Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks. (English) Zbl 1400.92028
Summary: We study the effects of an autapse, which is mathematically described as a self-feedback loop, on the propagation of weak, localized pacemaker activity across a Newman-Watts small-world network consisting of stochastic Hodgkin-Huxley neurons. We consider that only the pacemaker neuron, which is stimulated by a subthreshold periodic signal, has an electrical autapse that is characterized by a coupling strength and a delay time. We focus on the impact of the coupling strength, the network structure, the properties of the weak periodic stimulus, and the properties of the autapse on the transmission of localized pacemaker activity. Obtained results indicate the existence of optimal channel noise intensity for the propagation of the localized rhythm. Under optimal conditions, the autapse can significantly improve the propagation of pacemaker activity, but only for a specific range of the autaptic coupling strength. Moreover, the autaptic delay time has to be equal to the intrinsic oscillation period of the Hodgkin-Huxley neuron or its integer multiples. We analyze the inter-spike interval histogram and show that the autapse enhances or suppresses the propagation of the localized rhythm by increasing or decreasing the phase locking between the spiking of the pacemaker neuron and the weak periodic signal. In particular, when the autaptic delay time is equal to the intrinsic period of oscillations an optimal phase locking takes place, resulting in a dominant time scale of the spiking activity. We also investigate the effects of the network structure and the coupling strength on the propagation of pacemaker activity. We find that there exist an optimal coupling strength and an optimal network structure that together warrant an optimal propagation of the localized rhythm.
MSC:
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
References:
| [1] | McNamara, B.; Wiesenfeld, K.; Roy, R., Observation of stochastic resonance in a ring laser, Phys. Rev. Lett., 60, 2626-2629 (1988) |
| [2] | Gammaitoni, L.; Hänggi, P.; Jung, P.; Marchesoni, F., Stochastic resonance, Rev. Modern Phys., 70, 223-288 (1998) |
| [3] | Hänggi, P., Stochastic resonance in biology, Chem. Phys. Chem., 3, 285-290 (2002) |
| [4] | Longtin, A., Stochastic resonance in neuron models, J. Stat. Phys., 70, 309-327 (1993) · Zbl 1002.92503 |
| [5] | Ozer, M.; Perc, M.; Uzuntarla, M., Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving, Phys. Lett. A, 373, 964-968 (2009) · Zbl 1228.92013 |
| [6] | Yilmaz, E.; Uzuntarla, M.; Ozer, M.; Perc, M., Stochastic resonance in hybrid scale-free neuronal networks, Physica A, 392, 5735-5741 (2013) · Zbl 1395.34067 |
| [7] | Guo, D.; Li, C., Stochastic and coherence resonance in the feed-forward-loop neuronal network motifs, Phys. Rev. E, 79, Article 051921 pp. (2009) |
| [8] | Hille, B., Ionic channels in nerve membranes, Prog. Biophys. Mol. Biol., 21, 1-32 (1970) |
| [9] | White, J. A.; Rubinstein, J. T.; Kay, A. R., Channel noise in neurons, Trends Neurosci., 23, 131-137 (2000) |
| [10] | Schneidman, E.; Freedman, B.; Segev, I., Ion channel stochasticity may be critical in determining the reliability and precision of spike timing, Neural Comput., 10, 1679-1703 (1998) |
| [11] | Hänggi, P.; Schmid, G.; Goychuk, I., Excitable membranes: Channel noise, synchronization, and stochastic resonance, Adv. Solid State Phys., 42, 359-370 (2002) |
| [12] | Ozer, M.; Perc, M.; Uzuntarla, M.; Koklukaya, E., Weak signal propagation through noisy feedforward neuronal networks, NeuroReport, 21, 338-343 (2010) |
| [13] | Yilmaz, E.; Ozer, M., Collective firing regularity of a scale-free Hodgkin-Huxley neuronal network in response to a subthreshold signal, Phys. Lett. A, 377, 1301-1307 (2013) · Zbl 1288.92007 |
| [14] | Van der Loos, H.; Glaser, E. M., Autapses in neocortex cerehri: synapses between a pyramidal cell’s axon and its own dendrites, Brain Res., 48, 355-360 (1972) |
| [15] | Park, M. R.; Lighthall, J. W.; Kitai, S. T., Recurrent inhibition in the rat neostriatum, Brain Res., 194, 359-369 (1980) |
| [16] | Preston, R. C.; Bishop, G. A.; Kitai, S. T., Medium spiny neuron projection from the rat striatum: An intracellular horseradish peroxidase study, Brain Res., 183, 253-263 (1980) |
| [17] | Karabelas, A. B.; Purpura, D. P., Evidence for autapses in the substantia nigra, Brain Res., 200, 467-473 (1980) |
| [18] | Tamás, G.; Buhl, E. H.; Somogyi, P., Massive autaptic self-innervation of GABA ergic neurons in cat visual cortex, J. Neurosci., 17, 6352-6364 (1997) |
