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

Inverse stochastic resonance in networks of spiking neurons

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron's intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.

Improved proprioceptive function by application of subsensory electrical noise: Effects of aging and task-demand

The application of subsensory noise stimulation over the lower limbs has been shown to improve proprioception and postural control under certain conditions. Whereas the effect specificity seems to depend on several factors, studies are still needed to determine the appropriate method for training and rehabilitation purposes. In the current study, we investigated whether the application of subsensory electrical noise over the legs improves proprioceptive function in young and older adults. We aimed to provide evidence that stronger and age-related differential effects occur in more demanding tasks. Proprioceptive function was initially assessed by testing the detection of passive ankle movement (kinesthetic perception) in twenty-eight subjects (14 young and 14 older adults). Thereafter, postural control was assessed during tasks with different sensory challenges: i) by removing visual information (eyes closed) and; ii) by moving the visual scene (moving room paradigm). Tests performed with the application of electrical noise stimulation were compared to those performed without noise. The results showed that electrical noise applied over the legs led to a reduction in the response time to kinesthetic perception in both young and older adults. On the other hand, the magnitude of postural sway was reduced by noise stimulation only during a more challenging task, namely, when the optical flow was changing in an unpredictable (nonperiodic) manner. No differential effects of stimulation between groups were observed. These findings suggest that the relevance of proprioceptive inputs in tasks with different challenges, but not the subjects' age, is a determining factor for sensorimotor improvements due to electrical noise stimulation.

Cortical Spike Synchrony as a Measure of Input Familiarity

Spike synchrony, which occurs in various cortical areas in response to specific perception, action, and memory tasks, has sparked a long-standing debate on the nature of temporal organization in cortex. One prominent view is that this type of synchrony facilitates the binding or grouping of separate stimulus components. We argue instead for a more general function: a measure of the prior probability of incoming stimuli, implemented by long-range, horizontal, intracortical connections. We show that networks of this kind-pulse-coupled excitatory spiking networks in a noisy environment-can provide a sufficient substrate for stimulus-dependent spike synchrony. This allows for a quick (few spikes) estimate of the match between inputs and the input history as encoded in the network structure. Given the ubiquity of small, strongly excitatory subnetworks in cortex, we thus propose that many experimental observations of spike synchrony can be viewed as signs of input patterns that resemble long-term experience-that is, of patterns with high prior probability.

Transcranial Random Noise Stimulation (tRNS) Shapes the Processing of Rapidly Changing Auditory Information

Neural oscillations in the gamma range are the dominant rhythmic activation pattern in the human auditory cortex. These gamma oscillations are functionally relevant for the processing of rapidly changing acoustic information in both speech and non-speech sounds. Accordingly, there is a tight link between the temporal resolution ability of the auditory system and inherent neural gamma oscillations. Transcranial random noise stimulation (tRNS) has been demonstrated to specifically increase gamma oscillation in the human auditory cortex. However, neither the physiological mechanisms of tRNS nor the behavioral consequences of this intervention are completely understood. In the present study we stimulated the human auditory cortex bilaterally with tRNS while EEG was continuously measured. Modulations in the participants’ temporal and spectral resolution ability were investigated by means of a gap detection task and a pitch discrimination task. Compared to sham, auditory tRNS increased the detection rate for near-threshold stimuli in the temporal domain only, while no such effect was present for the discrimination of spectral features. Behavioral findings were paralleled by reduced peak latencies of the P50 and N1 component of the auditory event-related potentials (ERP) indicating an impact on early sensory processing. The facilitating effect of tRNS was limited to the processing of near-threshold stimuli while stimuli clearly below and above the individual perception threshold were not affected by tRNS. This non-linear relationship between the signal-to-noise level of the presented stimuli and the effect of stimulation further qualifies stochastic resonance (SR) as the underlying mechanism of tRNS on auditory processing. Our results demonstrate a tRNS related improvement in acoustic perception of time critical auditory information and, thus, provide further indices that auditory tRNS can amplify the resonance frequency of the auditory system.

Noise-induced stabilization of collective dynamics

We illustrate a counterintuitive effect of an additive stochastic force, which acts independently on each element of an ensemble of globally coupled oscillators. We show that a very small white noise not only broadens the clusters, wherever they are induced by the deterministic forces, but can also stabilize a linearly unstable collective periodic regime: self-consistent partial synchrony. With the help of microscopic simulations we are able to identify two noise-induced bifurcations. A macroscopic analysis, based on a perturbative solution of the associated nonlinear Fokker-Planck equation, confirms the numerical studies and allows determining the eigenvalues of the stability problem. We finally argue about the generality of the phenomenon.

Optically levitated nanoparticle as a model system for stochastic bistable dynamics

Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.

Synchronization and variability imbalance underlie cognitive impairment in primary-progressive multiple sclerosis

We aimed to investigate functional connectivity and variability across multiple frequency bands in brain networks underlying cognitive deficits in primary-progressive multiple sclerosis (PP-MS) and to explore how they are affected by the presence of cortical lesions (CLs). We analyzed functional connectivity and variability (measured as the standard deviation of BOLD signal amplitude) in resting state networks (RSNs) associated with cognitive deficits in different frequency bands in 25 PP-MS patients (12 M, mean age 50.9 ± 10.5 years) and 20 healthy subjects (9 M, mean age 51.0 ± 9.8 years). We confirmed the presence of a widespread cognitive deterioration in PP-MS patients, with main involvement of visuo-spatial and executive domains. Cognitively impaired patients showed increased variability, reduced synchronicity between networks involved in the control of cognitive macro-domains and hyper-synchronicity limited to the connections between networks functionally more segregated. CL volume was higher in patients with cognitive impairment and was correlated with functional connectivity and variability. We demonstrate, for the first time, that a functional reorganization characterized by hypo-synchronicity of functionally-related/hyper-synchronicity of functionally-segregated large scale networks and an abnormal pattern of neural activity underlie cognitive dysfunction in PP-MS, and that CLs possibly play a role in variability and functional connectivity abnormalities.

