Behavioral stochastic resonance: how the noise from a Daphnia swarm enhances individual prey capture by juvenile paddlefish

The ecology of electricity and electroreception

Electricity, the interaction between electrically charged objects, is widely known to be fundamental to the functioning of living systems. However, this appreciation has largely been restricted to the scale of atoms, molecules, and cells. By contrast, the role of electricity at the ecological scale has historically been largely neglected, characterised by punctuated islands of research infrequently connected to one another. Recently, however, an understanding of the ubiquity of electrical forces within the natural environment has begun to grow, along with a realisation of the multitude of ecological interactions that these forces may influence. Herein, we provide the first comprehensive collation and synthesis of research in this emerging field of electric ecology. This includes assessments of the role electricity plays in the natural ecology of predator-prey interactions, pollination, and animal dispersal, among many others, as well as the impact of anthropogenic activity on these systems. A detailed introduction to the ecology and physiology of electroreception - the biological detection of ecologically relevant electric fields - is also provided. Further to this, we suggest avenues for future research that show particular promise, most notably those investigating the recently discovered sense of aerial electroreception.

Natural ELF fields in the atmosphere and in living organisms

Most electrical activity in vertebrates and invertebrates occurs at extremely low frequencies (ELF), with characteristic maxima below 50 Hz. The origin of these frequency maxima is unknown and remains a mystery. We propose that over billions of years during the evolutionary history of living organisms on Earth, the natural electromagnetic resonant frequencies in the atmosphere, continuously generated by global lightning activity, provided the background electric fields for the development of cellular electrical activity. In some animals, the electrical spectrum is difficult to differentiate from the natural background atmospheric electric field produced by lightning. In this paper, we present evidence for the link between the natural ELF fields and those found in many living organisms, including humans.

Challenges in coupling atmospheric electricity with biological systems

The atmosphere is host to a complex electric environment, ranging from a global electric circuit generating fluctuating atmospheric electric fields to local lightning strikes and ions. While research on interactions of organisms with their electrical environment is deeply rooted in the aquatic environment, it has hitherto been confined to interactions with local electrical phenomena and organismal perception of electric fields. However, there is emerging evidence of coupling between large- and small-scale atmospheric electrical phenomena and various biological processes in terrestrial environments that even appear to be tied to continental waters. Here, we synthesize our current understanding of this connectivity, discussing how atmospheric electricity can affect various levels of biological organization across multiple ecosystems. We identify opportunities for research, highlighting its complexity and interdisciplinary nature and draw attention to both conceptual and technical challenges lying ahead of our future understanding of the relationship between atmospheric electricity and the organization and functioning of biological systems.

Stochastic resonance in MoS2 photodetector

In this article, we adopt a radical approach for next generation ultra-low-power sensor design by embracing the evolutionary success of animals with extraordinary sensory information processing capabilities that allow them to survive in extreme and resource constrained environments. Stochastic resonance (SR) is one of those astounding phenomena, where noise, which is considered detrimental for electronic circuits and communication systems, plays a constructive role in the detection of weak signals. Here, we show SR in a photodetector based on monolayer MoS₂ for detecting ultra-low-intensity subthreshold optical signals from a distant light emitting diode (LED). We demonstrate that weak periodic LED signals, which are otherwise undetectable, can be detected by a MoS₂ photodetector in the presence of a finite and optimum amount of white Gaussian noise at a frugal energy expenditure of few tens of nano-Joules. The concept of SR is generic in nature and can be extended beyond photodetector to any other sensors.

Here, the authors take advantage of stochastic resonance in a photodetector based on monolayer MoS₂ for measuring otherwise undetectable, ultra-low-intensity, subthreshold optical signals from a distant light emitting diode in the presence of a finite and optimum amount of white Gaussian noise.

