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  • Review Article
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Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding

Key Points

  • One of the central problems in neuroscience is the characterization and understanding of the neural code. In 1968 Perkel and Bullock defined four key functions for a candidate neural code: stimulus representation, interpretation, transformation and transmission. Although the first three have been studied extensively, surprisingly, the fourth has been largely ignored in experiments. Yet, signal transmission is a vital functions for a neural code in ensuring communication among highly specialized brain regions.

  • Feedforward networks with convergent or divergent connections between subsequent groups of neurons have been the model system of choice in the study of spiking-activity propagation. The simple feedforward topology captures key features of the modular architecture of the brain. Moreover, from a functional perspective, certain classes of recurrent networks can be treated as feedforward networks.

  • Theoretical studies have identified two dominant modes for propagating spiking activity in feedforward networks: the aynchronous rate mode, in which the average spike count is propagated across the sub-networks; and the synchronous event mode, in which only synchronous volleys of spikes are propagated.

  • Various properties of individual neurons and the structure of feedforward networks can amplify even weak correlations in spiking-activity propagation. Such amplification rapidly degenerates the fidelity of an asynchronous rate code. Thus, only feedforward networks with weak shared connectivity are suitable for propagating asynchronous firing rates. Large, shared connectivity favours the propagation of a synchrony code.

  • Structural properties of feedforward networks, in particular connection probability and synaptic strengths, have a crucial role in determining whether asynchronous firing rates or synchronous spikes are propagated. Thus, appropriate architecture of the FFN may support stable propagation of asynchronous and synchronous neural codes simultaneously.

  • Indirect experimental evidence suggests that neural networks in vivo may indeed induce synchrony in their propagating activity. However, a direct testing of theoretical predictions is currently lacking. Controlled stimulation of appropriately selected neural networks in vivo to generate activity patterns mimicking either asynchronous or synchronous input and monitoring of their temporal evolution downstream could provide an effective paradigm for testing these predicitions.

Abstract

The brain is a highly modular structure. To exploit modularity, it is necessary that spiking activity can propagate from one module to another while preserving the information it carries. Therefore, reliable propagation is one of the key properties of a candidate neural code. Surprisingly, the conditions under which spiking activity can be propagated have received comparatively little attention in the experimental literature. By contrast, several computational studies in the last decade have addressed this issue. Using feedforward networks (FFNs) as a generic network model, they have identified two dynamical activity modes that support the propagation of either asynchronous (rate code) or synchronous (temporal code) spiking. Here, we review the dichotomy of asynchronous and synchronous propagation in FFNs, propose their integration into a single extended conceptual framework and suggest experimental strategies to test our hypothesis.

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Figure 1: The feedforward network as a model of information processing in the brain.
Figure 2: Cascaded neural assemblies.
Figure 3: Transmission of asynchronous firing rate in an FFN.
Figure 4: Propagation of a pulse packet in an FFN.
Figure 5: Coexistence of firing rate propagation and synchrony propagation.

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References

  1. James, W. Psychology: The Briefer Course. (Henry Holt and Company, New York, 1890).

    Google Scholar 

  2. Perkel, D. H. & Bullock, T. H. Neural coding: a report based on an NRP work session. Neurosci. Res. Program Bull. 6, 219–349 (1968). A seminal report that defines key properties of a neural code and describes various candidate neural codes.

    Google Scholar 

  3. Reyes, A. D. Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nature Neurosci. 6, 593–599 (2003). The only study that has addressed the issue of spiking-activity propagation in experiments. Using an innovative method this study showed the emergence of synchrony in feedforward networks.

    CAS  PubMed  Google Scholar 

  4. Diesmann, M., Gewaltig, M. & Aertsen, A. Stable propagation of synchronous spiking in cortical neural networks. Nature 402, 529–533 (1999). The first study to systematically investigate the propagation of synchronous spiking in computer simulations of feedforward networks.