Noise-tunable nonlinearity in a dispersively coupled diffusion-resonator system using superconducting circuits

The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a result, the circuit's response to forcing can become multistable. The strength of the nonlinearity is tuned by the level of noise in the system, and increases with decreasing noise. This tunable nonlinearity could potentially find application in the field of sensitive detection, whereas increased understanding of the classical harmonic oscillator is relevant for studies of the quantum-to-classical crossover of Jaynes-Cummings systems.

Vection Latency Is Reduced by Bone-Conducted Vibration and Noisy Galvanic Vestibular Stimulation

Studies of the illusory sense of self-motion elicited by a moving visual surround (‘vection’) have revealed key insights about how sensory information is integrated. Vection usually occurs after a delay of several seconds following visual motion onset, whereas self-motion in the natural environment is perceived immediately. It has been suggested that this latency relates to the sensory mismatch between visual and vestibular signals at motion onset. Here, we tested three techniques with the potential to reduce sensory mismatch in order to shorten vection onset latency: noisy galvanic vestibular stimulation (GVS) and bone conducted vibration (BCV) at the mastoid processes, and body vibration applied to the lower back. In Experiment 1, we examined vection latency for wide field visual rotations about the roll axis and applied a burst of stimulation at the start of visual motion. Both GVS and BCV reduced vection latency by two seconds compared to the control condition, whereas body vibration had no effect on latency. In Experiment 2, the visual stimulus rotated about the pitch, roll, or yaw axis and we found a similar facilitation of vection by both BCV and GVS in each case. In a control experiment, we confirmed that air-conducted sound administered through headphones was not sufficient to reduce vection onset latency. Together the results suggest that noisy vestibular stimulation facilitates vection, likely due to an upweighting of visual information caused by a reduction in vestibular sensory reliability.

Pre-stimulus alpha oscillations over somatosensory cortex predict tactile misperceptions

Fluctuations of pre-stimulus oscillatory activity in the somatosensory alpha band (8-14Hz) observed using human EEG and MEG have been shown to influence the detection of supra- and peri-threshold somatosensory stimuli. However, some reports of touch occur even without a stimulus. We investigated the possibility that pre-stimulus alpha oscillations might also influence these false reports of touch - known as tactile misperceptions. We recorded EEG while participants performed the Somatic Signal Detection Task (SSDT), in which participants must detect brief, peri-threshold somatosensory targets. We found that pre-stimulus oscillatory power in the somatosensory alpha range exhibited a negative linear relationship with reporting of touch at electrode clusters over both contralateral and ipsilateral somatosensory regions. As pre-stimulus alpha power increased, the probability of reporting a touch declined; as it decreased, the probability of reporting a touch increased. This relationship was stronger on trials without a somatosensory stimulus than on trials with a somatosensory stimulus, although was present for both trial types. Spatio-temporal cluster-based permutation analysis also found that pre-stimulus alpha was lower on trials when touch was reported - irrespective of whether it was present - over contralateral and ipsilateral somatosensory cortices, as well as left frontocentral areas. We argue that alpha power may reflect changes in response criterion rather than sensitivity alone. Low alpha power relates to a low barrier to reporting a touch even when one is not present, while high alpha power is linked to less frequent reporting of touch overall.

The emergence of waves in random discrete systems

Essential criteria for the emergence of wave-like manifestations occurring in an entirely discrete system are identified using a simple model for the movement of particles through a network. The dynamics are entirely stochastic and memoryless involving a birth-death-migration process. The requirements are that the network should have at least three nodes, that migration should have a directional bias, and that the particle dynamics have a non-local dependence. Well defined bifurcations mark transitions between amorphous, wave-like and collapsed states with an intermittent regime between the latter two.

Stochastic phenotypic interconversion in tumors can generate heterogeneity

Phenotype variations define heterogeneity in biological and molecular systems, and play a crucial mechanistic role, and heterogeneity has been demonstrated in tumor cells. In this work, cells from blood of patients affected by colon cancer were analyzed and sorted using a microfluidic assay based on galactose-active moieties and incubated for culturing in severe combined immunodeficiency (SCID) mice. Based on the results of these experiments, a model based on Markov theory is implemented and discussed to explain the equilibrium existing between phenotypes of cell subpopulations sorted using the microfluidic assay. In combination with the experimental results, the model has many implications for tumor heterogeneity; For example, it displays interconversion of phenotypes, confirming the experiments. Such interconversion generates metastatic cells and implies that targeting circulating tumor cells (CTC) will not be an efficient method for prevention of tumor recurrence. Most importantly, understanding the transitions between cell phenotypes in the cell population can improve understanding of tumor generation and growth.

Emergent Structural Mechanisms for High-Density Collective Motion Inspired by Human Crowds

Collective motion of large human crowds often depends on their density. In extreme cases like heavy metal concerts and black Friday sales events, motion is dominated by physical interactions instead of conventional social norms. Here, we study an active matter model inspired by situations when large groups of people gather at a point of common interest. Our analysis takes an approach developed for jammed granular media and identifies Goldstone modes, soft spots, and stochastic resonance as structurally driven mechanisms for potentially dangerous emergent collective motion.

