Voltage fluctuations in neurons: signal or noise?

Mechanisms of stationary voltage fluctuation in the neuromuscular junction endplate and corresponding denoising paradigms

The neuromuscular junction (NMJ) has an elaborate anatomy to ensure agile and accurate signal transmission. Based on our formerly obtained expressions of the thermal and conductance induced voltage fluctuations, in this paper, the mechanisms underlying the conductance-induced voltage fluctuation are characterized from two aspects: the scaling laws with respect to either of the two system-size factors, the number of receptors or the membrane area; and the "seesaw effect" with respect to the intensive parameter, the concentration of acetylcholine. According to these mechanisms, several aspects of the NMJ anatomy are explained from a denoising perspective. Finally, the power spectra of the two types of voltage fluctuations are characterized by their specific scaling laws, based on which we explain why the endplate noise has the low-frequency property that is described by the term "seashell sound".

Modeling the effect of magnetoelectric nanoparticles on neuronal electrical activity: An analog circuit approach

This paper introduces a physical neuron model that incorporates magnetoelectric nanoparticles (MENPs) as an essential electrical circuit component to wirelessly control local neural activity. Availability of such a model is important as MENPs, due to their magnetoelectric effect, can wirelessly and noninvasively modulate neural activity, which, in turn, has implications for both finding cures for neurological diseases and creating a wireless noninvasive high-resolution brain-machine interface. When placed on a neuronal membrane, MENPs act as magnetic-field-controlled finite-size electric dipoles that generate local electric fields across the membrane in response to magnetic fields, thus allowing to controllably activate local ion channels and locally initiate an action potential. Herein, the neuronal electrical characteristic description is based on ion channel activation and inhibition mechanisms. A MENP-based memristive Hodgkin-Huxley circuit model is extracted by combining the Hodgkin-Huxley model and an equivalent circuit model for a single MENP. In this model, each MENP becomes an integral part of the neuron, thus enabling wireless local control of the neuron's electric circuit itself. Furthermore, the model is expanded to include multiple MENPs to describe collective effects in neural systems.

Cellular mechanisms underlying carry-over effects after magnetic stimulation

Magnetic fields are widely used for neuromodulation in clinical settings. The intended effect of magnetic stimulation is that neural activity resumes its pre-stimulation state right after stimulation. Many theoretical and experimental works have focused on the cellular and molecular basis of the acute neural response to magnetic field. However, effects of magnetic stimulation can still last after the termination of the magnetic stimulation (named "carry-over effects"), which could generate profound effects to the outcome of the stimulation. However, the cellular and molecular mechanisms of carry-over effects are largely unknown, which renders the neural modulation practice using magnetic stimulation unpredictable. Here, we investigated carry-over effects at the cellular level, using the combination of micro-magnetic stimulation (µMS), electrophysiology, and computation modeling. We found that high frequency magnetic stimulation could lead to immediate neural inhibition in ganglion neurons from Aplysia californica, as well as persistent, carry-over inhibition after withdrawing the magnetic stimulus. Carry-over effects were found in the neurons that fired action potentials under a variety of conditions. The carry-over effects were also observed in the neurons when the magnetic field was applied across the ganglion sheath. The state of the neuron, specifically synaptic input and membrane potential fluctuation, plays a significant role in generating the carry-over effects after magnetic stimulation. To elucidate the cellular mechanisms of such carry-over effects under magnetic stimulation, we simulated a single neuron under magnetic stimulation with multi-compartment modeling. The model successfully replicated the carry-over effects in the neuron, and revealed that the carry-over effect was due to the dysfunction of the ion channel dynamics that were responsible for the initiation and sustaining of membrane excitability. A virtual voltage-clamp experiment revealed a compromised Na conductance and enhanced K conductance post magnetic stimulation, rendering the neurons incapable of generating action potentials and, therefore, leading to the carry over effects. Finally, both simulation and experimental results demonstrated that the carry-over effects could be controlled by disturbing the membrane potential during the post-stimulus inhibition period. Delineating the cellular and ion channel mechanisms underlying carry-over effects could provide insights to the clinical outcomes in brain stimulation using TMS and other modalities. This research incentivizes the development of novel neural engineering or pharmacological approaches to better control the carry-over effects for optimized clinical outcomes.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons allow signals from the cerebellar cortex to influence the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many PC inputs are thought to converge onto each CbN neuron to suppress its firing. It has been proposed that PCs convey information using a rate code, a synchrony and timing code, or both. The influence of PCs on CbN neuron firing was primarily examined for the combined effects of many PC inputs with comparable strengths, and the influence of individual PC inputs has not been extensively studied. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modeling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, individual PC-CbN synapses are suited to concurrently convey rate codes and generate precisely timed responses in CbN neurons. Either synchronous firing or synchronous pauses of PCs promote CbN neuron firing on rapid time scales for nonuniform inputs, but less effectively than for uniform inputs. This is a secondary consequence of variable input sizes elevating the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. These findings may generalize to other brain regions with highly variable inhibitory synapse sizes.