    CAS  PubMed  Google Scholar 

  5. Cateau, H. & Fukai, T. Fokker–Planck approach to the pulse packet propagation in synfire chain. Neural Netw. 14, 657–685 (2001).

    Google Scholar 

  6. van Rossum, M. C., Turrigiano, G. G. & Nelson, S. B. Fast propagation of firing rates through layered networks of noisy neurons. J. Neurosci. 22, 1956–1966 (2002).

    CAS  PubMed  PubMed Central  Google Scholar 

  7. Kistler, W. M. & Gerstner, W. Stable propagation of activity pulses in populations of spiking neurons. Neural Comput. 14, 987–997 (2002).

    PubMed  Google Scholar 

  8. Litvak, V. et al. On the transmission of rate code in long feedforward networks with excitatory-inhibitory balance. J. Neurosci. 23, 3006–3015 (2003).

    CAS  PubMed  PubMed Central  Google Scholar 

  9. Kumar, A., Rotter, S. & Aertsen, A. Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model. J. Neurosci. 28, 5268–5280 (2008). The first study to show that asynchronous–irregular ongoing activity in a recurrent network facilitates propagation of both synchronous spiking and asynchronous firing rates in an embedded feedforward network.

    CAS  PubMed  PubMed Central  Google Scholar 

  10. Vogels, T. P. & Abbott, L. F. Signal propagation and logic gating in networks of integrate-and-fire neurons. J. Neurosci. 25, 10786–10795 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. Vogels, T. P. & Abbott, L. F. Gating multiple signals through detailed balance of excitation and inhibition in spiking networks. Nature Neurosci. 12, 483–491 (2009).

    CAS  PubMed  Google Scholar 

  12. Aertsen, A., Diesmann, M. & Gewaltig, M. Propagation of synchronous spiking activity in feedforward neural networks. J. Physiol. (Paris) 90, 243–247 (1996).

    CAS  Google Scholar 

  13. Gewaltig, M., Diesmann, M. & Aertsen, A. Propagation of cortical synfire activity: survival probability in single trials and stability in the mean. Neural Netw. 14, 657–673 (2001).

    CAS  PubMed  Google Scholar 

  14. Gerstein, G., Bedenbaugh, P. & Aertsen, A. Neural assemblies. IEEE Trans. Biomed. Eng. 36, 1–11 (1989).

    Google Scholar 

  15. Harris, K. D. Neural signatures of cell assembly organization. Nature Rev. Neurosci. 6, 399–407 (2005).

    CAS  Google Scholar 

  16. Hebb, D. O. The Organization of Behavior: A Neuropsychological Theory. (John Wiley & Sons, New York, 1949).

    Google Scholar 

  17. Arieli, A. et al. Dynamics of ongoing activity: explanation of the larger variability in evoked cortical responses. Science 273, 1868–1871 (1996).

    Article  CAS  PubMed  Google Scholar 

  18. Kenet, T. et al. Spontaneously emerging cortical representations of visual attributes. Nature 425, 954–956 (2003).

    CAS  PubMed  Google Scholar 

  19. Shadlen, M. N. & Newsome, W. T. The variable discharge of cortical neurons: implication for connectivity, computation, and information coding. J. Neurosci. 18, 3870–3896 (1998).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. Binzegger, T. A quantitative map of the circuit of cat primary visual cortex. J. Neurosci. 24, 8441–8453 (2004).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Braitenberg, V. & Schüz, A. Cortex: Statistics and Geometry of Neuronal Connectivity. (Springer-Verlag, Berlin, 1998).

    Google Scholar 

  22. Gulyás, A. I. et al. Hippocampal pyramidal cells excite inhibitory neurons through a single release site. Nature 366, 683–687 (1993).

    PubMed  Google Scholar 

  23. Hessler, N. A., Shirke, A. M. & Malinow, R. The probability of transmitter release at a mammalian central synapse. Nature 366, 569–572 (1993).

    CAS  PubMed  Google Scholar 

  24. Shaw, G. L., Harth, E. & Scheibel, A. B. Cooperativity in brain function: assemblies of approximately 30 neurons. Exp. Neurol. 77, 324–358 (1982).

