Abstract
Simulations of neural activity are commonly based on differential equations. We address the question what can be achieved with a simplified discrete model. The proposed model resembles artificial neural networks enriched with additional biologically inspired features. A neuron has several states, and the state transitions follow endogenous patterns which roughly correspond to firing behavior observed in biological neurons: oscillatory, tonic, plateauing, etc. Neural interactions consist of two components: synaptic connections and extrasynaptic emission of neurotransmitters. The dynamics is asynchronous and event-based; the events correspond to the changes in neurons activity. This model is innovative in introducing discrete framework for modeling neurotransmitter interactions which play the important role in neuromodulation. We simulate rhythmic activity of small neural ensembles like central pattern generators (CPG). The modeled examples include: the biphasic rhythm generated by the half-center mechanism with the post-inhibitory rebound (like the leech heartbeat CPG), the triphasic rhythm (like in pond snail feeding CPG) and the pattern switch in the system of several neurons (like the switch between ingestion and egestion in Aplysia feeding CPG). The asynchronous dynamics allows to obtain multi-phasic rhythms with phase durations close to their biological prototypes. The perspectives of discrete modeling in biological research are discussed in the conclusion.
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Communicated by Benjamin Lindner.
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The research was partially supported by the Russian Foundation for Basic Research (projects 17-29-07029, 19-04-00628)
We thank Liudmila Zhilyakova, Sergei Kulivets, Dmitry Vorontsov and Ilya Chistopolsky for fruitful discussion and Prof. Dmitry Sakharov for the strong biological motivation. We also thank Dmitry Kuznetsov for language editing.
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Bazenkov, N.I., Boldyshev, B.A., Dyakonova, V. et al. Simulating Small Neural Circuits with a Discrete Computational Model. Biol Cybern 114, 349–362 (2020). https://doi.org/10.1007/s00422-020-00826-w
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DOI: https://doi.org/10.1007/s00422-020-00826-w