Activity-dependent ectopic action potentials in regular-spiking neurons of the neocortex

Introduction

Action potentials usually travel orthodromically along a neuron's axon, from the axon initial segment (AIS) toward the presynaptic terminals. Under some circumstances action potentials also travel in the opposite direction, antidromically, after being initiated at a distal location. Given their initiation at an atypical site, we refer to these events as "ectopic action potentials." Ectopic action potentials (EAPs) were initially observed in pathological conditions including seizures and nerve injury. Several studies have described regular-spiking (RS) pyramidal neurons firing EAPs in seizure models. Under nonpathological conditions, EAPs were reported in a few populations of neurons, and our group has found that EAPs can be induced in a large proportion of parvalbumin-expressing interneurons in the neocortex. Nevertheless, to our knowledge there have been no prior reports of ectopic firing in the largest population of neurons in the neocortex, pyramidal neurons, under nonpathological conditions.

Methods

We performed in vitro recordings utilizing the whole-cell patch clamp technique. To elicit EAPs, we triggered orthodromic action potentialswith either long, progressively increasing current steps, or with trains of brief pulses at 30, 60, or 100 Hz delivered in 3 different ways, varying in stimulus and resting period duration.

Results

We found that a large proportion (72.7%) of neocortical RS cells from mice can fire EAPs after a specific stimulus in vitro, and that most RS cells (56.1%) are capable of firing EAPs across a broad range of stimulus conditions. Of the 37 RS neurons in which we were able to elicit EAPs, it took an average of 863.8 orthodromic action potentials delivered over the course of an average of ~81.4 s before the first EAP was seen. We observed that some cells responded to specific stimulus frequencies while less selective, suggesting frequency tuning in a subset of the cells.

Discussion

Our findings suggest that pyramidal cells can integrate information over long time-scales before briefly entering a mode of self-generated firing that originates in distal axons. The surprising ubiquity of EAP generation in RS cells raises interesting questions about the potential roles of ectopic spiking in information processing, cortical oscillations, and seizure susceptibility.

Autogenous cerebral processes: an invitation to look at the brain from inside out

While external stimulation can reliably trigger neuronal activity, cerebral processes can operate independently from the environment. In this study, we conceptualize autogenous cerebral processes (ACPs) as intrinsic operations of the brain that exist on multiple scales and can influence or shape stimulus responses, behavior, homeostasis, and the physiological state of an organism. We further propose that the field should consider exploring to what extent perception, arousal, behavior, or movement, as well as other cognitive functions previously investigated mainly regarding their stimulus-response dynamics, are ACP-driven.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons convey signals from the cerebellar cortex to the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many uniform sized PC inputs are thought to converge onto each CbN neuron to suppress or eliminate firing. Leading theories maintain that PCs encode information using either a rate code, or by synchrony and precise timing. Individual PCs are thought to have limited influence on CbN neuron firing. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modelling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, PC-CbN synapses are suited to concurrently convey rate codes, and generate precisely-timed responses in CbN neurons. Variable input sizes also elevate the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. Although this reduces the relative influence of PC synchrony on the firing rate of CbN neurons, synchrony can still have important consequences, because synchronizing even two large inputs can significantly increase CbN neuron firing. These findings may be generalized to other brain regions with highly variable sized synapses.

Alzheimer's disease as a fundamental disease of information processing systems: An information theory perspective

The human brain is a dynamic multiplex of information, both neural (neurotransmitter-to-neuron, involving 1.5×10¹⁵ action potentials per minute) and immunological (cytokine-to-microglia, providing continuous immune surveillance via 1.5×10¹⁰ immunocompetent cells). This conceptualization highlights the opportunity of exploiting "information" not only in the mechanistic understanding of brain pathology, but also as a potential therapeutic modality. Arising from its parallel yet interconnected proteopathic-immunopathic pathogeneses, Alzheimer's disease (AD) enables an exploration of the mechanistic and therapeutic contributions of information as a physical process central to brain disease progression. This review first considers the definition of information and its relevance to neurobiology and thermodynamics. Then we focus on the roles of information in AD using its two classical hallmarks. We assess the pathological contributions of β-amyloid peptides to synaptic dysfunction and reconsider this as a source of noise that disrupts information transfer between presynaptic and postsynaptic neurons. Also, we treat the triggers that activate cytokine-microglial brain processes as information-rich three-dimensional patterns, including pathogen-associated molecular patterns and damage-associated molecular patterns. There are structural and functional similarities between neural and immunological information with both fundamentally contributing to brain anatomy and pathology in health and disease. Finally, the role of information as a therapeutic for AD is introduced, particularly cognitive reserve as a prophylactic protective factor and cognitive therapy as a therapeutic contributor to the comprehensive management of ongoing dementia.

