Balanced excitatory and inhibitory inputs to cortical neurons decouple firing irregularity from rate modulations

Preictal dysfunctions of inhibitory interneurons paradoxically lead to their rebound hyperactivity and to low-voltage-fast onset seizures in Dravet syndrome

Epilepsies have numerous specific mechanisms. The understanding of neural dynamics leading to seizures is important for disclosing pathological mechanisms and developing therapeutic approaches. We investigated electrographic activities and neural dynamics leading to convulsive seizures in patients and mouse models of Dravet syndrome (DS), a developmental and epileptic encephalopathy in which hypoexcitability of GABAergic neurons is considered to be the main dysfunction. We analyzed EEGs from DS patients carrying a SCN1A pathogenic variant, as well as epidural electrocorticograms, hippocampal local field potentials, and hippocampal single-unit neuronal activities in Scn1a+/- and Scn1aRH/+ DS mice. Strikingly, most seizures had low-voltage-fast onset in both patients and mice, which is thought to be generated by hyperactivity of GABAergic interneurons, the opposite of the main pathological mechanism of DS. Analyzing single-unit recordings, we observed that temporal disorganization of the firing of putative interneurons in the period immediately before the seizure (preictal) precedes the increase of their activity at seizure onset, together with the entire neuronal network. Moreover, we found early signatures of the preictal period in the spectral features of hippocampal and cortical field potential of Scn1a mice and of patients' EEG, which are consistent with the dysfunctions that we observed in single neurons and that allowed seizure prediction. Therefore, the perturbed preictal activity of interneurons leads to their hyperactivity at the onset of generalized seizures, which have low-voltage-fast features that are similar to those observed in other epilepsies and are triggered by hyperactivity of GABAergic neurons. Preictal spectral features may be used as predictive seizure biomarkers.

Logarithmically scaled, gamma distributed neuronal spiking

Naturally log-scaled quantities abound in the nervous system. Distributions of these quantities have non-intuitive properties, which have implications for data analysis and the understanding of neural circuits. Here, we review the log-scaled statistics of neuronal spiking and the relevant analytical probability distributions. Recent work using log-scaling revealed that interspike intervals of forebrain neurons segregate into discrete modes reflecting spiking at different timescales and are each well-approximated by a gamma distribution. Each neuron spends most of the time in an irregular spiking 'ground state' with the longest intervals, which determines the mean firing rate of the neuron. Across the entire neuronal population, firing rates are log-scaled and well approximated by the gamma distribution, with a small number of highly active neurons and an overabundance of low rate neurons (the 'dark matter'). These results are intricately linked to a heterogeneous balanced operating regime, which confers upon neuronal circuits multiple computational advantages and has evolutionarily ancient origins.

Reconstruction of sparse recurrent connectivity and inputs from the nonlinear dynamics of neuronal networks

Reconstructing the recurrent structural connectivity of neuronal networks is a challenge crucial to address in characterizing neuronal computations. While directly measuring the detailed connectivity structure is generally prohibitive for large networks, we develop a novel framework for reverse-engineering large-scale recurrent network connectivity matrices from neuronal dynamics by utilizing the widespread sparsity of neuronal connections. We derive a linear input-output mapping that underlies the irregular dynamics of a model network composed of both excitatory and inhibitory integrate-and-fire neurons with pulse coupling, thereby relating network inputs to evoked neuronal activity. Using this embedded mapping and experimentally feasible measurements of the firing rate as well as voltage dynamics in response to a relatively small ensemble of random input stimuli, we efficiently reconstruct the recurrent network connectivity via compressive sensing techniques. Through analogous analysis, we then recover high dimensional natural stimuli from evoked neuronal network dynamics over a short time horizon. This work provides a generalizable methodology for rapidly recovering sparse neuronal network data and underlines the natural role of sparsity in facilitating the efficient encoding of network data in neuronal dynamics.

New insights into binocular rivalry from the reconstruction of evolving percepts using model network dynamics

When the two eyes are presented with highly distinct stimuli, the resulting visual percept generally switches every few seconds between the two monocular images in an irregular fashion, giving rise to a phenomenon known as binocular rivalry. While a host of theoretical studies have explored potential mechanisms for binocular rivalry in the context of evoked model dynamics in response to simple stimuli, here we investigate binocular rivalry directly through complex stimulus reconstructions based on the activity of a two-layer neuronal network model with competing downstream pools driven by disparate monocular stimuli composed of image pixels. To estimate the dynamic percept, we derive a linear input-output mapping rooted in the non-linear network dynamics and iteratively apply compressive sensing techniques for signal recovery. Utilizing a dominance metric, we are able to identify when percept alternations occur and use data collected during each dominance period to generate a sequence of percept reconstructions. We show that despite the approximate nature of the input-output mapping and the significant reduction in neurons downstream relative to stimulus pixels, the dominant monocular image is well-encoded in the network dynamics and improvements are garnered when realistic spatial receptive field structure is incorporated into the feedforward connectivity. Our model demonstrates gamma-distributed dominance durations and well obeys Levelt's four laws for how dominance durations change with stimulus strength, agreeing with key recurring experimental observations often used to benchmark rivalry models. In light of evidence that individuals with autism exhibit relatively slow percept switching in binocular rivalry, we corroborate the ubiquitous hypothesis that autism manifests from reduced inhibition in the brain by systematically probing our model alternation rate across choices of inhibition strength. We exhibit sufficient conditions for producing binocular rivalry in the context of natural scene stimuli, opening a clearer window into the dynamic brain computations that vary with the generated percept and a potential path toward further understanding neurological disorders.

Stimulus presentation can enhance spiking irregularity across subcortical and cortical regions

Stimulus presentation is believed to quench neural response variability as measured by fano-factor (FF). However, the relative contributions of within-trial spike irregularity and trial-to-trial rate variability to FF fluctuations have remained elusive. Here, we introduce a principled approach for accurate estimation of spiking irregularity and rate variability in time for doubly stochastic point processes. Consistent with previous evidence, analysis showed stimulus-induced reduction in rate variability across multiple cortical and subcortical areas. However, unlike what was previously thought, spiking irregularity, was not constant in time but could be enhanced due to factors such as bursting abating the quench in the post-stimulus FF. Simulations confirmed plausibility of a time varying spiking irregularity arising from within and between pool correlations of excitatory and inhibitory neural inputs. By accurate parsing of neural variability, our approach reveals previously unnoticed changes in neural response variability and constrains candidate mechanisms that give rise to observed rate variability and spiking irregularity within brain regions.