Bodily motion fluctuation improves reaching success rate in a neurophysical agent via geometric-stochastic resonance

Organisms generate a variety of noise types, including neural noise, sensory noise, and noise resulting from fluctuations associated with movement. Sensory and neural noises are known to induce stochastic resonance (SR), which improves information transfer to the subjects control systems, including the brain. As a consequence, sensory and neural noise provide behavioral benefits, such as stabilization of posture and enhancement of feeding efficiency. In contrast, the benefits of fluctuations in the movements of a biological system remain largely unclear. Here, we describe a novel type of noise-induced order (NIO) that is realized by actively exploiting the motion fluctuations of an embodied system. In particular, we describe the theoretical analysis of a feedback-controlled embodied agent system that has a geometric end-effector. Furthermore, through several numerical simulations we demonstrate that the ratio of successful reaches to goal positions and capture of moving targets are improved by the exploitation of motion fluctuations. We report that reaching success rate improvement (RSRI) is based on the interaction of the geometric size of an end-effector, the agents motion fluctuations, and the desired motion frequency. Therefore, RSRI is a geometrically induced SR-like phenomenon. We also report an interesting result obtained through numerical simulations indicating that the agents neural and motion noise must be optimized to match the prey's motion noise in order to maximize the capture rate. Our study provides a new understanding of body motion fluctuations, as they were found to be the active noise sources for a behavioral NIO.

First insights into the function of the sawshark rostrum through examination of rostral tooth microwear

Potential roles of the rostrum of sawsharks (Pristiophoridae), including predation and self-defence, were assessed through a variety of inferential methods. Comparison of microwear on the surface of the rostral teeth of sawsharks and sawfishes (Pristidae) show that microwear patterns are alike and suggest that the elongate rostra in these two elasmobranch families are used for a similar purpose (predation). Raman spectroscopy indicates that the rostral teeth of both sawsharks and sawfishes are composed of hydroxyapatite, but differ in their collagen content. Sawfishes possess collagen throughout their rostral teeth whereas collagen is present only in the centre of the rostral teeth of sawsharks, which may relate to differences in ecological use. The ratio of rostrum length to total length in the common sawshark Pristiophorus cirratus was found to be similar to the largetooth sawfish Pristis pristis but not the knifetooth sawfish Anoxypristis cuspidata. Analysis of the stomach contents of P. cirratus indicates that the diet consists of demersal fishes and crustaceans, with shrimp from the family Pandalidae being the most important dietary component. No prey item showed evidence of wounds inflicted by the rostral teeth. In light of the similarities in microwear patterns, rostral tooth chemistry and diet with sawfishes, it is hypothesised that sawsharks use their rostrum in a similar manner for predation (sensing and capturing prey) and possibly for self-defence.

Sound production in the tiger-tail seahorse Hippocampus comes: Insights into the sound producing mechanisms

Acoustic signals of the tiger-tail seahorse (Hippocampus comes) during feeding were studied using wavelet transform analysis. The seahorse "click" appears to be a compounded sound, comprising three acoustic components that likely come from two sound producing mechanisms. The click sound begins with a low-frequency precursor signal, followed by a sudden high-frequency spike that decays quickly, and a final, low-frequency sinusoidal component. The first two components can, respectively, be traced to the sliding movement and forceful knock between the supraorbital bone and coronet bone of the cranium, while the third one (purr) although appearing to be initiated here is produced elsewhere. The seahorse also produces a growling sound when under duress. Growling is accompanied by the highest recorded vibration at the cheek indicating another sound producing mechanism here. The purr has the same low frequency as the growl; both are likely produced by the same structural mechanism. However, growl and purr are triggered and produced under different conditions, suggesting that such "vocalization" may have significance in communication between seahorses.

Mating behavior of Daphnia: impacts of predation risk, food quantity, and reproductive phase of females

High predation risk and food depletion lead to sexual reproduction in cyclically parthenogenetic Daphnia. Mating, the core of sexual reproduction, also occurs under these conditions. Assessment of the environmental conditions and alteration of mating efforts may aid in determining the success of sexual reproduction. Here, we evaluated the impacts of predation risk, food quantity, and reproductive phase of females on the mating behavior of Daphnia obtusa males including contact frequency and duration using video analysis. Mating-related behavior involved male-female contact (mating) as well as male-male contact (fighting). Mating frequency increased while unnecessary fighting decreased in the presence of predation risk. In addition, low food concentration reduced fighting between males. Males attempted to attach to sexual females more than asexual females, and fighting occurred more frequently in the presence of sexual females. Duration of mating was relatively long; however, males separated shortly after contact in terms of fighting behavior. Thus, assessment of environmental factors and primary sexing of mates were performed before actual contact, possibly mechanically, and precise sex discrimination was conducted after contact. These results suggest that mating in Daphnia is not a random process but rather a balance between predation risk and energetic cost that results in changes in mating and fighting strategies.

