×

Influence of autapse on mode-locking structure of a Hodgkin-Huxley neuron under sinusoidal stimulus. (English) Zbl 1412.92041

Summary: We investigated the mode-locking behaviors of a Hodgkin-Huxley neuron with an autapse under sinusoidal stimulus. A neuron without an autapse can exhibit rich \(p:q\) mode-locking (i.e. \(p\) output action potentials generated by \(q\) cycles stimulations) behaviors with periodic stimuli. In the presence of the autaptic connection, the \(p:q\) mode-locking behaviors are completely reset. The autapse extends the scope of mode-locking. The autapse can enhance or suppress the status of mode-locking. Even for some specified autaptic parameters, the neuron could be driven into the sub-threshold oscillation. Our results suggested that the autapse can serve as a potential control option for adjusting the mode-locking firing behaviors. We also found that changing the delay time is much more effectively operable to regulate the response behavior than the autaptic intensity.

MSC:

92C20 Neural biology
Full Text: DOI

References:

[1] Atencio, C. A.; Schreiner, C. E., Columnar connectivity and laminar processing in cat primary auditory cortex, PLoS One, 5, e9521 (2010)
[2] Bacci, A.; Huguenard, J. R., Enhancement of spike-timing precision by autaptic transmission in neocortical inhibitory interneurons, Neuron, 49, 119-130 (2006)
[3] Bekkers, J. M., Neurophysiologyare autapses prodigal synapses?, Curr. Biol., 8, R52-R55 (1998)
[4] Bekkers, J. M., Synaptic transmissionfunctional autapses in the cortex, Curr. Biol., 13, R433-R435 (2003)
[5] Borkowski, L. S., Response of a Hodgkin-Huxley neuron to a high-frequency input, Phys. Rev. E, 80, 051914 (2009)
[6] Che, Y.-Q.; Wang, J.; Si, W.-J.; Fei, X.-Y., Phase-locking and chaos in a silent Hodgkin-Huxley neuron exposed to sinusoidal electric field, Chaos Solitons Fractals, 39, 454-462 (2009)
[7] Chen, Y.; Zhang, H.; Wang, H.; Yu, L.; Chen, Y., The role of coincidence—detector neurons in the reliability and precision of subthreshold signal detection in noise, PLoS One, 8, e56822 (2013)
[8] David, F. O.; Hugues, E.; Cenier, T.; Fourcaud-Trocme, N.; Buonviso, N., Specific entrainment of mitral cells during gamma oscillation in the rat olfactory bulb, PLoS Comput. Biol., 5, e1000551 (2009)
[9] Fellous, J.-M.; Houweling, A. R.; Modi, R. H.; Rao, R. P.N.; Tiesinga, P. H.E.; Sejnowski, T. J., Frequency dependence of spike timing reliability in cortical pyramidal cells and interneurons, J. Neurophysiol., 85, 1782-1787 (2001)
[10] Gaudreault, M.; Drolet, F.; Vials, J., Bifurcation threshold of the delayed van der Pol oscillator under stochastic modulation, Phys. Rev. E, 85, 056214 (2012)
[11] 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)
[12] Ikeda, K.; Bekkers, J. M., Autapses, Curr. Biol., 16, R308 (2006)
[13] Jensen, M. H.; Krishna, S., Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli, FEBS Lett., 586, 1664-1668 (2012)
[14] Jiang, M.; Zhu, J.; Liu, Y.; Yang, M.; Tian, C.; Jiang, S.; Wang, Y.; Guo, H.; Wang, K.; Shu, Y., Enhancement of asynchronous release from fast-spiking interneuron in human and rat epileptic neocortex, PLoS Biol., 10, e1001324 (2012)
[15] Kitano, H., Systems biologya brief overview, Science, 295, 1662-1664 (2002)
[16] Lee, S.-G.; Kim, S., Bifurcation analysis of mode-locking structure in a Hodgkin-Huxley neuron under sinusoidal current, Phys. Rev. E, 73, 041924 (2006)
[17] Li, Y.; Schmid, G.; Hänggi, P.; Schimansky-Geier, L., Spontaneous spiking in an autaptic Hodgkin-Huxley setup, Phys. Rev. E, 82, 061907 (2010)
[18] Lübke, J.; Markram, H.; Frotscher, M.; Sakmann, B., Frequency and dendritic distribution of autapses established by layer 5 pyramidal neurons in the developing rat neocortexcomparison with synaptic innervation of adjacent neurons of the same class, J. Neurosci., 16, 3209-3218 (1996)
[19] 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, 041907 (2008)
[20] Pedemonte, M.; Pena, J. L.; Velluti, R. A., Firing of inferior colliculus auditory neurons is phase-locked to the hippocampus theta rhythm during paradoxical sleep and waking, Exp Brain Res., 112, 41-46 (1996)
[21] Postlethwaite, C. M.; Silber, M., Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control, Phys. Rev. E, 76, 056214 (2007)
[22] Reppert, S. M.; Weaver, D. R., Molecular analysis of mammalian circadian rhythms, Annu. Rev. Physiol., 63, 647-676 (2001)
[23] Sato, S.; Doi, S., Response characteristics of the BVP neuron model to periodic pulse inputs, Math. Biosci., 112, 243-259 (1992) · Zbl 0825.92046
[24] Seung, H. S.; Lee, D. D.; Reis, B. Y.; Tank, D. W., The autapsea simple illustration of short-term analog memory storage by tuned synaptic feedback, J. Comput. Neurosci., 9, 171-185 (2000) · Zbl 1044.92018
[25] Shi, X.; Wang, Z., Adaptive synchronization of time delay Hindmarsh-Rose neuron system via self-feedback, Nonlinear Dyn., 69, 2147-2153 (2012)
[26] Varela, F.; Lachaux, J. P.; Rodriguez, E.; Martinerie, J., The brainweb: phase synchronization and large-scale integration, Nat. Rev. Neurosci., 2, 229-239 (2001)
[27] Wang, H.; Wang, L.; Yu, L.; Chen, Y., Response of Morris-Lecar neurons to various stimuli, Phys. Rev. E, 83, 021915 (2011)
[28] Wang, H.; Chen, Y.; Chen, Y., First-spike latency in Hodgkin׳s three classes of neurons, J. Theor. Biol., 328, 19-25 (2013) · Zbl 1330.92032
[29] 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
[30] Zhang, H.; Chen, Y.; Chen, Y., Noise propagation in gene regulation networks involving interlinked positive and negative feedback loops, PLoS One, 7, e51840 (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.