Oscillation and noise determine signal transduction in shark multimodal sensory cells

Mutual information measure of visual perception based on noisy spiking neural networks

Note that images of low-illumination are weak aperiodic signals, while mutual information can be used as an effective measure for the shared information between the input stimulus and the output response of nonlinear systems, thus it is possible to develop novel visual perception algorithm based on the principle of aperiodic stochastic resonance within the frame of information theory. To confirm this, we reveal this phenomenon using the integrate-and-fire neural networks of neurons with noisy binary random signal as input first. And then, we propose an improved visual perception algorithm with the image mutual information as assessment index. The numerical experiences show that the target image can be picked up with more easiness by the maximal mutual information than by the minimum of natural image quality evaluation (NIQE), which is one of the most frequently used indexes. Moreover, the advantage of choosing quantile as spike threshold has also been confirmed. The improvement of this research should provide large convenience for potential applications including video tracking in environments of low illumination.

Nonlinear mechanism for the enhanced bursting activities induced by fast inhibitory autapse and reduced activities by fast excitatory autapse

The paradoxical phenomena that excitatory modulation does not enhance but reduces or inhibitory modulation not suppresses but promotes neural firing activities have attracted increasing attention. In the present study, paradoxical phenomena induced by both fast excitatory and inhibitory autapses in a "Fold/Big Homoclinic" bursting are simulated, and the corresponding nonlinear and biophysical mechanisms are presented. Firstly, the enhanced conductance of excitatory autapse induces the number of spikes per burst and firing rate reduced, while the enhanced inhibitory autapse cause both indicators increased. Secondly, with fast-slow variable dissection, the burst of bursting is identified to locate between a fold bifurcation and a big saddle-homoclinic orbit bifurcation of the fast subsystem. Enhanced excitatory or inhibitory autapses cannot induce changes of both bifurcation points, i.e., burst width. However, width of slow variable between two successive spikes within a burst becomes wider for the excitatory autapse and narrower for the inhibitory autapse, resulting in the less and more spikes per burst, respectively. Last, the autaptic current of fast autapse mainly plays a role during the peak of action potential, differing from the slow autaptic current with exponential decay, which can play roles following the peak of action potential. The fast excitatory autaptic current enhances the amplitude of the action potential and reduces the repolarization of the action potential to lengthen the interspike interval (ISI) of the spiking of the fast subsystem, resulting in the wide width of slow variable between successive spikes. The fast inhibitory autaptic current reduces the amplitude of action potential and ISI of spiking, resulting in narrow width of slow variable. The novel example of the paradoxical responses for both fast modulations and nonlinear mechanism extend the contents of neurodynamics, which presents potential functions of the fast autapse.

Research on constrained localization of ultrasound geometric distribution based on FHN neurons

The autopilot positioning process is mainly affected by three aspects: the first is the spatial geometric distribution of positioning sensors; the second is the screening of spurious observations; and the third is the equivalent ranging error. A constrained positioning method based on the geometric distribution of FitzHugh-Nagumo (FHN) neurons is proposed. To reduce the geometric accuracy factor, a Horizontal Dilution Of Precision value algorithm with a weight factor was proposed by considering the spatial geometric distribution of base stations and the geometric relationship of anchor points. This paper proposes a geometric constraint data processing method for the error of the pseudo-observation value. Finally, considering the significant weak signal perception ability of the biological nervous system, and the stochastic resonance phenomenon caused by noise can enhance the ability of the neuronal system to detect weak signals, an ultrasonic receiving method based on the stochastic resonance characteristics of FHN neuronal system is proposed, to enhance the signal and reduce noise. The results show that under the optimized base station layout and data geometric constraint processing, the ultrasonic wave based on FHN neuron improves the accuracy of spurious observations, reduces the calculation amount of geometric constraint processing, and reduces the positioning error by 66.67%, which provides a new direction for improving the positioning accuracy.

Obstacle induced spiral waves in a multilayered Huber-Braun (HB) neuron model

Various dynamical properties of four-dimensional mammalian cold receptor model have been discussed widely in the literature considering noise and temperature as important parameters of discussion. Though various spiking and bursting behaviors of the neuron under various noise and temperature conditions studied for a single neuron, no much discussions have been done on the collective behavior. We investigate the collective behavior of these temperature dependent stochastic neurons and unlike the neuron models when forced by periodic external force there is no wave reentry or spiral waves in the network. Hence, we introduce obstacle in the network and depending on the orientation and size of the introduced obstacle, we could show their effects on the wave reentry in the network. Various significant discussions are produced in this paper to confirm that obstacles placed parallel to the wave entry affects the excitability of the tissues significantly compared to those obstacles place perpendicular. We could also show that those obstacles which are lesser in dimensions doesn't affect the excitabilities and hence doesn't contribute for wave reentry. We introduce a new technique to identify wave reentry and spiral waves using the period of individual nodes is proposed. This technique could help us identify even the lowest of excitability change which cannot be seen when using spatiotemporal snapshots.

A discrete Huber-Braun neuron model: from nodal properties to network performance

Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it's the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered obstacle as an important factor which changes the excitability of the neurons in the network. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. In a two-layer network, stimulus play an important role in spatiotemporal dynamics of the network.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09806-1.

Enhanced brainstem phase-locking in low-level noise reveals stochastic resonance in the frequency-following response (FFR)

In nonlinear systems, the inclusion of low-level noise can paradoxically improve signal detection, a phenomenon known as stochastic resonance (SR). SR has been observed in human hearing whereby sensory thresholds (e.g., signal detection and discrimination) are enhanced in the presence of noise. Here, we asked whether subcortical auditory processing (neural phase locking) shows evidence of SR. We recorded brainstem frequency-following-responses (FFRs) in young, normal-hearing listeners to near-electrophysiological-threshold (40 dB SPL) complex tones composed of 10 iso-amplitude harmonics of 150 Hz fundamental frequency (F0) presented concurrent with low-level noise (+20 to -20 dB SNRs). Though variable and weak across ears, some listeners showed improvement in auditory detection thresholds with subthreshold noise confirming SR psychophysically. At the neural level, low-level FFRs were initially eradicated by noise (expected masking effect) but were surprisingly reinvigorated at select masker levels (local maximum near ∼ 35 dB SPL). These data suggest brainstem phase-locking to near threshold periodic stimuli is enhanced in optimal levels of noise, the hallmark of SR. Our findings provide novel evidence for stochastic resonance in the human auditory brainstem and suggest that under some circumstances, noise can actually benefit both the behavioral and neural encoding of complex sounds.

