Skip to main content
Log in

Nonrenewal spike train statistics: causes and functional consequences on neural coding

  • Review
  • Published:
Experimental Brain Research Aims and scope Submit manuscript

An Erratum to this article was published on 31 March 2011

Abstract

Many neurons display significant patterning in their spike trains (e.g. oscillations, bursting), and there is accumulating evidence that information is contained in these patterns. In many cases, this patterning is caused by intrinsic mechanisms rather than external signals. In this review, we focus on spiking activity that displays nonrenewal statistics (i.e. memory that persists from one firing to the next). Such statistics are seen in both peripheral and central neurons and appear to be ubiquitous in the CNS. We review the principal mechanisms that can give rise to nonrenewal spike train statistics. These are separated into intrinsic mechanisms such as relative refractoriness and network mechanisms such as coupling with delayed inhibitory feedback. Next, we focus on the functional roles for nonrenewal spike train statistics. These can either increase or decrease information transmission. We also focus on how such statistics can give rise to an optimal integration timescale at which spike train variability is minimal and how this might be exploited by sensory systems to maximize the detection of weak signals. We finish by pointing out some interesting future directions for research in this area. In particular, we explore the interesting possibility that synaptic dynamics might be matched with the nonrenewal spiking statistics of presynaptic spike trains in order to further improve information transmission.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abeles M (1991) Corticonics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Averbeck BB, Lee D (2006) Effects of noise correlations on information encoding and decoding. J Neurophysiol 95:3633–3644

    Article  PubMed  Google Scholar 

  • Averbeck BB, Latham PE, Pouget A (2006) Neural correlations, population coding and computation. Nat Rev Neurosci 7:358–366

    Article  PubMed  CAS  Google Scholar 

  • Avila Akerberg O, Chacron MJ (2009) Noise shaping in neural populations. Phys Rev E 79:011914

    Article  CAS  Google Scholar 

  • Avila Akerberg O, Chacron MJ (2010) Noise shaping in neural populations with global delayed feedback. Math Model Nat Phenom 5:100–124

    Article  Google Scholar 

  • Avila Akerberg O, Krahe R, Chacron MJ (2010) Neural heterogeneities and stimulus properties affect burst coding in vivo. Neuroscience 168:300–313

    Article  PubMed  CAS  Google Scholar 

  • Azouz R, Gray CM (1999) Cellular mechanisms contributing to response variability of cortical neurons in vivo. J Neurosci 19:2209–2223

    PubMed  CAS  Google Scholar 

  • Azouz R, Gray CM (2000) Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo. Proc Natl Acad Sci USA 97:8110–8115

    Article  PubMed  CAS  Google Scholar 

  • Azouz R, Gray CM (2003) Adaptive coincidence detection and dynamic gain control in visual cortical neurons in vivo. Neuron 37:513–523

    Article  PubMed  CAS  Google Scholar 

  • Bahar S, Kantelhardt JW, Neiman A, Rego HHA, Russell DF, Wilkens L, Bunde A, Moss F (2001) Long-range temporal anti-correlations in paddlefish electroreceptors. Eur Phys Lett 56:454–460

    Article  CAS  Google Scholar 

  • Barlow HB, Levick WR (1969) Three factors limiting the reliable detection of light by the retinal ganglion cells of the cat. J Physiol (Lond) 200:1–24

    CAS  Google Scholar 

  • Bastian J, Nguyenkim J (2001) Dendritic modulation of Burst-like firing in sensory neurons. J Neurophysiol 85:10–22

    PubMed  CAS  Google Scholar 

  • Benda J, Herz AV (2003) A universal model for spike-frequency adaptation. Neural Comput 15:2523–2564

    Article  PubMed  Google Scholar 

  • Benda J, Longtin A, Maler L (2005) Spike-frequency adaptation separates transient communication signals from background oscillations. J Neurosci 25:2312–2321

    Article  PubMed  CAS  Google Scholar 

  • Benda J, Longtin A, Maler L (2006) A synchronization-desynchronization code for natural communication signals. Neuron 52:347–358

    Article  PubMed  CAS  Google Scholar 

  • Benda J, Maler L, Longtin A (2010) Linear versus nonlinear signal transmission in neuron models with adaptation currents or dynamic thresholds. J Neurophysiol 104:2806–2820

    Article  PubMed  Google Scholar 

  • Birk JR (1972) Enhanced specificity of information in axons with negatively correlated adjacent interspike intervals. Kybernetik 10:201–203

