Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network
Tóm tắt
An autapse is an unusual synapse that occurs between the axon and the soma of the same neuron. Mathematically, it can be described as a self-delayed feedback loop that is defined by a specific time-delay and the so-called autaptic coupling strength. Recently, the role and function of autapses within the nervous system has been studied extensively. Here, we extend the scope of theoretical research by investigating the effects of an autapse on the transmission of a weak localized pacemaker activity in a scale-free neuronal network. Our results reveal that by mediating the spiking activity of the pacemaker neuron, an autapse increases the propagation of its rhythm across the whole network, if only the autaptic time delay and the autaptic coupling strength are properly adjusted. We show that the autapse-induced enhancement of the transmission of pacemaker activity occurs only when the autaptic time delay is close to an integer multiple of the intrinsic oscillation time of the neurons that form the network. In particular, we demonstrate the emergence of multiple resonances involving the weak signal, the intrinsic oscillations, and the time scale that is dictated by the autapse. Interestingly, we also show that the enhancement of the pacemaker rhythm across the network is the strongest if the degree of the pacemaker neuron is lowest. This is because the dissipation of the localized rhythm is contained to the few directly linked neurons, and only afterwards, through the secondary neurons, it propagates further. If the pacemaker neuron has a high degree, then its rhythm is simply too weak to excite all the neighboring neurons, and propagation therefore fails.
Tài liệu tham khảo
Gammaitoni L, Hänggi P, Jung P, et al. Stochastic resonance. Rev Modern Phys, 1998, 70: 223–287
Hänggi P. Stochastic resonance in biology. ChemPhysChem, 2002, 3: 285–290
Wiesenfeld K, Moss F. Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature, 1995, 373: 33–36
Longtin A. Stochastic resonance in neuron models. J Stat Phys, 1993, 70: 309–327
McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A, 1989, 39: 4854–4869
Pakdaman K, Tanabe S, Shimokawa T. Coherence resonance and discharge time reliability in neurons and neuronal model. Neural Netw, 2001, 14: 895–905
Pikovsky A S, Kurths J. Coherence resonance in a noise-driven excitable system. Phys Rev Lett, 1997, 78: 775–778
Longtin A. Autonomous stochastic resonance in bursting neurons. Phys Rev E, 1997, 55: 868–876
Lindner B, Schimansky-Geier L. Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance. Phys Rev E, 1999, 60: 7270–7276
Brunel N, Hansel D. How noise affects the synchronization properties of recurrent networks of inhibitory neurons. Neural Comput, 2006, 18: 1066–1110
Zhou C, Kurths J. Noise-induced synchronization and coherence resonance of a Hodgkin–Huxley model of thermally sensitive neurons. Chaos, 2003, 13: 401–409
Rulkov N F, Suschik M M, Tsimring L S, et al. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys Rev E, 1995, 51: 980–994
Rosenblum M G, Pikovsky A S, Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett, 1996, 76: 1804–1807
Huang X Y, Xu W F, Liang J M, et al. Spiral wave dynamics in neocortex. Neuron, 2010, 68: 978–990
Huang X Y, Troy W C, Yang Q, et al. Spiral waves in disinhibited mammalian neocortex. J Neurosci, 2004, 24: 9897–9902
Ma J, Wu Y, Ying H P, et al. Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons. Chin Sci Bull, 2011, 56: 151–157
Ma J, Wang C N, Jin W Y, et al. Transition from spiral wave to target wave and other coherent structures in the networks of Hodgkin–Huxley neurons. Appl Math Comput, 2010, 217: 3844–3852
Hille B. Ionic channels in nerve membranes. Prog Biophys Mol Biol, 1970, 21: 1–32
White J A, Rubinstein J T, Kay A R. Channel noise in neurons. Trends Neurosci, 2000, 23: 131–137
Schneidman E, Freedman B, Segev I. Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput, 1998, 10: 1679–1703
Hänggi P, Schmid G, Goychuk I. Excitable membranes: Channel noise, synchronization and stochastic resonance. Adv Solid State Phys, 2002, 42: 359–370
Ozer M, Perc M, Uzuntarla M. Stochastic resonance on Newman–Watts networks of Hodgkin–Huxley neurons with local periodic driving. Phys Lett A, 2009, 373: 964–968
Ozer M, Perc M, Uzuntarla M, et al. Weak signal propagation through noisy feedforward neuronal Networks. Neuroreport, 2010, 21: 338–343
Ozer M, Perc M, Uzuntarla M. Controlling The spontaneous spiking regularity via channel blocking on newman-watts networks of hodgkin-huxley neurons. Euro Phys Lett, 2009, 86: 40008
Ozer M, Uzuntarla M, Perc M, et al. Spike latency and jitter of neuronal membrane patches with stochastic hodgkin-huxley channels. J Theor Biol, 2009, 261:83–92
Yilmaz E, Ozer M. Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal. Phys Lett A, 2013, 377: 1301–1307
