Reliability and Redundancy of Neurons: Can We Distinguish Probabilistic, Stochastic, and Noisy Processes?

  • Theodore Holmes Bullock


The answer to the title question is: with great difficulty in the actual operation of living neurons, although these three properties are distinct and only overlap in their manifestation. The common belief that neurons are generally unreliable in the sense of inconsistent response to the same stimulus is here shown to be a special case and not necessarily due to system noise. The prevalent probabilistic view of neuronal firing remains plausible belief and is virtually untestable. This view models the nervous system with high redundancy of noisy neurons. The arguments usually cited, such as inconsistent response, can not be taken as cogent evidence for it. Several grounds for this conclusion are developed.

Three issues appear in the literature, two of them really irrelevant: (a) arguments that probabilistic methods in data reduction are necessary, (b) assertions that models assuming stochastic noise are valuable, and (c) claims that the nervous system actually works with noisy elements by large scale redundancy. These distinct propositions are usually blurred into one. I take no exception to the first two; the third claim is the issue addressed here.

Of two kinds of uncertainty, Heisenbergian is moot at the neuronal level, and statistical mechanical ( = practical unpredictability), as in a gas, surely exists. The questions are empirical, where and how much it exists; it is already clear that the relative strength of stochastic processes such as arrival times of converging spike trains varies widely among neurons.

Discussion should start by calling unexplained fluctuation “unexplained fluctuation,” not noise in the dictionary sense of undesirable antisignal. Several known causes of stochastic fluctuations are compatible with a highly reliable system. Although varying widely, many neurons are probably low in true noise but they may show a high level of apparent noise from any of several causes. Jitter is demonstrably adaptive in certain situations.

Redundancy in the sense of fully equivalent neurons is probably not as large in scale as commonly thought even of the brains of mammals. Chapter 7 proposes that few classes of fully equivalent neurons exceed 300–500. Overlap of input or output fields is much more general; neurons are commonly partially redundant, partially not. The value of overlap may not be so much for averaging internal noise as for signalling input and output by convergence that achieves sensitive, smooth, high resolution. To the extent that noise cancellation is accomplished, it is likely to depend not merely upon linear averaging or summing but to employ any of several nonlinear processes more robustly noise resistant. We do not assume indeterminate operation, absent good evidence. “Probabilistic” applies appropriately to the methods used for study but not to the actual operation of such a system, at least in a major degree, until adequate study has excluded deterministic or useful fluctuation. Reliability (consistent firing) is demonstrably high in many neurons, implying precision in connections and in dynamic properties. Evidence of this continuously increases, in contrast to evidence that true system noise explains observed fluctuation.