Electrical noise modulates perception of electrical pulses in humans: sensation enhancement via stochastic resonance

Although noise is usually considered to be harmful for signal detection and information transmission, stochastic resonance (SR) describes the counterintuitive phenomenon of noise enhancing the detection and transmission of weak input signals. In mammalian sensory systems, SR-related phenomena may arise both in the peripheral and the central nervous system. Here, we investigate behavioral SR effects of subliminal electrical noise stimulation on the perception of somatosensory stimuli in humans. We compare the likelihood to detect near-threshold pulses of different intensities applied on the left index finger during presence vs. absence of subliminal noise on the same or an adjacent finger. We show that (low-pass) noise can enhance signal detection when applied on the same finger. This enhancement is strong for near-threshold pulses below the 50% detection threshold and becomes stronger when near-threshold pulses are applied as brief trains. The effect reverses at pulse intensities above threshold, especially when noise is replaced by subliminal sinusoidal stimulation, arguing for a peripheral direct current addition. Unfiltered noise applied on longer pulses enhances detection of all pulse intensities. Noise applied to an adjacent finger has two opposing effects: an inhibiting effect (presumably due to lateral inhibition) and an enhancing effect (most likely due to SR in the central nervous system). In summary, we demonstrate that subliminal noise can significantly modulate detection performance of near-threshold stimuli. Our results indicate SR effects in the peripheral and central nervous system.

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.

Introduction to Focus Issue: nonlinear and stochastic physics in biology

Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.

Biased Brownian motion in extremely corrugated tubes

Biased Brownian motion of point-size particles in a three-dimensional tube with varying cross-section is investigated. In the fashion of our recent work, Martens et al. [Phys. Rev. E 83, 051135 (2011)] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density is derived. Using this expansion orders, we obtain that in the diffusion dominated regime the average particle current equals the zeroth order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular, we demonstrate that this estimate is more accurate for extremely corrugated geometries compared with the common applied method using a spatially-dependent diffusion coefficient D(x, f) which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation. The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.

Network model of chemical-sensing system inspired by mouse taste buds

Taste buds endure extreme changes in temperature, pH, osmolarity, so on. Even though taste bud cells are replaced in a short span, they contribute to consistent taste reception. Each taste bud consists of about 50 cells whose networks are assumed to process taste information, at least preliminarily. In this article, we describe a neural network model inspired by the taste bud cells of mice. It consists of two layers. In the first layer, the chemical stimulus is transduced into an irregular spike train. The synchronization of the output impulses is induced by the irregular spike train at the second layer. These results show that the intensity of the chemical stimulus is encoded as the degree of the synchronization of output impulses. The present algorithms for signal processing result in a robust chemical-sensing system.

Fast estimation of motion from selected populations of retinal ganglion cells

We explore how the reconstruction efficiency of fast spike population codes varies with population size, population composition and code complexity. Our study is based on experiments with moving light patterns which are projected onto the isolated retina of a turtle Pseudemys scripta elegans. The stimulus features to reconstruct are sequences of velocities kept constant throughout segments of 500 ms. The reconstruction is based on the spikes of a retinal ganglion cell (RGC) population recorded extracellularly via a multielectrode array. Subsequent spike sorting yields the parallel spike trains of 107 RGCs as input to the reconstruction method, here a discriminant analysis trained and tested in jack-knife fashion. Motivated by behavioral response times, we concentrate on fast reconstruction, i.e., within 150 ms following a trigger event defined via significant changes of the population spike rate. Therefore, valid codes involve only few (≤3) spikes per cell. Using only the latency t(1) of each cell (with reference to the trigger event) corresponds to the most parsimonious population code considered. We evaluate the gain in reconstruction efficiency when supplementing t(1) by spike times t(2) and t(3). Furthermore, we investigate whether sub-populations of smaller size benefit significantly from a selection process or whether random compilations are equally efficient. As selection criteria we try different concepts (directionality, reliability, and discriminability). Finally, we discuss the implications of a selection process and its inter-relation with code complexity for optimized reconstruction.

What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology

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.

