ISSN 2071-8594

Russian academy of sciences

Editor-in-Chief

Gennady Osipov

O. Kuznetsov, N. Bazenkov, B.Boldyshev, I.Chistopolsky, S. Kulivets, L. Zhilyakova Asynchronous discrete model of chemical interactions in simple neuronal systems

Abstract.

An asynchronous discrete model of nonsynaptic chemical interactions between neurons is proposed. The model significantly extends the previous work [1, 2] by novel concepts that make it more biologically plausible. In the model, neurons interact by emitting neurotransmitters to the shared extracellular space (ECS). We introduce dynamics of membrane potentials that comprises two factors: the endogenous rates of change depending on the neuron’s firing type and the exogenous rate of change, depending on the concentrations of neurotransmitters that the neuron is sensitive to. The neuron’s firing type is determined by the individual composition of endogenous rates. We consider three basic firing types: oscillatory, tonic and reactive. Each of them is essential for modeling central pattern generators – neural ensembles generating rhythmic activity in the absence of external stimuli. Differences in endogenous rates of different neurons leads to asynchronous neural interactions and significant variability of phase durations in the activity patterns present in simple neural systems. The algorithm computing the behavior of the proposed model is provided.

Keywords:

asynchronous discrete model, heterogeneous neuronal system, extracellular space, nonsynaptic interactions, neurotransmitters.

PP. 3-20.