Noise Improves Visual Motion Discrimination via a Stochastic Resonance-Like Phenomenon

The stochastic resonance (SR) is a phenomenon in which adding a moderate amount of noise can improve the signal-to-noise ratio and performance of non-linear systems. SR occurs in all sensory modalities including the visual system in which noise can enhance contrast detection sensitivity and the perception of ambiguous figures embedded in static scenes. Here, we explored how adding background white pixel-noise to a random dot motion (RDM) stimulus produced changes in visual motion discrimination in healthy human adults. We found that, although the average reaction times (RTs) remained constant, an intermediate level of noise improved the subjects’ ability to discriminate motion direction in the RDM task. The psychophysical responses followed an inverted U-like function of the input noise, whereas the incorrect responses with short RTs did not exhibit such modulation by external noise. Moreover, by applying stimulus and noisy signals to different eyes, we found that the SR phenomenon occurred presumably in the primary visual cortex, where these two signals first converge. Our results suggest that a SR-like phenomenon mediates the improvement of visual motion perception in the RDM task.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

Effectiveness Testing of a Piezoelectric Energy Harvester for an Automobile Wheel Using Stochastic Resonance

The collection of clean power from ambient vibrations is considered a promising method for energy harvesting. For the case of wheel rotation, the present study investigates the effectiveness of a piezoelectric energy harvester, with the application of stochastic resonance to optimize the efficiency of energy harvesting. It is hypothesized that when the wheel rotates at variable speeds, the energy harvester is subjected to on-road noise as ambient excitations and a tangentially acting gravity force as a periodic modulation force, which can stimulate stochastic resonance. The energy harvester was miniaturized with a bistable cantilever structure, and the on-road noise was measured for the implementation of a vibrator in an experimental setting. A validation experiment revealed that the harvesting system was optimized to capture power that was approximately 12 times that captured under only on-road noise excitation and 50 times that captured under only the periodic gravity force. Moreover, the investigation of up-sweep excitations with increasing rotational frequency confirmed that stochastic resonance is effective in optimizing the performance of the energy harvester, with a certain bandwidth of vehicle speeds. An actual-vehicle experiment validates that the prototype harvester using stochastic resonance is capable of improving power generation performance for practical tire application.

Identifying Anatomical Origins of Coexisting Oscillations in the Cortical Microcircuit

Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a close-to-irregular fashion at low rates. Using a combination of mean-field and linear response theory we predict the spectra generated in a layered microcircuit model of V1, composed of leaky integrate-and-fire neurons and based on connectivity compiled from anatomical and electrophysiological studies. The model exhibits low- and high-γ oscillations visible in all populations. Since locally generated frequencies are imposed onto other populations, the origin of the oscillations cannot be deduced from the spectra. We develop an universally applicable systematic approach that identifies the anatomical circuits underlying the generation of oscillations in a given network. Based on a theoretical reduction of the dynamics, we derive a sensitivity measure resulting in a frequency-dependent connectivity map that reveals connections crucial for the peak amplitude and frequency of the observed oscillations and identifies the minimal circuit generating a given frequency. The low-γ peak turns out to be generated in a sub-circuit located in layer 2/3 and 4, while the high-γ peak emerges from the inter-neurons in layer 4. Connections within and onto layer 5 are found to regulate slow rate fluctuations. We further demonstrate how small perturbations of the crucial connections have significant impact on the population spectra, while the impairment of other connections leaves the dynamics on the population level unaltered. The study uncovers connections where mechanisms controlling the spectra of the cortical microcircuit are most effective.

Recordings of brain activity show multiple coexisting oscillations. The generation of these oscillations has so far only been investigated in generic one- and two-population networks, neglecting their embedment into larger systems. We introduce a method that determines the mechanisms and sub-circuits generating oscillations in structured spiking networks. Analyzing a multi-layered model of the cortical microcircuit, we trace back characteristic oscillations to experimentally observed connectivity patterns. The approach exposes the influence of individual connections on frequency and amplitude of these oscillations and therefore reveals locations, where biological mechanisms controlling oscillations and experimental manipulations have the largest impact. The new analytical tool replaces parameter scans in computationally expensive models, guides circuit design, and can be employed to validate connectivity data.

Spintronic Nanodevices for Bioinspired Computing

Bioinspired hardware holds the promise of low-energy, intelligent, and highly adaptable computing systems. Applications span from automatic classification for big data management, through unmanned vehicle control, to control for biomedical prosthesis. However, one of the major challenges of fabricating bioinspired hardware is building ultra-high-density networks out of complex processing units interlinked by tunable connections. Nanometer-scale devices exploiting spin electronics (or spintronics) can be a key technology in this context. In particular, magnetic tunnel junctions (MTJs) are well suited for this purpose because of their multiple tunable functionalities. One such functionality, non-volatile memory, can provide massive embedded memory in unconventional circuits, thus escaping the von-Neumann bottleneck arising when memory and processors are located separately. Other features of spintronic devices that could be beneficial for bioinspired computing include tunable fast nonlinear dynamics, controlled stochasticity, and the ability of single devices to change functions in different operating conditions. Large networks of interacting spintronic nanodevices can have their interactions tuned to induce complex dynamics such as synchronization, chaos, soliton diffusion, phase transitions, criticality, and convergence to multiple metastable states. A number of groups have recently proposed bioinspired architectures that include one or several types of spintronic nanodevices. In this paper, we show how spintronics can be used for bioinspired computing. We review the different approaches that have been proposed, the recent advances in this direction, and the challenges toward fully integrated spintronics complementary metal-oxide-semiconductor (CMOS) bioinspired hardware.

