Discrete Modeling of Multi-transmitter Neural Networks with Neuronal Competition

  • Nikolay BazenkovEmail author
  • Varvara Dyakonova
  • Oleg Kuznetsov
  • Dmitri Sakharov
  • Dmitry Vorontsov
  • Liudmila Zhilyakova
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 636)


We propose a novel discrete model of central pattern generators (CPG), neuronal ensembles generating rhythmic activity. The model emphasizes the role of nonsynaptic interactions and the diversity of electrical properties in nervous systems. Neurons in the model release different neurotransmitters into the shared extracellular space (ECS) so each neuron with the appropriate set of receptors can receive signals from other neurons. We consider neurons, differing in their electrical activity, represented as finite-state machines functioning in discrete time steps. Discrete modeling is aimed to provide a computationally tractable and compact explanation of rhythmic pattern generation in nervous systems. The important feature of the model is the introduced mechanism of neuronal competition which is shown to be responsible for the generation of proper rhythms. The model is illustrated with an example of the well-studied feeding network of a pond snail. Future research will focus on the neuromodulatory effects ubiquitous in CPG networks and the whole nervous systems.


Discrete dynamics Multitransmitter neuronal system Neurotransmitters Neuromodulation Central Pattern Generator 


  1. 1.
    Bazenkov, N., Dyakonova, V., Kuznetsov, O., Sakharov, D., Vorontsov, D., Zhilyakova, L.: Discrete Modeling of Multi-Transmitter Neural Networks with Neuron Competition (2017). Scholar
  2. 2.
    Bargmann, C.: Beyond the connectome: how neuromodulators shape neural circuits. BioEssays 34(6), 458–465 (2012)CrossRefGoogle Scholar
  3. 3.
    Baronchelli, A., Ferrer-i-Cancho, R., Pastor-Satorras, R., Chater, N., Christiansen, M.: Networks in cognitive science. Trends Cogn. Sci. 17(7), 348–360 (2013)CrossRefGoogle Scholar
  4. 4.
    Dyakonova, V.: Neurotransmitter mechanisms of context-dependent behavior. Zh. Vyssh. Nerv. Deyat. 62(6), 1–17 (2012)Google Scholar
  5. 5.
    Ghigliazza, R., Holmes, P.: A minimal model of a central pattern generator and motoneurons for insect locomotion. SIAM J. Appl. Dyn. Syst. 3(4), 671–700 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Haykin, S.: Neural Networks and Learning Machines, 3rd edn. Prentice-Hall, Upper Saddle River (2009)Google Scholar
  7. 7.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its applications to conduction and excitation in nerve. J. Physiol. 116, 500–544 (1952)CrossRefGoogle Scholar
  8. 8.
    Kuznetsov, O.: Complex networks and activity spreading. Autom. Remote Control 76(12), 2091–2109 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Marder, E., Goeritz, M., Otopalik, A.: Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms. Curr. Opin. Neurobiol. 31, 156–163 (2015)CrossRefGoogle Scholar
  10. 10.
    McCulloch, W., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133 (1943)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Moroz, L., Kohn, A.: Independent origins of neurons and synapses: insights from ctenophores. Phil. Trans. R. Soc. Lond. B. Biol. Sci. 371(1685), 1–14 (2016)CrossRefGoogle Scholar
  12. 12.
    Roberts, P.: Classification of Temporal Patterns in Dynamic Biological Networks. Neural Comput. 10(7), 1831–1846 (1998)CrossRefGoogle Scholar
  13. 13.
    Sakharov, D.: The multiplicity of neurotransmitters: the functional significance. Zh. Evol. Biokhim. Fiziol. 26(5), 733–741 (1990)Google Scholar
  14. 14.
    Sterratt, D., Graham, B., Gillies, A., Willshaw, D.S.: Principles of Computational Modelling in Neuroscience. Cambridge University Press, Cambridge (2011)CrossRefGoogle Scholar
  15. 15.
    Vavoulis, D., Straub, V., Kemenes, I., Kemenes, G., Feng, J., Benjamin, P.: Dynamic control of a central pattern generator circuit: a computational model of the snail feeding network. Eur. J. Neurosci. 25, 2805–2818 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Nikolay Bazenkov
    • 1
    Email author
  • Varvara Dyakonova
    • 2
  • Oleg Kuznetsov
    • 1
  • Dmitri Sakharov
    • 2
  • Dmitry Vorontsov
    • 2
  • Liudmila Zhilyakova
    • 1
  1. 1.Trapeznikov Institute of Control Sciences of RASMoscowRussian Federation
  2. 2.Koltzov Institute of Developmental Biology of RASMoscowRussian Federation

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