    CAS  PubMed  Google Scholar 

  25. Abeles, M. Corticonics: Neural Circuits of the Cerebral Cortex. (Cambridge Univ. Press, Cambridge, UK, 1991).

    Google Scholar 

  26. Bullier, J. & Nowak, L. G. Parallel versus serial processing: new vistas on the distributed organization of the visual system. Curr. Opin. Neurobiol. 5, 497–503 (1995).

    CAS  PubMed  Google Scholar 

  27. Felleman, S. J. & Essen, D. C. Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1–46 (1991).

    CAS  PubMed  Google Scholar 

  28. Bain, A. Mind and Body: The Theories of Their Relation. (D. Appleton and Company, New York, 1875).

    Google Scholar 

  29. Sherrington, C. Man on his Nature. (Cambridge Univ. Press, Cambridge, UK, 1942).

    Google Scholar 

  30. Abeles, M. Local Cortical Circuits: An Electrophysiological Study. (Berlin, Heidelberg, New York, 1982).

    Google Scholar 

  31. Abeles, M. The quantification and graphic display of correlations among three spike trains. IEEE Trans. Biomed. Eng. 30, 235–239 (1983).

    CAS  PubMed  Google Scholar 

  32. Abeles, M. et al. Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J. Neurophysiol. 70, 1629–1638 (1993).

    CAS  PubMed  Google Scholar 

  33. Dayhoff, J. E. & Gerstein, G. L. Favored patterns in spike trains. II. Application. J. Neurophysiol. 49, 1349–1363 (1983).

    CAS  PubMed  Google Scholar 

  34. Frostig, R. D., Frysinger, R. C. & Harper, R. M. Recurring discharge patterns in multiple spike trains. II. Application in forebrain areas related to cardiac and respiratory control during different sleep–waking states. Biol. Cybern. 62, 495–502 (1990).

    CAS  PubMed  Google Scholar 

  35. Ikegaya, Y. et al. Synfire chains and cortical songs: temporal modules of cortical activity. Science 304, 559–564 (2004).

    CAS  PubMed  Google Scholar 

  36. Mokeichev, A. et al. Stochastic emergence of repeating cortical motifs in spontaneous membrane potential fluctuations in vivo. Neuron 53, 413–425 (2007).

    CAS  PubMed  Google Scholar 

  37. Prut, Y. et al. Spatiotemporal structure of cortical activity: properties and behavioral relevance. J. Neurophysiol. 79, 2857–2874 (1998).

    CAS  PubMed  Google Scholar 

  38. Roxin, A., Hakim, V. & Brunel, N. The statistics of repeating patterns of cortical activity can be reproduced by a model network of stochastic binary neurons. J. Neurosci. 28, 10734–10745 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  39. von der Malsburg, C. in Models of Neural Networks II Ch. 2 (eds Domany, E., van Hemmen, J. L. & Schulten, K.) 95–119 (Springer Verlag, Berlin, 1981).

    Google Scholar 

  40. Singer, W. & Gray, C. M. Visual feature integration and the temporal correlation hypothesis. Annu. Rev. Neurosci. 18, 555–586 (1995).

    CAS  PubMed  Google Scholar 

  41. Singer, W. The Cat Primary Visual Cortex (eds Payne, B. & Peters, A.) 521–559 (Academic Press, San Diego, 2002).

    Google Scholar 

  42. Griffith, J. S. On the stability of brain-like structures. Biophys. J. 3, 299–308 (1963).

    CAS  PubMed  PubMed Central  Google Scholar 

  43. Goldman, M. S. Memory without feedback in a neural network. Neuron 61, 621–634 (2009). This theoretical study and references 44 and 47 showed that, from a functional perspective, a certain class of recurrent networks can be considered as feedforward networks.

