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Endogenous fields enhanced stochastic resonance in a randomly coupled neuronal network
... Based on an array of CA1 16 neuron models, it is verified that uncorrelated noise can help the transmission of the 17 sub-threshold signal [16,17]. SR induced by uncorrelated noise is also found in other 18 network structures including the feedforward network [18], modular network [19], 19 random network [20] and small-world network [21,22]. During the above studies, 20 Gaussian noise is employed due to its convenience and universality. ...
... SR induced by uncorrelated noise is also found in other 18 network structures including the feedforward network [18], modular network [19], 19 random network [20] and small-world network [21,22]. During the above studies, 20 Gaussian noise is employed due to its convenience and universality. However, the 21 physiological noise in real should have self-correlations in time, which is not 22 4 consistent with the random distribution of Gaussian noise. 1 Recently, several kinds of noises attracted researchers' attentions in the 2 neuroscience field. ...
... 20 multiple SR[29]. In feedforward neural network, it is verified that the propagation of 21 weak signal can be affected by modulating the degree distribution of neurons in both22 5 the noisy and noise-free conditions [30, 31]. ...
We investigate the effects of sine-Wiener (SW)-noise on signal propagation in a randomly connected neural network based on Izhikevich neuron model in detail, in which the axonal conduction delays of synapses, the linkage probability between neurons and the ratio between excitatory and inhibitory neurons of the network are set similarly with the mammalian neocortex. It is found that the SW-noise can enhance the propagation of weak signal in the network. Besides the parameters of SW-noise, the characteristic parameters of the network also play important roles in signal propagation. Furthermore,
it is found that the neural network has its sensitive frequency that can optimally enhance the propagation of weak signal when the signal’s frequency is close to the network’s sensitive frequency. In summary, the results here suggest that the SW-noise with suitable self-correlation time and intensity can facilitate the propagation of weak
signal in the randomly connected neural network.
... Indeed, it was well demonstrated that TES can directly, likely through non-synaptic mechanisms, entrain/modulate subcortical neurons [360]. The TES-induced electric fields would act as endogenous electric fields, which are known to guide network activity, to modulate the timing of action potentials [419], and to enhance stochastic resonance [420]. This is valid for both tDCS (static electric field) and tACS (alternating electric field) with effects on brain function [387]. ...
Schizophrenia patients are waiting for a treatment free of detrimental effects. Psychotic disorders are devastating mental illnesses associated with dysfunctional brain networks. Ongoing brain network gamma frequency (30-80 Hz) oscillations, naturally implicated in integrative function, are excessively amplified during hallucinations, in at-risk mental states for psychosis and first-episode psychosis. So, gamma oscillations represent a bioelectrical marker for cerebral network disorders with prognostic and therapeutic potential. They accompany sensorimotor and cognitive deficits already present in prodromal schizophrenia. Abnormally amplified gamma oscillations are reproduced in the corticothalamic systems of healthy humans and rodents after a single systemic administration, at a psychotomimetic dose, of the glutamate N-methyl-d-aspartate receptor antagonist ketamine. These translational ketamine models of prodromal schizophrenia are thus promising to work out a preventive noninvasive treatment against first-episode psychosis and chronic schizophrenia. In the present essay, transcranial electric stimulation (TES) is considered an appropriate preventive therapeutic modality because it can influence cognitive performance and neural oscillations. Here, I highlight clinical and experimental findings showing that, together, the corticothalamic pathway, the thalamus, and the glutamatergic synaptic transmission form an etiopathophysiological backbone for schizophrenia and represent a potential therapeutic target for preventive TES of dysfunctional brain networks in at-risk mental state patients against psychotic disorders.
... Then a crucial experiment confirmed the mechanism of SR, which declared the existence of SR in practice through observing the signalto-noise-ratio (SNR) in Schmitt trigger circuit and tunnel diode [2,3] . In recent years, SR has been studied widely in many scientific fields and plays important roles, such as information transmission, especially in biomechanics, pattern formation, overdamped monostable potential, population dynamics, and superconducting devices [4][5][6][7][8][9][10] . SR was studied in biochemical system not only in theory but also in experiments. ...
Stochastic resonance is investigated to explain the beneficial effect of Lévy noise on gene expression of genetic toggle model with harmonic excitation. The dynamic change of protein concentration of genetic toggle model under combined drives of harmonic excitation and Lévy noise is obtained numerically. Stochastic resonance is presented through the classical measure of signal-to-noise-ratio. Then from two aspects of combined drives on the protein at high or low concentration, the changes of protein concentration and signal-to-noise-ratio are discussed, respectively. When combined drives are within the protein at high concentration, the increasing Lévy noise intensity can promote the transition between the high and low concentrations, and the low protein concentration hardly fluctuates under the small noise intensity. It is also shown that the increase of stability index, skewness parameter of Lévy noise and amplitude of harmonic excitation can suppress the optimum collaboration of stochastic resonance. On the other hand, when combined drives are within the protein at low concentration, the increasing noise intensity can enhance the transition between the high and low concentrations, and the increase of stability index, skewness parameter and amplitude can strengthen the optimum collaboration of stochastic resonance. By the synergic actions of stochastic resonance, it is demonstrated that combined effect of harmonic excitation and Lévy stimuli can be utilized to promote the gene expression of proteins in genetic toggle model.