Noise induced suppression of spiral waves in a hybrid FitzHugh-Nagumo neuron with discontinuous resetting

A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated, and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A N×N network of the neuron model is constructed to study the wave propagation and wave re-entry phenomena. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed, but for such values of the flux coupling, the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term, we showed that when noise is introduced for the entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely.

Stochasticity Versus Determinacy in Neurobiology: From Ion Channels to the Question of the "Free Will"

If one accepts that decisions are made by the brain and that neuronal mechanisms obey deterministic physical laws, it is hard to deny what some brain researchers postulate, such as "We do not do what we want, but we want what we do" and "We should stop talking about freedom. Our actions are determined by physical laws." This point of view has been substantially supported by spectacular neurophysiological experiments demonstrating action-related brain activity (readiness potentials, blood oxygen level-dependent signals) occurring up to several seconds before an individual becomes aware of his/her decision to perform the action. This report aims to counter the deterministic argument for the absence of free will by using experimental data, supplemented by computer simulations, to demonstrate that biological systems, specifically brain functions, are built on principle randomness, which is introduced already at the lowest level of neuronal information processing, the opening and closing of ion channels. Switching between open and closed states follows physiological laws but also makes use of randomness, which is apparently introduced by Brownian motion - principally unavoidable under all life-compatible conditions. Ion-channel stochasticity, manifested as noise, function is not smoothed out toward higher functional levels but can even be amplified by appropriate adjustment of the system's non-linearities. Examples shall be given to illustrate how stochasticity can propagate from ion channels to single neuron action potentials to neuronal network dynamics to the interactions between different brain nuclei up to the control of autonomic functions. It is proposed that this intrinsic stochasticity helps to keep the brain in a flexible state to explore diverse alternatives as a prerequisite of free decision-making.

Circadian actions of orexins on the retinorecipient lateral geniculate complex in rat

Key points

Rhythmic processes in living organisms are controlled by biological clocks. The orexinergic system of the lateral hypothalamus carries circadian information to provide arousal for the brain during the active phase.

Here, we show that orexins exert an excitatory action in three parts of the lateral geniculate nucleus (LGN), in particular upon directly retinorecipient neurons in the non‐image forming visual structures.

We provide evidence for the high nocturnal levels of orexins with stable circadian expression of predominant orexin receptor 2 in the LGN.

Our data additionally establish the convergence of orexinergic and pituitary adenylate cyclase (PAC)‐activating peptide/PAC1 receptor systems (used by melanopsin‐expressing retinal ganglion cells), which directly regulates responses to the retinal input.

These results help us better understand circadian orexinergic control over the non‐image forming subcortical visual system, forming the animal's preparedness for the behaviourally active night.

Abstract

The orexinergic system of the lateral hypothalamus is tightly interlinked with the master circadian clock and displays daily variation in activity to provide arousal‐related excitation for the plethora of brain structures in a circadian manner. Here, using a combination of electrophysiological, optogenetic, histological, molecular and neuronal tracing methods, we explore a particular link between orexinergic and visual systems in rat. The results of the present study demonstrate that orexinergic fibre density at the area of subcortical visual system exerts a clear day to night variability, reaching a maximum at behaviourally active night. We also show pronounced electrophysiological activations of neurons in the lateral geniculate nucleus by orexin A through 24 h, via identified distinct orexin receptors, with the ventrolateral geniculate displaying a daily cycle of responsiveness. In addition, for the first time, we provide a direct evidence for orexins to act on retinorecipient neurons with a high convergence of orexinergic and putatively retinal pituitary adenylate cyclase (PAC)‐activating peptide/PAC1 receptor systems. Altogether, the present study ties orexins to non‐image forming visual structures with implications for circadian orexinergic modulation of neurons, which process information on ambient light levels.

Rhythmic processes in living organisms are controlled by biological clocks. The orexinergic system of the lateral hypothalamus carries circadian information to provide arousal for the brain during the active phase.

Here, we show that orexins exert an excitatory action in three parts of the lateral geniculate nucleus (LGN), in particular upon directly retinorecipient neurons in the non‐image forming visual structures.

We provide evidence for the high nocturnal levels of orexins with stable circadian expression of predominant orexin receptor 2 in the LGN.

Our data additionally establish the convergence of orexinergic and pituitary adenylate cyclase (PAC)‐activating peptide/PAC1 receptor systems (used by melanopsin‐expressing retinal ganglion cells), which directly regulates responses to the retinal input.

These results help us better understand circadian orexinergic control over the non‐image forming subcortical visual system, forming the animal's preparedness for the behaviourally active night.

Coherence resonance for neuronal bursting with spike undershoot

Although the bursting patterns with spike undershoot are involved with the achievement of physiological or cognitive functions of brain with synaptic noise, noise induced-coherence resonance (CR) from resting state or subthreshold oscillations instead of bursting has been widely identified to play positive roles in information process. Instead, in the present paper, CR characterized by the increase firstly and then decease of peak value of power spectrum of spike trains is evoked from a bursting pattern with spike undershoot, which means that the minimal membrane potential within burst is lower than that of the subthreshold oscillations between bursts, while CR cannot be evoked from the bursting pattern without spike undershoot. With bifurcations and fast-slow variable dissection method, the bursting patterns with and without spike undershoot are classified into "Sub-Hopf/Fold" bursting and "Fold/Homoclinic" bursting, respectively. For the bursting with spike undershoot, the trajectory of the subthreshold oscillations is very close to that of the spikes within burst. Therefore, noise can induce more spikes from the subthreshold oscillations and modulate the bursting regularity, which leads to the appearance of CR. For the bursting pattern without spike undershoot, the trajectory of the quiescent state is not close to that of the spikes within burst, and noise cannot induce spikes from the quiescent state between bursts, which is cause for non-CR. The result provides a novel case of CR phenomenon and extends the scopes of CR concept, presents that noise can enhance rather than suppress information of the bursting patterns with spike undershoot, which are helpful for understanding the dynamics and the potential physiological or cognitive functions of the nerve fiber or brain neurons with such bursting patterns.

