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Information propagation in recurrent neuronal populations with mixed excitatory–inhibitory synaptic connections

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Abstract

Information propagation in the cortical neural network has attracted a large amount of attention. In this paper, a feedforward network is constructed with each subnetwork being a recurrent neuronal population, consisting of neurons coupled by excitatory and inhibitory synapses, in which neurons have both types of outgoing synapses. Namely, neurons in the constructed feedforward neuronal networks have mixed excitatory–inhibitory synapses. Here, propagation of population firing rate and pulse packets are investigated. For the propagation of population firing rate, it is found that proper feedforward connection probability and strength could promote the propagation of population firing rate. Properly larger feedforward synaptic time constant could considerably enhance the fidelity of the propagating population firing rate. For the propagation of pulse packet, we find suitably adjusting the relative strength, recurrent probability, and feedforward synaptic connection can promote propagation of pulse packet. Notably, different from each other, larger feedforward synaptic time constant can considerably promote the propagation of population firing rate while hindering the propagation of pulse packets.

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Notes

  1. In our model, neurons can generate either excitatory or inhibitory synapses to their postsynaptic neurons. The phenomenon that the firing rate of the sensory network increases with R shown in Fig. 4 can be explained as follows. Take an example network of three neurons, neuron No. 1 generates stronger inhibition on neuron No. 2, so temporarily the neuron No. 2 is inhibited and then generate firing activity with a lower rate. Thus, the neuron No. 2 can only generate weaker inhibition on the neuron No. 3. making the following neurons be excited with a higher firing rate. This seems the phenomenon ‘disinhibition’ as reported in former works [80, 81]. Such disinhibition may lead to the increasing in the sensory network’s firing rate.

References

  1. Buzsáki, G.: Neural syntax: cell assemblies, synapsembles, and readers. Neuron 68(3), 362–385 (2010)

    Article  Google Scholar 

  2. Newsome, W.T., Britten, K.H., Movshon, J.A.: Neuronal correlates of a perceptual decision. Nature 341, 52–54 (1989)

    Article  Google Scholar 

  3. Georgopoulos, A., Taira, M., Lukashin, A.: Cognitive neurophysiology of the motor cortex. Science 260(5104), 47–52 (1993)

    Article  Google Scholar 

  4. Shadlen, M.N., Newsome, W.T.: Noise, neural codes and cortical organization. Curr. Opin. Neurobiol. 4(4), 569–579 (1994)

    Article  Google Scholar 

  5. Marsalek, P., Koch, C., Maunsell, J.H.R.: On the relationship between synaptic input and spike output jitter in individual neurons. Proc. Nat. Acad. Sci. USA 94(2), 735–40 (1997)

    Article  Google Scholar 

  6. Mazurek, M.E., Shadlen, M.N.: Limits to the temporal fidelity of cortical spike rate signals. Nat. Neurosci. 5, 463–471 (2002)

    Article  Google Scholar 

  7. Gray, C.M.: Synchronous oscillations in neuronal systems: mechanisms and functions. J. Comput. Neurosci. 1(1), 11–38 (1994)

    Article  Google Scholar 

  8. Riehle, A., Grün, S., Diesmann, M., Aertsen, A.: Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278(5345), 1950–1953 (1997)

    Article  Google Scholar 

  9. Diesmann, M., Gewaltig, M.O., Aertsen, A.: Stable propagation of synchronous spiking in cortical neural networks. Nature 402, 529–533 (1999)

    Article  Google Scholar 

  10. Aertsen, A., Diesmann, M., Gewaltig, M.: Propagation of synchronous spiking activity in feedforward neural networks. J. Physiol.-Paris 90(3), 243–247 (1996)

    Article  Google Scholar 

  11. Shadlen, M.N., Newsome, W.T.: The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18(10), 3870–3896 (1998)

    Article  Google Scholar 

  12. Abeles, M., Bergman, H., Margalit, E., Vaadia, E.: Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J. Neurophysiol. 70(4), 1629–1638 (1993)

    Article  Google Scholar 

  13. Nowak, L.G., Sanchez-Vives, M.V., McCormick, D.A.: Influence of low and high frequency inputs on spike timing in visual cortical neurons. Cereb. Cortex 7(6), 487–501 (1997)

    Article  Google Scholar 

  14. Prut, Y., Vaadia, E., Bergman, H., Haalman, I., Slovin, H., Abeles, M.: Spatiotemporal structure of cortical activity: properties and behavioral relevance. J. Neurophysiol. 79(6), 2857–2874 (1998)