Stimulation from Cochlear Implant Electrodes Assists with Recovery from Asymmetric Perceptual Tilt: Evidence from the Subjective Visual Vertical Test

Vestibular end organ impairment is highly prevalent in children who have sensorineural hearing loss (SNHL) rehabilitated with cochlear implants (CIs). As a result, spatial perception is likely to be impacted in this population. Of particular interest is the perception of visual vertical because it reflects a perceptual tilt in the roll axis and is sensitive to an imbalance in otolith function. The objectives of the present study were thus to identify abnormalities in perception of the vertical plane in children with SNHL and determine whether such abnormalities could be resolved with stimulation from the CI. Participants included 53 children (15.2 ± 4.0 years of age) with SNHL and vestibular loss, confirmed with vestibular evoked myogenic potential (VEMP) testing. Testing protocol was validated in a sample of nine young adults with normal hearing (28.8 ± 7.7 years). Perception of visual vertical was assessed using the static Subjective Visual Vertical (SVV) test performed with and without stimulation in the participants with cochleovestibular loss. Trains of electrical pulses were delivered by an electrode in the left and/or right ear. Asymmetric spatial orientation deficits were found in nearly half of the participants with CIs (24/53 [45%]). The abnormal perception in this cohort was exacerbated by visual tilts in the direction of their deficit. Electric pulse trains delivered using the CI shifted this abnormal perception towards center (i.e., normal; p = 0.007). Importantly, this benefit was realized regardless of which ear was stimulated. These results suggest a role for CI stimulation beyond the auditory system, in particular, for improving vestibular/balance function.

Noise-assisted estimation of attractor invariants

In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K_{2}), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (D_{m}^{U}), the correlation entropy (K_{m}^{U}), and the noise level (σ_{m}^{U}). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators D_{m}^{U} and σ_{m}^{U} behave in a similar manner to those based on the GCI. However, for the calculation of K_{2}, the estimator K_{m}^{U} outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K_{2}, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.

Presynaptic Spontaneous Activity Enhances the Accuracy of Latency Coding

The time to the first spike after stimulus onset typically varies with the stimulation intensity. Experimental evidence suggests that neural systems use such response latency to encode information about the stimulus. We investigate the decoding accuracy of the latency code in relation to the level of noise in the form of presynaptic spontaneous activity. Paradoxically, the optimal performance is achieved at a nonzero level of noise and suprathreshold stimulus intensities. We argue that this phenomenon results from the influence of the spontaneous activity on the stabilization of the membrane potential in the absence of stimulation. The reported decoding accuracy improvement represents a novel manifestation of the noise-aided signal enhancement.

Noise Enhances Action Potential Generation in Mouse Sensory Neurons via Stochastic Resonance

Noise can enhance perception of tactile and proprioceptive stimuli by stochastic resonance processes. However, the mechanisms underlying this general phenomenon remain to be characterized. Here we studied how externally applied noise influences action potential firing in mouse primary sensory neurons of dorsal root ganglia, modelling a basic process in sensory perception. Since noisy mechanical stimuli may cause stochastic fluctuations in receptor potential, we examined the effects of sub-threshold depolarizing current steps with superimposed random fluctuations. We performed whole cell patch clamp recordings in cultured neurons of mouse dorsal root ganglia. Noise was added either before and during the step, or during the depolarizing step only, to focus onto the specific effects of external noise on action potential generation. In both cases, step + noise stimuli triggered significantly more action potentials than steps alone. The normalized power norm had a clear peak at intermediate noise levels, demonstrating that the phenomenon is driven by stochastic resonance. Spikes evoked in step + noise trials occur earlier and show faster rise time as compared to the occasional ones elicited by steps alone. These data suggest that external noise enhances, via stochastic resonance, the recruitment of transient voltage-gated Na channels, responsible for action potential firing in response to rapid step-wise depolarizing currents.

Noninvasive Brain Stimulation Techniques Can Modulate Cognitive Processing

Recent methods that allow a noninvasive modulation of brain activity are able to modulate human cognitive behavior. Among these methods are transcranial electric stimulation and transcranial magnetic stimulation that both come in multiple variants. A property of both types of brain stimulation is that they modulate brain activity and in turn modulate cognitive behavior. Here, we describe the methods with their assumed neural mechanisms for readers from the economic and social sciences and little prior knowledge of these techniques. Our emphasis is on available protocols and experimental parameters to choose from when designing a study. We also review a selection of recent studies that have successfully applied them in the respective field. We provide short pointers to limitations that need to be considered and refer to the relevant papers where appropriate.

Duration Dependent Effects of Transcranial Pulsed Current Stimulation (tPCS) Indexed by Electroencephalography

OBJECTIVE

To explore the duration of tPCS after effects given different durations of stimulation on power and interhemispheric coherence of the EEG frequency bands. Our hypothesis was that longer tPCS duration would induce a differential effect on the EEG analysis and a longer duration of after effects on the EEG frequency bands.

MATERIALS AND METHODS

We conducted a double blind, sham controlled study in which forty healthy subjects were randomized to receive a single session of either 10, 20, 30 min of active (2 mA, random frequency between 6 and 10 Hz, ear clip montage) or sham tPCS. EEG was recorded before and after the intervention to assess tPCS induced after effects.

RESULTS

We found that 10 and 20 min of active tPCS induced a significant increase in alpha (p = 0.004) and theta (p = 0.006) coherence in the frontal region as compared with the sham stimulation. No significant changes were found with 30 min of stimulation (p < 0.05). The Kaplan Meier analysis showed that 10 and 20 min of tPCS induced after effects that lasted 50 min.

CONCLUSIONS

These results evidence the nonlinear relationship between the stimulation duration and the tPCS after effects, suggesting the presence of homeostatic mechanisms.

Vestibular evoked myogenic potential testing as an objective measure of vestibular stimulation with cochlear implants

OBJECTIVES/HYPOTHESIS

To determine if vestibular potentials could be elicited with electrical stimulation from cochlear implants.

STUDY DESIGN

Prospective cohort study.