Mounting evidence suggest neural response variability to be important for understanding and constraining the underlying neural mechanisms in a given brain area. Here, by analyzing responses across multiple brain areas and by using a principled method for parsing variability components into rate variability and spiking irregularity, we show that unlike what was previously thought, event-related quench of variability is not a brain-wide phenomenon and that point process variability and nonrenewal bursting can enhance post-stimulus spiking irregularity across certain cortical and subcortical regions. We propose possible presynaptic mechanisms that may underlie the observed heterogeneities in spiking variability across the brain.

Controlling the spontaneous firing behavior of a neuron with astrocyte

Mounting evidence in recent years suggests that astrocytes, a sub-type of glial cells, not only serve metabolic and structural support for neurons and synapses but also play critical roles in the regulation of proper functioning of the nervous system. In this work, we investigate the effect of astrocytes on the spontaneous firing activity of a neuron through a combined model that includes a neuron-astrocyte pair. First, we show that an astrocyte may provide a kind of multistability in neuron dynamics by inducing different firing modes such as random and bursty spiking. Then, we identify the underlying mechanism of this behavior and search for the astrocytic factors that may have regulatory roles in different firing regimes. More specifically, we explore how an astrocyte can participate in the occurrence and control of spontaneous irregular spiking activity of a neuron in random spiking mode. Additionally, we systematically investigate the bursty firing regime dynamics of the neuron under the variation of biophysical facts related to the intracellular environment of the astrocyte. It is found that an astrocyte coupled to a neuron can provide a control mechanism for both spontaneous firing irregularity and burst firing statistics, i.e., burst regularity and size.

Functional Implications of Dale's Law in Balanced Neuronal Network Dynamics and Decision Making

The notion that a neuron transmits the same set of neurotransmitters at all of its post-synaptic connections, typically known as Dale's law, is well supported throughout the majority of the brain and is assumed in almost all theoretical studies investigating the mechanisms for computation in neuronal networks. Dale's law has numerous functional implications in fundamental sensory processing and decision-making tasks, and it plays a key role in the current understanding of the structure-function relationship in the brain. However, since exceptions to Dale's law have been discovered for certain neurons and because other biological systems with complex network structure incorporate individual units that send both positive and negative feedback signals, we investigate the functional implications of network model dynamics that violate Dale's law by allowing each neuron to send out both excitatory and inhibitory signals to its neighbors. We show how balanced network dynamics, in which large excitatory and inhibitory inputs are dynamically adjusted such that input fluctuations produce irregular firing events, are theoretically preserved for a single population of neurons violating Dale's law. We further leverage this single-population network model in the context of two competing pools of neurons to demonstrate that effective decision-making dynamics are also produced, agreeing with experimental observations from honeybee dynamics in selecting a food source and artificial neural networks trained in optimal selection. Through direct comparison with the classical two-population balanced neuronal network, we argue that the one-population network demonstrates more robust balanced activity for systems with less computational units, such as honeybee colonies, whereas the two-population network exhibits a more rapid response to temporal variations in network inputs, as required by the brain. We expect this study will shed light on the role of neurons violating Dale's law found in experiment as well as shared design principles across biological systems that perform complex computations.

Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons

The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects and nonstationary responses of the population activity to rapidly changing stimuli. Here we derive low-dimensional firing-rate models for homogeneous populations of neurons modeled as time-dependent renewal processes. The class of renewal neurons includes integrate-and-fire models driven by white noise and has been frequently used to model neuronal refractoriness and spike synchronization dynamics. The derivation is based on an eigenmode expansion of the associated refractory density equation, which generalizes previous spectral methods for Fokker-Planck equations to arbitrary renewal models. We find a simple relation between the eigenvalues characterizing the timescales of the firing rate dynamics and the Laplace transform of the interspike interval density, for which explicit expressions are available for many renewal models. Retaining only the first eigenmode already yields a reliable low-dimensional approximation of the firing-rate dynamics that captures spike synchronization effects and fast transient dynamics at stimulus onset. We explicitly demonstrate the validity of our model for a large homogeneous population of Poisson neurons with absolute refractoriness and other renewal models that admit an explicit analytical calculation of the eigenvalues. The eigenmode expansion presented here provides a systematic framework for alternative firing-rate models in computational neuroscience based on spiking neuron dynamics with refractoriness.

A Statistical View on Calcium Oscillations

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.

Compressive Sensing Inference of Neuronal Network Connectivity in Balanced Neuronal Dynamics

Determining the structure of a network is of central importance to understanding its function in both neuroscience and applied mathematics. However, recovering the structural connectivity of neuronal networks remains a fundamental challenge both theoretically and experimentally. While neuronal networks operate in certain dynamical regimes, which may influence their connectivity reconstruction, there is widespread experimental evidence of a balanced neuronal operating state in which strong excitatory and inhibitory inputs are dynamically adjusted such that neuronal voltages primarily remain near resting potential. Utilizing the dynamics of model neurons in such a balanced regime in conjunction with the ubiquitous sparse connectivity structure of neuronal networks, we develop a compressive sensing theoretical framework for efficiently reconstructing network connections by measuring individual neuronal activity in response to a relatively small ensemble of random stimuli injected over a short time scale. By tuning the network dynamical regime, we determine that the highest fidelity reconstructions are achievable in the balanced state. We hypothesize the balanced dynamics observed in vivo may therefore be a result of evolutionary selection for optimal information encoding and expect the methodology developed to be generalizable for alternative model networks as well as experimental paradigms.

Identification of midbrain dopamine neurons using features from spontaneous spike activity patterns. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2019;2019:2990-2993. [PMID: 31946517 DOI: 10.1109/embc.2019.8857574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Although dopamine neurons are considered essential in various brain functions, their specific roles are under debate, partially due to the difficulty to identify dopamine neurons among surrounding neurons deep in the brain based only on the extracellularly recorded electric activities. Thus, a handy method to identify dopamine and non-dopamine neurons based on the spontaneous activity patterns is desired. Here we tried to discriminate optogenetically-identified dopamine neurons from other types of neurons and obtained 86.0% success.

Assessing the Impacts of Correlated Variability with Dissociated Timescales

Despite the profound influence on coding capacity of sensory neurons, the measurements of noise correlations have been inconsistent. This is, possibly, because nonstationarity, i.e., drifting baselines, engendered the spurious long-term correlations even if no actual short-term correlation existed. Although attempts to separate them have been made previously, they were ad hoc for specific cases or computationally too demanding. Here we proposed an information-geometric method to unbiasedly estimate pure short-term noise correlations irrespective of the background brain activities without demanding computational resources. First, the benchmark simulations demonstrated that the proposed estimator is more accurate and computationally efficient than the conventional correlograms and the residual correlations with Kalman filters or moving averages of length three or more, while the best moving average of length two coincided with the propose method regarding correlation estimates. Next, we analyzed the cat V1 neural responses to demonstrate that the statistical test accompanying the proposed method combined with the existing nonstationarity test enabled us to dissociate short-term and long-term noise correlations. When we excluded the spurious noise correlations of purely long-term nature, only a small fraction of neuron pairs showed significant short-term correlations, possibly reconciling the previous inconsistent observations on existence of significant noise correlations. The decoding accuracy was slightly improved by the short-term correlations. Although the long-term correlations deteriorated the generalizability, the generalizability was recovered by the decoder with trend removal, suggesting that brains could overcome nonstationarity. Thus, the proposed method enables us to elucidate the impacts of short-term and long-term noise correlations in a dissociated manner.