    CAS  PubMed  PubMed Central  Google Scholar 

  44. Murphy, B. K. & Miller, K. D. Balanced amplification: a new mechanism of selective amplification of neural activity patterns. Neuron 61, 635–648 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  45. Schrader, S. et al. Detecting synfire chain activity using massively parallel spike train recording. J. Neurophysiol. 100, 2165–2176 (2008).

    PubMed  PubMed Central  Google Scholar 

  46. Liu, J. K. & Buonomano, D. V. Embedding multiple trajectories in simulated recurrent neural networks in a self-organizing manner. J. Neurosci. 29, 13172–13181 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  47. Ganguli, S., Huh, D. & Sompolinsky, H. Memory traces in dynamical systems. Proc. Natl Acad. Sci. 105, 18970–18975 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  48. Hehl, U. Embedding of synchronous spike activity in cortical networks. Deutsche National Bibliotek [online] (2001).

    Google Scholar 

  49. Izhikevich, E. M., Gally, J. A. & Edelman, G. M. Spike-timing dynamics of neuronal groups. Cereb. Cortex 14, 933–944 (2004).

    PubMed  Google Scholar 

  50. Aviel, Y. et al. On embedding synfire chains in a balanced network. Neural Comput. 15, 1321–1340 (2003).

    CAS  PubMed  Google Scholar 

  51. Mehring, C. et al. Activity dynamics and propagation of synchronous spiking in locally connected random networks. Biol. Cybern. 88, 395–408 (2003).

    PubMed  Google Scholar 

  52. Tetzlaff, T. et al. The spread of rate and correlation in stationary cortical networks. Neurocomputing 52–54, 949–954 (2003).

    Google Scholar 

  53. Tetzlaff, T., Geisel, T. & Diesmann, M. The ground state of cortical feed-forward networks. Neurocomputing 44–46, 673–678 (2002).

    Google Scholar 

  54. Mazurek, M. E. & Shadlen, M. N. Limits to the temporal fidelity of cortical spike rate signals. Nature Neurosci. 5, 463–471 (2002). This study showed for the first time that even weak correlations can impair stimulus encoding in the form of firing rates in an ensemble of neurons.

    CAS  PubMed  Google Scholar 

  55. Sompolinsky, H. et al. Population coding in neuronal systems with correlated noise. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64, 051904 (2001).

    CAS  PubMed  Google Scholar 

  56. de la Rocha, J. et al. Correlation between neural spike trains increases with firing rate. Nature 448, 802–807 (2007).

    CAS  PubMed  Google Scholar 

  57. Staude, B., Rotter, S. & Grün, S. Can. spike coordination be differentiated from rate covariation? Neural Comput. 20, 1973–1999 (2008).

    PubMed  Google Scholar 

  58. Aertsen, A. M. et al. Dynamics of neuronal firing correlation: modulation of 'effective connectivity.' J. Neurophysiol. 61, 900–917 (1989).

    CAS  PubMed  Google Scholar 

  59. Grün, S., Diesmann, M. & Aertsen, A. Unitary events in multiple single-neuron spiking activity: I. Detection and significance. Neural Comput. 14, 43–80 (2002).

    PubMed  Google Scholar 

  60. Grün, S., Diesmann, M. & Aertsen, A. Unitary events in multiple single-neuron spiking activity: II. Nonstationary data. Neural Comput. 14, 81–119 (2002).

    PubMed  Google Scholar 

  61. Guetig, R., Aertsen, A. & Rotter, S. Statistical significance of coincident spikes: count-based versus rate-based statistics. Neural Comput. 14, 121–153 (2002).

    Google Scholar 

  62. Staude, B. Gruen S. & Rotter S. Higher-order correlations in non-stationary parallel spike trains: statistical modeling and inference. Front. Comput. Neurosci. 4, 16 (2010).

    PubMed  PubMed Central  Google Scholar 

  63. Bair, W., Zohary, E. & Newsome, W. T. Correlated firing in macaque visual area MT: time scales and relationship to behavior. J. Neurosci. 21, 1676–1697 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  64. Chen, Y., Geisler, W. S. & Seidemann, E. Optimal decoding of correlated neural population responses in the primate visual cortex. Nature Neurosci. 9, 1412–1420 (2006).

