The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is optimized by the noise. The coupling of the network can enhance CR in two different ways. In particular, when the coupling is strong enough, the synchronization of the system is induced and optimized by the noise. This synchronization leads to a high and wide plateau in the local CR curve. A bell-shaped curve is found for the peak height of power spectra of the spike train, being significantly different from a monotonic behavior for the single neuron. The local-noise-induced limit cycle can evolve to a refined spatiotemporal order through the dynamical optimization among the autonomous oscillation of an individual neuron, the coupling of the network, and the local noise.
Post inhibitory rebound is a nonlinear phenomenon present in a variety of nerve cells. Following a period of hyper-polarization this effect allows a neuron to fire a spike or packet of spikes before returning to rest. It is an important mechanism underlying central pattern generation for heartbeat, swimming and other motor patterns in many neuronal systems. In this paper we consider how networks of neurons, which do not intrinsically oscillate, may make use of inhibitory synaptic connections to generate large scale coherent rhythms in the form of cluster states. We distinguish between two cases i) where the rebound mechanism is due to anode break excitation and ii) where rebound is due to a slow T-type calcium current. In the former case we use a geometric analysis of a McKean type model to obtain expressions for the number of clusters in terms of the speed and strength of synaptic coupling. Results are found to be in good qualitative agreement with numerical simulations of the more detailed Hodgkin-Huxley model. In the second case we consider a particular firing rate model of a neuron with a slow calcium current that admits to an exact analysis. Once again existence regions for cluster states are explicitly calculated. Both mechanisms are shown to prefer globally synchronous states for slow synapses as long as the strength of coupling is sufficiently large. With a decrease in the duration of synaptic inhibition both systems are found to break into clusters. A major difference between the two mechanisms for cluster generation is that anode break excitation can support clusters with several groups, whilst slow T-type calcium currents predominantly give rise to clusters of just two (anti-synchronous) populations.
This paper is concerned with the synthesis and reactions of enantiopure 1,8,9,16-tetraethynyltetraphenylene (3). We obtained 3 in 34% yield through four steps starting from 1,8,9,16-tetrahydroxytetraphenylene (2a) via a functional group interconversion strategy. On the basis of this chiral "helical" building block, three rigid helical macrocycles 14, 15, and 22 were designed. Complexes 14 and 15 were constructed via coordination-driven self-assembly with platinum(II) complexes 8 and 9b, while 22 cannot be obtained successfully. Then macrocycle 28 was designed on the structural basis of 22 to which octyl chains were introduced, in the hope of improving the solubility of the complex. Macrocycle 28 was finally formed and was characterized by NMR spectroscopy, elemental analysis, and electrospray mass spectrometry. For the enantiopure 15 and 28, circular dichroism (CD) spectra also exhibited chiral properties. Complexes 27 and 28 both exhibited an intense emission band at 621 nm in acetonitrile at 298 K upon excitation at λ > 420 nm.
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