Modeling the Impulse Transmission through a System of Two Synapses
DOI:
https://doi.org/10.15407/ujpe71.3.236Keywords:
impulse, synapse, mediator, membrane, receptor, activationAbstract
A model describing the process of nerve signal transmission through a system consisting of two interacting synapses has been proposed. The model is based on nonlinear differential equations that describe the activation of receptors on the postsynaptic membranes of two synaptic clefts. The interaction between the synapses is implemented in such a way that the activation of receptors on the first postsynaptic membrane determines the intensity of mediator injection into the second synapse. The peculiarities of the stationary state of this system have been studied, and the stability of this state has been shown. The influence of the intensity of mediator injection into the first synapse of the system on the concentration of activated receptors in the second synapse has also been analyzed. It has been demonstrated that the reliability of the entire system is not violated at a qualitative level, and the character of the receptor activation process on the postsynaptic membrane of the second synapse remains stable with respect to variations in the input signal.
References
1. Z.M. Bacq. Chemical Transmission of Nerve Impulses: A Historical Sketch (Pergamon, 1975).
https://doi.org/10.1016/B978-0-08-020512-0.50009-9
2. H.W. Davenport. Early history of the concept of chemical transmission of the nerve impulse. Physiologist 34, 129 (1991).
3. M.R. Bennett. History of the Synapse (Harwood Academic Publishers, 2001).
https://doi.org/10.1201/9781482284171
4. T.C. S¨udhof, R.C. Malenka. Understanding synapses: Past, present, and future. Neuron 60, 469 (2008).
https://doi.org/10.1016/j.neuron.2008.10.011
5. B. Wang, O.K. Dudko. A theory of synaptic transmission. eLife 10, e73585 (2021).
https://doi.org/10.7554/eLife.73585
6. A.L. Hodgkin, A.F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 4, 500 (1952).
https://doi.org/10.1113/jphysiol.1952.sp004764
7. J.C. Eccles. The Physiology of Synapses (Springer-Verlag, 1964).
https://doi.org/10.1007/978-3-642-64950-9
8. B. Katz, R. Miledi. The measurement of synaptic delay, and the time course of acetylcholine release at the neuromuscular junction. Proc. Roy. Soc. London B 161, 483 (1965).
https://doi.org/10.1098/rspb.1965.0016
9. R.W. Holz, S.K. Fisher. Synaptic transmission and cellular signaling: an overview. InBasic Neurochemistry (Elsevier, 2012).
https://doi.org/10.1016/B978-0-12-374947-5.00012-2
10. E.R. Kandel, J.D. Koester, S.H. Mack, S.A. Siegelbaum. Principles of Neural Science (McGraw-Hill, 2021).
11. A.V. Chalyi, L.M. Chernenko. Phase transition in finitesize systems and synaptic transmission. In: Dynamical Phenomena at Interfaces, Surfaces and Membranes (Nowa Science Publishers, 1993), p. 457.
12. A.V. Chalyi. Synergetic dialogue "physics-medicine": Hexagones in living and inanimate nature. J. Mol. Liq. 320, 114293 (2020).
https://doi.org/10.1016/j.molliq.2020.114293
13. A.V. Chalyi. What is Medicine?: Basic Principles of Physics in Medicine and Beyond (Springer Nature, 2025).
https://doi.org/10.1007/978-3-031-64979-0
14. O.V. Chalyi, O.V. Zaitseva. A kinetic model of synaptic transmission on intercell interaction. Ukr. J. Phys. 54, 366 (2009).
15. A.V. Chalyi, E.V. Zaitseva. Strange attractor in kinetic model of synaptic transmission. J. Phys. Stud. 11, 322 (2007).
https://doi.org/10.30970/jps.11.322
16. A.V. Chalyi, K.A. Chaliy, L.M. Chernenko, A.N. Vasil'ev. Critical phenomena in finite-size binary liquid mixtures with reduced geometry. J. Mol. Liq. 93, 1 (2001).
https://doi.org/10.1016/S0167-7322(01)00219-7
17. A.V. Chalyi, A.N. Vasilev, E.V. Zaitseva. Synaptic transmission as a cooperative phenomenon in confined systems. Condens. Matter Phys. 20, 13804 (2017).
https://doi.org/10.5488/CMP.20.13804
18. A.N. Vasilev, A.V. Chalyi. Cooperative operation mode of a synaptic channel. Ukr. J. Phys. 54, 1183 (2009).
19. O.M. Vasyliev, O.V. Zaitseva, O.V. Chalyi. Analysis of the synaptic signal transmission based on a kinetic model. Ukr. J. Phys. 69, 37 (2024).
https://doi.org/10.15407/ujpe69.1.37
20. S.I. Braichenko, A.N. Vasilev. Modeling of postsynaptic membrane activation. J. Phys. Stud. 16, 4802 (2012).
https://doi.org/10.30970/jps.16.4802
21. A.N. Vasilev, O.V. Kulish. Model of postsynaptic membrane deactivation. Ukr. J. Phys. 63, 919 (2018).
https://doi.org/10.15407/ujpe63.10.919
22. O.V. Kulish, A.N. Vasilev. Modeling the nerve impuls transmission in a synaptic cleft. J. Phys. Stud. 23, 1 (2019).
https://doi.org/10.30970/jps.23.1801
23. J. Trommershauser, R. Schneggenburger, A. Zippelius, E. Nehery. Heterogeneous presynaptic release probabilities: functional relevance for short-term plasticity. Biophys. J. 84, 1563 (2003).