Receptive Field Spike Train Optic Lobe Electric Organ Discharge Musca Domestica 
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  1. Adey WR (1972): Organization of brain tissue: is the brain a noisy processor. Int J Neurosci 3: 271–284CrossRefGoogle Scholar
  2. Allanson J’I’ (1956): The reliability of neurons. In: Proceedings of the 1st International Congress on Cybernetics, Paris: Namur Gauthier-Villars, pp 687–694Google Scholar
  3. Arbib MA (1964): Brains, Machine, and Mathematics. New York: McGraw-Hill Book CompanyGoogle Scholar
  4. Barlow HB, Levick WR (1969): Three factors limiting the reliable detection of light by retinal ganglion cells of the cat. J Physiol 200: 1–24Google Scholar
  5. Bartley SH, Bishop GH (1933): Factors determining the form of the electrical response from the optic cortex of the rabbit. Am J Physiol 103: 173–184Google Scholar
  6. Bennett MVL, Pappas GD, Giminez M, Nakajima Y (1967): Physiology and ultrastructure of electrotonic junctions. IV. Medullary electromotor nuclei in gymnotid fish. J Neurophysiol 30: 236–300Google Scholar
  7. Beurle RL (1962): Storage and manipulation of information in random networks. In: Aspects ofthe Theory of Artificial Intelligence. Proceedings of the 1st International Symposium on Biosimulation, Locarno, Muses CA, ed. New York: Plenum Press, pp 19–42Google Scholar
  8. Bishop LG, Keehn DG (1967): Neural correlates of the optomotor response in the fly. Kybernetik 3: 288–295Google Scholar
  9. Bishop LG, Keehn DG, McCann GD (1968): Motion detection by interneurons of optic lobes and brain of the flies Calliphora phaenicia and Musca domestica. J Neurophysiol 31: 509–525Google Scholar
  10. Bishop PO (1969): Neurophysiology of binocular single vision and stereopsis. In: Handbook of Sensory Physiology, Vol VII/3: Central Visual Information A, Jung R, ed. Berlin: Springer-Verlag, pp 255–305Google Scholar
  11. Bishop PO (1970): Beginning of form vision and binocular depth discrimination in cortex. In: The Neurosciences: A Second Study Program, Schmitt FO, ed. New York: Rockefeller University Press, pp 471–485Google Scholar
  12. Braitenberg V (1967): Patterns of projection in the visual system of the fly. I. Retinal-lamina projections. Exp Brain Res 3: 271–298CrossRefGoogle Scholar
  13. Burns DB (1968): The Uncertain Nervous System. London: Edward Arnold LtdGoogle Scholar
  14. Caianiello ER (1968): Neural Networks. New York: Springer-VerlagCrossRefGoogle Scholar
  15. Coggeshall RE (1967): A light and electron microscope study of the abdominal ganglion of Aplysia californica. J Neurophysiol 30: 1263–1287Google Scholar
  16. Cohen MJ (1970): A comparison of invertebrate and vertebrate central neurons. In: The Neurosciences: A Second Study Program, Schmitt FO, ed. New York: Rockefeller University Press, pp 798–812Google Scholar
  17. Cragg BG, Temperley HNV (1954): The organization of neurones: a co-operative analogy. Electroencephalogr Clin Neurophysiol 6: 85–92CrossRefGoogle Scholar
  18. Doupe AJ, Konishi M (1991): Song-selective auditory circuits in the vocal control system of the zebra finch. Proc Nail Acad Sci USA 88: 11339–11343CrossRefGoogle Scholar
  19. Eccles JC (1953): The Neurophysiological Basis of Mind. Oxford: The Clarendon PressGoogle Scholar
  20. Galambos R, Schwartzkopff J, Rupert A (1959): Microelectrode study of superior olivary nuclei. Am J Physiol 197: 527–536Google Scholar
  21. Gaze RM (1970): The Formation of Nerve Connections. New York: Academic PressGoogle Scholar
  22. Grinnell AD (1969): Comparative study of hearing. Annu Rev Physiol 31: 545–580CrossRefGoogle Scholar
  23. Grösser O-J, Grösser-Cornehls U (1969): Neurophysiologie des Bewegungssehens. Ergeb Physiol 61: 179–265Google Scholar
  24. Heiligenberg WF (1986): Jamming avoidance responses. In: Electroreception, Bullock TH, Heiligenberg W, eds. New York: John Wiley Sons, pp 613–649Google Scholar
  25. Howe DW Jr, Erskine FT, Granath LP (1966): Threshold sensitivity of Sternarchus albifrons to electric fields. Am Zoo/ 6: 521–522Google Scholar
  26. Hubel DH, Wiesel TN (1962): Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J Physiol 160: 106–154Google Scholar
  27. Hubel DH, Wiesel TN (1968): Receptive fields and functional architecture of monkey striate cortex. J Physiol 195: 215–243Google Scholar
  28. Isaacs JP, Lamb JC (1969): Complementarity in Biology: Quantization of Molecular Motion. Baltimore: The John Hopkins PressGoogle Scholar
  29. John ER (1972): Switchboard versus statistical theories of learning and memory. Science 177: 850–864CrossRefGoogle Scholar
  30. Kogan AB (1964): Statistical probability principle of the neuronal organization of the functional systems of the brain. Dokl Akad Nauk SSSR Biological Sci Sect (Transi) 154: 139–142Google Scholar