Balanced Active Core in Heterogeneous Neuronal Networks

It is hypothesized that cortical neuronal circuits operate in a global balanced state, i.e., the majority of neurons fire irregularly by receiving balanced inputs of excitation and inhibition. Meanwhile, it has been observed in experiments that sensory information is often sparsely encoded by only a small set of firing neurons, while neurons in the rest of the network are silent. The phenomenon of sparse coding challenges the hypothesis of a global balanced state in the brain. To reconcile this, here we address the issue of whether a balanced state can exist in a small number of firing neurons by taking account of the heterogeneity of network structure such as scale-free and small-world networks. We propose necessary conditions and show that, under these conditions, for sparsely but strongly connected heterogeneous networks with various types of single-neuron dynamics, despite the fact that the whole network receives external inputs, there is a small active subnetwork (active core) inherently embedded within it. The neurons in this active core have relatively high firing rates while the neurons in the rest of the network are quiescent. Surprisingly, although the whole network is heterogeneous and unbalanced, the active core possesses a balanced state and its connectivity structure is close to a homogeneous Erdös-Rényi network. The dynamics of the active core can be well-predicted using the Fokker-Planck equation. Our results suggest that the balanced state may be maintained by a small group of spiking neurons embedded in a large heterogeneous network in the brain. The existence of the small active core reconciles the balanced state and the sparse coding, and also provides a potential dynamical scenario underlying sparse coding in neuronal networks.

The impact of spike-frequency adaptation on balanced network dynamics

A dynamic balance between strong excitatory and inhibitory neuronal inputs is hypothesized to play a pivotal role in information processing in the brain. While there is evidence of the existence of a balanced operating regime in several cortical areas and idealized neuronal network models, it is important for the theory of balanced networks to be reconciled with more physiological neuronal modeling assumptions. In this work, we examine the impact of spike-frequency adaptation, observed widely across neurons in the brain, on balanced dynamics. We incorporate adaptation into binary and integrate-and-fire neuronal network models, analyzing the theoretical effect of adaptation in the large network limit and performing an extensive numerical investigation of the model adaptation parameter space. Our analysis demonstrates that balance is well preserved for moderate adaptation strength even if the entire network exhibits adaptation. In the common physiological case in which only excitatory neurons undergo adaptation, we show that the balanced operating regime in fact widens relative to the non-adaptive case. We hypothesize that spike-frequency adaptation may have been selected through evolution to robustly facilitate balanced dynamics across diverse cognitive operating states.

The Dynamics of Balanced Spiking Neuronal Networks Under Poisson Drive Is Not Chaotic

Some previous studies have shown that chaotic dynamics in the balanced state, i.e., one with balanced excitatory and inhibitory inputs into cortical neurons, is the underlying mechanism for the irregularity of neural activity. In this work, we focus on networks of current-based integrate-and-fire neurons with delta-pulse coupling. While we show that the balanced state robustly persists in this system within a broad range of parameters, we mathematically prove that the largest Lyapunov exponent of this type of neuronal networks is negative. Therefore, the irregular firing activity can exist in the system without the chaotic dynamics. That is the irregularity of balanced neuronal networks need not arise from chaos.

A single spike deteriorates synaptic conductance estimation

We investigated the estimation accuracy of synaptic conductances by analyzing simulated voltage traces generated by a Hodgkin-Huxley type model. We show that even a single spike substantially deteriorates the estimation. We also demonstrate that two approaches, namely, negative current injection and spike removal, can ameliorate this deterioration.

Efficiency of rate and latency coding with respect to metabolic cost and time

Recent studies on the theoretical performance of latency and rate code in single neurons have revealed that the ultimate accuracy is affected in a nontrivial way by aspects such as the level of spontaneous activity of presynaptic neurons, amount of neuronal noise or the duration of the time window used to determine the firing rate. This study explores how the optimal decoding performance and the corresponding conditions change when the energy expenditure of a neuron in order to spike and maintain the resting membrane potential is accounted for. It is shown that a nonzero amount of spontaneous activity remains essential for both the latency and the rate coding. Moreover, the optimal level of spontaneous activity does not change so much with respect to the intensity of the applied stimulus. Furthermore, the efficiency of the temporal and the rate code converge to an identical finite value if the neuronal activity is observed for an unlimited period of time.

Accuracy of rate coding: When shorter time window and higher spontaneous activity help

It is widely accepted that neuronal firing rates contain a significant amount of information about the stimulus intensity. Nevertheless, theoretical studies on the coding accuracy inferred from the exact spike counting distributions are rare. We present an analysis based on the number of observed spikes assuming the stochastic perfect integrate-and-fire model with a change point, representing the stimulus onset, for which we calculate the corresponding Fisher information to investigate the accuracy of rate coding. We analyze the effect of changing the duration of the time window and the influence of several parameters of the model, in particular the level of the presynaptic spontaneous activity and the level of random fluctuation of the membrane potential, which can be interpreted as noise of the system. The results show that the Fisher information is nonmonotonic with respect to the length of the observation period. This counterintuitive result is caused by the discrete nature of the count of spikes. We observe also that the signal can be enhanced by noise, since the Fisher information is nonmonotonic with respect to the level of spontaneous activity and, in some cases, also with respect to the level of fluctuation of the membrane potential.

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.

Optimal decoding and information transmission in Hodgkin-Huxley neurons under metabolic cost constraints

Information theory quantifies the ultimate limits on reliable information transfer by means of the channel capacity. However, the channel capacity is known to be an asymptotic quantity, assuming unlimited metabolic cost and computational power. We investigate a single-compartment Hodgkin-Huxley type neuronal model under the spike-rate coding scheme and address how the metabolic cost and the decoding complexity affects the optimal information transmission. We find that the sub-threshold stimulation regime, although attaining the smallest capacity, allows for the most efficient balance between the information transmission and the metabolic cost. Furthermore, we determine post-synaptic firing rate histograms that are optimal from the information-theoretic point of view, which enables the comparison of our results with experimental data.