The detecting mechanism of carbon nanotubes gas sensor based on multi-stable stochastic resonance (MSR) model was studied in this paper. A numerically stimulating model based on MSR was established. And gas-ionizing experiment by adding electronic white noise to induce 1.65 MHz periodic component in the carbon nanotubes gas sensor was performed. It was found that the signal-to-noise ratio (SNR) spectrum displayed two maximal values, which accorded to the change of the broken-line potential function. The experimental results of gas-ionizing experiment demonstrated that periodic component of 1.65 MHz had multiple MSR phenomena, which was in accordance with the numerical stimulation results. In this way, the numerical stimulation method provides an innovative method for the detecting mechanism research of carbon nanotubes gas sensor.
We study the phenomenon of stochastic resonance on diffusive, small-world and scale-free networks consisting of bistable overdamped oscillators. Important thereby is the fact that the external subthreshold periodic forcing is introduced only to a single oscillator of the network. Hence, the forcing acts as a pacemaker trying to impose its rhythm on the whole network through the unit to which it is introduced. Without the addition of additive spatiotemporal noise, however, the whole network, including the unit that is directly exposed to the pacemaker, remains trapped forever in one of the two stable steady states of the local dynamics. We show that the correlation between the frequency of subthreshold pacemaker activity and the response of the network is resonantly dependent on the intensity of additive noise. The reported pacemaker-driven stochastic resonance depends most significantly on the coupling strength and the underlying network structure. Namely, the outreach of the pacemaker obeys the classic diffusion law in the case of nearest-neighbor interactions, thus being proportional to the square root of the coupling strength, whereas it becomes superdiffusive by an appropriate small-world or scale-free topology of the interaction network. In particular, the scale-free topology is identified as being optimal for the dissemination of localized rhythmic activity across the whole network. Also, we show that the ratio between the clustering coefficient and the characteristic path length is the crucial quantity defining the ability of a small-world network to facilitate the outreach of the pacemaker-emitted subthreshold rhythm. We additionally confirm these findings by using the FitzHugh–Nagumo excitable system as an alternative to the bistable overdamped oscillator.
Networks of fast-spiking interneurons are crucial for the generation of
neural oscillations in the brain. Here we study the synchronous behavior of
interneuronal networks that are coupled by delayed inhibitory and fast
electrical synapses. We find that both coupling modes play a crucial role by
the synchronization of the network. In addition, delayed inhibitory synapses
affect the emerging oscillatory patterns. By increasing the inhibitory synaptic
delay, we observe a transition from regular to mixed oscillatory patterns at a
critical value. We also examine how the unreliability of inhibitory synapses
influences the emergence of synchronization and the oscillatory patterns. We
find that low levels of reliability tend to destroy synchronization, and
moreover, that interneuronal networks with long inhibitory synaptic delays
require a minimal level of reliability for the mixed oscillatory pattern to be
maintained.
Periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus: they tend to fire at a preferred phase of the stimulus cycle, but not at every cycle. Hence, the histogram of interspike intervals (ISIH), i.e., of times between successive firings, is multimodal for these neurons, with peaks centered at integer multiples of the driving period. A particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data. In the present paper, we show that an excitable cell model, the Fitzhugh-Nagumo equations, also reproduces these features when driven by additive periodic and stochastic forces. This model exhibits its own brand of stochastic resonance as the peaks of the ISIH successively go through a maximum when the noise intensity is increased. Further, the presence of a noise-induced limit cycle introduces a third time scale in the problem. This limit cycle is found to modify qualitatively the phase-locking picture, e.g., by suppressing certain peaks in the ISIH. Finally, the role of noise and possibly of stochastic resonance (SR) in the neural encoding of sensory information is discussed.
Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30-80 Hz gamma rhythm in which network oscillations arise through 'stochastic synchrony' capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs.
Efficient methods for Local Field Potential (LFP) signal analysis amenable to interpretation are becoming increasingly relevant. LFP signals are believed, in part, to reflect neural action potential activity, and LFP frequency modulations are linked to spiking events. Furthermore, LFP signals are increasingly accessible in human brain regions previously unreachable due to a proliferation of deep brain stimulation implantation procedures. Traditional LFP analysis involves computing power spectra densities (PSDs) of these signals, which captures power at various frequencies in the signal. However, PSDs are second order statistics and may not capture non-trivial temporal dependencies that exist in the raw data. In this paper, we propose an LFP analysis method that is useful for describing unique features of temporal dependencies in LFP signals. This method is based on autoregressive (AR) modeling and draws from the systems identification sub-field of systems and control. Specifically, we have built and analysed AR models of LFP activity, and have demonstrated statistically significant differences in temporal dependencies between diseased globus pallidus tissue and control regions in two dystonia patients receiving deep brain stimulation implantation. Differences in the PSDs of LFP signals between these two groups were not statistically significant.