  31. Kuhn TS (1962): The Structure of Scientific Revolutions. Chicago: University of Chicago PressGoogle Scholar
  32. Kuiper JW, Leutscher-Hazelhoff JT (1965): High-precision repetitive firing in the insect optic lobe and a hypothesis for its function in object location. Nature (Lund) 206: 1158–1160CrossRefGoogle Scholar
  33. Lamb JC, Isaacs JP (1966): Indeterminacy, the synapse, the mnemic microstate, and the psyche. Cond Reflex 4: 1–5Google Scholar
  34. Larimer JL, McDonald JA (1968): Sensory feedback from electroreceptors to electromotor pacemaker center in gymnotids. Am J Physiol 214: 12–53Google Scholar
  35. Levy M, Martin P, IanoT, Zieske H (1969): Paradoxical effect of vagus nerve stimulation on heart rate in dogs. Circ Res 25: 303–314Google Scholar
  36. Marchiafava PL, Pepeu G (1966): The responses of units in the superior colliculus of the cat to a moving visual stimulus. Experientia 22: 1–5CrossRefGoogle Scholar
  37. Margoliash D (1986): Preference for autogenous song by auditory neurons in a song system nucleus of the white-crowned sparrow. J Neurosci 6: 1643–1661Google Scholar
  38. Maturana HR, Frenk S (1963): Directional movement and horizontal edge detectors in the pigeon retina. Science 142: 977–979Google Scholar
  39. McCann GD, Dill JC (1969): Fundamental properties of intensity, form, and motion perception in the visual nervous systems of Calliphora phaenicia and Musca domestica. J Gen Physiol 53: 385–413CrossRefGoogle Scholar
  40. McDonald M (1964): A system for stabilizing evoked potentials obtained in the brain stem of the cat. Med Electron Bio! Eng 2: 417–423CrossRefGoogle Scholar
  41. Michael CR (1966): Receptive fields of directionally selective units in the optic nerve of the ground squirrel/receptive fields of opponent color units in the optic nerve of the ground squirrel. Science 152: 1092–1097CrossRefGoogle Scholar
  42. Moore GP, Perkel DH, Segundo JP (1966): Statistical analysis and functional interpretation of neuronal spike data. Annu Rev Physiol 28: 493–522CrossRefGoogle Scholar
  43. Mountcastle VB (1967): The problem of sensing and the neural coding of sensory events. In: The Neurosciences: A Study Program, Quarton CG, Melnechuk T, Schmitt FO, eds. New York: Rockefeller University Press, pp 393–408Google Scholar
  44. Nicholls JG, Baylor DA (1968): Specific modalities and receptive fields of sensory neurons in CNS of the leech. J Neurophysiol 31: 740–756Google Scholar
  45. Oyster CW (1968): The analysis of image motion by the rabbit retina. J Physiol 199: 613–635Google Scholar
  46. Perrett DI, Mistlin AJ, Harries MH (1987): Seeing faces: the representation of facial information in temporal cortex. In: Seeing Contour and Colour, Proceedings of the Third International Symposium of the Northern Eye Institute, Manchester UK 1987, Kuhrowski JJ, Dickinson CM, Murray U, eds. Oxford: Pergamon Press, pp 740–754Google Scholar
  47. Perrett DI, Harries MH, Bevan R, Thomas S, Benson Pi, Mistlin AJ, Chitty AJ, Hietanen JK, Ortega JE (1989): Frameworks of analysis for the neural representation of animate objects and actions. J Exp Biol 146: 87–113Google Scholar
  48. Perret DI, Harries MH, Mistlin AJ, Chitty AJ (1990): Recognition of objects and actions: frameworks for neuronal computation and perceptual experience. In: Higher Order Sensory Processing. Studies in Neuroscience Series Google Scholar
  49. Guthrie DM, ed. Manchester: Manchester University Press, pp 155–173Google Scholar
  50. Ratliff F, Hartline HK, Lange GD (1968): Variability of interspike intervals in optic nerve fibers of Limulus: effect of light and dark adaptation. Proc Natl Acad Sci USA 60: 464–469CrossRefGoogle Scholar
  51. Reid JVO (1969): The cardiac pacemaker: effects of regularly spaced nervous input. Am Heart J 78: 58–64CrossRefGoogle Scholar
  52. Roberge FA (1969): Paradoxical inhibition: a negative feedback principle in oscillatory systems. Automatika 5: 407–416CrossRefGoogle Scholar
  53. Rolls ET, Perrett DI, Caan AW, Wilson FAW (1982): Neuronal responses related to visual recognition. Brain 105: 611–646CrossRefGoogle Scholar
  54. Rupert A, Moushegian G, Galambos R (1962): Microelectrode studies of primary vestibular neurons in cat. Exp Neurol 5: 100–109CrossRefGoogle Scholar
  55. Scheibe! ME, Scheibel AB (1970): Elementary processes in selected thalamic and cortical subsystems—the structural substrates. In: The Neurosciences: A Second Study Program, Schmitt FO, ed. New York: Rockefeller University Press, pp 443–457Google Scholar
  56. Scholl DA (1956): The Organization of the Cerebral Cortex. New York: John Wiley Sons, IncGoogle Scholar
  57. Schulman J (1969): Information Transfer Across an Inhibitor to Pacemaker Synapse at the Crayfish Stretch Receptor. PhD Thesis. Zoology Department. Los Angeles CA: University of California, Los AngelesGoogle Scholar