Estimation of the synaptic input firing rates and characterization of the stimulation effects in an auditory neuron

To understand information processing in neuronal circuits, it is important to infer how a sensory stimulus impacts on the synaptic input to a neuron. An increase in neuronal firing during the stimulation results from pure excitation or from a combination of excitation and inhibition. Here, we develop a method for estimating the rates of the excitatory and inhibitory synaptic inputs from a membrane voltage trace of a neuron. The method is based on a modified Ornstein-Uhlenbeck neuronal model, which aims to describe the stimulation effects on the synaptic input. The method is tested using a single-compartment neuron model with a realistic description of synaptic inputs, and it is applied to an intracellular voltage trace recorded from an auditory neuron in vivo. We find that the excitatory and inhibitory inputs increase during stimulation, suggesting that the acoustic stimuli are encoded by a combination of excitation and inhibition.

Advantages and limitations of the use of optogenetic approach in studying fast-scale spike encoding

Understanding single-neuron computations and encoding performed by spike-generation mechanisms of cortical neurons is one of the central challenges for cell electrophysiology and computational neuroscience. An established paradigm to study spike encoding in controlled conditions in vitro uses intracellular injection of a mixture of signals with fluctuating currents that mimic in vivo-like background activity. However this technique has two serious limitations: it uses current injection, while synaptic activation leads to changes of conductance, and current injection is technically most feasible in the soma, while the vast majority of synaptic inputs are located on the dendrites. Recent progress in optogenetics provides an opportunity to circumvent these limitations. Transgenic expression of light-activated ionic channels, such as Channelrhodopsin2 (ChR2), allows induction of controlled conductance changes even in thin distant dendrites. Here we show that photostimulation provides a useful extension of the tools to study neuronal encoding, but it has its own limitations. Optically induced fluctuating currents have a low cutoff (~70Hz), thus limiting the dynamic range of frequency response of cortical neurons. This leads to severe underestimation of the ability of neurons to phase-lock their firing to high frequency components of the input. This limitation could be worked around by using short (2 ms) light stimuli which produce membrane potential responses resembling EPSPs by their fast onset and prolonged decay kinetics. We show that combining application of short light stimuli to different parts of dendritic tree for mimicking distant EPSCs with somatic injection of fluctuating current that mimics fluctuations of membrane potential in vivo, allowed us to study fast encoding of artificial EPSPs photoinduced at different distances from the soma. We conclude that dendritic photostimulation of ChR2 with short light pulses provides a powerful tool to investigate population encoding of simulated synaptic potentials generated in dendrites at different distances from the soma.

Analytical approximations of the firing rate of an adaptive exponential integrate-and-fire neuron in the presence of synaptic noise

Computational models offer a unique tool for understanding the network-dynamical mechanisms which mediate between physiological and biophysical properties, and behavioral function. A traditional challenge in computational neuroscience is, however, that simple neuronal models which can be studied analytically fail to reproduce the diversity of electrophysiological behaviors seen in real neurons, while detailed neuronal models which do reproduce such diversity are intractable analytically and computationally expensive. A number of intermediate models have been proposed whose aim is to capture the diversity of firing behaviors and spike times of real neurons while entailing the simplest possible mathematical description. One such model is the exponential integrate-and-fire neuron with spike rate adaptation (aEIF) which consists of two differential equations for the membrane potential (V) and an adaptation current (w). Despite its simplicity, it can reproduce a wide variety of physiologically observed spiking patterns, can be fit to physiological recordings quantitatively, and, once done so, is able to predict spike times on traces not used for model fitting. Here we compute the steady-state firing rate of aEIF in the presence of Gaussian synaptic noise, using two approaches. The first approach is based on the 2-dimensional Fokker-Planck equation that describes the (V,w)-probability distribution, which is solved using an expansion in the ratio between the time constants of the two variables. The second is based on the firing rate of the EIF model, which is averaged over the distribution of the w variable. These analytically derived closed-form expressions were tested on simulations from a large variety of model cells quantitatively fitted to in vitro electrophysiological recordings from pyramidal cells and interneurons. Theoretical predictions closely agreed with the firing rate of the simulated cells fed with in-vivo-like synaptic noise.

Chronic deep cerebellar stimulation promotes long-term potentiation, microstructural plasticity, and reorganization of perilesional cortical representation in a rodent model

Control over postinjury CNS plasticity is a major frontier of science that, if conquered, would open new avenues for treatment of neurological disorders. Here we investigate the functional, physiological, and structural changes in the cerebral cortex associated with chronic deep brain stimulation of the cerebellar output, a treatment approach that has been shown to improve postischemia motor recovery in a rodent model of cortical infarcts. Long-Evans rats were pretrained on the pasta-matrix retrieval task, followed by induction of focal cortical ischemia and implantation of a macroelectrode in the contralesional lateral cerebellar nucleus. Animals were assigned to one of three treatment groups pseudorandomly to balance severity of poststroke motor deficits: REGULAR stimulation, BURST stimulation, or SHAM. Treatment initiated 2 weeks post surgery and continued for 5 weeks. At the end, animals were randomly selected for perilesional intracortical microstimulation mapping and tissue sampling for Western blot analysis or contributed tissue for 3D electron microscopy. Evidence of enhanced cortical plasticity with therapeutically effective stimulation is shown, marked by greater perilesional reorganization in stimulation- treated animals versus SHAM. BURST stimulation was significantly effective for promoting distal forepaw cortical representation. Stimulation-treated animals showed a twofold increase in synaptic density compared with SHAM. In addition, treated animals demonstrated increased expression of synaptic markers of long-term potentiation and plasticity, including synaptophysin, NMDAR1, CaMKII, and PSD95. These findings provide a critical foundation of how deep cerebellar stimulation may guide plastic reparative reorganization after nonprogressive brain injury and indicate strong translational potential.

On how correlations between excitatory and inhibitory synaptic inputs maximize the information rate of neuronal firing

Cortical neurons receive barrages of excitatory and inhibitory inputs which are not independent, as network structure and synaptic kinetics impose statistical correlations. Experiments in vitro and in vivo have demonstrated correlations between inhibitory and excitatory synaptic inputs in which inhibition lags behind excitation in cortical neurons. This delay arises in feed-forward inhibition (FFI) circuits and ensures that coincident excitation and inhibition do not preclude neuronal firing. Conversely, inhibition that is too delayed broadens neuronal integration times, thereby diminishing spike-time precision and increasing the firing frequency. This led us to hypothesize that the correlation between excitatory and inhibitory synaptic inputs modulates the encoding of information of neural spike trains. We tested this hypothesis by investigating the effect of such correlations on the information rate (IR) of spike trains using the Hodgkin-Huxley model in which both synaptic and membrane conductances are stochastic. We investigated two different synaptic input regimes: balanced synaptic conductances and balanced currents. Our results show that correlations arising from the synaptic kinetics, τ, and millisecond lags, δ, of inhibition relative to excitation strongly affect the IR of spike trains. In the regime of balanced synaptic currents, for short time lags (δ ~ 1 ms) there is an optimal τ that maximizes the IR of the postsynaptic spike train. Given the short time scales for monosynaptic inhibitory lags and synaptic decay kinetics reported in cortical neurons under physiological contexts, we propose that FFI in cortical circuits is poised to maximize the rate of information transfer between cortical neurons. Our results also provide a possible explanation for how certain drugs and genetic mutations affecting the synaptic kinetics can deteriorate information processing in the brain.