METHODS

Vestibular responsiveness to electrical stimulation from cochlear implants was assessed via vestibular evoked myogenic potential (VEMP) testing in 53 pediatric and young adult patients.

RESULTS

Thirty-one participants (58%) showed at least one vestibular potential in response to acoustic stimulation; 33 (62%) had an electrically evoked vestibular response. A cervical VEMP (cVEMP) was present in 45 of the 96 tested ears (47%) in response to acoustic stimulation, and in 34 ears (35%) with electrical stimulation. An ocular VEMP (oVEMP) was elicited acoustically in 25 ears (26%) and electrically in 34 (35%) ears. In the ears with absent responses to acoustic stimuli, electrically evoked cVEMPs and oVEMPs were present in 14 (27%) and 18 (25%) ears, respectively. Electric VEMPs demonstrated shorter latencies than acoustic VEMPs (P < .01). Whereas an increased prevalence of VEMPs was seen at high stimulation levels (P < .01), there was no difference between prevalence proportions with basal (electrode 3) or apical (electrode 20) stimulation (P > .05).

CONCLUSIONS

VEMPs can be elicited with electrical stimulation in a proportion of children with cochlear implants, demonstrating current spread from the cochlea to the vestibular system. The presence of electric VEMPs in acoustically nonresponsive ears, along with the shorter latencies of electrically driven VEMPs, suggests that electrical current can bypass the otoliths and directly stimulate vestibular neural elements.

LEVEL OF EVIDENCE

4. Laryngoscope, 2016 127:E75-E81, 2017.

Optimal random frequency range in transcranial pulsed current stimulation indexed by quantitative electroencephalography

Given the recent results provided by previous investigations on transcranial pulsed current stimulation (tPCS) demonstrating its modulatory effects on cortical connectivity; we aimed to explore the application of different random pulsed frequencies. The utility of tPCS as a neuromodulatory technique for cognition performance will come as additional frequency ranges are tested with the purpose to find optimal operational parameters for tPCS. This study was designed to analyze the effects of tPCS using the following random frequencies; 1-5, 6-10, and 11-15 Hz compared with sham on quantitative electroencephalographic changes in the spectral power and interhemispheric coherence of each electroencephalographic frequency band. This was a parallel, randomized, double-blinded, sham-controlled trial. Forty healthy individuals older than 18 years were eligible to participate. The main outcomes were differences in the spectral power analysis and interhemispheric coherence as measured by quantitative electroencephalography. Participants were randomly allocated to four groups of random frequency stimulation and received a single session of stimulation for 20 min with a current intensity of 2 mA delivered by bilateral periauricular electrode clips. We found that a random pulsed frequency between 6-10 Hz significantly increased the power and coherence in frontal and central areas for the alpha band compared with sham stimulation, while 11-15 Hz tPCS decreased the power for the alpha and theta bandwidth. Our findings corroborate the hypothesis that a random frequency ranging into the boundaries of 6-10 Hz induces changes in the naturally occurring alpha oscillatory activity, providing additional data for further studies with tPCS.

Modulating Human Auditory Processing by Transcranial Electrical Stimulation

Transcranial electrical stimulation (tES) has become a valuable research tool for the investigation of neurophysiological processes underlying human action and cognition. In recent years, striking evidence for the neuromodulatory effects of transcranial direct current stimulation, transcranial alternating current stimulation, and transcranial random noise stimulation has emerged. While the wealth of knowledge has been gained about tES in the motor domain and, to a lesser extent, about its ability to modulate human cognition, surprisingly little is known about its impact on perceptual processing, particularly in the auditory domain. Moreover, while only a few studies systematically investigated the impact of auditory tES, it has already been applied in a large number of clinical trials, leading to a remarkable imbalance between basic and clinical research on auditory tES. Here, we review the state of the art of tES application in the auditory domain focussing on the impact of neuromodulation on acoustic perception and its potential for clinical application in the treatment of auditory related disorders.

Too good to be true: when overwhelming evidence fails to convince

Is it possible for a large sequence of measurements or observations, which support a hypothesis, to counterintuitively decrease our confidence? Can unanimous support be too good to be true? The assumption of independence is often made in good faith; however, rarely is consideration given to whether a systemic failure has occurred. Taking this into account can cause certainty in a hypothesis to decrease as the evidence for it becomes apparently stronger. We perform a probabilistic Bayesian analysis of this effect with examples based on (i) archaeological evidence, (ii) weighing of legal evidence and (iii) cryptographic primality testing. In this paper, we investigate the effects of small error rates in a set of measurements or observations. We find that even with very low systemic failure rates, high confidence is surprisingly difficult to achieve; in particular, we find that certain analyses of cryptographically important numerical tests are highly optimistic, underestimating their false-negative rate by as much as a factor of 2⁸⁰.

Stochastic resonance in the synaptic transmission between hair cells and vestibular primary afferents in development

The stochastic resonance (SR) is a phenomenon of nonlinear systems in which the addition of an intermediate level of noise improves the response of such system. Although SR has been studied in isolated hair cells and in the bullfrog sacculus, the occurrence of this phenomenon in the vestibular system in development is unknown. The purpose of the present study was to explore for the existence of SR via natural mechanical-stimulation in the hair cell-vestibular primary afferent transmission. In vitro experiments were performed on the posterior semicircular canal of the chicken inner ear during development. Our experiments showed that the signal-to-noise ratio of the afferent multiunit activity from E15 to P5 stages of development exhibited the SR phenomenon, which was characterized by an inverted U-like response as a function of the input noise level. The inverted U-like graphs of SR acquired their higher amplitude after the post-hatching stage of development. Blockage of the synaptic transmission with selective antagonists of the NMDA and AMPA/Kainate receptors abolished the SR of the afferent multiunit activity. Furthermore, computer simulations on a model of the hair cell - primary afferent synapse qualitatively reproduced this SR behavior and provided a possible explanation of how and where the SR could occur. These results demonstrate that a particular level of mechanical noise on the semicircular canals can improve the performance of the vestibular system in their peripheral sensory processing even during embryonic stages of development.