    Article  PubMed  CAS  Google Scholar 

  • Borst A, Theunissen F (1999) Information theory and neural coding. Nat Neurosci 2:947–957

    Article  PubMed  CAS  Google Scholar 

  • Brandman R, Nelson ME (2002) A simple model of long-term spike train regularization. Neural Comput 14:1575–1597

    Article  PubMed  Google Scholar 

  • Cajal RS (1909) Histologie du système nerveux de l’Homme et des vertébrés. Maloine, Paris

    Google Scholar 

  • Chacron MJ (2006) Nonlinear information processing in a model sensory system. J Neurophysiol 95:2933–2946

    Article  PubMed  Google Scholar 

  • Chacron MJ, Bastian J (2008) Population coding by electrosensory neurons. J Neurophysiol 99:1825–1835

    Article  PubMed  Google Scholar 

  • Chacron MJ, Longtin A, St-Hilaire M, Maler L (2000) Suprathreshold stochastic firing dynamics with memory in P-type electroreceptors. Phys Rev Lett 85:1576–1579

    Article  PubMed  CAS  Google Scholar 

  • Chacron MJ, Longtin A, Maler L (2001a) Negative interspike interval correlations increase the neuronal capacity for encoding time-varying stimuli. J Neurosci 21:5328–5343

    PubMed  CAS  Google Scholar 

  • Chacron MJ, Longtin A, Maler L (2001b) Simple models of bursting and non-bursting electroreceptors. Neurocomputing 38:129–139

    Article  Google Scholar 

  • Chacron MJ, Pakdaman K, Longtin A (2003) Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire model with threshold fatigue. Neural Comput 15:253–278

    Article  PubMed  Google Scholar 

  • Chacron MJ, Lindner B, Longtin A (2004a) ISI correlations and information transfer. Fluctuations Noise Lett 4:L195–L205

    Article  Google Scholar 

  • Chacron MJ, Lindner B, Longtin A (2004b) Noise shaping by interval correlations increases information transfer. Phys Rev Lett 92:080601

    Article  PubMed  CAS  Google Scholar 

  • Chacron MJ, Longtin A, Maler L (2004c) To burst or not to burst? J Comput Neurosci 17:127–136

    Article  PubMed  Google Scholar 

  • Chacron MJ, Lindner B, Longtin A, Maler L, Bastian J (2005a) Experimental and theoretical demonstration of noise shaping by interspike interval correlations. Proc SPIE 5841:150–163

    Article  Google Scholar 

  • Chacron MJ, Maler L, Bastian J (2005b) Electroreceptor neuron dynamics shape information transmission. Nat Neurosci 8:673–678

    Article  PubMed  CAS  Google Scholar 

  • Chacron MJ, Lindner B, Longtin A (2007) Threshold fatigue and information transfer. J Comput Neurosci 23:301–311

    Article  PubMed  Google Scholar 

  • Correia MJ, Landolt JP (1977) A point process analysis of the spontaneous activity of anterior semicircular canal units in the anesthetized pigeon. Biol Cybern 27:199–213

    Article  PubMed  CAS  Google Scholar 

  • Cover T, Thomas J (1991) Elements of information theory. Wiley, New York

    Book  Google Scholar 

  • Cox DR, Lewis PAW (1966) The statistical analysis of series of events. Methuen, London

    Google Scholar 

  • Dayan P, Abbott LF (2001) Theoretical neuroscience: computational and mathematical modeling of neural systems. MIT Press, Cambridge

    Google Scholar 

  • Destexhe A, Rudolph M, Pare D (2003) The high-conductance state of neocortical neurons in vivo. Nat Rev Neurosci 4:739–751

    Article  PubMed  CAS  Google Scholar 

  • Doiron B, Chacron MJ, Maler L, Longtin A, Bastian J (2003) Inhibitory feedback required for network oscillatory responses to communication but not prey stimuli. Nature 421:539–543

    Article  PubMed  CAS  Google Scholar 

  • Eccles JC (1953) The neurophysiological basis of mind. Oxford University Press, London

    Google Scholar 

  • Eckhorn R, Reitboeck HJ, Arndt M, Dicke P (1990) Feature linking via synchronization among distributed assemblies: simulations of results from cat visual cortex. Neural Comput 2:293–307