For a feedforward loop of oscillatory Hodgkin-Huxley neurons interacting via excitatory chemical synapses, we show that a great variety of spatiotemporal periodic firing patterns can be encoded by properly chosen communication delays and synaptic weights, which contributes to the concept of temporal coding by spikes. These patterns can be obtained by a modulation of the multiple coexisting stable in-phase synchronized states or traveling waves propagating along or against the direction of coupling. We derive explicit conditions for the network parameters allowing us to achieve a desired pattern. Interestingly, whereas the delays directly affect the time differences between spikes of interacting neurons, the synaptic weights control the phase differences. Our results show that already such a simple neural circuit may unfold an impressive spike coding capability.
Clinical effects of transcranial electrical stimulation with weak currents are remarkable considering the low amplitude of the electric fields acting on the brain. Elucidating the processes by which small currents affect ongoing brain activity is of paramount importance for the rational design of noninvasive electrotherapeutic strategies and to determine the relevance of endogenous fields. We propose that in active neuronal networks, weak electrical fields induce small but coherent changes in the firing rate and timing of neuronal populations that can be magnified by dynamic network activity. Specifically, we show that carbachol-induced gamma oscillations (25-35 Hz) in rat hippocampal slices have an inherent rate-limiting dynamic and timing precision that govern susceptibility to low-frequency weak electric fields (<50 Hz; <10 V/m). This leads to a range of nonlinear responses, including the following: (1) asymmetric power modulation by DC fields resulting from balanced excitation and inhibition; (2) symmetric power modulation by lower frequency AC fields with a net-zero change in firing rate; and (3) half-harmonic oscillations for higher frequency AC fields resulting from increased spike timing precision. These underlying mechanisms were elucidated by slice experiments and a parsimonious computational network model of single-compartment spiking neurons responding to electric field stimulation with small incremental polarization. Intracellular recordings confirmed model predictions on neuronal timing and rate changes, as well as spike phase-entrainment resonance at 0.2 V/m. Finally, our data and mechanistic framework provide a functional role for endogenous electric fields, specifically illustrating that modulation of gamma oscillations during theta-modulated gamma activity can result from field effects alone.
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.
Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations--e.g., random noise--cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being "suboptimal". Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the "neural code". Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise--via stochastic resonance or otherwise--than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing "noise benefits", and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.
We present first numerical evidence that in an excitable medium the synchronization of spatiotemporal patterns with external excitatory waves shows a sharp peak at a finite, well-defined noise level independent of the system size. This effect can be understood as a generalization of the concept of stochastic resonance to spatially extended systems. We further show the impact of spatiotemporal stochastic resonance for the spreading of spiral waves, where the noise level controls the scale and size of the spiral.
Stochastic resonance, a nonlinear phenomenon in which random noise optimizes a system's response to a signal, has been postulated to provide a role for noise in information processing in the brain. In these experiments, a time varying electric field was used to deliver both signal and noise directly to a network of neurons from mammalian brain. As the magnitude of the stochastic component of the field was increased, resonance was observed in the response of the neuronal network to a weak periodic signal. This is the first demonstration of stochastic resonance in neuronal networks from the brain.
Local field potentials and pairs of neurones in the subthalamic nucleus (STN) of patients with Parkinson's disease show high-frequency oscillations (HFOs) at 15-30 Hz. This study explores how these HFOs are modulated by voluntary movements and by dopaminergic medication. We examined 15 patients undergoing implantation of bilateral deep brain stimulating electrodes using microelectrode recordings of pairs of STN neurones (eight patients) and macroelectrode recordings of local field potentials from the STN (14 patients). Synchronized HFOs between STN neurones were observed in 28 out of 37 pairs in five patients who had tremor in the operating room and none of 45 pairs in three patients who did not. In two of the three non-tremulous patients, HFOs in the frequency spectra of local field potentials were detected but were weaker than in those patients with tremor. Active movement suppressed synchronized HFOs in three out of five pairs of neurones, independent of changes in firing rate. HFOs observed in the local field potentials in nine out of 14 patients were reduced with voluntary movement in six of the eight patients tested. Dopaminergic medication decreased the incidence of synchronized HFOs in STN neurone pairs, reduced HFO synchrony in a pair of tremor cells concurrent with a reduction in firing rate and limb tremor, and decreased HFOs of local field potentials in the STN. These results demonstrate that HFO synchronization in the STN is reduced by voluntary movements and by exogenous dopaminergic medication. A mechanism for neuronal oscillatory synchronization in basal ganglia is proposed. It is suggested that the firing of STN neurones can be synchronized by 15-30 Hz cortical beta oscillatory activity, particularly when dopamine deficiency results in a higher background firing rate of STN neurones, and that this synchronization contributes to parkinsonian pathophysiology.