Intermittent Failure of Spike Propagation in Primary Afferent Neurons during Tactile Stimulation

Primary afferent neurons convey somatosensory information to the CNS. Low-threshold mechanoreceptors are classified as slow-adapting (SA) or rapid-adapting (RA) based on whether or not they spike repetitively during sustained tactile stimulation; the former are subclassified as Type 1 or 2 based on the regularity of their spiking. Recording in vivo from DRGs of mice, we observed irregular- and regular-spiking units consistent with SA1 and SA2 low-threshold mechanoreceptors, but some units, which we labeled "semiregular," did not fit cleanly into the existing classification scheme. Analysis of their spiking revealed integer-multiple patterning in which spike trains comprised a fundamental interspike interval and multiples thereof. Integer-multiple-patterned spiking was reproduced by randomly removing spikes from an otherwise regular spike train, suggesting that semiregular units represent SA2 units in which some spikes are "missing." We hypothesized that missing spikes arose from intermittent failure of spikes to initiate or to propagate. Intermittent failure of spike initiation was ruled out by several observations: integer-multiple-patterned spiking was not induced by intradermal lidocaine, was independent of stimulus modality (mechanical vs optogenetic), and could not be reproduced in a conductance-based model neuron given constant input. On the other hand, integer-multiple-patterned spiking was induced by application of lidocaine to the DRG, thus pinpointing intermittent failure of spike propagation as the basis for integer-multiple-patterned spiking. Indeed, half of all SA2 units exhibited some missing spikes, mostly at low rate (<5%), which suggests that axons are efficient in using the lowest safety factor capable of producing near-perfect propagation reliability.SIGNIFICANCE STATEMENT The impedance mismatch at axon branch points can impede spike propagation. Reliability of spike propagation across branch points remains an open question and is especially important for primary afferents whose spikes must cross a T-junction to reach the CNS. Past research on propagation reliability has relied almost entirely on simulations and in vitro experiments. Here, recording in vivo, we linked a distinctive pattern of spiking to the intermittent failure of spike propagation at the T-junction. The rarity of failures argues that safety factor is high under physiological conditions, yet the occurrence of such failures argues that safety factor is just high enough to ensure near-perfect reliability, consistent with a good balance between propagation reliability and energy efficiency.

Noise-induced desynchronization and stochastic escape from equilibrium in complex networks

Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. If these terms are large enough, they can push the system from an initial stable equilibrium point, over a nearby saddle point, outside of the basin of attraction of the stable point. Except in some specific cases, the distance between these two points is not known analytically. Focusing on Kuramoto-like models and under simple assumptions on this distance, we derive conditions under which such noise terms perturb the dynamics strongly enough that they lead to stochastic escape from the initial basin of attraction. We numerically confirm the validity of that criterion for coupled oscillators on four very different complex networks. We find in particular that, quite counterintuitively, systems with inertia leave their initial basin faster than or at the same time as systems without inertia, except for strong white-noise perturbations.

Front-propagation in bacterial inter-colony communication

Many bacterial species exchange signaling molecules to coordinate population-wide responses. For this process, known as quorum sensing, the concentration of the respective molecules is crucial. Here, we consider the interaction between spatially distributed bacterial colonies so that the spreading of the signaling molecules in space becomes important. The exponential growth of the signal-producing populations and the corresponding increase in signaling molecule production result in an exponential concentration profile that spreads with uniform speed. The theoretical predictions are supported by experiments with different strains of the soil bacterium Sinorhizobium meliloti that display fluorescence when either producing or responding to the signaling molecules.

Modeling effects of neural fluctuations and inter-scale interactions

One of the greatest challenges to science, in particular, to neuroscience, is to understand how processes at different levels of organization are related to each other. In connection with this problem is the question of the functional significance of fluctuations, noise, and chaos. This paper deals with three related issues: (1) how processes at different organizational levels of neural systems might be related, (2) the functional significance of non-linear neurodynamics, including oscillations, chaos, and noise, and (3) how computational models can serve as useful tools in elucidating these types of issues. In order to capture and describe phenomena at different micro (molecular), meso (cellular), and macro (network) scales, the computational models need to be of appropriate complexity making use of available experimental data. I exemplify by two major types of computational models, those of Hans Braun and colleagues and those of my own group, which both aim at bridging gaps between different levels of neural systems. In particular, the constructive role of noise and chaos in such systems is modelled and related to functions, such as sensation, perception, learning/memory, decision making, and transitions between different (un-)conscious states. While there is, in general, a focus on upward causation, I will also discuss downward causation, where higher level activity may affect the activity at lower levels, which should be a condition for any functional role of consciousness and free will, often considered to be problematic to science.

Activity patterns with silent states in a heterogeneous network of gap-junction coupled Huber-Braun model neurons

A mathematical model of a network of nearest neighbor gap-junction coupled neurons has been used to examine the impact of neuronal heterogeneity on the networks' activity during increasing coupling strength. Heterogeneity has been introduced by Huber-Braun model neurons with randomization of the temperature as a scaling factor. This leads to neurons of an enormous diversity of impulse pattern, including burst discharges, chaotic activity, and two different types of tonic firing-all of them experimentally observed in the peripheral as well as central nervous system. When the network is composed of all these types of neurons, randomly selected, a particular phenomenon can be observed. At a certain coupling strength, the network goes into a completely silent state. Examination of voltage traces and inter-spike intervals of individual neurons suggests that all neurons, irrespective of their original pattern, go through a well-known bifurcation scenario, resembling those of single neurons especially on external current injection. All the originally spontaneously firing neurons can achieve constant membrane potentials at which all intrinsic and gap-junction currents are balanced. With limited diversity, i.e., taking out neurons of specific patterns from the lower and upper temperature range, spontaneous firing can be reinstalled with further increasing coupling strength, especially when the tonic firing regimes are missing. Reinstalled firing develops from slowly increasing subthreshold oscillations leading to tonic firing activity with already fairly well synchronized action potentials, while the subthreshold potentials can still be significantly different. Full in phase synchronization is not achieved. Additional studies are needed elucidating the underlying mechanisms and the conditions under which such particular transitions can appear.