Large coefficient of variation of inter-spike intervals induced by noise current in the resonate-and-fire model neuron

Neuronal spike variability is a statistical property associated with the noise environment. Considering a linearised Hodgkin-Huxley model, we investigate how large spike variability can be induced in a typical stellate cell when submitted to constant and noise current amplitudes. For low noise current, we observe only periodic firing (active) or silence activities. For intermediate noise values, in addition to only active or inactive periods, we also identify a single transition from an initial spike-train (active) to silence dynamics over time, where the spike variability is low. However, for high noise current, we find intermittent active and silence periods with different values. The spike intervals during active and silent states follow the exponential distribution, which is similar to the Poisson process. For non-maximal noise current, we observe the highest values of inter-spike variability. Our results suggest sub-threshold oscillations as a possible mechanism for the appearance of high spike variability in a single neuron due to noise currents.

Oscillations and variability in neuronal systems: interplay of autonomous transient dynamics and fast deterministic fluctuations

Neuronal systems are subject to rapid fluctuations both intrinsically and externally. These fluctuations can be disruptive or constructive. We investigate the dynamic mechanisms underlying the interactions between rapidly fluctuating signals and the intrinsic properties of the target cells to produce variable and/or coherent responses. We use linearized and non-linear conductance-based models and piecewise constant (PWC) inputs with short duration pieces. The amplitude distributions of the constant pieces consist of arbitrary permutations of a baseline PWC function. In each trial within a given protocol we use one of these permutations and each protocol consists of a subset of all possible permutations, which is the only source of uncertainty in the protocol. We show that sustained oscillatory behavior can be generated in response to various forms of PWC inputs independently of whether the stable equilibria of the corresponding unperturbed systems are foci or nodes. The oscillatory voltage responses are amplified by the model nonlinearities and attenuated for conductance-based PWC inputs as compared to current-based PWC inputs, consistent with previous theoretical and experimental work. In addition, the voltage responses to PWC inputs exhibited variability across trials, which is reminiscent of the variability generated by stochastic noise (e.g., Gaussian white noise). Our analysis demonstrates that both oscillations and variability are the result of the interaction between the PWC input and the target cell's autonomous transient dynamics with little to no contribution from the dynamics in vicinities of the steady-state, and do not require input stochasticity.

Exploiting Non-idealities of Resistive Switching Memories for Efficient Machine Learning

Novel computing architectures based on resistive switching memories (also known as memristors or RRAMs) have been shown to be promising approaches for tackling the energy inefficiency of deep learning and spiking neural networks. However, resistive switch technology is immature and suffers from numerous imperfections, which are often considered limitations on implementations of artificial neural networks. Nevertheless, a reasonable amount of variability can be harnessed to implement efficient probabilistic or approximate computing. This approach turns out to improve robustness, decrease overfitting and reduce energy consumption for specific applications, such as Bayesian and spiking neural networks. Thus, certain non-idealities could become opportunities if we adapt machine learning methods to the intrinsic characteristics of resistive switching memories. In this short review, we introduce some key considerations for circuit design and the most common non-idealities. We illustrate the possible benefits of stochasticity and compression with examples of well-established software methods. We then present an overview of recent neural network implementations that exploit the imperfections of resistive switching memory, and discuss the potential and limitations of these approaches.

Robust multi-input multi-output adaptive fuzzy terminal sliding mode control of deep brain stimulation in Parkinson's disease: a simulation study

Deep brain stimulation (DBS) has become an effective therapeutic solution for Parkinson’s disease (PD). Adaptive closed-loop DBS can be used to minimize stimulation-induced side effects by automatically determining the stimulation parameters based on the PD dynamics. In this paper, by modeling the interaction between the neurons in populations of the thalamic, the network-level modulation of thalamic is represented in a standard canonical form as a multi-input multi-output (MIMO) nonlinear first-order system with uncertainty and external disturbances. A class of fast and robust MIMO adaptive fuzzy terminal sliding mode control (AFTSMC) has been presented for control of membrane potential of thalamic neuron populations through continuous adaptive DBS current applied to the thalamus. A fuzzy logic system (FLS) is used to estimate the unknown nonlinear dynamics of the model, and the weights of FLS are adjusted online to guarantee the convergence of FLS parameters to optimal values. The simulation results show that the proposed AFTSMC not only significantly produces lower tracking errors in comparison with the classical adaptive fuzzy sliding mode control (AFSMC), but also makes more robust and reliable outputs. The results suggest that the proposed AFTSMC provides a more robust and smooth control input which is highly desirable for hardware design and implementation.