Sustainability of Transient Kinetic Regimes and Origins of Death

It is generally recognized that a distinguishing feature of life is its peculiar capability to avoid equilibration. The origin of this capability and its evolution along the timeline of abiogenesis is not yet understood. We propose to study an analog of this phenomenon that could emerge in non-biological systems. To this end, we introduce the concept of sustainability of transient kinetic regimes. This concept is illustrated via investigation of cooperative effects in an extended system of compartmentalized chemical oscillators under batch and semi-batch conditions. The computational study of a model system shows robust enhancement of lifetimes of the decaying oscillations which translates into the evolution of the survival function of the transient non-equilibrium regime. This model does not rely on any form of replication. Rather, it explores the role of a structured effective environment as a contributor to the system-bath interactions that define non-equilibrium regimes. We implicate the noise produced by the effective environment of a compartmentalized oscillator as the cause of the lifetime extension.

Intertrial auditory neural stability supports beat synchronization in preschoolers

The ability to synchronize motor movements along with an auditory beat places stringent demands on the temporal processing and sensorimotor integration capabilities of the nervous system. Links between millisecond-level precision of auditory processing and the consistency of sensorimotor beat synchronization implicate fine auditory neural timing as a mechanism for forming stable internal representations of, and behavioral reactions to, sound. Here, for the first time, we demonstrate a systematic relationship between consistency of beat synchronization and trial-by-trial stability of subcortical speech processing in preschoolers (ages 3 and 4 years old). We conclude that beat synchronization might provide a useful window into millisecond-level neural precision for encoding sound in early childhood, when speech processing is especially important for language acquisition and development.

Random noise can help to improve synchronization of excimer laser pulses

Recently, we have reported on a compact microcontroller-based unit developed to accurately synchronize excimer laser pulses (Mingesz et al. 2012 Fluct. Noise Lett. 11, 1240007 (doi:10.1142/S021947751240007X)). We have shown that dithering based on random jitter noise plus pseudorandom numbers can be used in the digital control system to radically reduce the long-term drift of the laser pulse from the trigger and to improve the accuracy of the synchronization. In this update paper, we present our new experimental results obtained by the use of the delay-controller unit to tune the timing of a KrF excimer laser as an addition to our previous numerical simulation results. The hardware was interfaced to the laser using optical signal paths in order to reduce sensitivity to electromagnetic interference and the control algorithm tested by simulations was applied in the experiments. We have found that the system is able to reduce the delay uncertainty very close to the theoretical limit and performs well in real applications. The simple, compact and flexible system is universal enough to also be used in various multidisciplinary applications.

Stochastic resonance is a method to improve the biosynthetic response of chondrocytes to mechanical stimulation

Cellular mechanosensitivity is an important factor during the mechanical stimulation of tissue engineered cartilage. While the application of mechanical stimuli improves tissue growth and properties, chondrocytes also rapidly desensitize under prolonged loading thereby limiting its effectiveness. One potential method to mitigate load-induced desensitization is by superimposing noise on the loading waveforms ("stochastic resonance"). Thus, the purpose of this study was to investigate the effects of stochastic resonance on chondrocyte matrix metabolism. Chondrocyte-seeded agarose gels were subjected to dynamic compressive loading, with or without, superimposed vibrations of different amplitudes and frequency bandwidths. Changes in matrix biosynthesis were determined by radioisotope incorporation and subsequent effects on intracellular calcium signaling were evaluated by confocal microscopy. Although dependent on the duration of loading, superimposed vibrations improved cellular sensitivity to mechanical loading by further increasing matrix synthesis between 20-60%. Stochastic resonance also appeared to limit load-induced desensitization by maintaining sensitivity under desensitized loading conditions. While superimposed vibrations had little effect on the magnitude of intracellular calcium signaling, recovery of mechanosensitivity after stimulation was achieved at a faster rate suggesting that less time may be required between successive loading applications. Thus, stochastic resonance appears to be a valuable tool during the mechanical stimulation of cartilage constructs, even when suboptimal stimulation conditions are used.

Differences in Speech Recognition Between Children with Attention Deficits and Typically Developed Children Disappear When Exposed to 65 dB of Auditory Noise

The most common neuropsychiatric condition in the in children is attention deficit hyperactivity disorder (ADHD), affecting ∼6–9% of the population. ADHD is distinguished by inattention and hyperactive, impulsive behaviors as well as poor performance in various cognitive tasks often leading to failures at school. Sensory and perceptual dysfunctions have also been noticed. Prior research has mainly focused on limitations in executive functioning where differences are often explained by deficits in pre-frontal cortex activation. Less notice has been given to sensory perception and subcortical functioning in ADHD. Recent research has shown that children with ADHD diagnosis have a deviant auditory brain stem response compared to healthy controls. The aim of the present study was to investigate if the speech recognition threshold differs between attentive and children with ADHD symptoms in two environmental sound conditions, with and without external noise. Previous research has namely shown that children with attention deficits can benefit from white noise exposure during cognitive tasks and here we investigate if noise benefit is present during an auditory perceptual task. For this purpose we used a modified Hagerman’s speech recognition test where children with and without attention deficits performed a binaural speech recognition task to assess the speech recognition threshold in no noise and noise conditions (65 dB). Results showed that the inattentive group displayed a higher speech recognition threshold than typically developed children and that the difference in speech recognition threshold disappeared when exposed to noise at supra threshold level. From this we conclude that inattention can partly be explained by sensory perceptual limitations that can possibly be ameliorated through noise exposure.