    Article  Google Scholar 

  15. McCormick, D.A., Prince, D.A.: Post-natal development of electrophysiological properties of rat cerebral cortical pyramidal neurones. J. Physiol. 393(1), 743–762 (1987)

    Article  Google Scholar 

  16. Câteau, H., Fukai, T.: Fokker–Planck approach to the pulse packet propagation in synfire chain. Neural Netw. 14(6–7), 675–85 (2001)

    Article  Google Scholar 

  17. Gewaltig, M.O., Diesmann, M., Aertsen, A.: Propagation of cortical synfire activity: survival probability in single trials and stability in the mean. Neural Netw. 14(6), 657–673 (2001)

    Article  Google Scholar 

  18. Fries, P.: A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends Cogn. Sci. 9(10), 474–480 (2005)

    Article  Google Scholar 

  19. Masuda, N., Aihara, K.: Bridging rate coding and temporal spike coding by effect of noise. Phys. Rev. Lett. 88, 248101 (2002)

    Article  Google Scholar 

  20. Masuda, N., Aihara, K.: Duality of rate coding and temporal coding in multilayered feedforward networks. Neural Comput. 15, 103–125 (2003)

    Article  MATH  Google Scholar 

  21. Masuda, N., Aihara, K.: Dual coding and effects of global feedback in multilayered neural networks. Neurocomputing 58–60, 33–39 (2004)

    Article  Google Scholar 

  22. Bruno, R.M., Sakmann, B.: Cortex is driven by weak but synchronously active thalamocortical synapses. Science 312(5780), 1622–1627 (2006)

    Article  Google Scholar 

  23. DeMarse, T.B., Pan, L., Alagapan, S., Brewer, G.J., Wheeler, B.C.: Feed-forward propagation of temporal and rate information between cortical populations during coherent activation in engineered in vitro networks. Front. Neural Circuits 10, 32 (2016)

    Article  Google Scholar 

  24. Kumar, A., Rotter, S., Aertsen, A.: Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model. J. Neurosci. 28(20), 5268–5280 (2008)

    Article  Google Scholar 

  25. 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)

    Article  Google Scholar 

  26. Barral, J., Wang, X.J., Reyes, A.: Propagation of temporal and rate signals in cultured multilayer networks. Nature Commun. 10, 1–14 (2019)

    Article  Google Scholar 

  27. Essen, D., Anderson, C., Felleman, D.: Information processing in the primate visual system: an integrated systems perspective. Science (New York, NY) 255, 419–23 (1992)

    Article  Google Scholar 

  28. Abeles, M.: Corticonics: Neural circuits of the cerebral cortex. Cambridge University Press, Cambridge, New York (1991)

    Book  Google Scholar 

  29. Diesmann, M., Gewaltig, M.O., Rotter, S., Aertsen, A.: State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 38–40, 565–571 (2001)

    Article  Google Scholar 

  30. Kistler, W.M., Gerstner, W.: Stable propagation of activity pulses in populations of spiking neurons. Neural Comput. 14(5), 987–997 (2002)

    Article  MATH  Google Scholar 

  31. van Rossum, M.C.W., Turrigiano, G.G., Nelson, S.B.: Fast propagation of firing rates through layered networks of noisy neurons. J. Neurosci. 22(5), 1956–1966 (2002)

    Article  Google Scholar 

  32. Litvak, V., Sompolinsky, H., Segev, I., Abeles, M.: On the transmission of rate code in long feedforward networks with excitatory–inhibitory balance. J. Neurosci. 23(7), 3006–3015 (2003)

    Article  Google Scholar 

  33. Reyes, A.D.: Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nat. Neurosci. 6, 593–599 (2003)

    Article  Google Scholar 

  34. Wang, S., Wang, W., Liu, F.: Propagation of firing rate in a feed-forward neuronal network. Phys. Rev. Lett. 96, 018103 (2006)

    Article  Google Scholar 

  35. Kremkow, J., Aertsen, A., Kumar, A.: Gating of signal propagation in spiking neural networks by balanced and correlated excitation and inhibition. J. Neurosci. 30(47), 15760–15768 (2010)

    Article  Google Scholar 

  36. Moldakarimov, S., Bazhenov, M., Sejnowski, T.J.: Feedback stabilizes propagation of synchronous spiking in cortical neural networks. Proc. Nat. Acad. Sci. USA 112(8), 2545–50 (2015)