Increased firing irregularity as an emergent property of neural-state transition in monkey prefrontal cortex

Flexible behaviors are organized by complex neural networks in the prefrontal cortex. Recent studies have suggested that such networks exhibit multiple dynamical states, and can switch rapidly from one state to another. In many complex systems such as the brain, the early-warning signals that may predict whether a critical threshold for state transitions is approaching are extremely difficult to detect. We hypothesized that increases in firing irregularity are a crucial measure for predicting state transitions in the underlying neuronal circuits of the prefrontal cortex. We used both experimental and theoretical approaches to test this hypothesis. Experimentally, we analyzed activities of neurons in the prefrontal cortex while monkeys performed a maze task that required them to perform actions to reach a goal. We observed increased firing irregularity before the activity changed to encode goal-to-action information. Theoretically, we constructed theoretical generic neural networks and demonstrated that changes in neuronal gain on functional connectivity resulted in a loss of stability and an altered state of the networks, accompanied by increased firing irregularity. These results suggest that assessing the temporal pattern of neuronal fluctuations provides important clues regarding the state stability of the prefrontal network. We also introduce a novel scheme that the prefrontal cortex functions in a metastable state near the critical point of bifurcation. According to this scheme, firing irregularity in the prefrontal cortex indicates that the system is about to change its state and the flow of information in a flexible manner, which is essential for executive functions. This metastable and/or critical dynamical state of the prefrontal cortex may account for distractibility and loss of flexibility in the prefrontal cortex in major mental illnesses such as schizophrenia.

The aging motor system as a model for plastic changes of GABA-mediated intracortical inhibition and their behavioral relevance

Since GABAA-mediated intracortical inhibition has been shown to underlie plastic changes throughout the lifespan from development to aging, here, the aging motor system was used as a model to analyze the interdependence of plastic alterations within the inhibitory motorcortical network and level of behavioral performance. Double-pulse transcranial magnetic stimulation (dpTMS) was used to examine inhibition by means of short-interval intracortical inhibition (SICI) of the contralateral primary motor cortex in a sample of 64 healthy right-handed human subjects covering a wide range of the adult lifespan (age range 20-88 years, mean 47.6 ± 20.7, 34 female). SICI was evaluated during resting state and in an event-related condition during movement preparation in a visually triggered simple reaction time task. In a subgroup (N = 23), manual motor performance was tested with tasks of graded dexterous demand. Weak resting-state inhibition was associated with an overall lower manual motor performance. Better event-related modulation of inhibition correlated with better performance in more demanding tasks, in which fast alternating activation of cortical representations are necessary. Declining resting-state inhibition was associated with weakened event-related modulation of inhibition. Therefore, reduced resting-state inhibition might lead to a subsequent loss of modulatory capacity, possibly reflecting malfunctioning precision in GABAAergic neurotransmission; the consequence is an inevitable decline in motor function.

Neural dynamics and information representation in microcircuits of motor cortex

The brain has to analyze and respond to external events that can change rapidly from time to time, suggesting that information processing by the brain may be essentially dynamic rather than static. The dynamical features of neural computation are of significant importance in motor cortex that governs the process of movement generation and learning. In this paper, we discuss these features based primarily on our recent findings on neural dynamics and information coding in the microcircuit of rat motor cortex. In fact, cortical neurons show a variety of dynamical behavior from rhythmic activity in various frequency bands to highly irregular spike firing. Of particular interest are the similarity and dissimilarity of the neuronal response properties in different layers of motor cortex. By conducting electrophysiological recordings in slice preparation, we report the phase response curves (PRCs) of neurons in different cortical layers to demonstrate their layer-dependent synchronization properties. We then study how motor cortex recruits task-related neurons in different layers for voluntary arm movements by simultaneous juxtacellular and multiunit recordings from behaving rats. The results suggest an interesting difference in the spectrum of functional activity between the superficial and deep layers. Furthermore, the task-related activities recorded from various layers exhibited power law distributions of inter-spike intervals (ISIs), in contrast to a general belief that ISIs obey Poisson or Gamma distributions in cortical neurons. We present a theoretical argument that this power law of in vivo neurons may represent the maximization of the entropy of firing rate with limited energy consumption of spike generation. Though further studies are required to fully clarify the functional implications of this coding principle, it may shed new light on information representations by neurons and circuits in motor cortex.

Optimal balance of the striatal medium spiny neuron network

Slowly varying activity in the striatum, the main Basal Ganglia input structure, is important for the learning and execution of movement sequences. Striatal medium spiny neurons (MSNs) form cell assemblies whose population firing rates vary coherently on slow behaviourally relevant timescales. It has been shown that such activity emerges in a model of a local MSN network but only at realistic connectivities of 10 ~ 20% and only when MSN generated inhibitory post-synaptic potentials (IPSPs) are realistically sized. Here we suggest a reason for this. We investigate how MSN network generated population activity interacts with temporally varying cortical driving activity, as would occur in a behavioural task. We find that at unrealistically high connectivity a stable winners-take-all type regime is found where network activity separates into fixed stimulus dependent regularly firing and quiescent components. In this regime only a small number of population firing rate components interact with cortical stimulus variations. Around 15% connectivity a transition to a more dynamically active regime occurs where all cells constantly switch between activity and quiescence. In this low connectivity regime, MSN population components wander randomly and here too are independent of variations in cortical driving. Only in the transition regime do weak changes in cortical driving interact with many population components so that sequential cell assemblies are reproducibly activated for many hundreds of milliseconds after stimulus onset and peri-stimulus time histograms display strong stimulus and temporal specificity. We show that, remarkably, this activity is maximized at striatally realistic connectivities and IPSP sizes. Thus, we suggest the local MSN network has optimal characteristics - it is neither too stable to respond in a dynamically complex temporally extended way to cortical variations, nor is it too unstable to respond in a consistent repeatable way. Rather, it is optimized to generate stimulus dependent activity patterns for long periods after variations in cortical excitation.