Stochastic and sinusoidal electrical stimuli increase the irregularity and gain of Type A and B medial vestibular nucleus neurons, in vitro

Galvanic vestibular stimulation (GVS) has been shown to improve vestibular function potentially via stochastic resonance, however, it remains unknown how central vestibular nuclei process these signals. In vivo work applying electrical stimuli to the vestibular apparatus of animals has shown changes in neuronal discharge at the level of the primary vestibular afferents and hair cells. This study aimed to determine the cellular impacts of stochastic, sinusoidal, and stochastic + sinusoidal stimuli on individual medial vestibular nucleus (MVN) neurons of male and female C57BL/6 mice. All stimuli increased the irregularity of MVN neuronal discharge, while differentially affecting neuronal gain. This suggests that the heterogeneous MVN neuronal population (marked by differential expression of ion channels), may influence the impact of electrical stimuli on neuronal discharge. Neuronal subtypes showed increased variability of neuronal firing, where Type A and B neurons experienced the largest gain changes in response to stochastic and sinusoidal stimuli. Type C neurons were the least affected regarding neuronal firing variability and gain changes. The membrane potential (MP) of neurons was altered by sinusoidal and stochastic + sinusoidal stimuli, with Type B and C neuronal MP significantly affected. These results indicate that GVS-like electrical stimuli impact MVN neuronal discharge differentially, likely as a result of heterogeneous ion channel expression.

Cortical mechanisms underlying variability in intermittent theta-burst stimulation-induced plasticity: A TMS-EEG study

OBJECTIVE

To test the hypothesis that intermittent theta burst stimulation (iTBS) variability depends on the ability to engage specific neurons in the primary motor cortex (M1).

METHODS

In a sham-controlled interventional study on 31 healthy volunteers, we used concomitant transcranial magnetic stimulation (TMS) and electroencephalography (EEG). We compared baseline motor evoked potentials (MEPs), M1 iTBS-evoked EEG oscillations, and resting-state EEG (rsEEG) between subjects who did and did not show MEP facilitation following iTBS. We also investigated whether baseline MEP and iTBS-evoked EEG oscillations could explain inter and intraindividual variability in iTBS aftereffects.

RESULTS

The facilitation group had smaller baseline MEPs than the no-facilitation group and showed more iTBS-evoked EEG oscillation synchronization in the alpha and beta frequency bands. Resting-state EEG power was similar between groups and iTBS had a similar non-significant effect on rsEEG in both groups. Baseline MEP amplitude and beta iTBS-evoked EEG oscillation power explained both inter and intraindividual variability in MEP modulation following iTBS.

CONCLUSIONS

The results show that variability in iTBS-associated plasticity depends on baseline corticospinal excitability and on the ability of iTBS to engage M1 beta oscillations.

SIGNIFICANCE

These observations can be used to optimize iTBS investigational and therapeutic applications.

Noise effect on the temporal patterns of neural synchrony

Neural synchrony in the brain is often present in an intermittent fashion, i.e., there are intervals of synchronized activity interspersed with intervals of desynchronized activity. A series of experimental studies showed that this kind of temporal patterning of neural synchronization may be very specific and may be correlated with behaviour (even if the average synchrony strength is not changed). Prior studies showed that a network with many short desynchronized intervals may be functionally different from a network with few long desynchronized intervals as it may be more sensitive to synchronizing input signals. In this study, we investigated the effect of channel noise on the temporal patterns of neural synchronization. We employed a small network of conductance-based model neurons that were mutually connected via excitatory synapses. The resulting dynamics of the network was studied using the same time-series analysis methods as used in prior experimental and computational studies. While it is well known that synchrony strength generally degrades with noise, we found that noise also affects the temporal patterning of synchrony. Noise, at a sufficient intensity (yet too weak to substantially affect synchrony strength), promotes dynamics with predominantly short (although potentially very numerous) desynchronizations. Thus, channel noise may be one of the mechanisms contributing to the short desynchronization dynamics observed in multiple experimental studies.

Noisy Synaptic Conductance: Bug or a Feature?

More often than not, action potentials fail to trigger neurotransmitter release. And even when neurotransmitter is released, the resulting change in synaptic conductance is highly variable. Given the energetic cost of generating and propagating action potentials, and the importance of information transmission across synapses, this seems both wasteful and inefficient. However, synaptic noise arising from variable transmission can improve, in certain restricted conditions, information transmission. Under broader conditions, it can improve information transmission per release, a quantity that is relevant given the energetic constraints on computing in the brain. Here we discuss the role, both positive and negative, synaptic noise plays in information transmission and computation in the brain.

Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage

The cerebellar granule cells (GrCs) are classically described as a homogeneous neuronal population discharging regularly without adaptation. We show that GrCs in fact generate diverse response patterns to current injection and synaptic activation, ranging from adaptation to acceleration of firing. Adaptation was predicted by parameter optimization in detailed computational models based on available knowledge on GrC ionic channels. The models also predicted that acceleration required additional mechanisms. We found that yet unrecognized TRPM4 currents specifically accounted for firing acceleration and that adapting GrCs outperformed accelerating GrCs in transmitting high-frequency mossy fiber (MF) bursts over a background discharge. This implied that GrC subtypes identified by their electroresponsiveness corresponded to specific neurotransmitter release probability values. Simulations showed that fine-tuning of pre- and post-synaptic parameters generated effective MF-GrC transmission channels, which could enrich the processing of input spike patterns and enhance spatio-temporal recoding at the cerebellar input stage.