    Article  Google Scholar 

  37. Claverol-Tinturé, E., Gross, G.: Commentary: Feedback stabilizes propagation of synchronous spiking in cortical neural networks. Front. Comput. Neurosci. 9, 71 (2015)

    Google Scholar 

  38. Sornborger, A.T., Wang, Z., Tao, L.: A mechanism for graded, dynamically routable current propagation in pulse-gated synfire chains and implications for information coding. J. Comput. Neurosci. 39, 181–195 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  39. Wang, C., Xiao, Z., Wang, Z., Sornborger, A.T., Tao, L.: A fokker-planck approach to graded information propagation in pulse-gated feedforward neuronal networks. (2015) arXiv preprint arXiv:1512.00520

  40. Wang, Z., Sornborger, A.T., Tao, L.: Graded, dynamically routable information processing with synfire-gated synfire chains. PLoS Comput. Biol. 12(6) (2016)

  41. Shao, Y., Sornborger, A.T., Tao, L.: A pulse-gated, predictive neural circuit. In: 2016 50th Asilomar Conference on Signals, Systems and Computers, pp. 1051–1055 (2016)

  42. Xiao, Z., Zhang, J., Sornborger, A.T., Tao, L.: Cusps enable line attractors for neural computation. Phys. Rev. E 96(5–1), 052308 (2017)

    Article  MathSciNet  Google Scholar 

  43. Xiao, Z., Wang, B., Sornborger, A.T., Tao, L.: Mutual information and information gating in synfire chains. Entropy 20, 102 (2018)

    Article  Google Scholar 

  44. Vogel, A., Ronacher, B.: Neural correlations increase between consecutive processing levels in the auditory system of locusts. J. Neurophysiol. 97(5), 3376–85 (2007)

    Article  Google Scholar 

  45. Kimpo, R.R., Theunissen, F.E., Doupe, A.J.: Propagation of correlated activity through multiple stages of a neural circuit. J. Neurosci. 23(13), 5750–61 (2003)

    Article  Google Scholar 

  46. Long, M., Jin, D., Fee, M.: Support for a synaptic chain model of neuronal sequence generation. Nature 468, 394–9 (2010)

    Article  Google Scholar 

  47. Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D., Yuste, R.: Synfire chains and cortical songs: temporal modules of cortical activity. Science 304(5670), 559–564 (2004)

    Article  Google Scholar 

  48. Nowotny, T., Huerta, R.: Explaining synchrony in feed-forward networks. Biol. Cybern. 89, 237–241 (2003)

    Article  MATH  Google Scholar 

  49. Segev, I.: Synchrony is stubborn in feedforward cortical networks. Nat. Neurosci. 6(6), 543–544 (2003)

    Article  Google Scholar 

  50. Li, J., Liu, F., Xu, D., Wang, W.: Signal propagation through feedforward neuronal networks with different operational modes. EPL (Europhys. Lett.) 85(3), 38006 (2009)

    Article  Google Scholar 

  51. Mehring, C., Hehl, U., Kubo, M., Diesmann, M., Aertsen, A.: Activity dynamics and propagation of synchronous spiking in locally connected random networks. Biol. Cybern. 88, 395–408 (2003)

    Article  MATH  Google Scholar 

  52. Vogels, T.P., Abbott, L.F.: Signal propagation and logic gating in networks of integrate-and-fire neurons. J. Neurosci. 25(46), 10786–10795 (2005)

    Article  Google Scholar 

  53. Kumar, A., Schrader, S., Aertsen, A., Rotter, S.: The high-conductance state of cortical networks. Neural Comput. 20, 1–43 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  54. Jahnke, S., Memmesheimer, R.M., Timme, M.: Propagating synchrony in feed-forward networks. Front. Comput. Neurosci. 7, 153 (2013)

    Article  Google Scholar 

  55. Jeanne, J.M., Wilson, R.I.: Convergence, divergence, and reconvergence in a feedforward network improves neural speed and accuracy. Neuron 88, 1014–1026 (2015)

    Article  Google Scholar 

  56. Salinas, E., Sejnowski, T.J.: Correlated neuronal activity and the flow of neural information. Nat. Rev. Neurosci. 2, 539–550 (2001)

