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Neuronal firing plays a key role in the neuronal information transmission, and different neuronal firing patterns are reported, such as spiking, bursting. A number of neuron models are introduced to reproduce the firing patterns of single neuron or neuronal network. The key factors determining the firing pattern gain more and more attention in the study of neuron system, such as noise, network topology. Noise is able to induce sub-or super-threshold coherent neuronal firing easily, and a number of coherence resonances are reported in the noise induced firing. The network topology determines the synchronization of the firing patterns of the neuronal network, and the change of network topology may induce fruitful synchronization transitions. It is well known that synapses exhibit a high variability with a diverse origin during information transmission, such as the stochastic release of neurotransmitters, variations in chemical concentration through synapses, and spatial heterogeneity of synaptic response over dendrite tree. The collective effect of all of these factors might result in the notion of dynamic synapses. In reality, the neuronal network often involves time delay due to the ?nite signal propagation time in biological networks. Recently, neuronal networks with time delay have received considerable attention. Delay-sustained neuronal firing patterns may be relevant to neuronal networks for establishing a concept of collective information processing in the presence of delayed information transmission. According to the above-mentioned motivations, the firing dynamics of the single postsynapic neuron is investigated based on a simple postsynaptic neuron model by using numerical simulation and Fourier transform analysis. In this model, the postsynapic neuron receives dynamic synaptic currents from a population of presynaptic neurons. It is found that the firing rate resonance between the pre-and postsynaptic neuron determines the firing of the postsynaptic neuron. Stimulus currents in specific frequency range are easy to stimulate postsynaptic neuron firing. The random currents released from dynamic synapses determine the postsynaptic firing rate. Then the single postsynaptic neuron is extended to a neuronal network, in which 100 neurons connect to its 4 nearest neighbors regularly and receive delayed synaptic currents from connected neurons. All the neurons in the network receive the same dynamic synaptic currents from the presynaptic neurons. The results show that the synaptic coupling in the network is able to promote the neuron firing in the network, and time delay in the synaptic coupling could reinforce the promotion, but the mode of the promotion is not changed.
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Keywords:
- neuron /
- synaptic stimulation /
- Flourier transform /
- time delay
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[27] Braitenberg V, Schz A 1991 Anatomy of the Cortex:Statistics and Geometry (Berlin:Springer-Verlag)
[28] Torres J J, Kappen J H 2013 Front. Comput. Neurosci. 7 30
[29] Abbott L F, Varela J A, Sen K, Nelson S B 1997 Science 275 221
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[31] Mishra J, Fellous J M, Sejnowski T J 2006 Neural Networks 19 1329
[32] Fan D, Wang Z, Wang Q 2015 Commun. Nonlinear Sci. Numer. Simulat. 36 219
[33] Uzuntarla M, Ozer M, Ileri U, Calim A, Torres J J 2015 Phys. Rev. E 92 062710
[34] Qian Y, Zhao Y, Liu F, Huang X, Zhang Z, Mi Y 2013 Commun. Nonlinear. Sci. 18 3509
[35] Qian Y, Liao X, Huang X, Mi Y, Zhang L, Hu G 2010 Phys. Rev. E 82 026107