Noise-Induced Transition to Bursting in Responses of Paddlefish Electroreceptor Afferents

The response properties of ampullary electroreceptors of paddlefish, Polyodon spathula, were studied in vivo, as single-unit afferent responses to external electrical stimulation with varied intensities of several types of noise waveforms, all Gaussian and zero-mean. They included broadband white noise, Ornstein–Uhlenbeck noise, low- or high-frequency band-limited noise, or natural noise recorded from swarms of Daphnia zooplankton prey, or from individual prey. Normally the afferents fire spontaneously in a tonic manner, which is actually quasiperiodic due to embedded oscillators. 1) Weak noise stimuli increased the variability of afferent firing, but it remained tonic. 2) In contrast, stimulation with less-weak broadband noise led to a qualitative change of the firing patterns, to parabolic bursting, even though the mean firing rate was scarcely affected. 3) The transition to afferent bursting was marked by the development of two well-separated timescales: the fast frequency of spiking inside bursts at ≤250 spikes/s and the slow frequency of burst occurrences at about 9 (range 5–13) bursts/s. These two timescales were manifested as two regimes in afferent power spectra, bimodal interspike interval histograms, return maps, and autocorrelation functions of afferent spike trains. 4) The stochastic approximately 9-Hz bursts were not simply driven by similar-frequency components of noise stimuli because bursts could be dissociated from stimulus waveforms using high-pass filtered noise, or a 0.1-Hz sine-wave stimulus. 5) Arrhenius plots showed that the threshold noise intensity required to elicit bursting depended on the frequency content of a noise stimulus, being lowest, about 1.2 μV/cm, for stimuli matching the 1- to 20-Hz best response band of these cathodally excited ampullary electroreceptors. This is only slightly higher than previous behavioral estimates of the electrosensory threshold as 0.5 μV/cm. 6) Comparable threshold values for bursting came from an alternate analytical approach, based on correlation times of spike trains. 7) Simultaneous recordings from pairs of afferents showed that their bursting frequencies (bursts/s) always converged as the amplitude of a noise stimulus was raised. Thus the slow timescale of bursting is similar for different electroreceptors, even though their mean spiking rates can differ. In conclusion, the ampullary electroreceptors of paddlefish have two distinct modes of operation: their spontaneous tonic firing is modulated by the weakest stimuli, but they switch to bursting output for less-weak stimuli. We propose that afferent bursting may mediate close-range tracking of planktonic prey.

Temporal analysis of moving DC electric fields in aquatic media

Many aquatic vertebrates can sense the weak electric fields generated by other animals and may also sense geoelectric or electromagnetic phenomena for use in orientation. All these sources generate stationary (dc) fields. In addition, fields from animals are modulated by respiration and other body movements. Since electroreceptors are insensitive to a pure dc field, it has been suggested that the ac modulation carries most of the relevant information for electrosensory animals. However, in a natural situation pure dc fields are rare since any relative movement between source and receiver will transform a dc field into a time varying signal. In this paper, we will describe the properties of such signals and how they are filtered at the first stage of electrosensory information processing in the brain. We will show that the signal perceived by an animal traversing a dc electric field contains all the information necessary to reconstruct the distance to the source and that the signal conditioning algorithms are perfectly adapted to preserve such information.

Optimal signal in sensory neurons under an extended rate coding concept

We define an optimal signal in parametric neuronal models on the basis of interspike interval data and rate coding schema. Under the classical approach the optimal signal is located where the frequency transfer function is steepest. Its position coincides with the inflection point of this curve. This concept is extended here by using Fisher information which is the inverse asymptotic variance of the best estimator and its dependence on the parameter value indicates accuracy of estimation. We compare the signal producing maximal Fisher information with the inflection point of the sigmoidal frequency transfer function.

Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

We investigate the stimulus-dependent tuning properties of a noisy ionic conductance model for intrinsic subthreshold oscillations in membrane potential and associated spike generation. Upon depolarization by an applied current, the model exhibits subthreshold oscillatory activity with an occasional spike generation when oscillations reach the spike threshold. We consider how the amount of applied current, the noise intensity, variation of maximum conductance values, and scaling to different temperature ranges alter the responses of the model with respect to voltage traces, interspike intervals and their statistics, and the mean spike frequency curves. We demonstrate that subthreshold oscillatory neurons in the presence of noise can sensitively and also selectively be tuned by the stimulus-dependent variation of model parameters.