Statistical analysis of sleep spindle occurrences

Spindles - a hallmark of stage II sleep - are a transient oscillatory phenomenon in the EEG believed to reflect thalamocortical activity contributing to unresponsiveness during sleep. Currently spindles are often classified into two classes: fast spindles, with a frequency of around 14 Hz, occurring in the centro-parietal region; and slow spindles, with a frequency of around 12 Hz, prevalent in the frontal region. Here we aim to establish whether the spindle generation process also exhibits spatial heterogeneity. Electroencephalographic recordings from 20 subjects were automatically scanned to detect spindles and the time occurrences of spindles were used for statistical analysis. Gamma distribution parameters were fit to each inter-spindle interval distribution, and a modified Wald-Wolfowitz lag-1 correlation test was applied. Results indicate that not all spindles are generated by the same statistical process, but this dissociation is not spindle-type specific. Although this dissociation is not topographically specific, a single generator for all spindle types appears unlikely.

Integrate-and-fire vs Poisson models of LGN input to V1 cortex: noisier inputs reduce orientation selectivity

One of the reasons the visual cortex has attracted the interest of computational neuroscience is that it has well-defined inputs. The lateral geniculate nucleus (LGN) of the thalamus is the source of visual signals to the primary visual cortex (V1). Most large-scale cortical network models approximate the spike trains of LGN neurons as simple Poisson point processes. However, many studies have shown that neurons in the early visual pathway are capable of spiking with high temporal precision and their discharges are not Poisson-like. To gain an understanding of how response variability in the LGN influences the behavior of V1, we study response properties of model V1 neurons that receive purely feedforward inputs from LGN cells modeled either as noisy leaky integrate-and-fire (NLIF) neurons or as inhomogeneous Poisson processes. We first demonstrate that the NLIF model is capable of reproducing many experimentally observed statistical properties of LGN neurons. Then we show that a V1 model in which the LGN input to a V1 neuron is modeled as a group of NLIF neurons produces higher orientation selectivity than the one with Poisson LGN input. The second result implies that statistical characteristics of LGN spike trains are important for V1's function. We conclude that physiologically motivated models of V1 need to include more realistic LGN spike trains that are less noisy than inhomogeneous Poisson processes.

Neuronal variability of MSTd neurons changes differentially with eye movement and visually related variables

Neurons in macaque cortical area MSTd are driven by visual motion and eye movement related signals. This multimodal characteristic makes MSTd an ideal system for studying the dependence of neuronal activity on different variables. Here, we analyzed the temporal structure of spiking patterns during visual motion stimulation using 2 distinct behavioral paradigms: fixation (FIX) and optokinetic response. For the FIX condition, inter- and intra-trial variability of spiking activity decreased with increasing stimulus strength, complying with a recent neurophysiological study reporting stimulus-related decline of neuronal variability. In contrast, for the optokinetic condition variability increased together with increasing eye velocity while retinal image velocity remained low. Analysis of stimulus signal variability revealed a correlation between the normalized variance of image velocity and neuronal variability, but no correlation with normalized eye velocity variance. We further show that the observed difference in neuronal variability allows classifying spike trains according to the paradigm used, even when mean firing rates (FRs) were similar. The stimulus-dependence of neuronal variability may result from the local network structure and/or the variability characteristics of the input signals, but may also reflect additional timing-based mechanisms independent of the neuron's mean FR and related to the modality driving the neuron.

Age-based comparison of human dendritic spine structure using complete three-dimensional reconstructions

Dendritic spines of pyramidal neurons are targets of most excitatory synapses in the cerebral cortex. Recent evidence suggests that the morphology of the dendritic spine could determine its synaptic strength and learning rules. However, unfortunately, there are scant data available regarding the detailed morphology of these structures for the human cerebral cortex. In the present study, we analyzed over 8900 individual dendritic spines that were completely 3D reconstructed along the length of apical and basal dendrites of layer III pyramidal neurons in the cingulate cortex of 2 male humans (aged 40 and 85 years old), using intracellular injections of Lucifer Yellow in fixed tissue. We assembled a large, quantitative database, which revealed a major reduction in spine densities in the aged case. Specifically, small and short spines of basal dendrites and long spines of apical dendrites were lost, regardless of the distance from the soma. Given the age difference between the cases, our results suggest selective alterations in spines with aging in humans and indicate that the spine volume and length are regulated by different biological mechanisms.

Power-law inter-spike interval distributions infer a conditional maximization of entropy in cortical neurons

The brain is considered to use a relatively small amount of energy for its efficient information processing. Under a severe restriction on the energy consumption, the maximization of mutual information (MMI), which is adequate for designing artificial processing machines, may not suit for the brain. The MMI attempts to send information as accurate as possible and this usually requires a sufficient energy supply for establishing clearly discretized communication bands. Here, we derive an alternative hypothesis for neural code from the neuronal activities recorded juxtacellularly in the sensorimotor cortex of behaving rats. Our hypothesis states that in vivo cortical neurons maximize the entropy of neuronal firing under two constraints, one limiting the energy consumption (as assumed previously) and one restricting the uncertainty in output spike sequences at given firing rate. Thus, the conditional maximization of firing-rate entropy (CMFE) solves a tradeoff between the energy cost and noise in neuronal response. In short, the CMFE sends a rich variety of information through broader communication bands (i.e., widely distributed firing rates) at the cost of accuracy. We demonstrate that the CMFE is reflected in the long-tailed, typically power law, distributions of inter-spike intervals obtained for the majority of recorded neurons. In other words, the power-law tails are more consistent with the CMFE rather than the MMI. Thus, we propose the mathematical principle by which cortical neurons may represent information about synaptic input into their output spike trains.

Input dependent cell assembly dynamics in a model of the striatal medium spiny neuron network

The striatal medium spiny neuron (MSN) network is sparsely connected with fairly weak GABAergic collaterals receiving an excitatory glutamatergic cortical projection. Peri-stimulus time histograms (PSTH) of MSN population response investigated in various experimental studies display strong firing rate modulations distributed throughout behavioral task epochs. In previous work we have shown by numerical simulation that sparse random networks of inhibitory spiking neurons with characteristics appropriate for UP state MSNs form cell assemblies which fire together coherently in sequences on long behaviorally relevant timescales when the network receives a fixed pattern of constant input excitation. Here we first extend that model to the case where cortical excitation is composed of many independent noisy Poisson processes and demonstrate that cell assembly dynamics is still observed when the input is sufficiently weak. However if cortical excitation strength is increased more regularly firing and completely quiescent cells are found, which depend on the cortical stimulation. Subsequently we further extend previous work to consider what happens when the excitatory input varies as it would when the animal is engaged in behavior. We investigate how sudden switches in excitation interact with network generated patterned activity. We show that sequences of cell assembly activations can be locked to the excitatory input sequence and outline the range of parameters where this behavior is shown. Model cell population PSTH display both stimulus and temporal specificity, with large population firing rate modulations locked to elapsed time from task events. Thus the random network can generate a large diversity of temporally evolving stimulus dependent responses even though the input is fixed between switches. We suggest the MSN network is well suited to the generation of such slow coherent task dependent response which could be utilized by the animal in behavior.