A stochastic mechanism for signal propagation in the brain: Force of rapid random fluctuations in membrane potentials of individual neurons

There are two functionally important factors in signal propagation in a brain structural network: the very first synaptic delay-a time delay about 1ms-from the moment when signals originate to the moment when observation on the signal propagation can begin; and rapid random fluctuations in membrane potentials of every individual neuron in the network at a timescale of microseconds. We provide a stochastic analysis of signal propagation in a general setting. The analysis shows that the two factors together result in a stochastic mechanism for the signal propagation as described below. A brain structural network is not a rigid circuit rather a very flexible framework that guides signals to propagate but does not guarantee success of the signal propagation. In such a framework, with the very first synaptic delay, rapid random fluctuations in every individual neuron in the network cause an "alter-and-concentrate effect" that almost surely forces signals to successfully propagate. By the stochastic mechanism we provide analytic evidence for the existence of a force behind signal propagation in a brain structural network caused by rapid random fluctuations in every individual neuron in the network at a timescale of microseconds with a time delay of 1ms.

Use of stochastic resonance methods for improving laparoscopic surgery performance

BACKGROUND

Vibrotactile feedback (VIB) has been utilized in previous research as sensory augmentation to improve performance during minimally invasive surgical tasks. Stochastic resonance (SR), introduced into the human control system as white noise at a subthreshold level, has shown promise to improve the sensitivity of tactile receptors resulting in performance enhancement for sensorimotor tasks. The purpose of this study was to determine whether SR could improve performance (accuracy, speed) in a simulated laparoscopic palpation task.

METHODS

Sixteen subjects performed a palpation task using a laparoscopic tool to detect the presence of tumors (compacted felt) embedded in simulated tissue samples (silicone gel) inside a laparoscopic trainer box. Subjects were randomly assigned to one of the four different conditions: (1) SR, (2) VIB, (3) VIB + SR, and (4) Control. The VIB and SR signals were administered via two separate haptic actuators attached to the subjects' dominant upper arms and forearms, respectively. All subjects were presented with 36 tissue samples with no sensory augmentation (Control) to establish baseline, followed by another 36 samples under one of the randomly assigned vibration conditions (SR, VIB, VIB + SR, or Control).

RESULTS

Results show a significantly larger improvement in tumor detection accuracy in the SR group compared to the VIB and Control groups. There was no difference in the time to task completion, indicating that there was no speed-accuracy trade-off.

CONCLUSIONS

The results have implications for the design of instruments and methods for increasing detection accuracy such as in palpation tasks. This technology could help surgeons better identify tumors located in healthy surrounding tissue.

Age-Related Changes in 1/f Neural Electrophysiological Noise

Aging is associated with performance decrements across multiple cognitive domains. The neural noise hypothesis, a dominant view of the basis of this decline, posits that aging is accompanied by an increase in spontaneous, noisy baseline neural activity. Here we analyze data from two different groups of human subjects: intracranial electrocorticography from 15 participants over a 38 year age range (15-53 years) and scalp EEG data from healthy younger (20-30 years) and older (60-70 years) adults to test the neural noise hypothesis from a 1/f noise perspective. Many natural phenomena, including electrophysiology, are characterized by 1/f noise. The defining characteristic of 1/f is that the power of the signal frequency content decreases rapidly as a function of the frequency (f) itself. The slope of this decay, the noise exponent (χ), is often <-1 for electrophysiological data and has been shown to approach white noise (defined as χ = 0) with increasing task difficulty. We observed, in both electrophysiological datasets, that aging is associated with a flatter (more noisy) 1/f power spectral density, even at rest, and that visual cortical 1/f noise statistically mediates age-related impairments in visual working memory. These results provide electrophysiological support for the neural noise hypothesis of aging. Significance statement: Understanding the neurobiological origins of age-related cognitive decline is of critical scientific, medical, and public health importance, especially considering the rapid aging of the world's population. We find, in two separate human studies, that 1/f electrophysiological noise increases with aging. In addition, we observe that this age-related 1/f noise statistically mediates age-related working memory decline. These results significantly add to this understanding and contextualize a long-standing problem in cognition by encapsulating age-related cognitive decline within a neurocomputational model of 1/f noise-induced deficits in neural communication.

Corticothalamic Synaptic Noise as a Mechanism for Selective Attention in Thalamic Neurons

A reason why the thalamus is more than a passive gateway for sensory signals is that two-third of the synapses of thalamocortical neurons are directly or indirectly related to the activity of corticothalamic axons. While the responses of thalamocortical neurons evoked by sensory stimuli are well characterized, with ON- and OFF-center receptive field structures, the prevalence of synaptic noise resulting from neocortical feedback in intracellularly recorded thalamocortical neurons in vivo has attracted little attention. However, in vitro and modeling experiments point to its critical role for the integration of sensory signals. Here we combine our recent findings in a unified framework suggesting the hypothesis that corticothalamic synaptic activity is adapted to modulate the transfer efficiency of thalamocortical neurons during selective attention at three different levels: First, on ionic channels by interacting with intrinsic membrane properties, second at the neuron level by impacting on the input-output gain, and third even more effectively at the cell assembly level by boosting the information transfer of sensory features encoded in thalamic subnetworks. This top-down population control is achieved by tuning the correlations in subthreshold membrane potential fluctuations and is adapted to modulate the transfer of sensory features encoded by assemblies of thalamocortical relay neurons. We thus propose that cortically-controlled (de-)correlation of subthreshold noise is an efficient and swift dynamic mechanism for selective attention in the thalamus.