    Article  Google Scholar 

  57. Brunel, N.: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci. 8(3), 183–208 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  58. Teramae, J., Fukai, T.: Local cortical circuit model inferred from power-law distributed neuronal avalanches. J. Comput. Neurosci. 22(3), 301–312 (2007)

    Article  MathSciNet  Google Scholar 

  59. Wang, S., Zhou, C.: Information encoding in an oscillatory network. Phys. Rev. E 79, 061910 (2009)

    Article  MathSciNet  Google Scholar 

  60. Guo, D., Li, C.: Population rate coding in recurrent neuronal networks with unreliable synapses. Cogn. Neurodyn. 6(1), 75–87 (2012)

    Article  Google Scholar 

  61. Han, R., Wang, J., Yu, H., Deng, B., Wei, X., Qin, Y., Wang, H.: Intrinsic excitability state of local neuronal population modulates signal propagation in feed-forward neural networks. Interdiscipl. J. Nonlinear Sci. 25(4), 043108 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  62. Chenkov, N., Sprekeler, H., Kempter, R.: Memory replay in balanced recurrent networks. PLoS Comput. Biol. 13, e1005359 (2017)

    Article  Google Scholar 

  63. Eccles, J.C., Fatt, P., Koketsu, K.: Cholinergic and inhibitory synapses in a pathway from motor-axon collaterals to motoneurones. J. Physiol. 126(3), 524–562 (1954)

    Article  Google Scholar 

  64. Root, D.H., Mejias-Aponte, C.A., Zhang, S., Wang, H.L., Hoffman, A.F., Lupica, C.R., Morales, M.: Single rodent mesohabenular axons release glutamate and gaba. Nat. Neurosci. 17(11), 1543–1551 (2014)

    Article  Google Scholar 

  65. Uchida, N.: Bilingual neurons release glutamate and gaba. Nat. Neurosci. 17, 1432–4 (2014)

    Article  Google Scholar 

  66. Shrivastava, A., Triller, A., Sieghart, W.: Gabaa receptors: post-synaptic co-localization and cross-talk with other receptors. Front. Cell. Neurosci. 5, 7 (2011)

    Article  Google Scholar 

  67. Kantamneni, S.: Cross-talk and regulation between glutamate and gabab receptors. Front. Cell. Neurosci. 9, 135 (2015)

    Article  Google Scholar 

  68. Zhang, S., Qi, J., Li, X., Wang, N., Britt, J., Hoffman, A.A., Bonci, A., Lupica, C., Morales, M.: Dopaminergic and glutamatergic microdomains in a subset of rodent mesoaccumbens axons. Nat. Neurosci. 18, 386–392 (2015)

    Article  Google Scholar 

  69. Saunders, A., Granger, A.J., Sabatini, B.L.: Corelease of acetylcholine and gaba from cholinergic forebrain neurons. eLife 4 (2015)

  70. Tritsch, N., Granger, A., Sabatini, B.: Mechanisms and functions of gaba co-release. Nat. Rev. Neurosci. 17, 139–145 (2016)

    Article  Google Scholar 

  71. Granger, A., Mulder, N., Saunders, A., Sabatini, B.: Cotransmission of acetylcholine and gaba. Neuropharmacology 100, 40–46 (2015)

    Article  Google Scholar 

  72. Zhu, H., Zou, G., Wang, N., Zhuang, M., Xiong, W., Huang, G.: Single-neuron identification of chemical constituents, physiological changes, and metabolism using mass spectrometry. Proc. Nat. Acad. Sci. 114(10), 2586–2591 (2017)

    Article  Google Scholar 

  73. Trudeau, L.E., Hnasko, T.S., Wallén-Mackenzie, Å., Morales, M., Rayport, S., Sulzer, D.: The multilingual nature of dopamine neurons. In: Diana, M., Chiara, G.D., Spano, P. (Eds.) Dopamine, Progress in Brain Research, vol. 211. Elsevier, Amsterdam, pp. 141–164 (2014)

  74. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117(4), 500–544 (1952)

    Article  Google Scholar 

  75. Hansel, D., Mato, G., Meunier, C.: Phase dynamics for weakly coupled hodgkin–huxley neurons. EPL (Europhys. Lett.) 23(5), 367 (1993)

    Article  Google Scholar 

  76. Vogels, T., Abbott, L.: Gating multiple signals through detailed balance of excitation and inhibition in spiking networks. Nat. Neurosci. 12, 483–91 (2009)