Gamma and infra-slow oscillations shape neuronal firing in the rat subcortical visual system

KEY POINTS

Neuronal oscillations observed in sensory systems are physiological carriers of information about stimulus features. Rhythm in the infra-slow range, originating from the retina, was previously found in the firing of subcortical visual system nuclei involved in both image and non-image forming functions. The present study shows that the firing of neurons in the lateral geniculate nucleus is also governed by gamma oscillation (∼35 Hz) time-locked to high phase of infra-slow rhythm that codes the intensity of transient light stimulation. We show that both physiological rhythms are synchronized within and between ipsilateral nuclei of the subcortical visual system and are dependent on retinal activity. The present study shows that neurophysiological oscillations characterized by various frequencies not only coexist in the subcortical visual system, but also are subjected to complex interference and synchronization processes.

ABSTRACT

The physiological function of rhythmic firing in the neuronal networks of sensory systems has been linked with information coding. Also, neuronal oscillations in different frequency bands often change as a signature of brain state or sensory processing. Infra-slow oscillation (ISO) in the neuronal firing dependent on the retinal network has been described previously in the structures of the subcortical visual system. In the present study, we show for the first time that firing of ISO neurons in the lateral geniculate nucleus is also characterized by a harmonic discharge pattern (i.e. action potentials are separated by the intervals governed by fundamental frequency in the gamma range: ∼35 Hz). A similar phenomenon was recently described in the suprachiasmatic nuclei of the hypothalamus: the master biological clock. We found that both gamma and ISO rhythms were synchronized within and between ipsilateral nuclei of the subcortical visual system and were dependent on the retinal activity of the contralateral eye. These oscillatory patterns were differentially influenced by transient and prolonged light stimulation with respect to both frequency change direction and sustainability. The results of the present study show that the firing pattern of neurons in the subcortical visual system is shaped by oscillations from infra-slow and gamma frequency bands that are plausibly generated by the retinal network. Additionally, the results demonstrate that both rhythms are not a distinctive feature of image or non-image forming visual systems but, instead, they comprise two channels carrying distinctive properties of photic information.

Stochastic multiresonance in coupled excitable FHN neurons

In this paper, effects of noise on Watts-Strogatz small-world neuronal networks, which are stimulated by a subthreshold signal, have been investigated. With the numerical simulations, it is surprisingly found that there exist several optimal noise intensities at which the subthreshold signal can be detected efficiently. This indicates the occurrence of stochastic multiresonance in the studied neuronal networks. Moreover, it is revealed that the occurrence of stochastic multiresonance has close relationship with the period of subthreshold signal T_e and the noise-induced mean period of the neuronal networks T₀. In detail, we find that noise could induce the neuronal networks to generate stochastic resonance for M times if T_e is not very large and falls into the interval (M×T₀,(M+1)×T₀) with M being a positive integer. In real neuronal system, subthreshold signal detection is very meaningful. Thus, the obtained results in this paper could give some important implications on detecting subthreshold signal and propagating neuronal information in neuronal systems.

Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network

We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). However, STDP was not considered in previous works on stochastic burst synchronization (SBS) between noise-induced burstings of sub-threshold neurons. Here, we study the effect of additive STDP on SBS by varying the noise intensity D in the Barabási-Albert scale-free network (SFN). One of our main findings is a Matthew effect in synaptic plasticity which occurs due to a positive feedback process. Good burst synchronization (with higher bursting measure) gets better via long-term potentiation (LTP) of synaptic strengths, while bad burst synchronization (with lower bursting measure) gets worse via long-term depression (LTD). Consequently, a step-like rapid transition to SBS occurs by changing D, in contrast to a relatively smooth transition in the absence of STDP. We also investigate the effects of network architecture on SBS by varying the symmetric attachment degree [Formula: see text] and the asymmetry parameter [Formula: see text] in the SFN, and Matthew effects are also found to occur by varying [Formula: see text] and [Formula: see text]. Furthermore, emergences of LTP and LTD of synaptic strengths are investigated in details via our own microscopic methods based on both the distributions of time delays between the burst onset times of the pre- and the post-synaptic neurons and the pair-correlations between the pre- and the post-synaptic instantaneous individual burst rates (IIBRs). Finally, a multiplicative STDP case (depending on states) with soft bounds is also investigated in comparison with the additive STDP case (independent of states) with hard bounds. Due to the soft bounds, a Matthew effect with some quantitative differences is also found to occur for the case of multiplicative STDP.

Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity

We consider the Watts-Strogatz small-world network (SWN) consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a "Matthew" effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation of synaptic strengths, while bad synchronization gets worse via long-term depression. Emergences of long-term potentiation and long-term depression of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre- and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on states) on the SSS are studied and discussed in comparison with the case of additive STDP (independent of states). These effects of STDP on the SSS in the SWN are also compared with those in the regular lattice and the random graph.

Noise activated bistable sensor based on chaotic system with output defined by temporal coding and firing rate

Traditional bistable sensors use external bias signal to drive its response between states and their detection strategy is based on the output power spectral density or the residence time difference (RTD) in two sensor states. Recently, the noise activated nonlinear dynamic sensors driven only by noise based on RTD technique have been proposed. Here, we present experimental results of dc voltage measurements by noise-driven bistable sensor based on electronic Chua's circuit operating in a chaotic regime where two single scroll attractors coexist. The output of the sensor is quantified by the proportion of the time the sensor stays in one state to the total observation time and by the spike-count rate with spikes defined by crossings between attractors. The relationship between the stimuli and particular observable for different noise intensities is obtained, the usefulness of each coding scheme is discussed, and the optimal noise intensity for detection is indicated. It is shown that the obtained relationship is the same for any observation time when population coding is used. The optimal time window for both detection and the number of units in population coding is found. Our results may be useful for analyses and understanding of the neural activity and in designing bistable storage elements at length scales where thermal fluctuations drastically increase and the effect of noise must be taken into consideration.