We study the interplay among noise, weak driving signal and coupling in excitable FitzHugh-Nagumo neurons. Due to coupling, noise-sustained oscillations become locked to the signal as functions of both signal frequency and noise intensity. Higher order m:n locking tongues and various array-enhanced resonance features are demonstrated. This resonance and locking behavior due to a time scale matching between noise-sustained oscillations and the signal is fundamentally different from stochastic resonance in usual noisy threshold elements.
This review focuses on the experimental evidence supporting a role for endogenous electric fields in wound healing in vertebrates. Most wounds involve the disruption of epithelial layers composing the epidermis or surrounding organs in the body. These epithelia generate a steady voltage across themselves that will drive an injury current out of the wounded region, generating a lateral electric field that has been measured in four different cases to be 40-200 mV/mm. Many epithelial cells, including human keratinocytes, have the ability to detect electric fields of this magnitude and respond with directed migration. Their response typically requires Ca2+ influx, the presence of specific growth factors and intracellular kinase activity. Protein kinase C is required by neural crest cells and cAMP-dependent protein kinase is used in keratinocytes while mitogen-activated protein kinase is required by corneal epithelial cells. Several recent experiments support a role for electric fields in the stimulation of wound healing in the developing frog neurula, adult newt skin and adult mammalian cornea. Some experiments indicate that when the electric field is removed the wound healing rate is 25% slower. In addition, nearly every clinical trial using electric fields to stimulate healing in mammalian wounds reports a significant increase in the rate of healing from 13 to 50%. However, these trials have utilized many different field strengths and polarities, so much work is needed to optimize this approach for the treatment of mammalian wounds.
Biological roles for naturally occurring, extracellular physiological electric fields have been proposed over the past century. However, in the molecular era, many biologists presume that electric fields have little physiological relevance because there has been no unequivocal demonstration of their importance at the single-cell level in vivo. We have used an in vivo rat corneal model, which generates its own endogenous electric field and show that nerve sprouting, the direction of nerve growth and the rate of epithelial wound healing are controlled coordinately by the wound-induced electric field.
Despite compelling phenomenological evidence that small electric fields (<5 mV/mm) can affect brain function, a quantitative and experimentally verified theory is currently lacking. Here we demonstrate a novel mechanism by which the nonlinear properties of single neurons "amplify" the effect of small electric fields: when concurrent to suprathreshold synaptic input, small electric fields can have significant effects on spike timing. For low-frequency fields, our theory predicts a linear dependency of spike timing changes on field strength. For high-frequency fields (relative to the synaptic input), the theory predicts coherent firing, with mean firing phase and coherence each increasing monotonically with field strength. Importantly, in both cases, the effects of fields on spike timing are amplified with decreasing synaptic input slope and increased cell susceptibility (millivolt membrane polarization per field amplitude). We confirmed these predictions experimentally using CA1 hippocampal neurons in vitro exposed to static (direct current) and oscillating (alternating current) uniform electric fields. In addition, we develop a robust method to quantify cell susceptibility using spike timing. Our results provide a precise mechanism for a functional role of endogenous field oscillations (e.g., gamma) in brain function and introduce a framework for considering the effects of environmental fields and design of low-intensity therapeutic neurostimulation technologies.
Here, we consider a noisy, bistable, single neuron model in the presence of periodic external modulation. The modulation induces a correlated switching between states driven by the noise. The information flow through the system, from the modulation, or signal, to the output switching events, leads to a succession of strong peaks in the power spectrum. The signal-to-noise ratio (SNR) obtained from this power spectrum is a measure of the information content in the neuron response. With increasing noise intensity, the SNR passes through a maximum: an effect which has been called stochastic resonance, and which was first advanced as a possible explanation of the observed periodicity in the recurrences of the Earth's ice ages. We treat the problem within the framework of a recently developed approximate theory, valid in the limits of weak noise intensity, weak periodic forcing and low forcing frequency, for both additive and multiplicative noise. Moreover, we have constructed an analog simulator of the neuron which demonstrates the stochastic resonance effect, and with which we have measured the SNRs for comparison with the theoretical results. Our model should be of interest in situations where a single inherently noisy neuron is the receptor of a periodic signal, which is itself noisy, either from the network or from an external source.
We study the phenomenon of stochastic resonance in a system of coupled
neurons that are globally excited by a weak periodic input signal. We
make the realistic assumption that the chemical and electrical synapses
interact in the same neuronal network, hence constituting a hybrid
network. By considering a hybrid coupling scheme embedded in the
scale-free topology, we show that the electrical synapses are more
efficient than chemical synapses in promoting the best correlation
between the weak input signal and the response of the system. We also
demonstrate that the average degree of neurons within the hybrid
scale-free network significantly influences the optimal amount of noise
for the occurrence of stochastic resonance, indicating that there also
exists an optimal topology for the amplification of the response to the
weak input signal. Lastly, we verify that the presented results are
robust to variations of the system size.
We consider here the effect of temporal correlations on the transmission of spike trains in an integrate-and-fire neuron. We find that if the noisy input spike train is variable enough, the signal-to-noise ratio can display more than one peak as a function of the noise strength. This result is analyzed in terms of a simple probabilistic description of the problem.