References

1. Bazenkov N., Vorontsov D., Dyakonova V., Zhilyakova L., Zakharov I., Kuznetsov O., Kulivets S., Sakharov D. 2017. Diskretnoe modelirovanie mezhneironnyh vzaimodeistvii v multitransmitternih setyah [Discrete modeling of neuronal interactions in multi-neurotransmitter networks]. Iskusstvenny Intellekt i Prinyatie Reshenii [Artificial Intelligence and Decision Making], 2: 55–73.
2. Bazenkov N., Dyakonova V., Kuznetsov O., Sakharov D., Vorontsov D., and Zhilyakova L. Discrete Modeling of Multitransmitter Neural Networks with Neuronal Competition. Springer International Publishing AG. 2018. Biologically Inspired Cognitive Architectures (BICA) for Young Scientists, Advances in Intelligent Systems and Computing V.636. P. 10 – 16.
3. McCulloch W.S., Pitts W. 1943. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys., v.5, pp.115-133
4. Hopfield J.J. 1982. Neural networks and physical systems with emergent collective computational abilities, Proceedings of National Academy of Sciences, vol. 79 no. 8.
5. Haykin S. 2009. Neural Networks and Learning Machines (3rd Edition), Prentice Hall.
6. LeCun, Y., Bengio, Y., Hinton. 2015.G. Deep learning. Nature 521 (7553). P. 436–444.
7. Goodfellow, I., Bengio,Y., and Courville, A. 2016. Deep Learning. MIT Press. 787 p.
8. Deng, L.; Yu, D. 2014. Deep Learning: Methods and Applications. Foundations and Trends in Signal Processing. 7 (3-4): 1–199.
9. Bengio, Y., Lamblin, P., Popovici, P., Larochelle, H. 2007. Greedy Layer-Wise Training of Deep Networks, Advances in Neural Information Processing Systems 19, MIT Press, Cambridge, MA.
10. Hinton, G.E., Osindero, S., and Teh, Y.W. 2006. A fast learning algorithm for deep belief nets. Neural Computation, 18:1527-1554.
11. Shumsky S.A. 2017. Glubokoe obuchenie. 10 let spustya [Deep Learning. 10 years later]. XIX mezhdunarodnaya nauchnotekhnicheskaya konferencia “Neiroinformatika-2017”: Lekcii po neiroinformatike. P. 98-131.
12. Abbott, L.F. 1999. Lapique’s introduction of the integrate-and-fire model neuron (1907). Brain Research Bulletin 50 (5/6): 303–304.
13. Hodgkin, A. L. and Huxley, A. F. 1952. A quantitative description of membrane current and its applications to conduction and excitation in nerve. J. Physiol. (Lond.), 116. P. 500–544.
14. FitzHugh R. 1969. Mathematical models of excitation and propagation in nerve. Chapter 1 (pp. 1–85 in H.P. Schwan, ed. Biological Engineering, McGraw–Hill Book Co., N.Y.)
15. Nagumo J., Arimoto S., and Yoshizawa S. 1962. An active pulse transmission line simulating nerve axon. Proc. IRE. 50:2061–2070.
16. Morris, C., Lecar, H., 1981. Voltage Oscillations in the barnacle giant muscle fiber, Biophys. J., 35 (1): 193–213.
17. Vavoulis D., Straub V., Kemenes I., Kemenes G., Feng J., Benjamin P. 2007. Dynamic control of a central pattern generator circuit: a computational model of the snail feeding network. European Journal of Neuroscience, Vol. 25, pp. 2805–2818, 2007.
18. Izhikevich E. 2000. International Journal of Bifurcation and Chaos, Vol. 10, No. 6, 1171–1266.
19. Izhikevich E. 2004. Which Model to Use for Cortical Spiking Neurons? IEEE Transactions on Neural Networks, Vol. 15, No. 5.
20. Brunel N. 2000. Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons. Journal of Computational Neuroscience, Vol. 8, No. 3, P.183–208. https://doi.org/10.1023/A:1008925309027
21. Ladenbauer J., Augustin M., Shiau L., Obermayer K. 2012. Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons. PLoS Computational Biology, Vol. 8, No. 4, e1002478, https://doi.org/10.1371/journal.pcbi.1002478
22. Delahunt C.B., Riffell J.A., Kutz J.N. 2018 Biological Mechanisms for Learning: A Computational Model of Olfactory Learning in the Manduca sexta Moth, with Applications to Neural Nets. ArXiv.org: 1802.02678. URL:
https://arxiv.org/abs/1802.02678 (по состоянию на 10.04.2018)
23. Balaban P.M., Vorontsov D.D., D'yakonova V.Ye., D'yakonova T.L., Zakharov I.S., Korshunova T.A., Orlov O.YU., Pavlova G.A., Panchin YU.V., Sakharov D.A., Falikman M.V. 2013. Tsentral'nyye generatory patterna (CPGs). Zhurn. vyssh. nerv. deyat. 63(5):1-21.
24. Mulloney B., Smarandache C. 2010. Fifty years of CPGs: two neuroethological papers that shaped the course of neuroscience. Front. Behav. Neurosci. V. 4. № 45. P. 1-8.
25. Harris-Warrick R.M., Marder E., Selverston A.I., Moulins M. (eds). 1992. Dynamic Biological Networks: The Stomatogastric Nervous System. Cambridge, MA: MIT Press.
26. Vizi E.S., Kiss J.P., Lendvai B. 2004. Nonsynaptic communication in the central nervous system. Review. Neurochem. Int. 45:443-451.
27. De-Miguel F.F., Trueta C. 2005. Synaptic and extrasynaptic secretion of serotonin. Cell Mol Neurobiol 25:297-312.
28. Sem'yanov A.V. 2005. Diffusional extrasynaptic neurotransmission via glutamate and GABA. Neurosci Behav Physiol 35:253-266.
29. Dyakonova T.L. and Dyakonova V.E. 2010. Coordination of rhythm-generating units via NO and extrasynaptic neurotransmitter release. J. Comp. Physiol. A 196(8):529-541.
30. Bargmann C.I. 2012. Beyond the connectome: How neuromodulators shape neural circuits. BioEssays 34(6):458–465.
31. Artemov N.M. and Sakharov D.A. 1986. Khachatur Sedrakovich Koshtoyants. M. Nauka. Chapter 3. Raboty po khimicheskim osnovam mekhanizmov nervnoy deyatelnosti. P. 106-162.
32. Brezina V. 2010. Beyond the wiring diagram: signalling through complex neuromodulator networks.
Philos. Trans. R. Soc. Lond. B. Biol. Sci. 12; 365(1551):2363-2374.
33. Sakharov D.A. 2012. Biologicheskiy substrat generatsii povedencheskikh aktov. Zhurn. obshch. biologii. 73(5):334-348.
34. Agnati L.F., Guidolin D., Guescini M., Genedani S., Fuxe K. 2010. Understanding wiring and volume transmission. Brain Res. Rev. 64:137-159.
35. Dyakonova V.Ye. 2012. Neyrotransmitternyye mekhanizmy kontekst-zavisimogo povedeniya. Zhurn. vyssh. nerv. deyat. 62(6):1–17.
36. Marder E. and Bucher D. Central pattern generators and the control of rhythmic movements. Curr. Biol., vol. 11, no. 23, p. R986–996, 2001.
37. Amari S.I. Learning patterns and pattern sequences by self-organizing nets of threshold elements. IEEE Transactions on Computers. 1972, 100 (21), n.11: 1197-1206.
38. Wang R.-S., Albert R. 2013. Effects of community structure on the dynamics of random threshold networks. Physical Review, v. E87.