A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

Two different bifurcation scenarios of firing patterns with decreasing extracellular calcium concentrations were observed in identical sciatic nerve fibers of a chronic constriction injury (CCI) model when the extracellular 4-aminopyridine concentrations were fixed at two different levels. Both processes proceeded from period-1 bursting to period-1 spiking via complex or simple processes. Multiple typical experimental examples manifested dynamics closely matching those simulated in a recently proposed 4-dimensional model to describe the nonlinear dynamics of the CCI model, which included most cases of the bifurcation scenarios. As the extracellular 4-aminopyridine concentrations is increased, the structure of the bifurcation scenario becomes more complex. The results provide a basic framework for identifying the relationships between different neural firing patterns and different bifurcation scenarios and for revealing the complex nonlinear dynamics of neural firing patterns. The potential roles of the basic bifurcation structures in identifying the information process mechanism are discussed.

Identification of neural firing patterns, frequency and temporal coding mechanisms in individual aortic baroreceptors

In rabbit depressor nerve fibers, an on-off firing pattern, period-1 firing, and integer multiple firing with quiescent state were observed as the static pressure level was increased. A bursting pattern with bursts at the systolic phase of blood pressure, continuous firing, and bursting with burst at diastolic phase and quiescent state at systolic phase were observed as the mean level of the dynamic blood pressure was increased. For both static and dynamic pressures, the firing frequency of the first two firing patterns increased and of the last firing pattern decreased due to the quiescent state. If the quiescent state is disregarded, the spike frequency becomes an increasing trend. The instantaneous spike frequency of the systolic phase bursting, continuous firing, and diastolic phase bursting can reflect the temporal process of the systolic phase, whole procedure, and diastolic phase of the dynamic blood pressure signal, respectively. With increasing the static current corresponding to pressure level, the deterministic Hodgkin-Huxley (HH) model manifests a process from a resting state first to period-1 firing via a subcritical Hopf bifurcation and then to a resting state via a supercritical Hopf bifurcation, and the firing frequency increases. The on-off firing and integer multiple firing were here identified as noise-induced firing patterns near the subcritical and supercritical Hopf bifurcation points, respectively, using the stochastic HH model. The systolic phase bursting and diastolic phase bursting were identified as pressure-induced firings near the subcritical and supercritical Hopf bifurcation points, respectively, using an HH model with a dynamic signal. The firing, spike frequency, and instantaneous spike frequency observed in the experiment were simulated and explained using HH models. The results illustrate the dynamics of different firing patterns and the frequency and temporal coding mechanisms of aortic baroreceptor.

Dynamics of on-off neural firing patterns and stochastic effects near a sub-critical Hopf bifurcation

On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris-Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to discriminate bifurcation types and neural excitability types.

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the [Formula: see text]-[Formula: see text] plane ([Formula: see text]: synaptic inhibition strength and [Formula: see text]: noise intensity). As the rewiring probability [Formula: see text] is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the [Formula: see text]-[Formula: see text] plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.

Phase-locked regimes in delay-coupled oscillator networks

For an ensemble of globally coupled oscillators with time-delayed interactions, an explicit relation for the frequency of synchronized dynamics corresponding to different phase behaviors is obtained. One class of solutions corresponds to globally synchronized in-phase oscillations. The other class of solutions have mixed phases, and these can be either randomly distributed or can be a splay state, namely with phases distributed uniformly on a circle. In the strong coupling limit and for larger networks, the in-phase synchronized configuration alone remains. Upon variation of the coupling strength or the size of the system, the frequency can change discontinuously, when there is a transition from one class of solutions to another. This can be from the in-phase state to a mixed-phase state, but can also occur between two in-phase configurations of different frequency. Analytical and numerical results are presented for coupled Landau-Stuart oscillators, while numerical results are shown for Rössler and FitzHugh-Nagumo systems.

Characterizing spiking in noisy type II neurons

Understanding the dynamics of noisy neurons remains an important challenge in neuroscience. Here, we describe a simple probabilistic model that accurately describes the firing behavior in a large class (type II) of neurons. To demonstrate the usefulness of this model, we show how it accurately predicts the interspike interval (ISI) distributions, bursting patterns and mean firing rates found by: (1) simulations of the classic Hodgkin-Huxley model with channel noise, (2) experimental data from squid giant axon with a noisy input current and (3) experimental data on noisy firing from a neuron within the suprachiasmatic nucleus (SCN). This simple model has 6 parameters, however, in some cases, two of these parameters are coupled and only 5 parameters account for much of the known behavior. From these parameters, many properties of spiking can be found through simple calculation. Thus, we show how the complex effects of noise can be understood through a simple and general probabilistic model.

Low endogenous neural noise in autism

‘Heuristic’ theories of autism postulate that a single mechanism or process underpins the diverse psychological features of autism spectrum disorder. Although no such theory can offer a comprehensive account, the parsimonious descriptions they provide are powerful catalysts to autism research. One recent proposal holds that ‘noisy’ neuronal signalling explains not only some deficits in autism spectrum disorder, but also some superior abilities, due to ‘stochastic resonance’. Here, we discuss three distinct actions of noise in neural networks, arguing in each case that autism spectrum disorder symptoms reflect too little, rather than too much, neural noise. Such reduced noise, perhaps a function of atypical brainstem activation, would enhance detection and discrimination in autism spectrum disorder but at significant cost, foregoing the widespread benefits of noise in neural networks.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.

