Biological Cybernetics

, Volume 102, Issue 5, pp 389–412 | Cite as

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

Original Paper

Abstract

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.

Keywords

Sensory network Phase oscillator Stochastic network Network encoding 

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References

  1. Abbott LF, van Vreeswijk CA (1993) Asynchronous states in networks of pulse-coupled oscillators. Phys Rev E 48: 1483CrossRefGoogle Scholar
  2. Alkon DL, Fuortes MGF (1972) Responses of photoreceptors in Hermissenda. J Gen Phisiol 60: 631–649CrossRefGoogle Scholar
  3. Amit DJ, Brunel N (1997) Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex 7(3): 237–252CrossRefPubMedGoogle Scholar
  4. Berman N, Maler L (1998) Inhibition evoked from primary afferents in the electrosensory lateral line lobe of the weakly electric fish (Apteronotus leptorhynchus). J Neurophysiol 80: 3173–3196PubMedGoogle Scholar
  5. Blackwell KT (2006) Ionic currents underlying difference in light responses between type A and type B photoreceptors. J Neurophysiol 95: 3060–3072CrossRefPubMedGoogle Scholar
  6. Bressloff P, Coombes S (2000) Dynamics of strongly coupled spiking neurons. Neural Comput 12: 91–129CrossRefPubMedGoogle Scholar
  7. Brown E, Moehlis J, Holmes P (2004) On the phase reduction and response dynamics of neural oscillator populations. Neural Comput 16: 673–715CrossRefPubMedGoogle Scholar
  8. Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput 11: 1621–1671CrossRefPubMedGoogle Scholar
  9. Brunel N, Hansel D (2006) How noise affects the synchronization properties of recurrent networks of inhibitory neurons. Neural Comput 18: 1066–1110CrossRefPubMedGoogle Scholar
  10. Bryant HL, Segundo JP (1976) Spike initiation by transmembrane current: a white noise analysis. J Physiol 260: 279–314PubMedGoogle Scholar
  11. Butson CR, Clark GA (2008a) Random noise paradoxically improves light-intensity encoding in Hermissenda photoreceptor network. J Neurophysiol 99: 146–154CrossRefPubMedGoogle Scholar
  12. Butson CR, Clark GA (2008b) Mechanisms of noise-induced improvement in light-intensity encoding in Hermissenda photoreceptor network. J Neurophysiol 99: 155–165CrossRefPubMedGoogle Scholar
  13. Chacron MJ, Longtin A, St-Hilaire M, Maler L (2000) Suprathreshold stochastic firing dynamics with memory in P-type electroreceptors. Phys Rev Lett 85: 1576–1579CrossRefPubMedGoogle Scholar
  14. Eakin RM, Westfall JA, Dennis MJ (1967) Fine structure of the eye of a nudibranch mollusc Hermissenda Crassicornis. J Cell Sci 2: 349–358PubMedGoogle Scholar
  15. Ermentrout GB, Galán RF, Urban NN (2007) Relating neural dynamics to neural coding. Phys Rev Lett 99: 248103CrossRefPubMedGoogle Scholar
  16. Ermentrout GB, Kopell N (1990) Oscillator death in systems of coupled neural oscillators. SIAM J Appl Math 50: 125CrossRefGoogle Scholar
  17. Ermentrout GB, Saunders D (2006) Phase resetting and coupling of noisy neural oscillators. J Comput Neurosci 20: 179–190CrossRefPubMedGoogle Scholar
  18. Fusi S, Mattia M (1999) Collective behavior of networks with linear (VLSI) integrate-and-fire neurons. Neural Comput 11: 633–652CrossRefPubMedGoogle Scholar
  19. Gardner CW (1994) Handbook of stochastic methods. Springer, BerlinGoogle Scholar
  20. Gerstner W (2000) Population dynamics of spiking neurons: fast transients, asynchronous states, and locking. Neural Comput 12: 43–89CrossRefPubMedGoogle Scholar
