On the Synchronizability of Quadratic Integrate and Fire Neurons

Yıl 2024, Cilt: 10 Sayı: 1, 80 - 90, 15.03.2024

Koray Çiftçi

https://doi.org/10.28979/jarnas.1140961

Öz

Synchronization is a property of complex systems that manifests itself as the emergence of collective behavior from local interactions. Neurons are the basic building blocks of the nervous system, and in neuronal networks, the firing times of the neurons get synchronized via the electrical and chemical synapses among them. This property has been observed in both computational models and experimental studies. However, this synchronization's mechanisms have not yet been totally revealed. Here, we investigate the synchronization properties of quadratic integrate and fire (QIF) neurons from a computational modeling perspective. QIF neurons are simple yet effective models in the sense that they have the ability to capture complex behavior observed in neurons. We present analytical results concerning the spiking frequency of the QIF neurons and the relationships between membrane voltage and phase of the neurons. We give simulation results for a simple network of all-to-all coupled QIF neurons, demonstrating the effects of different types of coupling among the network members. We show that electrical and inhibitory chemical synapses play complementary roles in the formation of synchronized behavior in a neuronal network. Our results contribute to our understanding of the brain to produce cognitive abilities and coordinated action.

Anahtar Kelimeler

Integrate and fire, neuron, phase, synchronization

Kaynakça

• A. L. Hodgkin, A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology 117 (4) (1952) 500.
• R. Jolivet, T. J. Lewis, W. Gerstner, Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy, Journal of Neurophysiology 92 (2) (2004) 959–976.
• N. Brunel, M. C. Van Rossum, Lapicque’s 1907 paper: From frogs to integrate-and-fire, Biological Cybernetics 97 (5–6) (2007) 337–339.
• A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biological Cybernetics 95 (2006). 1–19.
• E. M. Izhikevich, Dynamical systems in neuroscience, MIT Press, London, 2007.
• D. Mishra, A. Yadav, P. K. Kalra, Learning with single quadratic integrate-and-fire neuron, in: J. Wang, Z. Yi, J. M. Zurada, B. L. Lu, H. Yin, (Eds.) Advances in Neural Networks - ISNN 2006, Vol. 3971 of Lecture Notes in Computer Science, Springer, Berlin, 2006, pp. 424–429.
• D. Hansel, G. Mato, Existence and stability of persistent states in large neuronal networks, Physical Review Letters 86 (18) (2001) 4175–4178.
• Á. Byrne, M. J.Brookes, S. Coombes, A mean field model for movement induced changes in the beta rhythm, Journal of Computational Neuroscience 43 (2) (2017) 143–158.
• G. B. Ermentrout, C. C. Chow, Modeling neural oscillations, Physiology and Behavior 77 (4) (2002) 629–633.
• S. Keeley, Á. Byrne, A. Fenton, J. Rinzel, Firing rate models for gamma oscillations, Journal of Neurophysiology 121(6) (2019) 2181–2190.
• G. Buzsaki, A. Draguhn, Neuronal oscillations in cortical networks, Science 304 (5679) (2004) 1926–1929.
• T. Womelsdorf, J. M. Schoffelen, R. Oostenveld, W. Singer, R. Desimone, A. K. Engel, P. Fries, Modulation of neuronal interactions through neuronal synchronization, Science 316 (5831) (2007) 1609–1612.
• T. Womelsdorf, P. Fries, The role of neuronal synchronization in selective attention, Current Opinion in Neurobiology 17 (2) (2007) 154–160.
• N. Axmacher, F. Mormann, G. Fernández, C. E. Elger, J. Fell, Memory formation by neuronal synchronization, Brain Research Reviews 52 (1) (2006) 170–182.
• J. Van Der Werf, O. Jensen, P. Fries, W. P. Medendorp, Neuronal synchronization in human posterior parietal cortex during reach planning, Journal of Neuroscience 30 (4) (2010) 1402–1412.
• F. Varela, J. P. Lachaux, E. Rodriguez, J. Martinerie, The brainweb: Phase synchronization and large-scale integration, Nature Reviews Neuroscience 2 (4) (2001) 229–239.