    CAS  PubMed  Google Scholar 

  65. Riehle, A. et al. Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278, 1950–1953 (1997).

    CAS  PubMed  Google Scholar 

  66. Stopfer, M. & Laurent, G. Short-term memory in olfactory network dynamics. Nature 402, 664–668 (1999).

    CAS  PubMed  Google Scholar 

  67. Vaadia, E. et al. Dynamics of neuronal interactions in monkey cortex in relation to behavioural events. Nature 373, 515–518 (1995).

    CAS  PubMed  Google Scholar 

  68. Wehr, M. & Laurent, G. Odour encoding by temporal sequences of firing in oscillating neural assemblies. Nature 384, 162–166 (1996).

    CAS  PubMed  Google Scholar 

  69. Wehr, M. & Laurent, G. Relationship between afferent and central temporal patterns in the locust olfactory system. J. Neurosci. 19, 381–390 (1999).

    CAS  PubMed  PubMed Central  Google Scholar 

  70. Zohary, E., Shadlen, M. N. & Newsome, W. T. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370, 140–143 (1994).

    CAS  PubMed  Google Scholar 

  71. Adrian, E. D. & Zotterman, Y. The impulses produced by sensory nerve-endings: part II. The response of a Single End-Organ. J. Physiol. 61, 151–171 (1926).

    CAS  PubMed  PubMed Central  Google Scholar 

  72. Barlow, H. B. Single units and sensation: a neuron doctrine for perceptual psychology? Perception 1, 371–394 (1972).

    CAS  PubMed  Google Scholar 

  73. Cui, H. & Andersen, R. A. Posterior parietal cortex encodes autonomously selected motor plans. Neuron 56, 552–559 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  74. Romo, R. et al. Neuronal correlates of parametric working memory in the prefrontal cortex. Nature 399, 470–473 (1999).

    CAS  PubMed  Google Scholar 

  75. Wilson, M. A. & McNaughton, B. L. Dynamics of the hippocampal ensemble code for space. Science 261, 1055–1058 (1993).

    CAS  PubMed  Google Scholar 

  76. Knutsen, P. M. & Ahissar, E. Orthogonal coding of object location. Trends Neurosci. 32, 101–108 (2009).

    CAS  PubMed  Google Scholar 

  77. Huxter, J., Burgess, N. & O'keefe, J. Independent rate and temporal coding in hippocampal pyramidal cells. Nature 425, 828–832 (2003).

    CAS  PubMed  PubMed Central  Google Scholar 

  78. Abbott, L. F. & Nelson, S. B. Synaptic plasticity: taming the beast. Nature Neurosci. 3, 1178–1183 (2000).

    CAS  PubMed  Google Scholar 

  79. Guetig, R. et al. Learning input correlations through nonlinear temporally asymmetric hebbian plasticity. J. Neurosci. 23, 3697–3714 (2003).

    Google Scholar 

  80. van Rossum, M. C., Bi, G. Q. & Turrigiano, G. G. Stable Hebbian learning from spike timing-dependent plasticity. J. Neurosci. 20, 8812–8821 (2000).

    CAS  PubMed  PubMed Central  Google Scholar 

  81. Kuhn, A., Aertsen, A. & Rotter, S. Neuronal integration of synaptic input in the fluctuation-driven regime. J. Neurosci. 24, 2345–2356 (2004).

    CAS  PubMed  PubMed Central  Google Scholar 

  82. Kuhn, A., Aertsen, A. & Rotter, S. Higher-order statistics of input ensembles and the response of simple model neurons. Neural Comput. 16, 67–101 (2003).

    Google Scholar 

  83. Marsalek, P., Koch, C. & Maunsell, J. On the relationship between synaptic input and spike output jitter in individual neurons. Proc. Natl Acad. Sci. 94, 736–740 (1997).