[36] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[37] Tsodyks M V, Pawelzik K, Markram H 1998 Neural Comput. 10 821
[38] Fitzpatrick J S, Akopian G, Walsh J P 2001 J. Neurophysiol. 85 2088
[39] Tecuapetla F, Carrillo-Reid L, Bargas J, Galarraga E 2007 Proc. Natl. Acad. Sci. USA 104 10258
[40] Ma Y, Hu H, Agmon A 2012 J. Neurosci. 32 983
[41] Barroso-Flores J, Herrera-Valdez M A, Lopez-Huerta V G, Galarraga E 2015 J. Bargas Neural Plast. 2015 573543
[42] Tsodyks M, Uziel A, Markram H 2000 J. Neurosci. 20 RC50
[43] Tsodyks M V, Markram H 1997 Proc. Natl. Acad. Sci. USA 94 719
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[1] Hartmann G, Hauske G, Eckmiller R 1990 Parallel Processing in Neural Systems and Computers (Amsterdam:Computing and Computers)
[2] Vanrullen R, Guyonneau R, Thorpe S J 2005 Trends Neurosci. 28 1
[3] Pankratova E V, Polovinkin A V, Mosekilde E 2005 Eur. Phys. J. B 45 391
[4] Levin J E, Miller J P 1996 Nature 380 165
[5] Tang J, Liu T B, Ma J, Luo J M, Yang X Q 2016 Commun. Nonlinear Sci. Numer. Simulat. 32 262
[6] Duan W L, Zeng C 2017 Appl. Math. Comput. 292 400
[7] Yu W T, Tang J, Luo J M 2015 Acta Phys. Sin. 64 068702 (in Chinese)[于文婷, 唐军, 罗进明2015 64 068702]
[8] Yu W T, Tang J, Ma J, Luo J M, Yang X Q 2015 Eur. Biophys. J. 44 677
[9] Zeng J, Zeng C, Xie Q, Guan L, Dong X, Yang F 2016 Physica A 462 1273
[10] Johnson J B 1928 Phys. Rev. 32 97
[11] Gu H, Zhao Z 2015 Plos One 10 e0138593
[12] Qian Y 2014 Plos One 9 e96415
[13] Guo D, Wang Q, Perc M 2012 Phys. Rev. E 85 878
[14] Liu S, Wang Q, Fan D 2016 Front. Comput. Neurosc. 10 81
[15] Mainen Z F, Sejnowski T J 1995 Science 268 1503
[16] Jun M A, Tang J 2015 Sci. China:Technol. Sc. 58 2038
[17] Chialvo D R, Longtin A, Mautllergerking J 1997 Phys. Rev. E 55 1798
[18] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 254
[19] Guo D, Li C 2012 J. Theor. Biol. 308 105
[20] Xiao W W, Gu H G, Liu M R 2016 Sci. China:Technol. Sci. 59 1
[21] Liu F, Yu Y, Wang W 2001 Phys. Rev. E 63 051912
[22] Sakumura Y, Aihara K 2002 Neural Proc. Lett. 16 235
[23] Tang J, Ma J, Yi M, Xia H, Yang X Q 2011 Phys. Rev. E 83 046207
[24] Yu W T, Tang J, Ma J, Yang X Q 2016 Europhys. Lett. 114 50006
[25] Song X L, Wang C N, Ma J, Tang J 2015 Sci. China:Technol. Sci. 58 1
[26] Markram H, Wang Y, Tsodyks M 1998 Proc. Natl. Acad. Sci. USA 95 5323
[27] Braitenberg V, Schz A 1991 Anatomy of the Cortex:Statistics and Geometry (Berlin:Springer-Verlag)
[28] Torres J J, Kappen J H 2013 Front. Comput. Neurosci. 7 30
[29] Abbott L F, Varela J A, Sen K, Nelson S B 1997 Science 275 221
[30] Torres J J, Pantic L, Kappen H J 2002 Phys. Rev. E 66 061910
[31] Mishra J, Fellous J M, Sejnowski T J 2006 Neural Networks 19 1329
[32] Fan D, Wang Z, Wang Q 2015 Commun. Nonlinear Sci. Numer. Simulat. 36 219
[33] Uzuntarla M, Ozer M, Ileri U, Calim A, Torres J J 2015 Phys. Rev. E 92 062710
[34] Qian Y, Zhao Y, Liu F, Huang X, Zhang Z, Mi Y 2013 Commun. Nonlinear. Sci. 18 3509
[35] Qian Y, Liao X, Huang X, Mi Y, Zhang L, Hu G 2010 Phys. Rev. E 82 026107
[36] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[37] Tsodyks M V, Pawelzik K, Markram H 1998 Neural Comput. 10 821
[38] Fitzpatrick J S, Akopian G, Walsh J P 2001 J. Neurophysiol. 85 2088
[39] Tecuapetla F, Carrillo-Reid L, Bargas J, Galarraga E 2007 Proc. Natl. Acad. Sci. USA 104 10258
[40] Ma Y, Hu H, Agmon A 2012 J. Neurosci. 32 983
[41] Barroso-Flores J, Herrera-Valdez M A, Lopez-Huerta V G, Galarraga E 2015 J. Bargas Neural Plast. 2015 573543
[42] Tsodyks M, Uziel A, Markram H 2000 J. Neurosci. 20 RC50
[43] Tsodyks M V, Markram H 1997 Proc. Natl. Acad. Sci. USA 94 719
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