• M. V. L. Bennett, R. S. Zukin, Electrical Coupling and Neuronal Synchronization in the Mammalian Brain, Neuron 41 (4) (2004) 495–511.
• S. H. Strogatz, I. Stewart, Coupled oscillators and biological synchronization, Scientific American 269 (6) (1993) 102–109.
• L. Glass, Synchronization and rhythmic processes in physiology, Nature 410 (6825) (2001) 277–284.
• X. Li, G. Chen, Synchronization and desynchronization of complex dynamical networks: An engineering viewpoint, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 50 (11) (2003) 1381–1390.
• Y. Kuramoto, Collective synchronization of pulse-coupled oscillators and excitable units, Physica D: Nonlinear Phenomena 50 (1) (1991) 15–30.
• P. Clusella, B. Pietras, E. Montbrió, Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling. Chaos: An interdisciplinary, Journal of Nonlinear Science 32 (1) (2022) 013105.
• M. Jafarian, K. H. Johansson, (2019). Synchronization of quadratic integrate-and-fire spiking neurons: Constant versus voltage-dependent couplings. 2019 IEEE 58th Conference on Decision and Control (CDC), 4711-4716.
• W. Ye, Dynamics of a large-scale spiking neural network with quadratic integrate-and-fire neurons, Neural Plasticity 2021 (2021) Article ID 6623926 10 pages.
• I. Ratas, K. Pyragas, Interplay of different synchronization modes and synaptic plasticity in a system of class I neurons, Scientific Reports 12 (1) (2022) Article Number 19631 17 pages.
• E. H. Buhl, G. Tamás, A. Fisahn, Cholinergic activation and tonic excitation induce persistent gamma oscillations in mouse somatosensory cortex in vitro, The Journal of Physiology 513 (1) (1998) 117–126.
• M. Beierlein, J. R. Gibson, B. W. Connors, A network of electrically coupled interneurons drives synchronized inhibition in neocortex, Nature Neuroscience 3 (9) (2000) 904–910.
• C. Van Vreeswijk, L. F. Abbott, G. Bard Ermentrout, When inhibition not excitation synchronizes neural firing, Journal of computational neuroscience 1 (4) (1994) 313–321.
• M. A. Whittington, R. D. Traub, N. Kopell, B. Ermentrout, E. H. Buhl, Inhibition-based rhythms: Experimental and mathematical observations on network dynamics, International Journal of Psychophysiology 38 (3) (2000) 315–336.
• R. D. Traub, Model of synchronized population bursts in electrically coupled interneurons containing active dendritic conductances, Journal of Computational Neuroscience 2 (1995) 283–289.
• C. C. Chow, N. Kopell, Dynamics of spiking neurons with electrical coupling, Neural Computation 12 (7) (2000) 1643–1678.
• C. C. Canavier, S. Achuthan, Pulse coupled oscillators and the phase resetting curve, Mathematical Biosciences 226 (2) (2010) 77–96.
• N. Kopell, B. Ermentrout, Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks, Proceedings of the National Academy of Sciences 101 (43) (2004) 15482–15487.
• M. S. Baptista, F. M. Moukam Kakmeni, C. Grebogi, Combined effect of chemical and electrical synapses in Hindmarsh-Rose neural networks on synchronization and the rate of information, Physical Review E 82 (3) (2010) 036203.
• L. Koban, A. Ramamoorthy, I. Konvalinka, Why do we fall into sync with others? Interpersonal synchronization and the brain’s optimization principle, Social Neuroscience 14 (1) (2019) 1–9.
• H. Adesnik, Layer-specific excitation/inhibition balances during neuronal synchronization in the visual cortex, The Journal of Physiology 596 (9) (2018) 1639–1657.
• A. Navarrete, C. P. Van Schaik, K. Isler, Energetics and the evolution of human brain size, Nature 480 (7375) (2011).
• J. A. White, C. C. Chow, J. Rit, C. Soto-Treviño, N. Kopell, Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons, Journal of Computational Neuroscience 5 (1) (1998) 5–16.
• T. J. Lewis, J. Rinzel, Dynamics of spiking neurons connected by both inhibitory and electrical coupling, Journal of Computational Neuroscience 14 (3) (2003) 283–309.