Chaotic resonance: two-state model with chaos-induced escape over potential barrier

We consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation. We derive analytical expressions of chaos-induced transition rate between the neighboring potential wells based on the inhomogeneous Smoluchowski equation. Our first-order analysis reveals that the transition rate has the form of the Kramers escape rate except for a perturbed prefactor. This modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise. By means of the two-state model and the chaos-induced transition rate, we arrive at an analytical expression of the signal-to-noise ratio (SNR). Our first-order SNR shows that chaotic resonance can correspond directly to stochastic resonance.

Optimum signal in a simple neuronal model with signal-dependent noise

How does the information about a signal in neural threshold crossings depend on the noise acting upon it? Two models are explored, a binary McCulloch and Pitts (threshold exceedance) model and a model of waiting time to exceedance--a discrete-time version of interspike intervals. If noise grows linearly with the signal, we find the best identification of the signal in terms of the Fisher information is for signals that do not reach the threshold in the absence of noise. Identification attains the same precision under weak and strong signals, but the coding range decreases at both extremes of signal level. We compare the results obtained for Fisher information with those using related first and second moment measures. The maximum obtainable information is plotted as a function of the ratio of noise to signal.

Comparison of Stochastic vs. Conventional Transcutaneous Electrical Stimulation for Pain Modulation in Patients with Electromyographically Documented Radiculopathy

OBJECTIVE

To determine if a transcutaneous electrical stimulation (TENS) unit modified to deliver electrical impulses at random (R) or stochastic frequency, called TENS-R, provided better pain relief than conventional TENS.

DESIGN

A prospective, randomized, double-blinded, placebo-controlled study at an urban teaching hospital. A total of 13 adult subjects with radiculopathy on electromyogram and chronic radicular pain rated pain before and after walking 100 feet with proximal (axial) placement of TENS leads with randomized settings on conventional TENS, placebo, or TENS-R and, subsequently, with distal (limb) placement of TENS leads with randomized settings, all on the same day. The pain measures used were the McGill Pain Questionnaire, parts 1 and 2, and the Visual Analog Scale. The functional measure was speed of walking.

RESULTS

Four men and seven women completed the study pain scores, measured by McGill Pain Questionnaire part 2, significantly improved when the patient used TENS-R vs. conventional TENS (P = 0.006, analysis of variance). Placement of TENS electrodes on the back significantly decreased pain compared with lead placement on the legs for McGill Pain Questionnaire part 1 (P = 0.007), McGill Pain Questionnaire part 2 (P = 0.042), and the Visual Analog Scale (P = 0.026) measures.

CONCLUSIONS

Qualitative pain scores significantly improved when the patient used TENS-R vs. conventional TENS. Lead placement of any TENS modality over the back vs. over the leg improved all pain scores.

Stochastic resonance and synchronization in the crayfish caudal photoreceptor

Stochastic resonance is the process by which noise added to a weak external stimulus can enhance encoding efficiency in the sensory periphery and thence in the central nervous system. Stochastic synchronization is the process by which noisy phase synchronization of two periodic (or aperiodic) signals can occur. Together with a brief review of both concepts, we illustrate their applications to the encoding of weak external hydrodynamic signals in the mechanosensory system of the crayfish.

On episode sensitization in recurrent affective disorders: the role of noise

Episode sensitization is postulated as a key mechanism underlying the long-term course of recurrent affective disorders. Functionally, episode sensitization represents positive feedback between a disease process and its disease episodes resulting in a transition from externally triggered to autonomous episode generation. Recently, we introduced computational approaches to elucidate the functional properties of sensitization. Specifically, we considered the dynamics of episode sensitization with a simple computational model. The present study extends this work by investigating how naturally occurring, internal or external, random influences ("noise") affect episode sensitization. Our simulations demonstrate that actions of noise differ qualitatively in dependence on both the model's activity state as well as the noise intensity. Thereby induction as well as suppression of sensitization can be observed. Most interestingly, externally triggered sensitization development can be minimized by tuning the noise to intermediate intensities. Our findings contribute to the conceptual understanding of the clinical kindling model for affective disorders and also indicate interesting roles for random fluctuations in kindling and sensitization at the neuronal level.