Versatile stochastic dot product circuits based on nonvolatile memories for high performance neurocomputing and neurooptimization

The key operation in stochastic neural networks, which have become the state-of-the-art approach for solving problems in machine learning, information theory, and statistics, is a stochastic dot-product. While there have been many demonstrations of dot-product circuits and, separately, of stochastic neurons, the efficient hardware implementation combining both functionalities is still missing. Here we report compact, fast, energy-efficient, and scalable stochastic dot-product circuits based on either passively integrated metal-oxide memristors or embedded floating-gate memories. The circuit’s high performance is due to mixed-signal implementation, while the efficient stochastic operation is achieved by utilizing circuit’s noise, intrinsic and/or extrinsic to the memory cell array. The dynamic scaling of weights, enabled by analog memory devices, allows for efficient realization of different annealing approaches to improve functionality. The proposed approach is experimentally verified for two representative applications, namely by implementing neural network for solving a four-node graph-partitioning problem, and a Boltzmann machine with 10-input and 8-hidden neurons.

Providing efficient and scalable specialized hardware for stochastic neural networks remains a challenge. Here, the authors propose a fast, energy-efficient and scalable stochastic dot-product circuit that may use either of two types of memory devices – metal-oxide memristors and floating-gate memories.

Stochasticity from function - Why the Bayesian brain may need no noise

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functional Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial.

Inhomogeneities in Network Structure and Excitability Govern Initiation and Propagation of Spontaneous Burst Activity

The mesoscale architecture of neuronal networks strongly influences the initiation of spontaneous activity and its pathways of propagation. Spontaneous activity has been studied extensively in networks of cultured cortical neurons that generate complex yet reproducible patterns of synchronous bursting events that resemble the activity dynamics in developing neuronal networks in vivo. Synchronous bursts are mostly thought to be triggered at burst initiation sites due to build-up of noise or by highly active neurons, or to reflect reverberating activity that circulates within larger networks, although neither of these has been observed directly. Inferring such collective dynamics in neuronal populations from electrophysiological recordings crucially depends on the spatial resolution and sampling ratio relative to the size of the networks assessed. Using large-scale microelectrode arrays with 1024 electrodes at 0.3 mm pitch that covered the full extent of in vitro networks on about 1 cm², we investigated where bursts of spontaneous activity arise and how their propagation patterns relate to the regions of origin, the network's structure, and to the overall distribution of activity. A set of alternating burst initiation zones (BIZ) dominated the initiation of distinct bursting events and triggered specific propagation patterns. Moreover, BIZs were typically located in areas with moderate activity levels, i.e., at transitions between hot and cold spots. The activity-dependent alternation between these zones suggests that the local networks forming the dominating BIZ enter a transient depressed state after several cycles (similar to Eytan et al., 2003), allowing other BIZs to take over temporarily. We propose that inhomogeneities in the network structure define such BIZs and that the depletion of local synaptic resources limit repetitive burst initiation.

The Dynamic Basis of Respiratory Rhythm Generation: One Breath at a Time

Rhythmicity is a universal timing mechanism in the brain, and the rhythmogenic mechanisms are generally dynamic. This is illustrated for the neuronal control of breathing, a behavior that occurs as a one-, two-, or three-phase rhythm. Each breath is assembled stochastically, and increasing evidence suggests that each phase can be generated independently by a dedicated excitatory microcircuit. Within each microcircuit, rhythmicity emerges through three entangled mechanisms: ( a) glutamatergic transmission, which is amplified by ( b) intrinsic bursting and opposed by ( c) concurrent inhibition. This rhythmogenic triangle is dynamically tuned by neuromodulators and other network interactions. The ability of coupled oscillators to reconfigure and recombine may allow breathing to remain robust yet plastic enough to conform to nonventilatory behaviors such as vocalization, swallowing, and coughing. Lessons learned from the respiratory network may translate to other highly dynamic and integrated rhythmic systems, if approached one breath at a time.

Variability and Predictors of Response to Continuous Theta Burst Stimulation: A TMS-EEG Study

Continuous theta-burst stimulation (cTBS) is a repetitive transcranial magnetic stimulation paradigm reported to decrease the excitability of the stimulated cortical area and which is thought to reflect a form of inhibitory synaptic plasticity. However, since its introduction, the effect of cTBS has shown a remarkable variability in its effects, which are often quantified by measuring the amplitude of motor evoked potentials (MEPs). Part of this inconsistency in experimental results might be due to an intrinsic variability of TMS effects caused by genetic or neurophysiologic factors. However, it is also possible that MEP only reflect the excitability of a sub-population of output neurons; resting EEG power and measures combining TMS and electroencephalography (TMS-EEG) might represent a more thorough reflection of cortical excitability. The aim of the present study was to verify the robustness of several predictors of cTBS response, such as I wave recruitment and baseline MEP amplitude, and to test cTBS after-effects on multiple neurophysiologic measurements such as MEP, resting EEG power, local mean field power (LMFP), TMS-related spectral perturbation (TRSP), and inter-trial phase clustering (ITPC). As a result, we were not able to confirm either the expected decrease of MEP amplitude after cTBS or the ability of I wave recruitment and MEP amplitude to predict the response to cTBS. Resting EEG power, LMFP, TRSP, and ITPC showed a more consistent trend toward a decrease after cTBS. Overall, our data suggest that the effect of cTBS on corticospinal excitability is variable and difficult to predict with common electrophysiologic markers, while its effect might be clearer when probed with combined TMS and EEG.