Interspike interval distributions of spiking neurons driven by fluctuating inputs

Interspike interval (ISI) distributions of cortical neurons exhibit a range of different shapes. Wide ISI distributions are believed to stem from a balance of excitatory and inhibitory inputs that leads to a strongly fluctuating total drive. An important question is whether the full range of experimentally observed ISI distributions can be reproduced by modulating this balance. To address this issue, we investigate the shape of the ISI distributions of spiking neuron models receiving fluctuating inputs. Using analytical tools to describe the ISI distribution of a leaky integrate-and-fire (LIF) neuron, we identify three key features: 1) the ISI distribution displays an exponential decay at long ISIs independently of the strength of the fluctuating input; 2) as the amplitude of the input fluctuations is increased, the ISI distribution evolves progressively between three types, a narrow distribution (suprathreshold input), an exponential with an effective refractory period (subthreshold but suprareset input), and a bursting exponential (subreset input); 3) the shape of the ISI distribution is approximately independent of the mean ISI and determined only by the coefficient of variation. Numerical simulations show that these features are not specific to the LIF model but are also present in the ISI distributions of the exponential integrate-and-fire model and a Hodgkin-Huxley-like model. Moreover, we observe that for a fixed mean and coefficient of variation of ISIs, the full ISI distributions of the three models are nearly identical. We conclude that the ISI distributions of spiking neurons in the presence of fluctuating inputs are well described by gamma distributions.

Dual amplification strategy for the fabrication of highly sensitive interleukin-6 amperometric immunosensor based on poly-dopamine

An electrochemical immunosensor was studied for sensitive detection of Interleukin-6 (IL-6) based on a dual amplification mechanism resulting from Au nanoparticles (AuNP)-Poly-dopamine (PDOP) as the sensor platform and multienzyme-antibody functionalized AuNP-PDOP@carbon nanotubes (CNT). The stable and robust film, PDOP, was used to immobilize biomolecules not only for the construction of the sensor platform, but also for the signal labeling. Sensitivity was greatly amplified by using the special platform of AuNP-PDOP and synthesizing horseradish peroxidase (HRP)-antibody (Ab(2)) functionalized AuNP-PDOP@carbon nanotubes (CNT). A linear response range of IL-6 from 4.0 to 8.0 × 10(2) pg mL(-1) with a low detection limit of 1.0 pg mL(-1) was obtained by the amperometry determination. Measurements of IL-6 in human serum gave excellent correlations with standard ELISA assays. Moreover, the immunosensor exhibited high selectivity, good reproducibility, and stability.

Correlation of cognitive performance and morphological changes in neocortical pyramidal neurons in aging

It is well established that the cerebral cortex undergoes extensive remodeling in aging. In this study, we used behaviorally characterized rats to correlate age-related morphological changes with cognitive impairment. For this, young and aged animals were tested in the Morris water maze to evaluate their cognitive performance. Following behavioral characterization, the animals were perfused and a combination of intracellular labeling and immunohistochemistry was applied. Using this approach, we characterized the dendritic morphology of cortical pyramidal neurons as well as the pattern of glutamatergic and GABAergic appositions on their cell bodies and dendrites. We focused on the association region of the parietal cortex (LtPA) and the medial prefrontal cortex (mPFC) for their involvement in the Morris water maze task. We found an age-related atrophy of distal basal dendrites that did not differ between aged cognitively unimpaired (AU) and aged cognitively impaired animals (AI). Dendritic spines and glutamatergic appositions generally decreased from young to AU and from AU to AI rats. On the other hand, GABAergic appositions only showed a trend towards a decrease in AU rats. Collectively, the data show that the ratio of excitatory/inhibitory inputs was only altered in AI animals. When cortical cholinergic varicosities were labeled on alternate sections, we found that AI animals also had a significant reduction of cortical cholinergic boutons compared with AU or young animals. In aged animals, the density of cortical cholinergic varicosities correlated with the excitatory/inhibitory ratio. Our data suggest that both cholinergic atrophy and an imbalance towards inhibition may contribute to the observed age-associated behavioral impairment.

Estimating network parameters from combined dynamics of firing rate and irregularity of single neurons

High firing irregularity is a hallmark of cortical neurons in vivo, and modeling studies suggest a balance of excitation and inhibition is necessary to explain this high irregularity. Such a balance must be generated, at least partly, from local interconnected networks of excitatory and inhibitory neurons, but the details of the local network structure are largely unknown. The dynamics of the neural activity depends on the local network structure; this in turn suggests the possibility of estimating network structure from the dynamics of the firing statistics. Here we report a new method to estimate properties of the local cortical network from the instantaneous firing rate and irregularity (CV(2)) under the assumption that recorded neurons are a part of a randomly connected sparse network. The firing irregularity, measured in monkey motor cortex, exhibits two features; many neurons show relatively stable firing irregularity in time and across different task conditions; the time-averaged CV(2) is widely distributed from quasi-regular to irregular (CV(2) = 0.3-1.0). For each recorded neuron, we estimate the three parameters of a local network [balance of local excitation-inhibition, number of recurrent connections per neuron, and excitatory postsynaptic potential (EPSP) size] that best describe the dynamics of the measured firing rates and irregularities. Our analysis shows that optimal parameter sets form a two-dimensional manifold in the three-dimensional parameter space that is confined for most of the neurons to the inhibition-dominated region. High irregularity neurons tend to be more strongly connected to the local network, either in terms of larger EPSP and inhibitory PSP size or larger number of recurrent connections, compared with the low irregularity neurons, for a given excitatory/inhibitory balance. Incorporating either synaptic short-term depression or conductance-based synapses leads many low CV(2) neurons to move to the excitation-dominated region as well as to an increase of EPSP size.

Chasing the cell assembly

Although we know enormous amounts of detailed information about the neurons that make up the cortex, placing this information back into the context of the behaving animal is a serious challenge. The functional cell assembly hypothesis first described by Hebb (The Organization of Behavior; a Neuropsychological Theory. New York: Wiley; 1949) aimed to provide a mechanistic explanation of how groups of neurons, acting together, form a percept. The vast number of neurons potentially involved make testing this hypothesis exceedingly difficult as neither the number nor locations of assembly members are known. Although increasing the number of neurons from which simultaneous recordings are made is of benefit, providing evidence for or against a hypothesis like Hebb's requires more than this. In this review, we aim to outline some recent technical advances, which may light the way in the chase for the functional cell assembly.