    Google Scholar 

  84. Salinas, E. & Sejnowski, T. J. Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. J. Neurosci. 20, 6193–6209 (2000).

    CAS  PubMed  PubMed Central  Google Scholar 

  85. Salinas, E. & Sejnowski, T. J. Integrate-and-fire neurons driven by correlated stochastic input. Neural Comput. 14, 2111–2155 (2002).

    PubMed  PubMed Central  Google Scholar 

  86. Burkitt, A. N. & Clark, G. M. Analysis of integrate-and-fire neurons: synchronization of synaptic input and spike output. Neural Comput. 11, 871–901 (1999).

    CAS  PubMed  Google Scholar 

  87. Brunel, N. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci. 8, 183–208 (2000).

    CAS  PubMed  Google Scholar 

  88. Kumar, A. et al. The high-conductance state of cortical networks. Neural Comput. 20, 1–43 (2008).

    PubMed  Google Scholar 

  89. Renart, A. et al. The asynchronous state in cortical circuits. Science 327, 587–590 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  90. Ecker, A. S. et al. Decorrelated neuronal firing in cortical microcircuits. Science 327, 584–587 (2010).

    CAS  PubMed  Google Scholar 

  91. Vogel, A. & Ronacher, B. Neural correlations increase between consecutive processing levels in the auditory system of locusts. J. Neurophysiol. 97, 3376–3385 (2007).

    CAS  PubMed  Google Scholar 

  92. Kremkow, J. et al. Functional consequences of correlated excitatory and inhibitory conductances in cortical networks. J. Comput. Neurosci. 28, 579–594 (2010). The first study to systematically investigate the role of correlated excitatory and inhibitory inputs on the stability and propagation of spiking activity in feedforward networks that are embedded in recurrent networks.

    PubMed  Google Scholar 

  93. Yazdanbakhsh, A. et al. New attractor states for synchronous activity in synfire chains with excitatory and inhibitory coupling. Biol. Cybern. 86, 367–378 (2002).

    PubMed  Google Scholar 

  94. Teramae, J. & Fukai, T. Local cortical circuit model inferred from power-law distributed neuronal avalanches. J. Comput. Neurosci. 22, 301–312 (2007).

    PubMed  Google Scholar 

  95. Goedeke, S. & Diesmann, M. The mechanism of synchronization in feed-forward neuronal networks. New J. Phys. 10, 015007 (2008).

    Google Scholar 

  96. Doupe, A. J. et al. Cellular, circuit, and synaptic mechanisms in song learning. Ann. NY Acad. Sci. 1016, 495–523 (2004).

    PubMed  Google Scholar 

  97. Kao, M. H., Wright, B. D. & Doupe, A. J. Neurons in a forebrain nucleus required for vocal plasticity rapidly switch between precise firing and variable bursting depending on social context. J. Neurosci. 28, 13232–13247 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  98. Kimpo, R. R., Theunissen, F. E. & Doupe, A. J. Propagation of correlated activity through multiple stages of a neural circuit. J. Neurosci. 23, 5750–5761 (2003).

    CAS  PubMed  PubMed Central  Google Scholar 

  99. Kojima, S. & Doupe, A. J. Activity propagation in an avian basal ganglia-thalamocortical circuit essential for vocal learning. J. Neurosci. 29, 4782–4793 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  100. Bruno, R. M. & Sakmann, B. Cortex is driven by weak but synchronously active thalamocortical synapses. Science 312, 1622–1627 (2006).

    CAS  PubMed  Google Scholar 

  101. Bienenstock, E. A model of neocortex. Netw. Comp. Neural Syst. 6, 179–224 (1995). This paper proposed a model of neocortex functioning based on interacting feedforward networks.

    Google Scholar 

  102. Yang, Y. et al. Millisecond-scale differences in neural activity in auditory cortex can drive decisions. Nature Neurosci. 11, 1262–1263 (2008).

    CAS  PubMed  Google Scholar 

  103. Alonso, J., Usrey, W. M. & Reid, R. C. Precisely correlated firing in cells of the lateral geniculate nucleus. Nature 383, 815–819 (1996).

