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Point process models of single-neuron discharges

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Abstract

In most neural systems, neurons communicate via sequences of action potentials. Contemporary models assume that the action potentials' times of occurrence rather than their waveforms convey information. The mathematical tool for describing sequences of events occurring in time and/or space is the theory of point processes. Using this theory, we show that neural discharge patterns convey time-varying information intermingled with the neuron's response characteristics. We review the basic techniques for analyzing single-neuron discharge patterns and describe what they reveal about the underlying point process model. By applying information theory and estimation theory to point processes, we describe the fundamental limits on how well information can be represented by and extracted from neural discharges. We illustrate applying these results by considering recordings from the lower auditory pathway.

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References

  • Adrian ED (1928) The Basis of Sensation. Christopher, London.

    Google Scholar 

  • Bialek W, Rieke F, de Ruyter, van Steveninck RR, Warland D (1991) Reading a neural code. Science 252:1852–1856.

    Google Scholar 

  • Brémaud P (1981) Point Processes and Queues. Springer-Verlag, New York.

    Google Scholar 

  • Cover TM, Thomas JA (1991) Elements of Information Theory. Wiley, New York. London.

    Google Scholar 

  • Cox DR (1962) Renewal Theory. Methuen, London.

    Google Scholar 

  • Cox DR, Lewis PAW (1966) The Statistical Analysis of Series of Events. Methuen, London.

    Google Scholar 

  • Davis MHA (1980) Capacity and cutoff rate for Poisson-type channels. IEEE Trans. Info. Th. IT-26:710–715.

    Google Scholar 

  • Devroye L (1986) Non-uniform Random Variate Generation. Springer-Verlag, New York.

    Google Scholar 

  • Devroye L (1987) A Course in Density Estimation. Birkhauser, Boston.

    Google Scholar 

  • Fienberg SE (1974) Stochastic models for single neuron firing trains. A survey. Biometrics 30: 399–427.

    Google Scholar 

  • Gaumond RP, Molnar CE, Kim DO (1982) Stimulus and recovery dependence of cat cochlear nerve fiber spike discharge probability. J. Neurophysiol. 48(3):856–873.

    Google Scholar 

  • Gerstein GL, Kiang NYS (1960) An approach to the quantitative analysis of electrophysiological data from single neurons. Biophysical J. 1:15–28.

    Google Scholar 

  • Hawkes AG (1971) Spectra of some self-exciting mutually exciting point processes. Biometrika 58:83–90.

    Google Scholar 

  • Holden AV (1976) Models of the Stochastic Activity of Neurones. Vol. 12 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin.

    Google Scholar 

  • Johnson DH (1974) The Response of Single Auditory-Nerve Fibers in the Cat to Single Tones: Synchrony and Average Discharge Rate. Ph.D. thesis, MIT, Cambridge, MA.

    Google Scholar 

  • Johnson DH (1978) The relationship of post-stimulus time and interval histograms to the timing characteristics of spike trains. Biophysical J. 22:413–430.

    Google Scholar 

  • Johnson DH (1980) The relationship between spike rate and synchrony in responses of auditory-nerve fibers to single tones. J. Acoust. Soc. Am. 68(4):1115–1122.

    Google Scholar 

  • Johnson DH, Swami A (1983) The transmission of signals by auditory-nerve fiber discharge patterns. J. Acoust. Soc. Am. 74:493–501.

    Google Scholar 

  • Johnson DH, Tsuchitani C, Linebarger DA, Johnson M (1986) The application of a point process model to the single unit responses of the cat lateral superior olive to ipsilaterally presented tones. Hearing Res. 21:135–159.

    Google Scholar 

  • Kabanov YM (1978) The capacity of a channel of the Poisson type. Theory Prob. and Applications 23:143–147.

    Google Scholar 

  • Kiang NYS, Watanabe T, Thomas EC, Clark LF (1965) Discharge Patterns of Single Fibers in the Cat's Auditory Nerve. MIT Press, Cambridge, MA.

    Google Scholar 

  • Kumar AR, Johnson DH (1990) A distribution-free model order estimation technique using entropy. Circuits, Systems, and Signal Processing 9:31–54.

    Google Scholar 

  • Kumar AR, Johnson DH (1993) Modeling and analyzing fractal point processes. J. Acoust. Soc. Am. 93:3365–3373.

    Google Scholar 

  • Lawrence AJ (1970) Selective interaction of a stationary point process and a renewal process. J. Appl. Prob. 7:483–489.

    Google Scholar 

  • Li J, Young ED (1993) Discharge-rate dependence of refractory behavior of cat auditory-nerve fibers. Hearing Res. 69:151–162.

    Google Scholar 

  • Linebarger DA, Johnson DH (1986) Superposition models of the discharge patterns of units in the lower auditory system. Hearing Res. 23:185–198.

    Google Scholar 

  • Mark KE, Miller MI (1992) Bayesian model selection and minimum description length estimation of auditory-nerve discharge rates. J. Acoust. Soc. Am. 91:989–1002.

    Google Scholar 

  • Miller MI (1985) Algorithms for removing recovery-related distortion from auditory-nerve discharge patterns. J. Acoust. Soc. Am. 77:1452–1464. Also see Erratum. J. Acoust. Soc. Am. 79:570, 1986.

    Google Scholar 

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

    Google Scholar 

  • Ozaki T (1979) Maximum likelihood estimation of Hawkes' self-exciting point processes. Ann. Inst. Statist. Math. 31, Part B:145–155.

    Google Scholar 

  • Rieke F, Warland D, Bialek W (1993) Coding efficiency and information rates in sensory neurons. Europhysics Letters 22:151–156.

    Google Scholar 

  • Rodieck RW, Kiang NYS, Gerstein GL (1962) Some quantitative methods for the study of spontaneous activity of single neurons. Biophysical J. 2:351–368.

    Google Scholar 

  • Sampath G, Srinivasan SK (1977) Stochastic Models for Spike Trains of Single Neurons. Vol. 16 of Lecture Notes in Biomathematics. S Levin, Ed. Springer-Verlag, New York.

    Google Scholar 

  • Shamai (Shitz) S, Lapidoth A (1993) Bounds on the capacity of a spectrally constrained Poisson channel. IEEE Trans. Info. Th. 39:19–29.

    Google Scholar 

  • Siebert WM, Gray PR (1963) Random process model for the firing pattern of single auditory neurons. In MIT Quart. Prog. Rep. 271:241–245. MIT Res. Lab. Electronics.

  • Snyder DL (1975) Random Point Processes. Wiley, New York.

    Google Scholar 

  • Snyder DL, Rhodes IB (1980) Some implications for the cutoff-rate criterion for coded direct-detection optical communication systems. IEEE Trans. Info. Th. IT-26:327–338.

    Google Scholar 

  • Ten Hoopen M, Reuver HA (1965) Selective interaction of two recurrent processes. J. Appl. Prob. 2:286–292.

    Google Scholar 

  • Tsao YH (1984) Tests for stationarity. J. Acoust. Soc. Am. 75:486–498.

    Google Scholar 

  • Zacksenhouse M, Johnson DH, Williams J (1995) Computer simulation of LSO discharge patterns. Unpublished manuscript.

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Authors and Affiliations

  1. Computer and Information Technology Institute, Department of Electrical and Computer Engineering, Rice University, MS #366, 77005-1892, Houston, Texas

    Don H. Johnson

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  1. Don H. Johnson
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Johnson, D.H. Point process models of single-neuron discharges. J Comput Neurosci 3, 275–299 (1996). https://doi.org/10.1007/BF00161089

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  • DOI: https://doi.org/10.1007/BF00161089

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