Yilmaz E, Baysal V, Ozer M. Enhancement of temporal coherence via time-periodic coupling strength in a scale-free network of stochastic Hodgkin-Huxley neuron. Phys Lett A, 2015, 379: 1594–1599
Sun X J, Shi X. Effects of channel blocks on the spiking regularity in clustered neuronal networks. Sci China Tech Sci, 2014, 57: 879–884
Van der Loos H, Glaser E M. Autapses in neocortex cerebri: synapses between a pyramidal cell’s axon and its own dendrites. Brain Res, 1972, 48: 355–360
Herrmann C S, Klaus A. Autapse turns neuron into oscillator. Int J Bifurcat Chaos, 2004, 14: 623–633
Park M R, Lighthall J W, Kitai S T. Recurrent inhibition in the rat neostriatum. Brain Res, 1980, 194: 359–369
Preston R J, Bishop G A, Kitai S T. Medium spiny neuron projection from the rat striatum: An intracellular horseradish peroxidase study. Brain Res, 1980, 183: 253–263
Karabelas A B, Purpura D P. Evidence for autapses in the substantia nigra. Brain Res, 1980, 200: 467–473
Tamás G, Buhl E H, Somogyi P. Massive autaptic self-innervation of GABAergic neurons in cat visual cortex. J Neurosci, 1997, 17: 6352–6364
Lübke J, Markram H, Frotscher M, et al. 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, 1996, 16: 3209–3218
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, 2003, 23: 859–866
Süel G M, García-Ojalvo J, Liberman L M, et al. An excitable gene regulatory circuit induces transient cellular differentiation. Nature, 2006, 440: 545–550
Cabrera J L, Milton J G. On-off intermittency in a human balancing task. Phys Rev Lett, 2002, 89: 158702
Beta C, Bertram M, Mikhailov A S, et al. Controlling turbulence in a surface chemical reaction by time-delay autosynchronization. Phys Rev E, 2003, 67: 046224
Sethia G C, Kurths J, Sen A. Coherence resonance in an excitable system with time delay. Phys Lett A, 2007, 364: 227–230
Bacci A, Huguenard J R. Enhancement of spike-timing precision by autaptic transmission in neocortical inhibitory interneurons. Neuron, 2006, 49: 119–130
Li Y, Schmid G, Hänggi P, et al. Spontaneous spiking in an autaptic Hodgkin-Huxley setup. Phys Rev E, 2010, 82: 061907
Connelly W M. Autaptic connections and synaptic depression constrain and promote gamma oscillations. PLoS One, 2014, 9: e89995
Wang H, Ma J, Chen Y, et al. Effect of an autapse on the firing pattern transition in a bursting neuron. Commun Nonlinear Sci Numer Simulat, 2014, 19: 3242–3254
Wang H, Sun Y, Li Y, et al. Influence of autapse on mode-locking structure of a Hodgkin-Huxley neuron under sinusoidal stimulus. J Theor Biol, 2014, 358: 25–30
Liu H, Chapman E R, Dean C. “Self” versus “non-self” connectivity dictates properties of synaptic transmission and plasticity. PLoS One, 2013, 8: e62414
Qin H X, Ma J, Wang C N, et al. Autapse-induced target wave, spiral wave in regular network of neurons. Sci China-Phys Mech Astron, 2014, 57: 1918–1926
Ma J, Song X, Tang J, et al. Wave emitting and propagation induced by autapse in a forward feedback neuronal network. Neurocomputing, 2015, 167: 378–389
Ma J, Song X, Jin W, et al. Autapse-induced synchronization in a coupled neuronal Network. Chaos Soliton Fract, 2015, 80: 31–38
Yilmaz E, Ozer M. Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron. Physica A, 2015, 421: 455–462
Katz A M. Physiology of the Heart. Philadelphia: Kluwer, 2000
Perc M. Stochastic resonance on excitable small-world networks via a pacemaker. Phys Rev E, 2007, 76: 066203
Perc M, Marhl M. Pacemaker enhanced noise-induced synchrony in cellular arrays. Phys Lett A, 2006, 353: 372–377
Gan C B, Perc M, Wang Q Y. Delay-aided stochastic multi resonances on scale-free FitzHugh–Nagumo neuronal networks. Chin Phys B, 2010, 19: 040508
Hodgkin A L, Huxley A F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 1952, 117: 500–544
Fox R F. Stochastic versions of the Hodgkin-Huxley equations. Biophys J, 1997, 72: 2068–2074
Barabasi A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286: 509–512
Yu H, Wang J, Sun J, et al. Effects of hybrid synapses on the vibrational resonance in small-world neuronal networks. Chaos, 2012, 22: 033105
Yilmaz E, Uzuntarla M, Ozer M, et al. Stochastic resonance in hybrid scale-free neuronal networks. Physica A, 2013, 392: 5735–5741
Yu Y, Wang W, Wang J F, et al. Resonance-enhanced signal detection and transduction in the Hodgkin-Huxley neuronal systems. Phys Rev E, 2001; 63: 021907
Qin H X, Ma J, Jin W Y, et al. Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Tech Sci, 2014, 57: 936–946.
Song X L, Wang C N, Ma J, et al. Transition of electric activity of neurons induced by chemical and electric autapses. Sci China Tech Sci, 2015, 58: 1007–1014
Yilmaz E, Baysal V, Ozer M, et al. Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks. Physica A, 2016, 444: 538–546
Li X, Wang J, Hu W. Effects of chemical synapses on the enhancement of signal. Phys Rev E, 2007, 76: 041902