  21. Glass L, Mackey MC (1988) From clocks to chaos: the rhythms of life. Princeton University Press, Princeton, NJGoogle Scholar
  22. Jazayeri M, Movshon A (2006) Optimal representation of sensory information by neural populations. Nat Neurosci 9: 690–696CrossRefPubMedGoogle Scholar
  23. Kohn AF, Freitasda Rocha A, Segundo JP (1981) Presynaptic irregularity and pacemaker inhibition. Biol Cybern 41: 5–18CrossRefGoogle Scholar
  24. Kuramoto Y (1984) Chemical oscillations, waves, and turbulence. Dover Books, New York, NYGoogle Scholar
  25. Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268: 1503–1506CrossRefPubMedGoogle Scholar
  26. Ma JM, Beck JM, Latham PE, Pouget A (2006) Bayesian inference with probabilistic population codes. Nat Neurosci 9: 1432–1438CrossRefPubMedGoogle Scholar
  27. Mar DJ, Chow CC, Gerstner W, Adams RW, Collins JJ (1999) Noise shaping in populations of coupled model neurons. Proc Natl Acad Sci USA 96: 10450–10455CrossRefPubMedGoogle Scholar
  28. Maran SK, Canavier C (2008) Using phase resetting to predict 1:1 and 2:2 locking in two neuron networks in which firing order is not always preserved. J Comput Neurosci 24: 37–55CrossRefPubMedGoogle Scholar
  29. Mo JL, Blackwell KT (2003) Comparisson of Hermissenda type A and type B photoreceptors: response to light as a function of intensity and duration. J Neurosci 23(22): 8020–8028PubMedGoogle Scholar
  30. Nesse WH, Borisyuk A, Bressloff PC (2008) Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation. J Comput Neurosci 25: 317–333CrossRefPubMedGoogle Scholar
  31. Nesse WH, Clark GA, Bressloff PC (2007) Spike patterning of a stochastic phase model neuron given periodic inhibition. Phys Rev E 75: 031912CrossRefGoogle Scholar
  32. Oh M, Matveev V (2009) Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons. J Comput Neurosci 26(2): 303–320CrossRefPubMedGoogle Scholar
  33. Perkel DH, Schulman JH, Bullock TH, Moore GP, Segundo JP (1964) Pacemaker neurons: effects of regularly spaced synaptic input. Science 145: 61–63CrossRefPubMedGoogle Scholar
  34. Roddey JC, Girish B, Miller JP (2000) assessing the performance of neural encoding models in the presence of noise. J Comput Neurosci 8: 95–112CrossRefPubMedGoogle Scholar
  35. Rubin J, Josić K (2007) The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs. Neural Comput 19: 1251–1294CrossRefPubMedGoogle Scholar
  36. Schultz LM, Clark GA (1997) GABA-induced synaptic facilitation at type B to A photoreceptor connections in Hermissenda. Brain Res Bull 42: 377–383CrossRefPubMedGoogle Scholar
  37. Steinmetz PN, Manwani A, Koch C, London M, Segev I (2000) Subthreshold voltage noise due to channel fluctuations in active neuronal membranes. J Comput Neurosci 9: 133–148CrossRefPubMedGoogle Scholar
  38. Stevens CF, Zador AM (1998) Input synchrony and the irregular firing of cortical neurons. Nat Neurosci 3: 210–217CrossRefGoogle Scholar
  39. Wehr M, Zador AM (2003) Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex. Nature 436: 442–446CrossRefGoogle Scholar
  40. White JA, Klink R, Alonso A, Kay AR (1998) Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J Neurophysiol 80: 262–269PubMedGoogle Scholar
  41. Yamanobe T, Pakdaman K (2002) Response of a pacemaker neuron model to stochastic pulse trains. Biol Cybern 86: 155–165CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Cellular and Molecular MedicineUniversity of OttawaOttawaCanada
  2. 2.Department of BioengineeringUniversity of UtahSalt Lake CityUSA

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