Addition of visual noise boosts evoked potential-based brain-computer interface

Although noise has a proven beneficial role in brain functions, there have not been any attempts on the dedication of stochastic resonance effect in neural engineering applications, especially in researches of brain-computer interfaces (BCIs). In our study, a steady-state motion visual evoked potential (SSMVEP)-based BCI with periodic visual stimulation plus moderate spatiotemporal noise can achieve better offline and online performance due to enhancement of periodic components in brain responses, which was accompanied by suppression of high harmonics. Offline results behaved with a bell-shaped resonance-like functionality and 7–36% online performance improvements can be achieved when identical visual noise was adopted for different stimulation frequencies. Using neural encoding modeling, these phenomena can be explained as noise-induced input-output synchronization in human sensory systems which commonly possess a low-pass property. Our work demonstrated that noise could boost BCIs in addressing human needs.

Fokker-Planck and Fortet Equation-Based Parameter Estimation for a Leaky Integrate-and-Fire Model with Sinusoidal and Stochastic Forcing

Analysis of sinusoidal noisy leaky integrate-and-fire models and comparison with experimental data are important to understand the neural code and neural synchronization and rhythms. In this paper, we propose two methods to estimate input parameters using interspike interval data only. One is based on numerical solutions of the Fokker-Planck equation, and the other is based on an integral equation, which is fulfilled by the interspike interval probability density. This generalizes previous methods tailored to stationary data to the case of time-dependent input. The main contribution is a binning method to circumvent the problems of nonstationarity, and an easy-to-implement initializer for the numerical procedures. The methods are compared on simulated data.

LIST OF ABBREVIATIONS LIF

Leaky integrate-and-fireISI: Interspike intervalSDE: Stochastic differential equationPDE: Partial differential equation.

Dynamics of Gene Silencing in a Live Cell: Stochastic Resonance

Binding of a specific siRNA to the target mRNA in a live cell (human breast cancer cell, MCF-7) is studied by confocal microscopy. The specific siRNA (labeled with a fluorophore, alexa 488) exhibits much higher intensity of fluorescence in the bound state than in the free (unbound) state. It is observed that repeated unbinding and rebinding of siRNA (to target mRNA) occur before gene silencing. 16 273 on-time periods (residence or dwell time of siRNA in bound form) are detected. They follow a strikingly simple pattern. All of the on-time periods are odd-integral multiples of 5.5 ± 0.05 ms. This is ascribed to stochastic resonance.

What is all the noise about in interval timing?

Cognitive processes such as decision-making, rate calculation and planning require an accurate estimation of durations in the supra-second range-interval timing. In addition to being accurate, interval timing is scale invariant: the time-estimation errors are proportional to the estimated duration. The origin and mechanisms of this fundamental property are unknown. We discuss the computational properties of a circuit consisting of a large number of (input) neural oscillators projecting on a small number of (output) coincidence detector neurons, which allows time to be coded by the pattern of coincidental activation of its inputs. We showed analytically and checked numerically that time-scale invariance emerges from the neural noise. In particular, we found that errors or noise during storing or retrieving information regarding the memorized criterion time produce symmetric, Gaussian-like output whose width increases linearly with the criterion time. In contrast, frequency variability produces an asymmetric, long-tailed Gaussian-like output, that also obeys scale invariant property. In this architecture, time-scale invariance depends neither on the details of the input population, nor on the distribution probability of noise.

Biological experimental observations of an unnoticed chaos as simulated by the Hindmarsh-Rose model

An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern.

Why noise is useful in functional and neural mechanisms of interval timing?

BACKGROUND

The ability to estimate durations in the seconds-to-minutes range - interval timing - is essential for survival, adaptation and its impairment leads to severe cognitive and/or motor dysfunctions. The response rate near a memorized duration has a Gaussian shape centered on the to-be-timed interval (criterion time). The width of the Gaussian-like distribution of responses increases linearly with the criterion time, i.e., interval timing obeys the scalar property.

RESULTS

We presented analytical and numerical results based on the striatal beat frequency (SBF) model showing that parameter variability (noise) mimics behavioral data. A key functional block of the SBF model is the set of oscillators that provide the time base for the entire timing network. The implementation of the oscillators block as simplified phase (cosine) oscillators has the additional advantage that is analytically tractable. We also checked numerically that the scalar property emerges in the presence of memory variability by using biophysically realistic Morris-Lecar oscillators. First, we predicted analytically and tested numerically that in a noise-free SBF model the output function could be approximated by a Gaussian. However, in a noise-free SBF model the width of the Gaussian envelope is independent of the criterion time, which violates the scalar property. We showed analytically and verified numerically that small fluctuations of the memorized criterion time leads to scalar property of interval timing.

CONCLUSIONS

Noise is ubiquitous in the form of small fluctuations of intrinsic frequencies of the neural oscillators, the errors in recording/retrieving stored information related to criterion time, fluctuation in neurotransmitters' concentration, etc. Our model suggests that the biological noise plays an essential functional role in the SBF interval timing.

Effects of time delay and random rewiring on the stochastic resonance in excitable small-world neuronal networks

The effects of time delay and rewiring probability on stochastic resonance and spatiotemporal order in small-world neuronal networks are studied in this paper. Numerical results show that, irrespective of the pacemaker introduced to one single neuron or all neurons of the network, the phenomenon of stochastic resonance occurs. The time delay in the coupling process can either enhance or destroy stochastic resonance on small-world neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of the pacemaker. More importantly, it is found that the small-world topology can significantly affect the stochastic resonance on excitable neuronal networks. For small time delays, increasing the rewiring probability can largely enhance the efficiency of pacemaker-driven stochastic resonance. We argue that the time delay and the rewiring probability both play a key role in determining the ability of the small-world neuronal network to improve the noise-induced outreach of the localized subthreshold pacemaker.