  58. Segundo JP, Perkel DH (1969): The nerve cell as an analyzer of spike trains. In: UCLA Forum in Medical Sciences, No. 11: The Interneuron, Brazier MAB, ed. Berkeley: University of California Press, pp 349–390Google Scholar
  59. Sperry RW (1963): Chemoaffinity in the orderly growth of nerve fiber patterns and connections. Proc Natl Acad Sci USA 50: 703–710CrossRefGoogle Scholar
  60. Stark L (1968): Neurological Control Systems. Studies in Bioengineering. New York: PlenumGoogle Scholar
  61. Stein RB (1970): The role of spike trains in transmitting and distorting sensory signals. In:,The Neurosciences: A Second Study Program, Schmitt FO, ed. New York: Rockefeller University Press, pp 597–6604Google Scholar
  62. Straschill M, Hoffmann KP (1968): Relationship between localization and functional properties of movement-sensitive neurons of the cat’s tectum opticum. Brain Res 8: 382–385CrossRefGoogle Scholar
  63. Strausfeld N (1970): Golgi studies on insects. Part II. The optic lobes of Diptera. Phil Trans R Soc Lond B Biol Sci 258: 135–223CrossRefGoogle Scholar
  64. Stuart AE (1969): Excitatory and inhibitory motoneurons in the central nervous system of the leech. Science 165: 817–819CrossRefGoogle Scholar
  65. Suga N (1967): Echo-detection by single neurons in the inferior colliculus of echo-locating bats. In: Animal Sonar Systems, Biology and Bionics, Busnel RG, ed. France: Jouy-en-Josas, pp 1004–1020Google Scholar
  66. Suga N (1969): Classification of inferior collicular neurones of bats in terms of responses to pure tones, FM sounds and noise bursts. J Physiol 200: 555–574Google Scholar
  67. Swihart SL (1968): Single unit activity in the visual pathway of the butterfly Heliconius erato. J Insect Physiol 14: 1589–1601CrossRefGoogle Scholar
  68. Szabo T, Enger PS (1964): Pacemaker activity of the medullary nucleus controlling electric organs in high-frequency gymnotid fish. Z Vgl Physiol 49: 285–300CrossRefGoogle Scholar
  69. Szentagothai J (1970): Glomerular synapses, complex synaptic arrangements, and their operational significance. In: The Neurosciences: A Second Study Program, Schmitt FO, ed. New York: The Rockefeller University Press, pp 427–443Google Scholar
  70. Ten Hoopen M (1966): Probabilistic firing of neurons consid- ered as a first passage problem. Biophys J 6: 435–451CrossRefGoogle Scholar
  71. Trujillo-Cenoz O (1965): Some aspects of the structural organization of the intermediate retina of dipterans. J Ultrastruct Res 13: 1–33CrossRefGoogle Scholar
  72. Verbeek LAM (1961): Reliable computation with unreliable circuitry. In: Bionics Symposium. Living Prototypes—the Key to New Technology. WADD Tech Rep 60–600 (Proc of the Bionics Symp, Dayton OH, 1960 ): Wright Patterson AFB Ohio: Wright Air Development Div, pp 83–93Google Scholar
  73. Von Neumann J (1956): Probabilistic logic and the synthesis of reliable organisms from unreliable components. In: Automata Studies, Shannon CE, McCarthy J, eds. Princeton: Princeton University Press, pp 43–98Google Scholar
  74. Vowles DM (1966): The receptive fields of cells in the retina of the housefly (Musca domestica). Proc R Soc Land B Biol Sci 164: 552–576CrossRefGoogle Scholar
  75. Wald G (1965): Determinacy, individuality, and the problem of free will. In: New Views of the Nature of Man, Platt JR, ed. Chicago: University of Chicago Press, pp 16–46Google Scholar
  76. Walter DO (1968): The indeterminacies of the brain. Perspect Biol Med 11:203–207 Google Scholar
  77. Watanabe A, Takeda K (1963): The change of discharge frequency by A.C. stimulus in a weak electric fish. J Exp Biol 40: 57–66Google Scholar
  78. Waterman TH, Wiersma CAG (1963): Electrical responses in decapod crustacean visual systems. J Cell Comp Physiol 61: 1–16CrossRefGoogle Scholar
  79. Wiersma CAG (1967): Visual central processing. In: Invertebrate Nervous Systems, Their Significance for Mammalian Neurophysiology, Wiersma CAG, ed. Chicago: University of Chicago, pp 269–284Google Scholar
  80. Wiersma CAG, Oberjat T (1968): The selective responsiveness of various crayfish oculomotor fibers to sensory stimuli. Comp Biochem Physiol 26: 1–16CrossRefGoogle Scholar
  81. Wiersma CAG, Yamaguchi T (1967): Integration of visual stimuli by crayfish central nervous system. J Exp Biol 47: 409–431Google Scholar
  82. Wilson DM (1970): Neural operations in arthropod ganglia. In: The Neurosciences: A Second Study Program, Schmitt FO, ed. New York: Rockefeller University Press, pp 397–409Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Theodore Holmes Bullock
    • 1
  1. 1.Department of Neurosciences 0201University of California, San DiegoLa JollaUSA

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