Three-Dimensional Model of Signal Processing in the Presynaptic Bouton of the Neuron

  • Andrzej Bielecki
  • Maciej GierdziewiczEmail author
  • Piotr Kalita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10841)


In this paper the model of a signal transmission in a synapse of the neuron is studied. The model is based on partial differential equations. The three-dimensional simulations based on the model are presented and discussed in details. The simulations enabled to estimate the value of the coefficient of diffusion transmission of neurotransmitters in the presynaptic bouton.


Presynaptic bouton Neurotransmitters Differential diffusive model Numerical three-dimensional simulations 


  1. 1.
    Aristizabal, F., Glavinovic, M.I.: Simulation and parameter estimation of dynamics of synaptic depression. Biol. Cybern. 90, 3–18 (2004)zbMATHCrossRefGoogle Scholar
  2. 2.
    Bielecki, A.: A model of human activity automatization as a basis of artificial intelligence systems. IEEE Trans. Auton. Ment. Dev. 6, 169–182 (2014)CrossRefGoogle Scholar
  3. 3.
    Bielecki, A., Bielecka, M., Bielecki, P.: Conditioned anxiety mechanism as a basis for a procedure of control module of an autonomous robot. Lect. Notes Artif. Intell. 10246, 390–398 (2017)Google Scholar
  4. 4.
    Bielecki, A., Kalita, P.: Model of neurotransmitter fast transport in axon terminal of presynaptic neuron. J. Math. Biol. 56, 559–576 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bielecki, A., Kalita, P.: Dynamical properties of the reaction-diffusion type model of fast synaptic transport. J. Math. Anal. Appl. 393, 329–340 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bielecki, A., Kalita, P., Lewandowski, M., Siwek, B.: Numerical simulation for a neurotransmitter transport model in the axon terminal of a presynaptic neuron. Biol. Cybern. 102, 489–502 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Bielecki, A., Kalita, P., Lewandowski, M., Skomorowski, M.: Compartment model of neuropeptide synaptic transport with impulse control. Biol. Cybern. 99, 443–458 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Bui, L., Glavinovic, M.: Temperature dependence of vesicular dynamics at excitatory synapses of rat hippocampus. Cogn. Neurodyn. 8, 277–286 (2014)CrossRefGoogle Scholar
  9. 9.
    Denker, A., Rizzoli, S.O.: Synaptic vesicle pools: an update. Front. Synaptic Neurosci. 2, 135 (2010)Google Scholar
  10. 10.
    Joensuu, M., Padmanabhan, P., Durisic, N., Adekunle, T.D., Bademosi Cooper-Williams, E., Morrow, I.C., Harper, C.B., Jung, W., Parton, R.G., Goodhill, G.J., Papadopulos, A., Meunier, F.A.: Subdiffractional tracking of internalized molecules reveals heterogeneous motion states of synaptic vesicles. J. Cell Biol. 215, 277–292 (2016)CrossRefGoogle Scholar
  11. 11.
    Knödel, M.M., Geiger, R., Ge, L., Bucher, D., Grillo, A., Wittum, G., Schuster, C., Queisser, G.: Synaptic bouton properties are tuned to best fit the prevailing firing pattern. Front. Comput. Neurosci. 8, 101 (2014)CrossRefGoogle Scholar
  12. 12.
    Rizzoli, S.O., Betz, W.J.: Synaptic vesicle pools. Nat. Rev. Neurosci. 6, 57–60 (2005)CrossRefGoogle Scholar
  13. 13.
    Tadeusiewicz, R.: New trends in neurocybernetics. Comput. Methods Mater. Sci. 10, 1–7 (2010)Google Scholar
  14. 14.
    von Gersdorff, H., Matthews, G.: Inhibition of endocytosis by elevated internal calcium in a synaptic terminal. Nature 370, 652–655 (1994)CrossRefGoogle Scholar
  15. 15.
    Wang, Y., Manis, P.B.: Short-term synaptic depression and recovery at the mature mammalian endbulb of held synapse in mice. J. Neurophysiol. 100(3), 1255–1264 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Andrzej Bielecki
    • 1
  • Maciej Gierdziewicz
    • 1
    Email author
  • Piotr Kalita
    • 2
  1. 1.Chair of Applied Computer Science, Faculty of Automation, Electrical Engineering, Computer Science and Biomedical EngineeringAGH University of Science and TechnologyKrakówPoland
  2. 2.Chair of Computer Mathematics, Institute of Computer Science and Computational Mathematics, Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland

Personalised recommendations