    CAS  PubMed  Google Scholar 

  104. Butts, D. A. et al. Temporal precision in the neural code and the timescales of natural vision. Nature 449, 92–96 (2007).

    CAS  PubMed  Google Scholar 

  105. Haider, B. et al. Synaptic and network nechanisms of sparse and reliable nisual cortical activity during nonclassical receptive field stimulation. Neuron 65, 107–121 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  106. Shinozaki, T. et al. Controlling synfire chain by inhibitory synaptic input. J. Physical Soc. Japan 76, 044806 (2007).

    Google Scholar 

  107. Abeles, M., Hayon, G. & Lehmann, D. Modeling compositionality by dynamic binding of synfire chains. J. Comput. Neurosci. 17, 179–201 (2004). One of the first papers to explore the computational properties of interacting feedforward networks exploiting synchrony propagation.

    PubMed  Google Scholar 

  108. Haykin, S. Neural Networks: A Comprehensive Foundation. (Prentice Hall, New Jersey, USA, 1999).

    Google Scholar 

  109. Thorpe, S., Fize, D. & Marlot, C. Speed of processing in the human visual system. Nature 381, 520–522 (1996).

    CAS  PubMed  Google Scholar 

  110. Thorpe, S., Delrome, A. & van Rullen, R. Spike-based strategies for rapid processing. Neural Netw. 14, 715–725 (2001).

    CAS  PubMed  Google Scholar 

  111. van Rullen, R. & Thorpe, S. J. Rate coding versus temporal order coding: what the retinal ganglion cells tell the visual cortex. Neural Comput. 13, 1255–1283 (2001).

    CAS  PubMed  Google Scholar 

  112. Gollisch, T. & Meister, M. Rapid neural coding in the retina with relative spike latencies. Science 319, 1108–1111 (2008).

    CAS  PubMed  Google Scholar 

  113. Kohn, A. & Smith, M. A. Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J. Neurosci. 25, 3661–3673 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  114. Olshausen, B. A. & Field, D. J. Sparse coding of sensory inputs. Curr. Opin. Neurobiol. 14, 481–487 (2004).

    CAS  PubMed  Google Scholar 

  115. Houweling, A. R. & Brecht, M. Behavioural report of single neuron stimulation in somatosensory cortex. Nature 451, 65–68 (2008).

    CAS  PubMed  Google Scholar 

  116. Rozell, C. J. et al. Sparse coding via thresholding and local competition in neural circuits. Neural Comput. 20, 2526–2563 (2008).

    PubMed  Google Scholar 

  117. Wolfe, J., Houweling, A. R. & Brecht, M. Sparse and powerful cortical spikes. Curr. Opin. Neurobiol. 20, 306–312 (2010).

    CAS  PubMed  Google Scholar 

  118. Luczak, A., Barthó, P. & Harris, K. D. Spontaneous events outline the realm of possible sensory responses in neocortical populations. Neuron 62, 413–425 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  119. Hertz, J. & Prügel-Bennett, A. Learning short synfire chains by self-organization. Netw. Comp. Neural Syst. 7, 357–363 (1996).

    CAS  Google Scholar 

  120. Morrison, A., Aertsen, A. & Diesmann, M. Spike-timing-dependent plasticity in balanced random networks. Neural Comput. 19, 1437–1467 (2007).

    PubMed  Google Scholar 

  121. Hebb, D. O. A Textbook of Psychology. (W. B. Saunders Company, Philadelphia and London, 1958).

    Google Scholar 

  122. Gerstein, G. L. & Kiang, N. Y.-S. An approach to the quantitative analysis of electrophysiological data from single neurons. Biophys. J. 1, 15–28 (1960).

    CAS  PubMed  PubMed Central  Google Scholar 

  123. Nawrot, M., Aertsen, A. & Rotter, S. Single-trial estimation of neuronal firing rates: from single-neuron spike trains to population activity. J. Neurosci. Methods 94, 82–92 (1999).