Noise-induced firing is studied in two major classes of bursting neuron models in the absence of periodic input. In the biologically relevant subthreshold regime where no deterministic firing occurs, additive noise induces spiking limit cycles. This noise makes the output firing patterns sensitive to the characteristics of autonomous subthreshold oscillations, which can change in response to various physicochemical stimuli. The nonmonotonic behavior with increasing noise of the phase locking between spikes and subthreshold oscillations, measured using spectral signal-to-noise ratios and line shape characteristics, are a manifestation of autonomous stochastic resonance in these systems. The type of bifurcation giving rise to bursting activity determines the behavior with noise of the mean firing frequency, interspike interval histogram, spike train power spectrum, and phase locking. In particular, it is shown that a saddle-node bifurcation is not required to see stochastic resonance (SR) without periodic input when there exists a stable deterministic subthreshold oscillation. This paper also studies SR in a detailed ionic neuron model, an approach that leads to tests of hypotheses regarding the nature of noise in real neurons.
We study the effect of heterogeneous neuron and information transmission delay on stochastic resonance of scale-free neuronal networks. For this purpose, we introduce the heterogeneity to the specified neuron with the highest degree. It is shown that in the absence of delay, an intermediate noise level can optimally assist spike firings of collective neurons so as to achieve stochastic resonance on scale-free neuronal networks for small and intermediate α(h), which plays a heterogeneous role. Maxima of stochastic resonance measure are enhanced as α(h) increases, which implies that the heterogeneity can improve stochastic resonance. However, as α(h) is beyond a certain large value, no obvious stochastic resonance can be observed. If the information transmission delay is introduced to neuronal networks, stochastic resonance is dramatically affected. In particular, the tuned information transmission delay can induce multiple stochastic resonance, which can be manifested as well-expressed maximum in the measure for stochastic resonance, appearing every multiple of one half of the subthreshold stimulus period. Furthermore, we can observe that stochastic resonance at odd multiple of one half of the subthreshold stimulus period is subharmonic, as opposed to the case of even multiple of one half of the subthreshold stimulus period. More interestingly, multiple stochastic resonance can also be improved by the suitable heterogeneous neuron. Presented results can provide good insights into the understanding of the heterogeneous neuron and information transmission delay on realistic neuronal networks.
The stochastic resonance in paced time-delayed scale-free FitzHugh–Nagumo (FHN) neuronal networks is investi-gated. We show that an intermediate intensity of additive noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble. Furthermore, we reveal that appropriately tuned delays can induce stochastic multires-onances, appearing at every integer multiple of the pacemaker's oscillation period. We conclude that fine-tuned delay lengths and locally acting pacemakers are vital for ensuring optimal conditions for stochastic resonance on complex neuronal networks.
We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instanta-neous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might neverthe-less preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the frac-tion of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.
We study the spatial dynamics of spiral waves in noisy Hodgkin–Huxley neuronal ensembles evoked by different information transmission delays and network topologies. In classical settings of coherence resonance the intensity of noise is fine-tuned so as to optimize the system's response. Here, we keep the noise intensity constant, and instead, vary the length of information transmission delay amongst coupled neurons. We show that there exists an intermediate transmission delay by which the spiral waves are optimally ordered, hence indicating the existence of delay-enhanced coherence of spatial dynamics in the examined system. Additionally, we examine the robustness of this phenomenon as the diffusive interaction topology changes towards the small-world type, and discover that shortcut links amongst distant neurons hinder the emergence of coherent spiral waves irrespective of transmission delay length. Presented results thus provide insights that could facilitate the understanding of information transmission delay on realistic neuronal networks.
We study the phenomenon of stochastic resonance on a modular neuronal network consisting of several small-world subnetworks with a subthreshold periodic pacemaker. Numerical results show that the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the intensity of additive spatiotemporal noise. This effect of pacemaker-driven stochastic resonance of the system depends extensively on the local and the global network structure, such as the intra- and inter-coupling strengths, rewiring probability of individual small-world subnetwork, the number of links between different subnetworks, and the number of subnetworks. All these parameters play a key role in determining the ability of the network to enhance the noise-induced outreach of the localized subthreshold pacemaker, and only they bounded to a rather sharp interval of values warrant the emergence of the pronounced stochastic resonance phenomenon. Considering the rather important role of pacemakers in real-life, the presented results could have important implications for many biological processes that rely on an effective pacemaker for their proper functioning.
The impact of inhibitory and excitatory synapses in delay-coupled
Hodgkin--Huxley neurons that are driven by noise is studied. If both synaptic
types are used for coupling, appropriately tuned delays in the inhibition
feedback induce multiple firing coherence resonances at sufficiently strong
coupling strengths, thus giving rise to tongues of coherency in the
corresponding delay-strength parameter plane. If only inhibitory synapses are
used, however, appropriately tuned delays also give rise to multiresonant
responses, yet the successive delays warranting an optimal coherence of
excitations obey different relations with regards to the inherent time scales
of neuronal dynamics. This leads to denser coherence resonance patterns in the
delay-strength parameter plane. The robustness of these findings to the
introduction of delay in the excitatory feedback, to noise, and to the number
of coupled neurons is determined. Mechanisms underlying our observations are
revealed, and it is suggested that the regularity of spiking across neuronal
networks can be optimized in an unexpectedly rich variety of ways, depending on
the type of coupling and the duration of delays.
