK channel activity selectively potentiates the afterhyperpolarizing current I(AHP) and modulates the firing properties of hippocampal pyramidal neurons. J Biol Chem 280:41404–41411CrossRefPubMedGoogle Scholar
  66. Pires A, Hoy RR (1992a) Temperature coupling in cricket acoustic communication. I. Field and laboratory studies of temperature effects on calling song production and recognition in Gryllus firmus. J Comp Physiol A 171:69–78CrossRefPubMedGoogle Scholar
  67. Pires A, Hoy RR (1992b) Temperature coupling in cricket acoustic communication. II. Localization of temperature effects on song production and recognition networks in Gryllus firmus. J Comp Physiol A 171:79–92CrossRefPubMedGoogle Scholar
  68. Pollack GS (1986) Discrimination of calling song models by the cricket, Teleogryllus oceanicus—the influence of sound direction on neural encoding of the stimulus temporal pattern and on phonotactic behavior. J Comp Physiol A 158:549–561CrossRefGoogle Scholar
  69. Pollack GS (1988) Selective attention in an insect auditory neuron. J Neurosci 8:2635–2639PubMedGoogle Scholar
  70. Pollack GS (1994) Synaptic inputs to the omega neuron of the cricket Teleogryllus oceanicus: differences in epsp wave-forms evoke by low and high sound frequencies. J Comp Physiol A 174:83–89CrossRefGoogle Scholar
  71. Pollack GS, Hoy RR (1979) Temporal pattern as a cue for species-specific calling song recognition in crickets. Science 204:429–432CrossRefPubMedGoogle Scholar
  72. Roper P, Callaway J, Shevchenko T, Teruyama R, Armstrong W (2003) AHP’s, HAP’s and DAP’s: how potassium currents regulate the excitability of rat supraoptic neurones. J Comput Neurosci 15:367–389CrossRefPubMedGoogle Scholar
  73. Rose GJ, Fortune ES (1999) Frequency-dependent PSP depression contributes to low-pass temporal filtering in Eigenmannia. J Neurosci 19:7629–7639PubMedGoogle Scholar
  74. Sabourin P, Pollack GS (2010) Temporal coding by populations of auditory receptor neurons. J Neurophysiol 103:1614–1621CrossRefPubMedGoogle Scholar
  75. Sabourin P, Gottlieb H, Pollack GS (2008) Carrier-dependent temporal processing in an auditory interneuron. J Acoust Soc Am 123:2910–2917CrossRefPubMedGoogle Scholar
  76. Sah P, Faber ESL (2002) Channels underlying neuronal calcium-activated potassium currents. Prog Neurobiol 66:345–353CrossRefPubMedGoogle Scholar
  77. Schildberger K (1984) Temporal selectivity of identified auditory neurons in the cricket brain. J Comp Physiol 155:171–185CrossRefGoogle Scholar
  78. Schildberger K, Huber F, Wohlers DW (1989) Central auditory pathway: neuronal correlates of phonotactic behavior. In: Huber F, Moore TE, Loher W (eds) Cricket behavior and neurobiology. Cornell University Press, Ithaca, pp 423–458Google Scholar
  79. Schul J (1998) Song recognition by temporal cues in a group of closely related bushcricket species (genus Tettigonia). J Comp Physiol A 183:401–410CrossRefGoogle Scholar
  80. Selverston AI, Kleindienst HU, Huber F (1985) Synaptic connectivity between cricket auditory interneurons as studied by selective photoinactivation. J Neurosci 5:1283–1292PubMedGoogle Scholar
  81. Shaw KL (2000) Interspecific genetics of mate recognition: Inheritance of female acoustic preference in Hawaiian crickets. Evolution 54:1303–1312PubMedGoogle Scholar
  82. Shaw KL, Herlihy DP (2000) Acoustic preference functions and song variability in the Hawaiian cricket Laupala cerasina. Proc R Soc Biol Sci 267:577–584CrossRefGoogle Scholar
  83. Shaw KL, Parsons YM, Lesnick SC (2007) QTL analysis of a rapidly evolving speciation phenotype in the Hawaiian cricket Laupala. Mol Ecol 16:2879–2892CrossRefPubMedGoogle Scholar
  84. Sobel EC, Tank DW (1994) In vivo Ca2+ dynamics in a cricket auditory neuron—an example of chemical computation. Science 263:823–826CrossRefPubMedGoogle Scholar
  85. Stocker M, Hirzel K, D’hoedt D, Pedarzani P (2004) Matching molecules to function: neuronal Ca2+-activated K+ channels and afterhyperpolarizations. Toxicon 43:933–949CrossRefPubMedGoogle Scholar
  86. Storm JF (1990) Potassium currents in hippocampal pyramidal cells. Prog Brain Res 83:161–187CrossRefPubMedGoogle Scholar
  87. Thorson J, Weber T, Huber F (1982) Auditory-behavior of the cricket. II. Simplicity of calling-song recognition in Gryllus, and anomalous phonotaxis at abnormal carrier frequencies. J Comp Physiol 146:361–378CrossRefGoogle Scholar
  88. Traub RD, Wong RK, Miles R, Michelson H (1991) A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J Neurophysiol 66:635–650PubMedGoogle Scholar
  89. Tucker TR, Fettiplace R (1996) Monitoring calcium in turtle hair cells with a calcium-activated potassium channel. J Physiol 494(Pt 3):613–626PubMedGoogle Scholar
  90. Tunstall DN, Pollack GS (2005) Temporal and directional processing by an identified interneuron, ON1, compared in cricket species that sing with different tempos. J Comp Physiol A 191:363–372CrossRefGoogle Scholar
  91. Walker TJ (1957) Specificity in the response of female tree crickets (Orthoptera: Gryllidae: Oecanthinae) to calling songs of the males. Ann Entomol Soc Am 50:626–636Google Scholar
  92. Walker TJ (1962) Factors responsible for intraspecific variation in calling songs of crickets. Evolution 16:407–428CrossRefGoogle Scholar
  93. Wang XJ (1998) Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J Neurophysiol 79:1549–1566PubMedGoogle Scholar
  94. Wei A, Jegla T, Salkoff L (1996) Eight potassium channel families revealed by the C. elegans genome project. Neuropharmacology 35:805–829CrossRefPubMedGoogle Scholar
  95. Wicher D, Penzlin H (1997) Ca2+ currents in central insect neurons: electrophysiological and pharmacological properties. J Neurophysiol 77:186–199PubMedGoogle Scholar
  96. Witte K, Farris HE, Ryan MJ, Wilczynski W (2005) How cricket frog females deal with a noisy world: habitat-related differences in auditory tuning. Behav Ecol 16:571–579CrossRefGoogle Scholar
  97. Xia XM, Fakler B, Rivard A, Wayman G, Johnson-Pais T, Keen JE, Ishii T, Hirschberg B, Bond CT, Lutsenko S, Maylie J, Adelman JP (1998) Mechanism of calcium gating in small-conductance calcium-activated potassium channels. Nature 395:503–507CrossRefPubMedGoogle Scholar
  98. Zakon HH (2003) Insight into the mechanisms of neuronal processing from electric fish. Curr Opin Neurobiol 13:744–750CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Center for Neuroscience and Kresge Hearing LaboratoriesLouisiana State University Health Sciences Center (LSUHSC)New OrleansUSA

Personalised recommendations