How noise contributes to time-scale invariance of interval timing

Time perception in the suprasecond range is crucial for fundamental cognitive processes such as decision making, rate calculation, and planning. In the vast majority of species, behavioral manipulations, and neurophysiological manipulations, interval timing is scale invariant: the time-estimation errors are proportional to the estimated duration. The origin and mechanisms of this fundamental property are unknown. We discuss the computational properties of a circuit consisting of a large number of (input) neural oscillators projecting on a small number of (output) coincidence detector neurons, which allows time to be coded by the pattern of coincidental activation of its inputs. We show that time-scale invariance emerges from the neural noise, such as small fluctuations in the firing patterns of its input neurons and in the errors with which information is encoded and retrieved by its output neurons. In this architecture, time-scale invariance is resistant to manipulations as it depends neither on the details of the input population nor on the distribution probability of noise.

Diversity and noise effects in a model of homeostatic regulation of the sleep-wake cycle

Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed examination of the underlying mechanisms. Neuronal systems in general, and those involved in sleep regulation in particular, are noisy and heterogeneous by their nature. It has been shown in various systems that certain levels of noise and diversity can significantly improve signal encoding. However, these phenomena, especially the effects of diversity, are rarely considered in the models of sleep regulation. The present paper is focused on a neuron-based physiologically motivated model of sleep-wake cycles that proposes a novel mechanism of the homeostatic regulation of sleep based on the dynamics of a wake-promoting neuropeptide orexin. Here this model is generalized by the introduction of intrinsic diversity and noise in the orexin-producing neurons, in order to study the effect of their presence on the sleep-wake cycle. A simple quantitative measure of the quality of a sleep-wake cycle is introduced and used to systematically study the generalized model for different levels of noise and diversity. The model is shown to exhibit a clear diversity-induced resonance: that is, the best wake-sleep cycle turns out to correspond to an intermediate level of diversity at the synapses of the orexin-producing neurons. On the other hand, only a mild evidence of stochastic resonance is found, when the level of noise is varied. These results show that disorder, especially in the form of quenched diversity, can be a key-element for an efficient or optimal functioning of the homeostatic regulation of the sleep-wake cycle. Furthermore, this study provides an example of a constructive role of diversity in a neuronal system that can be extended beyond the system studied here.

Time delay induced transition of gene switch and stochastic resonance in a genetic transcriptional regulatory model

Background

Noise, nonlinear interactions, positive and negative feedbacks within signaling pathways, time delays, protein oligomerization, and crosstalk between different pathways are main characters in the regulatory of gene expression. However, only a single noise source or only delay time in the deterministic model is considered in the gene transcriptional regulatory system in previous researches. The combined effects of correlated noise and time delays on the gene regulatory model still remain not to be fully understood.

Results

The roles of time delay on gene switch and stochastic resonance are systematically explored based on a famous gene transcriptional regulatory model subject to correlated noise. Two cases, including linear time delay appearing in the degradation process (case I) and nonlinear time delay appearing in the synthesis process (case II) are considered, respectively. For case I: Our theoretical results show that time delay can induce gene switch, i.e., the TF-A monomer concentration shifts from the high concentration state to the low concentration state ("on"→"off"). With increasing the time delay, the transition from "on" to "off" state can be further accelerated. Moreover, it is found that the stochastic resonance can be enhanced by both the time delay and correlated noise intensity. However, the additive noise original from the synthesis rate restrains the stochastic resonance. It is also very interesting that a resonance bi-peaks structure appears under large additive noise intensity. The theoretical results by using small-delay time-approximation approach are consistent well with our numerical simulation. For case II: Our numerical simulation results show that time delay can also induce the gene switch, however different with case I, the TF-A monomer concentration shifts from the low concentration state to the high concentration state ("off"→"on"). With increasing time delay, the transition from "on" to "off" state can be further enhanced. Moreover, it is found that the stochastic resonance can be weaken by the time delay.

Conclusions

The stochastic delay dynamic approach can identify key physiological control parameters to which the behavior of special genetic regulatory systems is particularly sensitive. Such parameters might provide targets for pharmacological intervention. Thus, it would be highly interesting to investigate if similar experimental techniques could be used to bring out the delay-induced switch and stochastic resonance in the stochastic gene transcriptional regulatory process.

Identifying type I excitability using dynamics of stochastic neural firing patterns

The stochastic firing patterns are simulated near saddle-node bifurcation on an invariant cycle corresponding to type I excitability in stochastic Morris-Lecar model. In absence of external periodic signal, the stochastic firing manifests continuous distribution in ISI histogram (ISIH), whose amplitude at first increases sharply and then decreases exponentially. In presence of the external periodic signal, stochastic firing patterns appear as two cases of integer multiple firing with multiple discrete peaks in ISIH. One manifests perfect exponential decay in all peaks and the other imperfect exponential decay except a lower first peak. These stochastic firing patterns simulated with or without external periodic signal can be demonstrated in the experiments on rat hippocampal CA1 pyramidal neurons. The exponential decay laws in the multiple peaks are also acquired using probability analysis method. The perfect decay law is determined by the independent characteristic within the firing while the imperfect decay law is from the inhibitory effect. In addition, the stochastic firing patterns corresponding to type I excitability are compared to those of type II excitability. The results not only reveal the dynamics of stochastic firing patterns with or without external signal corresponding to type I excitability, but also provide practical indicators to availably identify type I excitability.

Spike-interval triggered averaging reveals a quasi-periodic spiking alternative for stochastic resonance in catfish electroreceptors

Catfish detect and identify invisible prey by sensing their ultra-weak electric fields with electroreceptors. Any neuron that deals with small-amplitude input has to overcome sensitivity limitations arising from inherent threshold non-linearities in spike-generation mechanisms. Many sensory cells solve this issue with stochastic resonance, in which a moderate amount of intrinsic noise causes irregular spontaneous spiking activity with a probability that is modulated by the input signal. Here we show that catfish electroreceptors have adopted a fundamentally different strategy. Using a reverse correlation technique in which we take spike interval durations into account, we show that the electroreceptors generate a supra-threshold bias current that results in quasi-periodically produced spikes. In this regime stimuli modulate the interval between successive spikes rather than the instantaneous probability for a spike. This alternative for stochastic resonance combines threshold-free sensitivity for weak stimuli with similar sensitivity for excitations and inhibitions based on single interspike intervals.