Complexity in the temporal organization of neural systems may be a reflection of the diversity of their neural constituents. These constituents, excitatory and inhibitory neurons, comprise a well-defined ratio in vivo and form the substrate for rhythmic oscillatory activity. To begin to elucidate the dynamical implications that underlie this balance, we construct neural circuits not ordinarily found in nature and study the resulting temporal patterns. We culture several networks of neurons composed of varying fractions of excitatory and inhibitory cells and use a multielectrode array to study their temporal dynamics as this balance is modulated. We use the electrode burst as the temporal imprimatur to signify the presence of network activity. Burst durations, interburst intervals, and the number of spikes participating within a burst are used to illustrate the vivid differences in the temporal organization between the various cultured networks. When the network consists largely of excitatory neurons, no network temporal structure is apparent. However, the addition of inhibitory neurons evokes a temporal order. Calculation of the temporal autocorrelation shows that when the number of inhibitory neurons is a major fraction of the network, a striking network pattern materializes when none was previously present.
Local field potentials and the underlying endogenous electric fields (EFs) are traditionally considered to be epiphenomena of structured neuronal network activity. Recently, however, externally applied EFs have been shown to modulate pharmacologically evoked network activity in rodent hippocampus. In contrast, very little is known about the role of endogenous EFs during physiological activity states in neocortex. Here, we used the neocortical slow oscillation in vitro as a model system to show that weak sinusoidal and naturalistic EFs enhance and entrain physiological neocortical network activity with an amplitude threshold within the range of in vivo endogenous field strengths. Modulation of network activity by positive and negative feedback fields based on the network activity in real-time provide direct evidence for a feedback loop between neuronal activity and endogenous EF. This significant susceptibility of active networks to EFs that only cause small changes in membrane potential in individual neurons suggests that endogenous EFs could guide neocortical network activity.
The neocortex is the most common target of subdural electrotherapy and noninvasive brain stimulation modalities, including transcranial magnetic stimulation (TMS) and transcranial current simulation (TCS). Specific neuronal elements targeted by cortical stimulation are considered to underlie therapeutic effects, but the exact cell type(s) affected by these methods remains poorly understood.
We determined whether neuronal morphology or cell type predicted responses to subthreshold and suprathreshold uniform electric fields.
We characterized the effects of subthreshold and suprathreshold electrical stimulation on identified cortical neurons in vitro. Uniform electric fields were applied to rat motor cortex brain slices, while recording from interneurons and pyramidal cells across cortical layers, using a whole-cell patch clamp. Neuron morphology was reconstructed after intracellular dialysis of biocytin. Based solely on volume-weighted morphology, we developed a parsimonious model of neuronal soma polarization by subthreshold electric fields.
We found that neuronal morphology correlated with somatic subthreshold polarization. Based on neuronal morphology, we predict layer V pyramidal neuronal soma to be individually the most sensitive to polarization by optimally oriented subthreshold fields. Suprathreshold electric field action potential threshold was shown to reflect both direct cell polarization and synaptic (network) activation. Layer V/VI neuron absolute electric field action potential thresholds were lower than layer II/III pyramidal neurons and interneurons. Compared with somatic current injection, electric fields promoted burst firing and modulated action potential firing times.
We present experimental data indicating that cortical neuron morphology relative to electric fields and cortical cell type are factors in determining sensitivity to sub- and supra-threshold brain stimulation.
We propose an approach for desynchronization in an ensemble of globally coupled neural oscillators. The impact of washout filter aided mean field feedback on population synchronization process is investigated. By blocking the Hopf bifurcation of the mean field, the controller desynchronizes the ensemble. The technique is generally demand-controlled. It is robust and can be easily implemented practically. We suggest it for effective deep brain stimulation in neurological diseases characterized by pathological synchronization.
The relationships between noise and complex dynamic behaviors of neuronal ensembles are key questions in computational neuroscience, particularly in understanding some basic signal transmission mechanisms of the brain. Here we systemically investigate both the stochastic resonance (SR) and coherence resonance (CR) in the triple-neuron feed-forward-loop (FFL) network motifs by computational modeling. We use the Izhikevich neuron model as well as the chemical coupling to build the FFL motifs, and consider all possible motif types. The simulation results demonstrate that these motifs can exploit noise to enrich its dynamic performance. With a proper choice of noise intensities, both the SR and CR can be exhibited in many types of the FFLs. On the other hand, our results also indicate that the coupling strength serves as a control parameter, which has great impacts on the stochastic dynamics of the FFL motifs. Additionally, biological implications of presented results in the field of neuroscience are outlined.