Concept of an Active Amplification Mechanism in the Infrared Organ of Pyrophilous Melanophila Beetles

Jewel beetles of the genus Melanophila possess a pair of metathoracic infrared (IR) organs. These organs are used for forest fire detection because Melanophila larvae can only develop in fire killed trees. Several reports in the literature and a modeling of a historic oil tank fire suggest that beetles may be able to detect large fires by means of their IR organs from distances of more than 100 km. In contrast, the highest sensitivity of the IR organs, so far determined by behavioral and physiological experiments, allows a detection of large fires from distances up to 12 km only. Sensitivity thresholds, however, have always been determined in non-flying beetles. Therefore, the complete micromechanical environment of the IR organs in flying beetles has not been taken into consideration. Because the so-called photomechanic sensilla housed in the IR organs respond bimodally to mechanical as well as to IR stimuli, it is proposed that flying beetles make use of muscular energy coupled out of the flight motor to considerably increase the sensitivity of their IR sensilla during intermittent search flight sequences. In a search flight the beetle performs signal scanning with wing beat frequency while the inputs of the IR organs on both body sides are compared. By this procedure the detection of weak IR signals could be possible even if the signals are hidden in the thermal noise. If this proposed mechanism really exists in Melanophila beetles, their IR organs could even compete with cooled IR quantum detectors. The theoretical concept of an active amplification mechanism in a photon receptor innervated by highly sensitive mechanoreceptors is presented in this article.

Enhanced brain signal variability in children with autism spectrum disorder during early childhood

Extensive evidence shows that a core neurobiological mechanism of autism spectrum disorder (ASD) involves aberrant neural connectivity. Recent advances in the investigation of brain signal variability have yielded important information about neural network mechanisms. That information has been applied fruitfully to the assessment of aging and mental disorders. Multiscale entropy (MSE) analysis can characterize the complexity inherent in brain signal dynamics over multiple temporal scales in the dynamics of neural networks. For this investigation, we sought to characterize the magnetoencephalography (MEG) signal variability during free watching of videos without sound using MSE in 43 children with ASD and 72 typically developing controls (TD), emphasizing early childhood to older childhood: a critical period of neural network maturation. Results revealed an age‐related increase of brain signal variability in a specific timescale in TD children, whereas atypical age‐related alteration was observed in the ASD group. Additionally, enhanced brain signal variability was observed in children with ASD, and was confirmed particularly for younger children. In the ASD group, symptom severity was associated region‐specifically and timescale‐specifically with reduced brain signal variability. These results agree well with a recently reported theory of increased brain signal variability during development and aberrant neural connectivity in ASD, especially during early childhood. Results of this study suggest that MSE analytic method might serve as a useful approach for characterizing neurophysiological mechanisms of typical‐developing and its alterations in ASD through the detection of MEG signal variability at multiple timescales. Hum Brain Mapp 37:1038–1050, 2016. © 2015 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Transition from double coherence resonances to single coherence resonance in a neuronal network with phase noise

The effect of phase noise on the coherence dynamics of a neuronal network composed of FitzHugh-Nagumo (FHN) neurons is investigated. Phase noise can induce dissimilar coherence resonance (CR) effects for different coupling strength regimes. When the coupling strength is small, phase noise can induce double CRs. One corresponds to the average frequency of phase noise, and the other corresponds to the intrinsic firing frequency of the FHN neuron. When the coupling strength is large enough, phase noise can only induce single CR, and the CR corresponds to the intrinsic firing frequency of the FHN neuron. The results show a transition from double CRs to single CR with the increase in the coupling strength. The transition can be well interpreted based on the dynamics of a single neuron stimulated by both phase noise and the coupling current. When the coupling strength is small, the coupling current is weak, and phase noise mainly determines the dynamics of the neuron. Moreover, the phase-noise-induced double CRs in the neuronal network are similar to the phase-noise-induced double CRs in an isolated FHN neuron. When the coupling strength is large enough, the coupling current is strong and plays a key role in the occurrence of the single CR in the network. The results provide a novel phenomenon and may have important implications in understanding the dynamics of neuronal networks.

A technical guide to tDCS, and related non-invasive brain stimulation tools

Transcranial electrical stimulation (tES), including transcranial direct and alternating current stimulation (tDCS, tACS) are non-invasive brain stimulation techniques increasingly used for modulation of central nervous system excitability in humans. Here we address methodological issues required for tES application. This review covers technical aspects of tES, as well as applications like exploration of brain physiology, modelling approaches, tES in cognitive neurosciences, and interventional approaches. It aims to help the reader to appropriately design and conduct studies involving these brain stimulation techniques, understand limitations and avoid shortcomings, which might hamper the scientific rigor and potential applications in the clinical domain.

Differential effects of white noise in cognitive and perceptual tasks

Beneficial effects of noise on higher cognition have recently attracted attention. Hypothesizing an involvement of the mesolimbic dopamine system and its functional interactions with cortical areas, the current study aimed to demonstrate a facilitation of dopamine-dependent attentional and mnemonic functions by externally applying white noise in five behavioral experiments including a total sample of 167 healthy human subjects. During working memory, acoustic white noise impaired accuracy when presented during the maintenance period (Experiments 1-3). In a reward based long-term memory task, white noise accelerated perceptual judgments for scene images during encoding but left subsequent recognition memory unaffected (Experiment 4). In a modified Posner task (Experiment 5), the benefit due to white noise in attentional orienting correlated weakly with reward dependence, a personality trait that has been associated with the dopaminergic system. These results suggest that white noise has no general effect on cognitive functions. Instead, they indicate differential effects on perception and cognition depending on a variety of factors such as task demands and timing of white noise presentation.

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components.

Accurate Langevin approaches to simulate Markovian channel dynamics

The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu's classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.