Exponential decay characteristics of the stochastic integer multiple neural firing patterns

Integer multiple neural firing patterns exhibit multi-peaks in inter-spike interval (ISI) histogram (ISIH) and exponential decay in amplitude of peaks, which results from their stochastic mechanisms. But in previous experimental observation that the decay in ISIH frequently shows obvious bias from exponential law. This paper studied three typical cases of the decay, by transforming ISI series of the firing to discrete binary chain and calculating the probabilities or frequencies of symbols over the whole chain. The first case is the exponential decay without bias. An example of this case was discovered on hippocampal CA1 pyramidal neuron stimulated by external signal. Probability calculation shows that this decay without bias results from a stochastic renewal process, in which the successive spikes are independent. The second case is the exponential decay with a higher first peak, while the third case is that with a lower first peak. An example of the second case was discovered in experiment on a neural pacemaker. Simulation and calculation of the second and third cases indicate that the dependency in successive spikes of the firing leads to the bias seen in decay of ISIH peaks. The quantitative expression of the decay slope of three cases of firing patterns, as well as the excitatory effect in the second case of firing pattern and the inhibitory effect in the third case of firing pattern are identified. The results clearly reveal the mechanism of the exponential decay in ISIH peaks of a number of important neural firing patterns and provide new understanding for typical bias from the exponential decay law.

Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns

Period-doubling bifurcation to chaos were discovered in spontaneous firings of Onchidium pacemaker neurons. In this paper, we provide three cases of bifurcation processes related to period-doubling bifurcation cascades to chaos observed in the spontaneous firing patterns recorded from an injured site of rat sciatic nerve as a pacemaker. Period-doubling bifurcation cascades to period-4 (π(2,2)) firstly, and then to chaos, at last to a periodicity, which can be period-5, period-4 (π(4)) and period-3, respectively, in different pacemakers. The three bifurcation processes are labeled as case I, II and III, respectively, manifesting procedures different to those of period-adding bifurcation. Higher-dimensional unstable periodic orbits (UPOs) can be detected in the chaos, built close relationships to the periodic firing patterns. Case III bifurcation process is similar to that discovered in the Onchidium pacemaker neurons and simulated in theoretical model-Chay model. The extra-large Feigenbaum constant manifesting in the period-doubling bifurcation process, induced by quasi-discontinuous characteristics exhibited in the first return maps of both ISI series and slow variable of Chay model, shows that higher-dimensional periodic behaviors appeared difficult within the period-doubling bifurcation cascades. The results not only provide examples of period-doubling bifurcation to chaos and chaos with higher-dimensional UPOs, but also reveal the dynamical features of the period-doubling bifurcation cascades to chaos.

Sensory coding in oscillatory electroreceptors of paddlefish

Coherence and information theoretic analyses were applied to quantitate the response properties and the encoding of time-varying stimuli in paddlefish electroreceptors (ERs), studied in vivo. External electrical stimuli were Gaussian noise waveforms of varied frequency band and strength, including naturalistic waveforms derived from zooplankton prey. Our coherence analyses elucidated the role of internal oscillations and transduction processes in shaping the 0.5-20 Hz best frequency tuning of these electroreceptors, to match the electrical signals emitted by zooplankton prey. Stimulus-response coherence fell off above approximately 20 Hz, apparently due to intrinsic limits of transduction, but was detectable up to 40-50 Hz. Aligned with this upper fall off was a narrow band of intense internal noise at ∼25 Hz, due to prominent membrane potential oscillations in cells of sensory epithelia, which caused a narrow deadband of external insensitivity. Using coherence analysis, we showed that more than 76% of naturalistic stimuli of weak strength, ∼1 μV∕cm, was linearly encoded into an afferent spike train, which transmitted information at a rate of ∼30 bits∕s. Stimulus transfer to afferent spike timing became essentially nonlinear as the stimulus strength was increased to induce bursting firing. Strong stimuli, as from nearby zooplankton prey, acted to synchronize the bursting responses of afferents, including across populations of electroreceptors, providing a plausible mechanism for reliable information transfer to higher-order neurons through noisy synapses.

Temperature-dependent stochastic dynamics of the Huber-Braun neuron model

The response of a four-dimensional mammalian cold receptor model to different implementations of noise is studied across a wide temperature range. It is observed that for noisy activation kinetics, the parameter range decomposes into two regions in which the system reacts qualitatively completely different to small perturbations through noise, and these regions are separated by a homoclinic bifurcation. Noise implemented as an additional current yields a substantially different system response at low temperature values, while the response at high temperatures is comparable to activation-kinetic noise. We elucidate how this phenomenon can be understood in terms of state space dynamics and gives quantitative results on the statistics of interspike interval distributions across the relevant parameter range.

Stochastic resonance activity influences serum tryptophan metabolism in healthy human subjects

Background

Stochastic resonance therapy (SRT) is used for rehabilitation of patients with various neuropsychiatric diseases. An alteration in tryptophan metabolism along the kynurenine pathway has been identified in the central and peripheral nervous systems in patients with neuroinflammatory and neurodegenerative diseases and during the aging process. This study investigated the effect of SRT as an exercise activity on serum tryptophan metabolites in healthy subjects.

Methods

Serum L-tryptophan, L-kynurenine, kynurenic acid, and anthranilic acid levels were measured one minute before SRT and at one, 5, 15, 30, and 60 minutes after SRT. We found that SRT affected tryptophan metabolism. Serum levels of L-tryptophan, L-kynurenine, and kynurenic acid were significantly reduced for up to 60 minutes after SRT. Anthranilic acid levels were characterized by a moderate, non significant transient decrease for up to 15 minutes, followed by normalization at 60 minutes. Tryptophan metabolite ratios were moderately altered, suggesting activation of metabolism after SRT. Lowering of tryptophan would generally involve activation of tryptophan catabolism and neurotransmitter, protein, and bone biosynthesis. Lowering of kynurenic acid by SRT might be relevant for improving symptoms in patients with neuropsychiatric disorders, such as Parkinson’s disease, Alzheimer’s disease, schizophrenia, and depression, as well as certain pain conditions.