Kv3 K+ currents contribute to spike-timing in dorsal cochlear nucleus principal cells

Exposure to loud sound increases burst-firing of dorsal cochlear nucleus (DCN) fusiform cells in the auditory brainstem, which has been suggested to be an electrophysiological correlate of tinnitus. The altered activity of DCN fusiform cells may be due to down-regulation of high voltage-activated (Kv3-like) K⁺ currents. Whole cell current-clamp recordings were obtained from DCN fusiform cells in brain slices from P15-P18 CBA mice. We first studied whether acoustic over-exposure (performed at P15) or pharmacological inhibition of K⁺ currents with tetraethylamonium (TEA) affect fusiform cell action potential characteristics, firing frequency and spike-timing relative to evoking current stimuli. We then tested whether AUT1, a modulator of Kv3 K⁺ currents reverses the effects of sound exposure or TEA. Both loud sound exposure and TEA decreased the amplitude of action potential after-hyperpolarization, reduced the maximum firing frequency, and disrupted spike-timing. These treatments also increased post-synaptic voltage fluctuations at baseline. AUT1 applied in the presence of TEA or following acoustic over-exposure, did not affect the firing frequency, but enhanced action potential after-hyperpolarization, prevented the increased voltage fluctuations and restored spike-timing. Furthermore AUT1 prevented the occurrence of bursts. Our study shows that the effect on spike-timing is significantly correlated with the amplitude of the action potential after-hyperpolarization and the voltage fluctuations at baseline. In conclusion, modulation of putative Kv3 K⁺ currents may restore regular spike-timing of DCN fusiform cell firing following noise exposure, and could provide a means to restore deficits in temporal encoding observed during noise-induced tinnitus.

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Whole cell recordings were performed in dorsal cochlear nucleus fusiform cells.

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Spike-timing is dependent on the action potential after-hyperpolarization.

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Spike-timing is dependent on synaptic baseline voltage fluctuations.

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Inhibition of K⁺ currents using TEA or acoustic over-exposure disrupt spike-timing.

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AUT1, a Kv3.1/3.2 K⁺ current modulator, counteracts the disruptive effects on spike-timing.

A consensus layer V pyramidal neuron can sustain interpulse-interval coding

In terms of a single neuron's long-distance communication, interpulse intervals (IPIs) are an attractive alternative to rate and binary codes. As a proxy for an IPI, a neuron's time-to-spike can be found in the biophysical and experimental intracellular literature. Using the current, consensus layer V pyramidal neuron, the present study examines the feasibility of IPI-coding and examines the noise sources that limit the information rate of such an encoding. In descending order of importance, the noise sources are (i) synaptic variability, (ii) sodium channel shot-noise, followed by (iii) thermal noise. The biophysical simulations allow the calculation of mutual information, which is about 3.0 bits/spike. More importantly, while, by any conventional definition, the biophysical model is highly nonlinear, the underlying function that relates input intensity to the defined output variable is linear. When one assumes the perspective of a neuron coding via first hitting-time, this result justifies a pervasive and simplifying assumption of computational modelers-that a class of cortical neurons can be treated as linearly additive, computational devices.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware.

Matching Behavior as a Tradeoff Between Reward Maximization and Demands on Neural Computation

When faced with a choice, humans and animals commonly distribute their behavior in proportion to the frequency of payoff of each option. Such behavior is referred to as matching and has been captured by the matching law. However, matching is not a general law of economic choice. Matching in its strict sense seems to be specifically observed in tasks whose properties make matching an optimal or a near-optimal strategy. We engaged monkeys in a foraging task in which matching was not the optimal strategy. Over-matching the proportions of the mean offered reward magnitudes would yield more reward than matching, yet, surprisingly, the animals almost exactly matched them. To gain insight into this phenomenon, we modeled the animals' decision-making using a mechanistic model. The model accounted for the animals' macroscopic and microscopic choice behavior. When the models' three parameters were not constrained to mimic the monkeys' behavior, the model over-matched the reward proportions and in doing so, harvested substantially more reward than the monkeys. This optimized model revealed a marked bottleneck in the monkeys' choice function that compares the value of the two options. The model featured a very steep value comparison function relative to that of the monkeys. The steepness of the value comparison function had a profound effect on the earned reward and on the level of matching. We implemented this value comparison function through responses of simulated biological neurons. We found that due to the presence of neural noise, steepening the value comparison requires an exponential increase in the number of value-coding neurons. Matching may be a compromise between harvesting satisfactory reward and the high demands placed by neural noise on optimal neural computation.