    Google Scholar 

  124. Perkel, D. H., Gerstein, G. L. & Moore, G. P. Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys. J. 7, 419–440 (1967).

    CAS  PubMed  PubMed Central  Google Scholar 

  125. Palm, G., Aertsen, A. & Gerstein, G. L. On the significance of correlations among neuronal spike trains. Biol. Cybern. 59, 1–11 (1988).

    CAS  PubMed  Google Scholar 

  126. Tetzlaff, T. et al. Dependence of neuronal correlations on filter characteristics and marginal spike-train statistics. Neural Comput. 20, 2133–2184 (2008).

    PubMed  Google Scholar 

  127. Nakahara, H. & Amari, S. Information-geometric measure for neural spikes. Neural Comput. 14, 2269–2316 (2002).

    PubMed  Google Scholar 

  128. Martignon, L. et al. Detecting higher-order interactions among the spiking events in a group of neurons. Biol. Cybern. 73, 69–81 (1995).

    CAS  PubMed  Google Scholar 

  129. Panzeri, S., Brunel, N., Logothetis, N. K. & Kayser, C. Sensory neural codes using multiplexed temporal scales. Trends Neurosci. 33, 111–120 (2010).

    CAS  PubMed  Google Scholar 

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Acknowledgements

We thank J. Kremkow and T. Vogels for helpful discussions, G. Grah for preparing some of the graphical illustrations and U. Froriep for proofreading the manuscript. We also thank the editorial staff at the Nature Reviews Neuroscience for their continuous help in organizing the manuscript. This work was supported by the German Federal Ministry of Education and Research (grant 01GQ0420 to the Bernstein Center for Computational Neuroscience, Freiburg), the EU (grant no. 15,879-FACETS) and the German Research Foundation (Collaborative Research Center 780).

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Correspondence to Arvind Kumar.

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Network model (PDF 269 kb)

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FURTHER INFORMATION

A. Aertsen, C. Boucsein and A. Kumar's Brainworks homepage

The Bernstein Center Freiburg homepage

Glossary

Convergent–divergent connection

A connectivity scheme in which neurons in a group receive inputs from many neurons in a previous group (convergent connections) and at the same time project to many neurons in subsequent groups (divergent connections).

Unreliable synapses

Synapses may fail to induce a postsynaptic potential in the target neuron despite stimulation owing to the probabilistic nature of synaptic vesicle release.

Read-out problem

The problem of how the neural activity of a single neuron or group of neurons received and transformed ('decoded') by a postsynaptic group of neurons, to result in, for example, a decision, perception or motor act.

Embedding recurrent network

A large recurrent network typically composed of excitatory and inhibitory neurons that contain feedforward networks as subnetworks.

In- and out-degree

In-degree refers to the number of input synapses that a neuron receives. Out-degree refers to the number of synapses a neuron makes.

Asynchronous–irregular

A network state characterized by irregular firing of individual neurons (measured by the coefficient of variation of the inter-spike-interval distribution) and by asynchronous population activity (measured by pairwise correlation or fano factor) (Box 2).

Fixed point

If the system arrives at this point in its state-space, it remains there permanently in the absence of disturbances (a steady state). Fixed points can be stable or unstable.

Attractor

A fixed point in the state-space that attracts all of the system trajectories passing through its neighbourhood.

Saddle node

A fixed point that attracts some nearby trajectories but repels others.

State-space

A multi-dimensional space defined by variables that characterize the system state. If there are N such variables, each state is represented by a point in an N-dimensional state-space.

Rank-order coding

A spatiotemporal pattern of spikes in which the temporal rank of spikes carries information about a stimulus or cognitive state.

Sparse code

A coding scheme in which strong activation of a relatively small set of available neurons is used for information representation.

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Kumar, A., Rotter, S. & Aertsen, A. Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding. Nat Rev Neurosci 11, 615–627 (2010). https://doi.org/10.1038/nrn2886

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