    Article  Google Scholar 

  • Edwards CJ, Leary CJ, Rose GJ (2008) Mechanisms of long-interval selectivity in midbrain auditory neurons: roles of excitation, inhibition, and plasticity. J Neurophysiol 100:3407–3416

    Article  PubMed  Google Scholar 

  • Ellis LD, Mehaffey WH, Harvey-Girard E, Turner RW, Maler L, Dunn RJ (2007) SK channels provide a novel mechanism for the control of frequency tuning in electrosensory neurons. J Neurosci 27:9491–9502

    Article  PubMed  CAS  Google Scholar 

  • Engel TA, Schimansky-Geier L, Herz AV, Schreiber S, Erchova I (2008) Subthreshold membrane-potential resonances shape spike-train patterns in the entorhinal cortex. J Neurophysiol 100:1576–1589

    Article  PubMed  CAS  Google Scholar 

  • Engel TA, Helbig B, Russell DF, Schimansky-Geier L, Neiman AB (2009) Coherent stochastic oscillations enhance signal detection in spiking neurons. Phys Rev E Stat Nonlin Soft Matter Phys 80:021919

    Article  PubMed  CAS  Google Scholar 

  • Faber ES, Sah P (2003) Calcium-activated potassium channels: multiple contributions to neuronal function. Neuroscientist 9:181–194

    Article  PubMed  CAS  Google Scholar 

  • Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292–303

    Article  PubMed  CAS  Google Scholar 

  • Fano U (1947) Ionization yield of radiations. II. The fluctuations of the number of ions. Phys Rev 72:26–29

    Article  CAS  Google Scholar 

  • Farkhooi F, Strube-Bloss MF, Nawrot MP (2009) Serial correlation in neural spike trains: experimental evidence, stochastic modeling, and single neuron variability. Phys Rev E Stat Nonlin Soft Matter Phys 79:021905

    Article  PubMed  CAS  Google Scholar 

  • Floyd K, Hick VE, Holden AV, Koley J, Morrison JFB (1982) Non-Markov negative correlation between interspike intervals in mammalian efferent discharge. Biol Cybern 45:89–93

    Article  PubMed  CAS  Google Scholar 

  • Fuhrmann G, Segev I, Markram H, Tsodyks M (2002) Coding of temporal information by activity-dependent synapses. J Neurophysiol 87:140–148

    PubMed  Google Scholar 

  • Gabbiani FC (1996) Coding of time-varying signals in spike trains of integrate-and-fire neurons with random threshold. Neural Comput 8

  • Gabbiani F, Cox SJ (2010) Mathematics for neuroscientists. Academic Press, London

    Google Scholar 

  • Geisler CD, Goldberg JM (1966) A stochastic model of the repetitive activity of neurons. Biophys J 6:53–69

    Article  PubMed  CAS  Google Scholar 

  • Goense JB, Ratnam R (2003) Continuous detection of weak sensory signals in afferent spike trains: the role of anti-correlated interspike intervals in detection performance. J Comp Physiol A Neuroethol Sens Neural Behav Physiol 189:741–759

    Article  PubMed  CAS  Google Scholar 

  • Goldberg JM, Greenwood DD (1966) Response of neurons of the dorsal and posteroventral cochlear nuclei of the cat to acoustic stimuli of long duration. J Neurophysiol 29:72–93

    PubMed  CAS  Google Scholar 

  • Goldberg JM, Adrian HO, Smith FD (1964) Response of neurons of the superior olivary complex of the cat to acoustic stimuli of long duration. J Neurophysiol 27:706–749

    PubMed  CAS  Google Scholar 

  • Goldman MS, Maldonado P, Abbott LF (2002) Redundancy reduction and sustained firing with stochastic depressing synapses. J Neurosci 22:584–591

    PubMed  CAS  Google Scholar 

  • Green D, Swets J (1966) Signal detection theory and psychophysics. Wiley, New York

    Google Scholar 

  • Gussin D, Benda J, Maler L (2007) Limits of linear rate coding of dynamic stimuli by electroreceptor afferents. J Neurophysiol 97:2917–2929

    Article  PubMed  Google Scholar 

  • Hagiwara S (1949) On the fluctuations of the interval of the rhythmic excitation. I. The efferent impulse of the human motor unit during the voluntary contraction. Bull Physiogr Sci Res Inst Tokyo Univ 3:19–31

    Google Scholar 

  • Häusser M, Roth A (1997) Dendritic and somatic glutamate receptor channels in rat cerebellar Purkinje cells. J Physiol (Lond) 501:77–95