| [19] | Lübke, J.; Markram, H.; Frotscher, M.; Sakmann, B., Frequency and dendritic distribution of autapses established by layer 5 pyramidal neurons in the developing rat neocortex: Comparison with synaptic innervation of adjacent neurons of the same class, J. Neurosci., 16, 3209-3218 (1996) |
| [20] | Bacci, A.; Huguenard, J. R.; Prince, D. A., Functional autaptic neurotransmission in fast-spiking interneurons: a novel form of feedback inhibition in the neocortex, J. Neurosci., 23, 859-866 (2003) |
| [21] | Herrmann, C. S.; Klaus, A., Autapse turns neuron into oscillator, Int. J. Bifurcation Chaos, 14, 623-633 (2004) · Zbl 1064.92009 |
| [22] | Hashemi, M.; Valizadeh, A.; Azizi, Y., Effect of duration of synaptic activity on spike rate of a Hodgkin-Huxley neuron with delayed feedback, Phys. Rev. E, 85, Article 021917 pp. (2012) |
| [23] | Bacci, A.; Huguenard, J. R., Enhancement of spike-timing precision by autaptic transmission in neocortical inhibitory interneurons, Neuron, 49, 119-130 (2006) |
| [24] | Li, Y.; Schmid, G.; Hänggi, P.; Schimansky-Geier, L., Spontaneous spiking in an autaptic Hodgkin-Huxley setup, Phys. Rev. E, 82, Article 061907 pp. (2010) |
| [25] | Masoller, C.; Torrent, M. C.; García-Ojalvo, J., Interplay of subthreshold activity, time-delayed feedback, and noise on neuronal firing patterns, Phys. Rev. E, 78, Article 041907 pp. (2008) |
| [26] | Connelly, W. M., Autaptic connections and synaptic depression constrain and promote gamma oscillations, PLoS ONE, 9, e89995 (2014) |
| [27] | Wang, H.; Ma, J.; Chen, Y.; Chen, Y., Effect of an autapse on the firing pattern transition in a bursting neuron, Commun. Nonlinear Sci. Numer. Simul., 19, 3242-3254 (2014) · Zbl 1510.92054 |
| [28] | Wang, H.; Sun, Y.; Li, Y.; Chen, Y., Influence of autaptic self-feedback on mode-locking structure of a Hodgkin-Huxley neuron under sinusoidal stimulus, J. Theoret. Biol., 358, 25-30 (2014) · Zbl 1412.92041 |
| [29] | Sainz-Trapaga, M.; Maseller, C.; Braun, H. A.; Huber, M. T., Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons, Phys. Rev. E, 70, Article 031904 pp. (2004) |
| [30] | Yilmaz, E.; Ozer, M., Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin-Huxley neuron, Physica A, 421, 455-462 (2015) |
| [31] | Song, X. L.; Wang, C. N.; Ma, J.; Tang, J., Transition of electric activity of neurons induced by chemical and electric autapses, Sci. China Technol. Sci., 58, 1007-1014 (2015) |
| [32] | Qin, H. X.; Ma, J.; Jin, W. Y.; Wang, C. N., Dynamics of electric activities in neuron and neurons of network induced by autapses, Sci. China Technol. Sci., 57, 936-946 (2014) |
| [33] | Qin, H. X.; Wu, Y.; Wang, C. N.; Ma, J., Emitting waves from defects in network with autapses, Commun. Nonlinear Sci. Numer. Simul., 23, 164-174 (2015) · Zbl 1352.92035 |
| [34] | Katz, A. M., Physiology of the Heart (2000), Kluwer: Kluwer Philadelphia |
| [35] | Perc, M., Stochastic resonance on excitable small-world networks via a pacemaker, Phys. Rev. E, 76, Article 066203 pp. (2007) |
| [36] | Perc, M.; Marhl, M., Pacemaker enhanced noise-induced synchrony in cellular arrays, Phys. Lett. A, 353, 372-377 (2006) |
| [37] | Gun, C. B.; Perc, M.; Wang, Q., Delay-aided stochastic multiresonances on scale-free Fitz-Hugh-Nagumo neuronal networks, Chin. Phys. B, 19, Article 040508 pp. (2010) |
| [38] | Hodgkin, A. L.; Huxley, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117, 500-544 (1952) |
| [39] | Fox, R. F., Stochastic versions of the Hodgkin-Huxley equations, Biophys. J., 72, 2068-2074 (1997) |
| [40] | Ozer, M.; Uzuntarla, M.; Kayikcioglu, T.; Graham, L. J., Collective temporal coherence for subthreshold signal encoding on a stochastic small-world Hodgkin-Huxley neuronal network, Phys. Lett. A, 372, 6498-6503 (2008) · Zbl 1225.92009 |
| [41] | Wang, M.; Hou, Z.; Xin, H., Ordering spatiotemporal chaos in complex neuron networks, Chem. Phys. Chem., 7, 579-582 (2006) |
| [42] | Yu, Y.; Wang, W.; Wang, J. F.; Liu, F., Resonance-enhanced signal detection and transduction in the Hodgkin-Huxley neuronal systems, Phys. Rev. E, 63, Article 021907 pp. (2001) |
| [43] | Jiang, M.; Zhu, J.; Liu, Y.; Yang, M.; Tian, C.; Jiang, S., Enhancement of asynchronous release from fast-spiking interneuron in human and rat epileptic neocortex, PLoS Biol., 10, e1001324 (2012) |
| [44] | Guo, D.; Wang, Q.; Perc, M., Complex synchronous behavior in interneuronal networks with delayed inhibitory and fast electrical synapses, Phys. Rev. E, 85, Article 061905 pp. (2012) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
