Delay-induced multiple stochastic resonances on scale-free neuronal networks

We study the effects of periodic subthreshold pacemaker activity and time-delayed coupling on stochastic resonance over scale-free neuronal networks. As the two extreme options, we introduce the pacemaker respectively to the neuron with the highest degree and to one of the neurons with the lowest degree within the network, but we also consider the case when all neurons are exposed to the periodic forcing. In the absence of delay, we show that an intermediate intensity of noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble, irrespective to its placing, thus providing evidences for stochastic resonance on the scale-free neuronal networks. Interestingly thereby, if the forcing in form of a periodic pulse train is introduced to all neurons forming the network, the stochastic resonance decreases as compared to the case when only a single neuron is paced. Moreover, we show that finite delays in coupling can significantly affect the stochastic resonance on scale-free neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances independently of the placing of the pacemaker, but they can also altogether destroy stochastic resonance. Delay-induced multiple stochastic resonances manifest as well-expressed maxima of the correlation measure, appearing at every multiple of the pacemaker period. We argue that fine-tuned delays and locally active pacemakers are vital for assuring optimal conditions for stochastic resonance on complex neuronal networks.Comment: 7 two-column pages, 5 figures; accepted for publication in Chao

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.Comment: 5 pages, 9 figure

How single neuron properties shape chaotic dynamics and signal transmission in random neural networks

While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of nodes (such as single neurons) and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate units shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single units. For the case of two-dimensional rate units with strong adaptation, we find that the network exhibits a state of "resonant chaos", characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the resonance frequency can be predicted from the properties of isolated units, even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework can be applied to other mechanisms at the level of single nodes, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between the dynamics of single units and recurrent connectivity, which is a fundamental step toward the description of biologically realistic network models in the brain, or, more generally, networks of other physical or man-made complex dynamical units

Can intrinsic noise induce various resonant peaks?

We theoretically describe how weak signals may be efficiently transmitted throughout more than one frequency range in noisy excitable media by kind of stochastic multiresonance. This serves us here to reinterpret recent experiments in neuroscience, and to suggest that many other systems in nature might be able to exhibit several resonances. In fact, the observed behavior happens in our (network) model as a result of competition between (1) changes in the transmitted signals as if the units were varying their activation threshold, and (2) adaptive noise realized in the model as rapid activity-dependent fluctuations of the connection intensities. These two conditions are indeed known to characterize heterogeneously networked systems of excitable units, e.g., sets of neurons and synapses in the brain. Our results may find application also in the design of detector devices.Comment: 10 pages, 2 figure

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal response. Finally we show that the self-correlation of the colored noise causes a reduction of the effective noise intensity, which appears as a rescaling of the fluctuations affecting the FHN system.Comment: 13 pages, 10 figure

Resonant spike propagation in coupled neurons with subthreshold activity

Màster en Biofísica, curs 2006-2007Chemical coupling between neurons is only active when the presynaptic neuron is firing, and thus it does not allow for the propagation of subthreshold activity. Electrical coupling via gap junctions, on the other hand, is also ubiquitous and, due to its diffusive nature, transmits both subthreshold and suprathreshold activity between neurons. We study theoretically the propagation of spikes between two neurons that exhibit subthreshold oscillations, and which are coupled via both chemical synapses and gap junctions. Due to the electrical coupling, the periodic subthreshold activity is synchronized in the two neurons, and affects propagation of spikes in such a way that for certain values of the delay in the synaptic coupling, propagation is not possible. This effect could provide a mechanism for the modulation of information transmission in neuronal networks

Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors

We demonstrate, experimentally and theoretically, excitable nanosecond optical pulses in optoelectronic integrated circuits operating at telecommunication wavelengths (1550 nm) comprising a nanoscale double barrier quantum well resonant tunneling diode (RTD) photo-detector driving a laser diode (LD). When perturbed either electrically or optically by an input signal above a certain threshold, the optoelectronic circuit generates short electrical and optical excitable pulses mimicking the spiking behavior of biological neurons. Interestingly, the asymmetric nonlinear characteristic of the RTD-LD allows for two different regimes where one obtain either single pulses or a burst of multiple pulses. The high-speed excitable response capabilities are promising for neurally inspired information applications in photonics. (C) 2013 Optical Society of AmericaFCT [PTDC/EEA-TEL/100755/2008]; FCT Portugal [SFRH/BPD/84466/2012]; Ramon y Cajal fellowship; project RANGER [TEC2012-38864-C03-01]; Direcci General de Recerca del Govern de les Illes Balears; EU FEDER funds; Ministry of Economics and Competitivity of Spain [FIS2010-22322-C02-01

Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin-Huxley neurons

We investigate the regularity of spontaneous spiking activity on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise and fraction of blocked voltage-gated sodium and potassium ion channels embedded in neuronal membranes. We show that there exists an optimal fraction of shortcut links between physically distant neurons, as well as an optimal intensity of intrinsic noise, which warrant an optimally ordered spontaneous spiking activity. This doubly coherence resonance-like phenomenon depends significantly, and can be controlled via the fraction of closed sodium and potassium ion channels, whereby the impacts can be understood via the analysis of the firing rate function as well as the deterministic system dynamics. Potential biological implications of our findings for information propagation across neural networks are also discussed.Comment: 6 two-column pages, 5 figures; accepted for publication in Europhysics Letter

Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles

The firing of an action potential by a biological neuron represents a dramatic transition from small-scale linear stochastics (subthreshold voltage fluctuations) to gross-scale nonlinear dynamics (birth of a 1-ms voltage spike). In populations of neurons we see similar, but slower, switch-like there-and-back transitions between low-firing background states and high-firing activated states. These state transitions are controlled by varying levels of input current (single neuron), varying amounts of GABAergic drug (anesthesia), or varying concentrations of neuromodulators and neurotransmitters (natural sleep), and all occur within a milieu of unrelenting biological noise. By tracking the altering responsiveness of the excitable membrane to noisy stimulus, we can infer how close the neuronal system (single unit or entire population) is to switching threshold. We can quantify this “nearness to switching” in terms of the altering eigenvalue structure: the dominant eigenvalue approaches zero, leading to a growth in correlated, low-frequency power, with exaggerated responsiveness to small perturbations, the responses becoming larger and slower as the neural population approaches its critical point–-this is critical slowing. In this chapter we discuss phase-transition predictions for both single-neuron and neural-population models, comparing theory with laboratory and clinical measurement