    Article  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117:500–544

    CAS  Google Scholar 

  • Hollander H (1970) The projection from the visual cortex to the lateral geniculate body (LGB). An experimental study with silver impregnation methods in the cat. Exp Brain Res 10:219–235

    Article  PubMed  CAS  Google Scholar 

  • Horn D, Usher M (1989) Neural networks with dynamical thresholds. Phys Rev A 40:1036–1040

    Article  PubMed  Google Scholar 

  • Jolivet R, Rauch A, Luscher HR, Gerstner W (2006) Predicting spike timing of neocortical pyramidal neurons by simple threshold models. J Comput Neurosci 21:35–49

    Article  PubMed  Google Scholar 

  • Kara P, Reinagel P, Reid RC (2000) Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron 27:635–646

    Article  PubMed  CAS  Google Scholar 

  • Keat J, Reinagel P, Reid RC, Meister M (2001) Predicting every spike: a model for the responses of visual neurons. Neuron 30:803–817

    Article  PubMed  CAS  Google Scholar 

  • Khanbabaie R, Nesse WH, Longtin A, Maler L (2010) Kinetics of fast short-term depression are matched to spike train statistics to reduce noise. J Neurophysiol 103:3337–3348

    Article  PubMed  Google Scholar 

  • Krahe R, Gabbiani F (2004) Burst firing in sensory systems. Nat Rev Neurosci 5:13–23

    Article  PubMed  CAS  Google Scholar 

  • Kuffler SW, Fitzhugh R, Barlow HB (1957) Maintained activity in the cat’s retina in light and darkness. J Gen Physiol 40:683–702

    Article  PubMed  CAS  Google Scholar 

  • Lansky P, Radil T (1987) Statistical inference on spontaneous neuronal discharge patterns. I. Single neuron. Biol Cybern 55:299–311

    Article  PubMed  CAS  Google Scholar 

  • Lansky P, Musila M, Smith CE (1992) Effects of afterhyperpolarization on neuronal firing. Biosystems 27:25–38

    Article  PubMed  CAS  Google Scholar 

  • Latham PE, Nirenberg S (2005) Synergy, redundancy, and independence in population codes, revisited. J Neurosci 25:5195–5206

    Article  PubMed  CAS  Google Scholar 

  • Leary CJ, Edwards CJ, Rose GJ (2008) Midbrain auditory neurons integrate excitation and inhibition to generate duration selectivity: an in vivo whole-cell patch study in anurans. J Neurosci 28:5481–5493

    Article  PubMed  CAS  Google Scholar 

  • Lebedev MA, Nelson RJ (1996) High-frequency vibratory sensitive neurons in monkey primate somatosensory cortex: entrained and nonentrained responses to vibration during the performance of vibratory-cued hand movements. Exp Brain Res 111:313–325

    Article  PubMed  CAS  Google Scholar 

  • Levine MW (1980) Firing rate of a retinal neuron are not predictable from interspike interval statistics. Biophys J 30:9–25

    Article  PubMed  CAS  Google Scholar 

  • Lewis CD, Gebber GL, Larsen PD, Barman SM (2001) Long-term correlations in the spike trains of medullary sympathetic neurons. J Neurophysiol 85:1614–1622

    PubMed  CAS  Google Scholar 

  • Lindner B, Chacron MJ, Longtin A (2005) Integrate-and-fire neurons with threshold noise: a tractable model of how interspike interval correlations affect neuronal signal transmission. Phys Rev E 72:021911

    Article  CAS  Google Scholar 

  • Lindner B, Gangloff D, Longtin A, Lewis JE (2009) Broadband coding with dynamic synapses. J Neurosci 29:2076–2087

    Article  PubMed  CAS  Google Scholar 

  • Liu YH, Wang XJ (2001) Spike Frequency adaptation of a generalized leaky integrate-and-fire neuron. J Comput Neurosci 10:25–45

    Article  PubMed  CAS  Google Scholar 

  • London M, Roth A, Beeren L, Hausser M, Latham PE (2010) Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex. Nature 466:123–127

    Article  PubMed  CAS  Google Scholar 

  • Longtin A, Racicot DM (1997) Spike train patterning and forecastability. Biosystems 40:111–118