Mechanism and function of mixed-mode oscillations in vibrissa motoneurons

Vibrissa motoneurons in the facial nucleus innervate the intrinsic and extrinsic muscles that move the whiskers. Their intrinsic properties affect the way they process fast synaptic input from the vIRT and Bötzinger nuclei together with serotonergic neuromodulation. In response to constant current (I_app) injection, vibrissa motoneurons may respond with mixed mode oscillations (MMOs), in which sub-threshold oscillations (STOs) are intermittently mixed with spikes. This study investigates the mechanisms involved in generating MMOs in vibrissa motoneurons and their function in motor control. It presents a conductance-based model that includes the M-type K⁺ conductance, g_M, the persistent Na⁺ conductance, g_NaP, and the cationic h conductance, g_h. For g_h = 0 and moderate values of g_M and g_NaP, the model neuron generates STOs, but not MMOs, in response to I_app injection. STOs transform abruptly to tonic spiking as the current increases. In addition to STOs, MMOs are generated for g_h>0 for larger values of I_app; the I_app range in which MMOs appear increases linearly with g_h. In the MMOs regime, the firing rate increases with I_app like a Devil's staircase. Stochastic noise disrupts the temporal structure of the MMOs, but for a moderate noise level, the coefficient of variation (CV) is much less than one and varies non-monotonically with I_app. Furthermore, the estimated time period between voltage peaks, based on Bernoulli process statistics, is much higher in the MMOs regime than in the tonic regime. These two phenomena do not appear when moderate noise generates MMOs without an intrinsic MMO mechanism. Therefore, and since STOs do not appear in spinal motoneurons, the analysis can be used to differentiate different MMOs mechanisms. MMO firing activity in vibrissa motoneurons suggests a scenario in which moderate periodic inputs from the vIRT and Bötzinger nuclei control whisking frequency, whereas serotonergic neuromodulation controls whisking amplitude.

Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

Discharge properties of neurons recorded in the parvalbumin-positive (PV1) nucleus of the rat lateral hypothalamus

This study reports for the first time the extracellular activity recorded, in anesthetized rats, from cells located in an identified cluster of parvalbumin (PV)-positive neurons of the lateral hypothalamus forming the PV1-nucleus. Random-like firing characterized the majority (21/30) of the cells, termed regular cells, with a median firing rate of 1.7 spikes/s, Fano factor equal to 1, and evenly distributed along the rostro-caudal axis. Four cells exhibiting an oscillatory activity in the range 1.6-2.1Hz were observed only in the posterior part of the PV1-nucleus. The asynchronous activity of PV1 neurons is likely to produce a "network-driven" effect on their main target within the periaqueductal gray matter. The hypothesis is raised that background random-like firing of PV1-nucleus is associated with functional network activity likely to contribute dynamic information related to condition transitions of awareness and non-conscious perception.

Altering spinal cord excitability enables voluntary movements after chronic complete paralysis in humans

Previously, we reported that one individual who had a motor complete, but sensory incomplete spinal cord injury regained voluntary movement after 7 months of epidural stimulation and stand training. We presumed that the residual sensory pathways were critical in this recovery. However, we now report in three more individuals voluntary movement occurred with epidural stimulation immediately after implant even in two who were diagnosed with a motor and sensory complete lesion. We demonstrate that neuromodulating the spinal circuitry with epidural stimulation, enables completely paralysed individuals to process conceptual, auditory and visual input to regain relatively fine voluntary control of paralysed muscles. We show that neuromodulation of the sub-threshold motor state of excitability of the lumbosacral spinal networks was the key to recovery of intentional movement in four of four individuals diagnosed as having complete paralysis of the legs. We have uncovered a fundamentally new intervention strategy that can dramatically affect recovery of voluntary movement in individuals with complete paralysis even years after injury.

Stochastic computations in cortical microcircuit models

Experimental data from neuroscience suggest that a substantial amount of knowledge is stored in the brain in the form of probability distributions over network states and trajectories of network states. We provide a theoretical foundation for this hypothesis by showing that even very detailed models for cortical microcircuits, with data-based diverse nonlinear neurons and synapses, have a stationary distribution of network states and trajectories of network states to which they converge exponentially fast from any initial state. We demonstrate that this convergence holds in spite of the non-reversibility of the stochastic dynamics of cortical microcircuits. We further show that, in the presence of background network oscillations, separate stationary distributions emerge for different phases of the oscillation, in accordance with experimentally reported phase-specific codes. We complement these theoretical results by computer simulations that investigate resulting computation times for typical probabilistic inference tasks on these internally stored distributions, such as marginalization or marginal maximum-a-posteriori estimation. Furthermore, we show that the inherent stochastic dynamics of generic cortical microcircuits enables them to quickly generate approximate solutions to difficult constraint satisfaction problems, where stored knowledge and current inputs jointly constrain possible solutions. This provides a powerful new computing paradigm for networks of spiking neurons, that also throws new light on how networks of neurons in the brain could carry out complex computational tasks such as prediction, imagination, memory recall and problem solving.

