Article

Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons

Department of Physics, Lanzhou University of Technology, Lanzhou, 730050 China
Chinese Science Bulletin (Impact Factor: 1.37). 01/2011; 56(2):151-157. DOI: 10.1007/s11434-010-4281-2

ABSTRACT The phase transition of spiral waves in networks of Hodgkin-Huxley neurons induced by channel noise is investigated in detail.
All neurons in the networks are coupled with small-world connections, and the results are compared with the case for regular
networks, in which all neurons are completely coupled with nearest-neighbor connections. A statistical variable is defined
to study the collective behavior and phase transition of the spiral wave due to the channel noise and topology of the network.
The effect of small-world connection networks is described by local regular networks and long-range connection with certain
probability p. The numerical results confirm that (1) a stable rotating spiral wave can be developed and maintain robust with low p, where the breakup of the spiral wave and turbulence result from increasing the probability p to a certain threshold; (2) appropriate intensity of the optimized channel noise can develop a spiral wave among turbulent
states in small-world connection networks of H-H neurons; and (3) regular connection networks are more robust to channel noise
than small-world connection networks. A spiral wave in a small-world network encounters instability more easily as the membrane
temperature is increased to a certain high threshold.

Keywordsbreakup–channel noise–factor of synchronization–probability of long-range connection

Download full-text

Full-text

Available from: Ying Wu, Apr 17, 2014
0 Followers
 · 
100 Views
  • Source
    • "Experiments [40] [41] have confirmed that spiral wave can be observed in the mammalian neocortex, although the precise role of such complex patterns remains elusive. Accordingly, many works in the past [46] [47] [48] [49] simulated the formation and breakup of spiral waves on neuronal networks with the aim of clarifying their role and significance, in particularly suggesting that spiral waves can play a positive role in breaking through quiescent areas of the brain. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The electric activities of neurons are often affected by ion channel poisoning, in particularly, interrupting normal transduction of signals within the brain. This may be due to changes in conductance and the number of active channels. Tetraethylammonium, for example, is known to cause ion channel poisoning of potassium channels, while tetrodotoxin has similar detrimental effects on sodium channels. The occurrence of spiral waves in neuronal systems was observed frequently in the past, and it was argued that these waves of excitation may play an important role by the propagation of electric signals across the quiescent regions of the brain. In this work, the parameters xkxk and xNaxNa determine the ratio, with regards to the total number of ion channels, of active potassium and sodium channels, respectively, and they are taken to be representative also for the degree of channel poisoning. In the numerical studies, a well developed stable rotating spiral wave is used as the initial state to be controlled by the ion channel poisoning. We show that, under noise-free conditions, spiral waves are terminated whenever xkxk and xNaxNa are set lower than a given threshold. However, breakup of spiral wave occurs if the intensity of the channel noise increases. In order to quantify these observations, we use a simple but robust synchronization measure, which captures succinctly the transition from spiral waves to homogeneous neuronal activity and/or broken turbulent state. The critical thresholds can be inferred from the abrupt changes occurring in the corresponding dependencies of synchronization versus the xkxk and xNaxNa ratios. Furthermore, the sampled membrane potentials of a single neuron are recorded to detect the periodical spiral wave in a feasible way and the results could be dependent of the position of node (or site) to be monitored. Notably, small synchronization factors can be tightly associated to states where the formation of spiral waves is robust to channel poisoning and weak channel noise.
    Communications in Nonlinear Science and Numerical Simulation 11/2012; 17(11):4281–4293. DOI:10.1016/j.cnsns.2012.03.009 · 2.57 Impact Factor
  • Source
    • "However, amounts of consumed power (heat) and longer computation period are insurmountable when the original circuits are used to simulate the collective behaviors of neurons in domain or larger area, though single circuit is helpful to measure the electric activities of one or a few neurons [44], the reason is that amounts of heat is produced due to the Joule effect of resistance in the circuit, furthermore, some critical parameters could be changed due to the accumulation of heat and thus the simulated results are apart from the reliability. On the other hand, the functional domain of neuronal system is composed of a large number of neurons, it is critical and important to study the collective behaviors of neurons by using networks scheme and thus some potential clues could be found to give useful information to prevent the occurrence of neuronal disease [45] [46] [47]. Superconductivity of Josephson junction gives a potential way to avoid some defects and deficiencies of original circuits or dynamical system as mentioned above. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The chaotic circuit of resistive–capacitive–inductive-shunted Josephson junction is used to simulate behavior of Hindmarsh–Rose neuronal discharges. Based on tracking control theory, the controller contains two gain coefficients was constructed to control the chaotic system of Josephson junction to synchronize the chaotic Hindmarsh–Rose system, and the single controller was approached analytically. The results confirmed that the controller with appropriate gain coefficients was effective to reach complete synchronization (the amplitudes and rhythms of two systems are identical), phase synchronization (rhythms of two systems are identical) of Josephson junction and Hindmarsh–Rose neurons, respectively. The power consumption is estimated in a feasible way. As a result, the electric activities of Hindmarsh–Rose neurons could be simulated by using Josephson junction model completely.
    Communications in Nonlinear Science and Numerical Simulation 06/2012; 17(6):2659–2669. DOI:10.1016/j.cnsns.2011.10.029 · 2.57 Impact Factor
  • Source
    • "Experiments [40] [41] have confirmed that spiral wave can be observed in the mammalian neocortex, although the precise role of such complex patterns remains elusive. Accordingly, many works in the past [46] [47] [48] [49] simulated the formation and breakup of spiral waves on neuronal networks with the aim of clarifying their role and significance, in particularly suggesting that spiral waves can play a positive role in breaking through quiescent areas of the brain. "
    Communications in Nonlinear Science and Numerical Simulation 01/2012; · 2.57 Impact Factor