    Article  PubMed  CAS  Google Scholar 

  • Longtin A, Laing C, Chacron MJ (2003) Correlations and memory in neurodynamical systems. In: Rangarajan G, Ding M (eds) Long-range dependent stochastic processes. Springer, Berlin, pp 286–308

    Google Scholar 

  • Lowen SB, Teich MC (1992) Auditory-nerve action potentials form a nonrenewal point process over short as well as long time scales. J Acoust Soc Am 92:803–806

    Article  PubMed  CAS  Google Scholar 

  • Lowen SB, Teich MC (1996) The periodogram and Allan variance reveal fractal exponents greater than unity in auditory-nerve spike trains. J Acoust Soc Am 99:3585–3591

    Article  PubMed  CAS  Google Scholar 

  • Lowen SB, Cash SS, Poo M, Teich MC (1997) Quantal neurotransmitter secretion rate exhibits fractal behavior. J Neurosci 17:5666–5677

    PubMed  CAS  Google Scholar 

  • Maar DJ, Chow CC, Gerstner W, Adams RW, Collins JJ (1999) Noise shaping in populations of coupled model neurons. Proc Natl Acad Sci 96:10450–10455

    Article  Google Scholar 

  • MacGregor RJ, Oliver RM (1974) A model for repetitive firing in neurons. Kybernetik 16:53–64

    Article  PubMed  CAS  Google Scholar 

  • Maimon G, Assad JA (2009) Beyond Poisson: increased spike-time regularity across primate parietal cortex. Neuron 62:426–440

    Article  PubMed  CAS  Google Scholar 

  • Maler L, Sas E, Johnston S, Ellis W (1991) An atlas of the brain of the weakly electric fish Apteronotus Leptorhynchus. J Chem Neuroanat 4:1–38

    Article  PubMed  CAS  Google Scholar 

  • Mehaffey WH, Ellis LD, Krahe R, Dunn RJ, Chacron MJ (2008) Ionic and neuromodulatory regulation of burst discharge controls frequency tuning. J Physiol (Paris) 102:195–208

    Article  Google Scholar 

  • Meister M, Lagnado L, Baylor DA (1995) Concerted signaling by retinal ganglion cells. Science 270:1207–1210

    Article  PubMed  CAS  Google Scholar 

  • Mickus T, Jung HY, Spruston N (1999) Properties of slow cumulative sodium channel inactivation in rat hippocampal CA1 pyramidal neurons. Biophys J 76:846–860

    Article  PubMed  CAS  Google Scholar 

  • Middleton JW, Chacron MJ, Lindner B, Longtin A (2003a) Correlated noise and memory effects in neural firing dynamics. In: Beruzkov SM (ed) Unsolved problems of noise and fluctuations, vol 665. AIP Conference Proceedings, pp 183–190

  • Middleton JW, Chacron MJ, Lindner B, Longtin A (2003b) Firing statistics of a neuron driven by long-range correlated noise. Phys Rev E 68:021920

    Article  CAS  Google Scholar 

  • Moore GP, Perkel DH, Segundo JP (1966) Statistical analysis and functional interpretation of neuronal spike data. Annu Rev Physiol 28:493–522

    Article  PubMed  CAS  Google Scholar 

  • Nawrot MP, Boucsein C, Rodriguez-Molina V, Riehle A, Aertsen A, Grun S, Rotter S (2007) Serial interval statistics of spontaneous activity in cortical neurons in vivo and in vitro. Neurocomputing 70:1717–1722

    Article  Google Scholar 

  • Neiman A, Russell DF (2001) Stochastic byperiodic oscillations in the electroreceptors of paddlefish. Phys Rev Lett 86:3443–3446

    Article  PubMed  CAS  Google Scholar 

  • Neiman A, Russell DF (2002) Synchronization of noise-induced bursts in noncoupled sensory neurons. Phys Rev Lett 88:138103

    Article  PubMed  CAS  Google Scholar 

  • Neiman AB, Russell DF (2004) Two distinct types of noisy oscillators in electroreceptors of paddlefish. J Neurophysiol 92:492–509

    Article  PubMed  Google Scholar 

  • Neiman AB, Russell DF (2005) Models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish. Phys Rev E Stat Nonlin Soft Matter Phys 71:061915

    Article  PubMed  CAS  Google Scholar 

  • Nelson ME, MacIver MA (1999) Prey capture in the weakly electric fish Apteronotus albifrons: sensory acquisition strategies and electrosensory consequences. J Exp Biol 202:1195–1203