Synaptic inhibition and excitation estimated via the time constant of membrane potential fluctuations

When recording the membrane potential, V, of a neuron it is desirable to be able to extract the synaptic input. Critically, the synaptic input is stochastic and nonreproducible so one is therefore often restricted to single-trial data. Here, we introduce means of estimating the inhibition and excitation and their confidence limits from single sweep trials. The estimates are based on the mean membrane potential, V̄, and the membrane time constant, τ. The time constant provides the total conductance ( G = capacitance/τ) and is extracted from the autocorrelation of V. The synaptic conductances can then be inferred from V̄ when approximating the neuron as a single compartment. We further employ a stochastic model to establish limits of confidence. The method is verified on models and experimental data, where the synaptic input is manipulated pharmacologically or estimated by an alternative method. The method gives best results if the synaptic input is large compared with other conductances, the intrinsic conductances have little or no time dependence or are comparably small, the ligand-gated kinetics is faster than the membrane time constant, and the majority of synaptic contacts are electrotonically close to soma (recording site). Although our data are in current clamp, the method also works in V-clamp recordings, with some minor adaptations. All custom made procedures are provided in Matlab.

Patterned Brain Stimulation, What a Framework with Rhythmic and Noisy Components Might Tell Us about Recovery Maximization

Brain stimulation is having remarkable impact on clinical neurology. Brain stimulation can modulate neuronal activity in functionally segregated circumscribed regions of the human brain. Polarity, frequency, and noise specific stimulation can induce specific manipulations on neural activity. In contrast to neocortical stimulation, deep-brain stimulation has become a tool that can dramatically improve the impact clinicians can possibly have on movement disorders. In contrast, neocortical brain stimulation is proving to be remarkably susceptible to intrinsic brain-states. Although evidence is accumulating that brain stimulation can facilitate recovery processes in patients with cerebral stroke, the high variability of results impedes successful clinical implementation. Interestingly, recent data in healthy subjects suggests that brain-state dependent patterned stimulation might help resolve some of the intrinsic variability found in previous studies. In parallel, other studies suggest that noisy “stochastic resonance” (SR)-like processes are a non-negligible component in non-invasive brain stimulation studies. The hypothesis developed in this manuscript is that stimulation patterning with noisy and oscillatory components will help patients recover from stroke related deficits more reliably. To address this hypothesis we focus on two factors common to both neural computation (intrinsic variables) as well as brain stimulation (extrinsic variables): noise and oscillation. We review diverse theoretical and experimental evidence that demonstrates that subject-function specific brain-states are associated with specific oscillatory activity patterns. These states are transient and can be maintained by noisy processes. The resulting control procedures can resemble homeostatic or SR processes. In this context we try to extend awareness for inter-individual differences and the use of individualized stimulation in the recovery maximization of stroke patients.

Biologically inspired information processing and synchronization in ensembles of non-identical threshold-potential nanostructures

Nanotechnology produces basic structures that show a significant variability in their individual physical properties. This experimental fact may constitute a serious limitation for most applications requiring nominally identical building blocks. On the other hand, biological diversity is found in most natural systems. We show that reliable information processing can be achieved with heterogeneous groups of non-identical nanostructures by using some conceptual schemes characteristic of biological networks (diversity, frequency-based signal processing, rate and rank order coding, and synchronization). To this end, we simulate the integrated response of an ensemble of single-electron transistors (SET) whose individual threshold potentials show a high variability. A particular experimental realization of a SET is a metal nanoparticle-based transistor that mimics biological spiking synapses and can be modeled as an integrate-and-fire oscillator. The different shape and size distributions of nanoparticles inherent to the nanoscale fabrication procedures result in a significant variability in the threshold potentials of the SET. The statistical distributions of the nanoparticle physical parameters are characterized by experimental average and distribution width values. We consider simple but general information processing schemes to draw conclusions that should be of relevance for other threshold-based nanostructures. Monte Carlo simulations show that ensembles of non-identical SET may show some advantages over ensembles of identical nanostructures concerning the processing of weak signals. The results obtained are also relevant for understanding the role of diversity in biophysical networks.

The limits of brain determinacy

The genes do not control everything that happens in a cell or an organism, because thermally induced molecular movements and conformation changes are beyond genetic control. The importance of uncontrolled events has been argued from the differences between isogenic organisms reared in virtually identical environments, but these might alternatively be attributed to subtle, undetected differences in the environment. The present review focuses on the uncontrolled events themselves in the context of the developing brain. These are considered at cellular and circuit levels because even if cellular physiology was perfectly controlled by the genes (which it is not), the interactions between different cells might still be uncoordinated. A further complication is that the brain contains mechanisms that buffer noise and others that amplify it. The final resultant of the battle between these contrary mechanisms is that developmental stochasticity is sufficiently low to make neurobehavioural defects uncommon, but a chance component of neural development remains. Thus, our brains and behaviour are not entirely determined by a combination of genes-plus-environment.