    Article  Google Scholar 

  77. Liu, Y., Li, C.: Firing rate propagation through neuronal-astrocytic network. IEEE Trans. Neural Netw. Learn. Syst. 24(5), 789–799 (2013)

    Article  Google Scholar 

  78. Wang, X.J., Buzsáki, G.: Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci. 16(20), 6402–6413 (1996)

    Article  Google Scholar 

  79. Li, H., Sun, X., Xiao, J.: Degree of synchronization modulated by inhibitory neurons in clustered excitatory–inhibitory recurrent networks. EPL 121, 10003 (2018)

    Article  Google Scholar 

  80. Yang, G., Murray, J., Wang, X.J.: A dendritic disinhibitory circuit mechanism for pathway-specific gating. Nat. Commun. 7, 12815 (2016)

    Article  Google Scholar 

  81. Wang, X.J., Yang, G.: A disinhibitory circuit motif and flexible information routing in the brain. Curr. Opin. Neurobiol. 49, 75–83 (2018)

    Article  Google Scholar 

  82. Si, H., Sun, X.: Population rate coding in recurrent neuronal networks consisting of neurons with mixed excitatory–inhibitory synapses. Nonlinear Dyn. 100, 2673–2686 (2019)

    Google Scholar 

  83. König, P., Engel, A.K., Singer, W.: Integrator or coincidence detector? The role of the cortical neuron revisited. Trends Neurosci. 19(4), 130–137 (1996)

    Article  Google Scholar 

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

    Article  Google Scholar 

  85. Thorpe, S.J., Delorme, A., van Rullen, R.: Spike-based strategies for rapid processing. Neural Netw. 14(6–7), 715–25 (2001)

    Article  Google Scholar 

  86. 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)

    Article  MATH  Google Scholar 

  87. Gollisch, T., Meister, M.: Rapid neural coding in the retina with relative spike latencies. Science 319(5866), 1108–1111 (2008)

    Article  Google Scholar 

  88. Olshausen, B.A., Field, D.J.: Sparse coding of sensory inputs. Curr. Opin. Neurobiol. 14(4), 481–7 (2004)

    Article  Google Scholar 

  89. Fries, P.: Neuronal gamma-band synchronization as a fundamental process in cortical computation. Annu. Rev. Neurosci. 32, 209–24 (2009)

    Article  Google Scholar 

  90. Fries, P.: Rhythms for cognition: communication through coherence. Neuron 88, 220–235 (2015)

    Article  Google Scholar 

  91. Hahn, G., Bujan, A., Fr égnac, Y., Aertsen, A., Kumar, A.: Communication through resonance in spiking neuronal networks. PLoS Comput. Biol. 10, e1003811 (2014)

    Article  Google Scholar 

  92. Guo, D., Li, C.: Stochastic and coherence resonance in feed-forward-loop neuronal network motifs. Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 79(5 Pt 1), 051921 (2009)

    Article  Google Scholar 

  93. Wang, Q., Zhang, H., Chen, G.: Effect of the heterogeneous neuron and information transmission delay on stochastic resonance of neuronal networks. Chaos 22(4), 043123 (2012)

    Article  MathSciNet  Google Scholar 

  94. Zhao, J., Qin, Y., Che, Y., Ran, H., Li, J.: Effects of network topologies on stochastic resonance in feedforward neural network. Cogn. Neurodyn. 14 (2020)

  95. Di Maio, V., Santillo, S., Ventriglia, F.: Synaptic dendritic activity modulates the single synaptic event. Cogn. Neurodyn. (2020)

  96. Wu, S., Zhou, K., Ai, Y., Zhou, G., Yao, D., Guo, D.: Induction and propagation of transient synchronous activity in neural networks endowed with short-term plasticity. Cogn. Neurodyn. (2020)

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Acknowledgements

We thank all of the reviewers for their careful reading and creative questions and suggestions. We thank the editor’s suggestions on the figures. We thank Mr. Wenbin Liang for his effort to check and improve our English grammar and spelling.

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12072046 and 11772069) and the Fundamental Research Funds for the Central University (Nos. 2018XKJC02 and 2019XD-A10).

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  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, People’s Republic of China

    Hao Si & Xiaojuan Sun

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Si, H., Sun, X. Information propagation in recurrent neuronal populations with mixed excitatory–inhibitory synaptic connections. Nonlinear Dyn 104, 557–576 (2021). https://doi.org/10.1007/s11071-020-06192-3

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