    PubMed  CAS  Google Scholar 

  • Nesse W, Maler L, Longtin A (2010) Biophysical information representation in temporally correlated spike trains. Proc Natl Acad Sci USA 107:21973–21978

    Article  PubMed  CAS  Google Scholar 

  • Nirenberg S, Carcieri SM, Jacobs AL, Latham PE (2001) Retinal ganglion cells act largely as independent encoders. Nature 411:698–701

    Article  PubMed  CAS  Google Scholar 

  • Norsworthy SR, Schreier R, Temes GC (eds) (1997) Delta-sigma data converters. IEEE Press, Piscataway

    Google Scholar 

  • Ostapoff EM, Morest DK, Potashner SJ (1990) Uptake and retrograde transport of [3H]GABA from the cochlear nucleus to the superior olive in the guinea pig. J Chem Neuroanat 3:285–295

    PubMed  CAS  Google Scholar 

  • Perkel DH, Gerstein GL, Moore GP (1967a) Neuronal spike trains and stochastic point processes. I. The single spike train. Biophys J 7:391–418

    Article  PubMed  CAS  Google Scholar 

  • Perkel DH, Gerstein GL, Moore GP (1967b) Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys J 7:419–440

    Article  PubMed  CAS  Google Scholar 

  • Peron S, Gabbiani F (2009) Spike frequency adaptation mediates looming stimulus selectivity in a collision-detecting neuron. Nat Neurosci 12:318–326

    Article  PubMed  CAS  Google Scholar 

  • Poor HV (1994) An introduction to signal detection and estimation. Springer, New York

    Google Scholar 

  • Ratnam R, Nelson ME (2000) Non-renewal statistics of electrosensory afferent spike trains: implications for the detection of weak sensory signals. J Neurosci 20:6672–6683

    PubMed  CAS  Google Scholar 

  • Rieke F, Warland D, van Steveninck RR, Bialek W (1996) Spikes: exploring the neural code. MIT, Cambridge

    Google Scholar 

  • Roddey JC, Girish B, Miller JP (2000) Assessing the performance of neural encoding models in the presence of noise. J Comput Neurosci 8:95–112

    Article  PubMed  CAS  Google Scholar 

  • Rodieck RW (1967) Maintained activity of cat retinal ganglion cells. J Neurophysiol 30:1043–1071

    PubMed  CAS  Google Scholar 

  • Rose GJ, Leary CJ, Edwards CJ (2010) Interval-counting neurons in the anuran auditory midbrain: factors underlying diversity of interval tuning. J Comp Physiol A Neuroethol Sens Neural Behav Physiol 197:97–108

    Google Scholar 

  • Sadeghi SG, Chacron MJ, Taylor MC, Cullen KE (2007) Neural variability, detection thresholds, and information transmission in the vestibular system. J Neurosci 27:771–781

    Article  PubMed  CAS  Google Scholar 

  • Sah P (1996) Ca 2+-activated K+ currents in neurones: types, physiological roles and modulation. Trends Neurosci 19:150–154

    Article  PubMed  CAS  Google Scholar 

  • Sah P, Faber ES (2002) Channels underlying neuronal calcium-activated potassium currents. Progr Neurobiol 66:345–353

    Article  CAS  Google Scholar 

  • Savard M, Krahe R, Chacron MJ (2011) Neural heterogeneities influence envelope and temporal coding at the sensory periphery. Neuroscience 172:270–284

    Article  PubMed  CAS  Google Scholar 

  • Schäfer K, Braun HA, Peters C, Bretschneider F (1995) Periodic firing pattern in afferent discharges from electroreceptor organs of catfish. Eur J Physiol 429:378–385

    Article  Google Scholar 

  • Schneidman E, Bialek W, Berry MJ II (2003) Synergy, redundancy, and independence in population codes. J Neurosci 23:11539–11553

    PubMed  CAS  Google Scholar 

  • Schneidman E, Berry MJ II, Segev R, Bialek W (2006) Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440:1007–1012

    Article  PubMed  CAS  Google Scholar 

  • Schwalger T, Fisch K, Benda J, Lindner B (2010) How noisy adaptation of neurons shapes interspike interval histograms and correlations. PLoS Comput Biol 6:e1001026

    Article  PubMed  CAS  Google Scholar 

  • Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci 18:3870–3896

    PubMed  CAS  Google Scholar 

  • Shannon CE (1948) The mathematical theory of communication. Bell Syst Tech J 27(379–423):623–656