https://doi.org/10.1016/S0006-3495(03)74967-4
24. S.O. Rizzoli, W.J. Betz. Synaptic vesicle pools. Nature Rev. Neurosci. 6, 57 (2005).
https://doi.org/10.1038/nrn1583
25. J. Lichtenberger, P. Fromherz. A cell-semiconductor synapse: transistor recording of vesicle release in chromaffin cells. Biophys. J. 92, 2266 (2007).
https://doi.org/10.1529/biophysj.106.096446
26. K. Zheng, A. Scimemi, D.A. Rusakov. Receptor actions of synaptically released glutamate: The role of transporters on the scale from nanometers to microns. Biophys. J. 95, 4584 (2008).
https://doi.org/10.1529/biophysj.108.129874
27. E. Neher. What is rate-limiting during sustained synaptic activity: Vesicle supply or the availability of release sites? Front. Synap. Neurosci. 2, 144 (2010).
https://doi.org/10.3389/fnsyn.2010.00144
28. A.N. Vasilev, S.V. Kislyak. Double-pool kinetic model of synapse activation. J. Phys. Stud. 14, 4801 (2010).
https://doi.org/10.30970/jps.14.4801
29. P.S. Kaeser, W.G. Regehr. Molecular mechanisms for synchronous, asynchronous, and spontaneous neurotransmitter release. Annu. Rev. Physiol. 76, 333 (2014).
https://doi.org/10.1146/annurev-physiol-021113-170338
30. D.H. Kweon, B. Kong, Y.K. Shin. Hemifusion in synaptic vesicle cycle. Front. Mol. Neurosci. 10, 65 (2017).
https://doi.org/10.3389/fnmol.2017.00065
31. M.V. Gramlich, V.A. Klyachko. Nanoscale organization of vesicle release at central synapses. Trends Neurosci. 42, 425 (2019).
https://doi.org/10.1016/j.tins.2019.03.001
32. A.N. Vasilev, O.M. Khvyl. A pool model of the mediator exocytosis into the synapse. Ukr. J. Phys. 64, 822 (2019).
https://doi.org/10.15407/ujpe64.9.829
33. A.K. Vidybida. Fast cl-type inhibitory neuron with delayed feedback has non-markov output statistics. J. Phys. Stud. 22, 4801 (2018).
https://doi.org/10.30970/jps.22.4801
34. A.K. Vidybida, O.V. Shchur. Relation between firing statistics of spiking neuron with delayed fast inhibitory feedback and without feedback. Fluct. Noise Lett. 17, 1850005 (2018).
https://doi.org/10.1142/S0219477518500050
35. A. Vidybida, O. Shchur. First passage time distribution for spiking neuron with delayed excitatory feedback. Fluct. Noise Lett. 19, 01 (2020).
https://doi.org/10.1142/S0219477520500054
36. A. Vidybida, O. Shchur. Moment-generating function of output stream of leaky integrate-and-fire neuron. Ukr. J. Phys. 66, 254 (2021).
https://doi.org/10.15407/ujpe66.3.254
37. O.V. Shchur, A.K. Vidybida. Distribution of interspike intervals of a neuron with inhibitory autapse stimulated with a renewal process. Fluct. Noise Lett. 22, 2350003 (2023).
https://doi.org/10.1142/S0219477523500037
38. O.M. Vasyliev. A model of the synaptic channel with a feedback. J. Phys. Stud. 29, 4801 (2025).
https://doi.org/10.30970/jps.29.4801
39. A.V. Chalyi, A.N. Vasil'ev. Correlation properties, critical parameters and critical light scattering in finite-size systems. J. Mol. Liq. 84, 2 (2000).
https://doi.org/10.1016/S0167-7322(99)00187-7
40. D.A. Gavryushenko, K.V. Cherevko, V.M. Sysoev. The influence of the chemical reactions on the diffusion phenomena in the cylindrical systems bounded with the membranes. J. Mol. Liq. 127, 71 (2006).
https://doi.org/10.1016/j.molliq.2006.03.018
41. K.V. Cherevko, L.A. Bulavin, V.M. Sysoev. Thermodynamic analysis of multifragmentation phenomena. Phys. Rev. C 84, 044603 (2011).
https://doi.org/10.1103/PhysRevC.84.044603
42. K.V. Cherevko, D.A. Gavryushenko, O.V. Korobko, V.M. Sysoev. Entropy production in the diffusion of a Margules solution in a flat-parallel pore. Ukr. J. Phys. 58, 10 (2013).
https://doi.org/10.15407/ujpe58.10.0988
43. L.A. Bulavin, K.V. Cherevko, D.A. Gavryushenko, V.M. Sysoev, T.S. Vlasenko. Radiation influence on the temperature-dependent parameters of fluids. Phys. Rev. E 93, 032133 (2016).
https://doi.org/10.1103/PhysRevE.93.032133
44. K.V. Cherevko, D.A. Gavryushenko, L.A. Bulavin. Entropy production in a model biological system with facilitated diffusion. Ukr. J. Phys. 66, 8 (2021).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.