We study the impact of additive Gaussian noise and weak periodic forcing on the dynamics of a scale-free network of bistable overdamped oscillators. The periodic forcing is introduced to a single oscillator and therefore acts as a pacemaker trying to impose its rhythm on the whole ensemble. We show that an intermediate intensity of temporally and spatially uncorrelated noise is able to optimally assist the pacemaker in achieving this goal, thus providing evidence for stochastic resonance on weakly paced scale-free networks. Because of the inherent degree inhomogeneity of individual oscillators forming the scale-free network, the placement of the pacemaker within the network is thereby crucial. As two extremes, we consider separately the introduction of the pacemaker to the oscillator with the highest degree and to one of the oscillators having the lowest degree. In both cases the coupling strength plays a crucial role, since it determines to what extent the whole network will follow the pacemaker on the expense of a weaker correlation between the pacemaker and the units that are directly linked with the paced oscillator. Higher coupling strengths facilitate the global outreach of the pacemaker, but require higher noise intensities for the optimal response. In contrast, lower coupling strengths and comparatively low noise intensities localize the optimal response to immediate neighbors of the paced oscillator. If the pacemaker is introduced to the main hub, the transition between the locally and globally optimal responses is characterized by a double resonance that postulates the existence of an optimal coupling strength for the transmission of weak rhythmic activity across scale-free networks. We corroborate the importance of the inhomogeneous structure of scale-free networks by additionally considering regular networks of oscillators with different degrees of coupling.
Here, we consider a noisy, bistable, single neuron model in the presence of periodic external modulation. The modulation induces a correlated switching between states driven by the noise. The information flow through the system, from the modulation, or signal, to the output switching events, leads to a succession of strong peaks in the power spectrum. The signal-to-noise ratio (SNR) obtained from this power spectrum is a measure of the information content in the neuron response. With increasing noise intensity, the SNR passes through a maximum: an effect which has been called stochastic resonance, and which was first advanced as a possible explanation of the observed periodicity in the recurrences of the Earth's ice ages. We treat the problem within the framework of a recently developed approximate theory, valid in the limits of weak noise intensity, weak periodic forcing and low forcing frequency, for both additive and multiplicative noise. Moreover, we have constructed an analog simulator of the neuron which demonstrates the stochastic resonance effect, and with which we have measured the SNRs for comparison with the theoretical results. Our model should be of interest in situations where a single inherently noisy neuron is the receptor of a periodic signal, which is itself noisy, either from the network or from an external source.
1. The evoked EEG responses from the motor cortex of cats under Nembutal after electrical stimulation of nucleus VPL or VL of the thalamus, of midthalamic nuclei and of the cortex itself are compared with the cellular responses from the same area. The cellular responses were almost identical in different cells of a given experiment so that records from one cell can be taken as representative for the whole population of pyramidal cells from which the records were taken. The following correlations were found:
Recently, the phenomena of stochastic resonance (SR) have attracted much attention in the studies of the excitable systems under inherent noise, in particular, nervous systems. We study SR in a stochastic Hodgkin-Huxley neuron under Ornstein-Uhlenbeck noise and periodic stimulus, focusing on the dependence of properties of SR on stimulus parameters. We find that the dependence of the critical forcing amplitude on the frequency of the periodic stimulus shows a bell-shaped structure with a minimum at the stimulus frequency, which is quite different from the monotonous dependence observed in the bistable system at a small frequency range. The frequency dependence of the critical forcing amplitude is explained in connection with the firing onset bifurcation curve of the Hodgkin-Huxley neuron in the deterministic situation. The optimal noise intensity for maximal amplification is also found to show a similar structure.
We present an introductory overview of the subject of stochastic resonance. As researchers' interest in the phenomenon has spread from physics to biology, new questions both fundamental and practical have emerged. After reviewing some key aspects of the subject, we describe a promising candidate for exploring the possible beneficial effects of random noise in sensory transduction. (c) 1998 American Institute of Physics.
A neuronal network inspired by the anatomy of the cerebral cortex was simulated to study the self-organization of spiking neurons into neuronal groups. The network consisted of 100 000 reentrantly interconnected neurons exhibiting known types of cortical firing patterns, receptor kinetics, short-term plasticity and long-term spike-timing-dependent plasticity (STDP), as well as a distribution of axonal conduction delays. The dynamics of the network allowed us to study the fine temporal structure of emerging firing patterns with millisecond resolution. We found that the interplay between STDP and conduction delays gave rise to the spontaneous formation of neuronal groups--sets of strongly connected neurons capable of firing time-locked, although not necessarily synchronous, spikes. Despite the noise present in the model, such groups repeatedly generated patterns of activity with millisecond spike-timing precision. Exploration of the model allowed us to characterize various group properties, including spatial distribution, size, growth, rate of birth, lifespan, and persistence in the presence of synaptic turnover. Localized coherent input resulted in shifts of receptive and projective fields in the model similar to those observed in vivo.