    Google Scholar 

  • Sherman SM, Guillery RW (2002) The role of the thalamus in the flow of information to the cortex. Philos Trans R Soc Lond Ser B Biol Sci 357:1695–1708

    Article  Google Scholar 

  • Sherman SM, Guillery RW (2006) Exploring the thalamus and its role in cortical function. MIT Press, Cambridge

    Google Scholar 

  • Shin J (1993) Novel neural circuits based on stochastic pulse coding noise feedback pulse coding. Int J Electron 74:359–368

    Article  Google Scholar 

  • Shin J (2001) Adaptation in spiking neurons based on the noise shaping neural coding hypothesis. Neural Netw 14:907–919

    Article  PubMed  CAS  Google Scholar 

  • Smith CE, Goldberg JM (1986) A stochastic afterhyperpolarization model of repetitive activity in vestibular afferents. Biol Cybern 41–51

  • Snippe HP, Koenderink JJ (1992) Discrimination thresholds for channel-coded systems. Biol Cybern 66:543–551

    Article  Google Scholar 

  • Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci 13:334–350

    PubMed  CAS  Google Scholar 

  • Stein RB, Gossen ER, Jones KE (2005) Neuronal variability: noise or part of the signal? Nat Rev Neurosci 6:389–397

    Article  PubMed  CAS  Google Scholar 

  • Surmeier DJ, Honda CN, Willis WD (1989) Patterns of spontaneous discharge in primate spinothalamic neurons. J Neurophysiol 61:106–115

    PubMed  CAS  Google Scholar 

  • Teich MC (1992) Fractal neuronal firing patterns. In: McKenna T, Davis J, Zornetzer SF (eds) Single neuron computation. Academic Press, San Diego, pp 589–622

    Google Scholar 

  • Teich MC, Heneghan C, Lowen SB, Ozaki T, Kaplan E (1997) Fractal character of the neural spike train in the visual system of the cat. J Opt Soc Am A 14:529–546

    Article  CAS  Google Scholar 

  • Thomson EE, Kristan WB (2005) Quantifying stimulus discriminability: a comparison of information theory and ideal observer analysis. Neural Comput 17:741–778

    Article  PubMed  Google Scholar 

  • Toporikova N, Chacron MJ (2009) Dendritic SK channels gate information processing in vivo by regulating an intrinsic bursting mechanism seen in vitro. J Neurophysiol 102:2273–2287

    Article  PubMed  Google Scholar 

  • Tsuchitani C, Johnson DH (1985) The effects of ipsilateral tone burst stimulus level on the discharge patterns of cat lateral superior olivary units. J Acoust Soc Am 77:1484–1496

    Article  PubMed  CAS  Google Scholar 

  • Tuckwell HC (1988) Nonlinear and stochastic theories. Cambridge University Press, Cambridge

    Google Scholar 

  • Wang XJ (1998) Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J Neurophysiol 79:1549–1566

    PubMed  CAS  Google Scholar 

  • Weiss TF (1966) A model of the peripheral auditory system. Kybernetik 3:153–175

    Article  PubMed  CAS  Google Scholar 

  • Wiesenfeld K, Satija I (1987) Noise tolerance of frequency locked dynamics. Phys Rev B 36:2483–2492

    Article  Google Scholar 

  • Yacomotti AM, Eguia MC, Aliaga J, Martinez OE, Mindlin GB (1999) Interspike time distribution in noise driven excitable systems. Phys Rev Lett 83:292–295

    Article  CAS  Google Scholar 

  • Yamamoto M, Nakahama H (1983) Stochastic properties of spontaneous unit discharges in somatosensory cortex and mesencephalic reticular formation during sleep-waking states. J Neurophysiol 49:1182–1198

    PubMed  CAS  Google Scholar 

  • Zohary E, Shadlen MN, Newsome WT (1994) Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370:140–143

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

This research was supported by Conacyt (O.A.A.), as well as the Canadian Institutes of Health Research, the Canada Foundation for Innovation and the Canada Research Chairs program (M.J.C.).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maurice J. Chacron.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00221-011-2639-6

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avila-Akerberg, O., Chacron, M.J. Nonrenewal spike train statistics: causes and functional consequences on neural coding. Exp Brain Res 210, 353–371 (2011). https://doi.org/10.1007/s00221-011-2553-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00221-011-2553-y

Keywords

Navigation