Sequentially switching cell assemblies in random inhibitory networks of spiking neurons in the striatum

The striatum is composed of GABAergic medium spiny neurons with inhibitory collaterals forming a sparse random asymmetric network and receiving an excitatory glutamatergic cortical projection. Because the inhibitory collaterals are sparse and weak, their role in striatal network dynamics is puzzling. However, here we show by simulation of a striatal inhibitory network model composed of spiking neurons that cells form assemblies that fire in sequential coherent episodes and display complex identity-temporal spiking patterns even when cortical excitation is simply constant or fluctuating noisily. Strongly correlated large-scale firing rate fluctuations on slow behaviorally relevant timescales of hundreds of milliseconds are shown by members of the same assembly whereas members of different assemblies show strong negative correlation, and we show how randomly connected spiking networks can generate this activity. Cells display highly irregular spiking with high coefficients of variation, broadly distributed low firing rates, and interspike interval distributions that are consistent with exponentially tailed power laws. Although firing rates vary coherently on slow timescales, precise spiking synchronization is absent in general. Our model only requires the minimal but striatally realistic assumptions of sparse to intermediate random connectivity, weak inhibitory synapses, and sufficient cortical excitation so that some cells are depolarized above the firing threshold during up states. Our results are in good qualitative agreement with experimental studies, consistent with recently determined striatal anatomy and physiology, and support a new view of endogenously generated metastable state switching dynamics of the striatal network underlying its information processing operations.

Methods for estimating neural firing rates, and their application to brain-machine interfaces

Neural spike trains present analytical challenges due to their noisy, spiking nature. Many studies of neuroscientific and neural prosthetic importance rely on a smoothed, denoised estimate of a spike train's underlying firing rate. Numerous methods for estimating neural firing rates have been developed in recent years, but to date no systematic comparison has been made between them. In this study, we review both classic and current firing rate estimation techniques. We compare the advantages and drawbacks of these methods. Then, in an effort to understand their relevance to the field of neural prostheses, we also apply these estimators to experimentally gathered neural data from a prosthetic arm-reaching paradigm. Using these estimates of firing rate, we apply standard prosthetic decoding algorithms to compare the performance of the different firing rate estimators, and, perhaps surprisingly, we find minimal differences. This study serves as a review of available spike train smoothers and a first quantitative comparison of their performance for brain-machine interfaces.

Estimating instantaneous irregularity of neuronal firing

Cortical neurons in vivo had been regarded as Poisson spike generators that convey no information other than the rate of random firing. Recently, using a metric for analyzing local variation of interspike intervals, researchers have found that individual neurons express specific patterns in generating spikes, which may symbolically be termed regular, random, or bursty, rather invariantly in time. In order to study the dynamics of firing patterns in greater detail, we propose here a Bayesian method for estimating firing irregularity and the firing rate simultaneously for a given spike sequence, and we implement an algorithm that may render the empirical Bayesian estimation practicable for data comprising a large number of spikes. Application of this method to electrophysiological data revealed a subtle correlation between the degree of firing irregularity and the firing rate for individual neurons. Irregularity of firing did not deviate greatly around the low degree of dependence on the firing rate and remained practically unchanged for individual neurons in the cortical areas V1 and MT, whereas it fluctuated greatly in the lateral geniculate nucleus of the thalamus. This indicates the presence and absence of autocontrolling mechanisms for maintaining patterns of firing in the cortex and thalamus, respectively.

Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold

Information is transmitted in the brain through various kinds of neurons that respond differently to the same signal. Full characteristics including cognitive functions of the brain should ultimately be comprehended by building simulators capable of precisely mirroring spike responses of a variety of neurons. Neuronal modeling that had remained on a qualitative level has recently advanced to a quantitative level, but is still incapable of accurately predicting biological data and requires high computational cost. In this study, we devised a simple, fast computational model that can be tailored to any cortical neuron not only for reproducing but also for predicting a variety of spike responses to greatly fluctuating currents. The key features of this model are a multi-timescale adaptive threshold predictor and a nonresetting leaky integrator. This model is capable of reproducing a rich variety of neuronal spike responses, including regular spiking, intrinsic bursting, fast spiking, and chattering, by adjusting only three adaptive threshold parameters. This model can express a continuous variety of the firing characteristics in a three-dimensional parameter space rather than just those identified in the conventional discrete categorization. Both high flexibility and low computational cost would help to model the real brain function faithfully and examine how network properties may be influenced by the distributed characteristics of component neurons.

Relating neuronal firing patterns to functional differentiation of cerebral cortex

It has been empirically established that the cerebral cortical areas defined by Brodmann one hundred years ago solely on the basis of cellular organization are closely correlated to their function, such as sensation, association, and motion. Cytoarchitectonically distinct cortical areas have different densities and types of neurons. Thus, signaling patterns may also vary among cytoarchitectonically unique cortical areas. To examine how neuronal signaling patterns are related to innate cortical functions, we detected intrinsic features of cortical firing by devising a metric that efficiently isolates non-Poisson irregular characteristics, independent of spike rate fluctuations that are caused extrinsically by ever-changing behavioral conditions. Using the new metric, we analyzed spike trains from over 1,000 neurons in 15 cortical areas sampled by eight independent neurophysiological laboratories. Analysis of firing-pattern dissimilarities across cortical areas revealed a gradient of firing regularity that corresponded closely to the functional category of the cortical area; neuronal spiking patterns are regular in motor areas, random in the visual areas, and bursty in the prefrontal area. Thus, signaling patterns may play an important role in function-specific cerebral cortical computation.

Neurons, or nerve cells in the brain, communicate with each other using stereotyped electric pulses, called spikes. It is believed that neurons convey information mainly through the frequency of the transmitted spikes, called the firing rate. In addition, neurons may communicate some information through the finer temporal patterns of the spikes. Neuronal firing patterns may depend on cellular organization, which varies among the regions of the brain, according to the roles they play, such as sensation, association, and motion. In order to examine the relationship among signals, structure, and function, we devised a metric to detect firing irregularity intrinsic and specific to individual neurons and analyzed spike sequences from over 1,000 neurons in 15 different cortical areas. Here we report two results of this study. First, we found that neurons exhibit stable firing patterns that can be characterized as “regular”, “random”, and “bursty”. Second, we observed a strong correlation between the type of signaling pattern exhibited by neurons in a given area and the function of that area. This suggests that, in addition to reflecting the cellular organization of the brain, neuronal signaling patterns may also play a role in specific types of neuronal computations.