Depth recordings in patients with Parkinson's disease (PD) have demonstrated prominent oscillatory activity in the beta frequency (13-35 Hz) band in local field potentials (LFPs) recorded from the region of the subthalamic nucleus (STN). Although this activity has been hypothesized to contribute to bradykinesia, it is unclear to what extent the LFP oscillations arise in the STN and are synchronous with local neuronal discharge. We therefore recorded both LFPs and multi-neuronal activity from microelectrodes inserted into STN in six PD patients (8 sides) during functional neurosurgery. As microelectrodes passed from above STN into STN, there was a pronounced increase in beta frequency band LFP activity. Furthermore, spike-triggered averages of LFP activity suggested that the discharges of neurons in STN were locked to beta oscillations in the LFP. The LFP is therefore likely to represent synchronous activity in populations of neurons in the STN of patients with PD.
In sensory systems, the presence of a particular nonzero level of noise may significantly enhance the ability of an individual to detect weak sensory stimuli through a phenomenon known as stochastic resonance (SR). The aim of this study was to demonstrate if such phenomenon is also exhibited by the motor system; in particular, in the Ia-motoneuron synapse of the cat spinal cord. Monosynaptic reflexes elicited by periodic electrical stimulation to the medial gastrocnemius nerve were recorded in the L(7) ventral root (or in single motoneurons) of decerebrated cats. Random stretches (mechanical noise) were applied to the lateral gastrocnemius plus soleus muscle by means of a closed-loop mechanical stimulator-transducer. In all cats, we observed the SR phenomenon. The amplitude of the monosynaptic reflexes (or number of action potentials recorded in the motoneurons) evoked by the weak electrical stimuli applied to the medial gastrocnemius nerve were an inverted U-like function of the mechanical noise applied to the lateral gastrocnemius plus soleus muscle. A significant maximum value in the amplitude of the monosynaptic responses was reached with a particular noise amplitude value. Numerical simulations on a model of the monosynaptic reflex pathway qualitatively reproduce this stochastic resonance behavior. We conclude that the monosynaptic reflex response elicited by Ia afferents is optimized by the noisy stretching of a synergistic muscle. Our study provides the first direct demonstration that the motor system, and not only the sensory systems, exhibits the SR phenomenon.
The sensitivity of brain tissue to weak extracellular electric fields is important in assessing potential public health risks of extremely low frequency (ELF) fields, and potential roles of endogenous fields in brain function. Here we determine the effect of applied electric fields on membrane potentials and coherent network oscillations. Applied DC electric fields change transmembrane potentials in CA3 pyramidal cell somata by 0.18 mV per V m(-1) applied. AC sinusoidal electric fields have smaller effects on transmembrane potentials: sensitivity drops as an exponential decay function of frequency. At 50 and 60 Hz it is approximately 0.4 that for DC fields. Effects of fields of < or = 16 V m(-1) peak-to-peak (p-p) did not outlast application. Kainic acid (100 nm) induced coherent network oscillations in the beta and gamma bands (15-100 Hz). Applied fields of > or = 6 V m(-1) p-p (2.1 V m(-1) r.m.s.) shifted the gamma peak in the power spectrum to centre on the applied field frequency or a subharmonic. Statistically significant effects on the timing of pyramidal cell firing within the oscillation appeared at distinct thresholds: at 50 Hz, 1 V m(-1) p-p (354 mV m(-1) r.m.s.) had statistically significant effects in 71% of slices, and 0.5 V m(-1) p-p (177 mV m(-1) r.m.s.) in 20%. These threshold fields are consistent with current environmental guidelines. They correspond to changes in somatic potential of approximately 70 microV, below membrane potential noise levels for neurons, demonstrating the emergent properties of neuronal networks can be more sensitive than measurable effects in single neurons.
We show that the correlation between the frequency of subthreshold pacemaker activity and the response of an excitable array is resonantly dependent on the intensity of additive spatiotemporal noise. Thereby, the effect of the underlying network, defining the interactions among excitable units, largely depends on the coupling strength. Only for intermediate coupling strengths is the small world property able to enhance the stochastic resonance, whereas for smaller and larger couplings the impact of the transition from diffusive to random networks is less profound. Thus, the optimal interplay between a localized source of weak rhythmic activity and the response of the whole array demands a delicate balance between the strength of excitation transfer and the effectiveness of the network structure to support it.
A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons. The model combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC.
Nonlinear physics of complex systems -current status and future trends. Lecture notes in physics
- P Hänggi
- R Bartussek
- J Parisi
- S C Müller
- W Zimmermman
Hänggi P, Bartussek R, Parisi J, Müller SC, Zimmermman W, editors.
Nonlinear physics of complex systems -current status and future
trends. Lecture notes in physics. New York: Springer; 1999.
Frequency sensitivity in Hodgkin-Huxley systems
- C S Zhou
- J Kurths
- B Hu
Zhou CS, Kurths J, Hu B. Frequency sensitivity in Hodgkin-Huxley
systems. Phys Rev E 2003;67:030101.