Neural variability, or lack thereof

Temporal dynamics and neural variabilities underlying the interplay between emotion and inhibition in Chinese autistic children

This study investigated the neural dynamics underlying the interplay between emotion and inhibition in Chinese autistic children. Electroencephalography (EEG) signals were recorded from 50 autistic and 46 non-autistic children during an emotional Go/Nogo task. Based on single-trial ERP analyses, autistic children, compared to their non-autistic peers, showed a larger Nogo-N170 for angry faces and an increased Nogo-N170 amplitude variation for happy faces during early visual perception. They also displayed a smaller N200 for all faces and a diminished Nogo-N200 amplitude variation for happy and neutral faces during inhibition monitoring and preparation. During the late stage, autistic children showed a larger posterior-Go-P300 for angry faces and an augmented posterior-Nogo-P300 for happy and neutral faces. These findings clarify the differences in neural processing of emotional stimuli and inhibition between Chinese autistic and non-autistic children, highlighting the importance of considering these dynamics when designing intervention to improve emotion regulation in autistic children.

Low frequency independent components: Internal neuromarkers linking cortical LFPs to behavior

Local field potentials (LFPs) in the primate motor cortex have been shown to reflect information related to volitional movements. However, LFPs are composite signals that receive contributions from multiple neural sources, producing a complex mix of component signals. Using a blind source separation approach, we examined the components of neural activity recorded using multielectrode arrays in motor areas of macaque monkeys during a grasping and lifting task. We found a set of independent components in the low-frequency LFP with high temporal and spatial consistency associated with each task stage. We observed that ICs often arise from electrodes distributed across multiple cortical areas and provide complementary information to external behavioral markers, specifically in task stage detection and trial alignment. Taken together, our results show that it is possible to separate useful independent components of the LFP associated with specific task-related events, potentially representing internal markers of transition between cortical network states.

Neural synchrony in cortical networks: mechanisms and implications for neural information processing and coding

Synchronization of neuronal discharges on the millisecond scale has long been recognized as a prevalent and functionally important attribute of neural activity. In this article, I review classical concepts and corresponding evidence of the mechanisms that govern the synchronization of distributed discharges in cortical networks and relate those mechanisms to their possible roles in coding and cognitive functions. To accommodate the need for a selective, directed synchronization of cells, I propose that synchronous firing of distributed neurons is a natural consequence of spike-timing-dependent plasticity (STDP) that associates cells repetitively receiving temporally coherent input: the “synchrony through synaptic plasticity” hypothesis. Neurons that are excited by a repeated sequence of synaptic inputs may learn to selectively respond to the onset of this sequence through synaptic plasticity. Multiple neurons receiving coherent input could thus actively synchronize their firing by learning to selectively respond at corresponding temporal positions. The hypothesis makes several predictions: first, the position of the cells in the network, as well as the source of their input signals, would be irrelevant as long as their input signals arrive simultaneously; second, repeating discharge patterns should get compressed until all or some part of the signals are synchronized; and third, this compression should be accompanied by a sparsening of signals. In this way, selective groups of cells could emerge that would respond to some recurring event with synchronous firing. Such a learned response pattern could further be modulated by synchronous network oscillations that provide a dynamic, flexible context for the synaptic integration of distributed signals. I conclude by suggesting experimental approaches to further test this new hypothesis.

The prefrontal cortex of the Mexican free-tailed bat is more selective to communication calls than primary auditory cortex

In this study, we examined the auditory responses of a prefrontal area, the frontal auditory field (FAF), of an echolocating bat (Tadarida brasiliensis) and presented a comparative analysis of the neuronal response properties between the FAF and the primary auditory cortex (A1). We compared single-unit responses from the A1 and the FAF elicited by pure tones, downward frequency-modulated sweeps (dFMs), and species-specific vocalizations. Unlike the A1, FAFs were not frequency tuned. However, progressive increases in dFM sweep rate elicited a systematic increase of response precision, a phenomenon that does not take place in the A1. Call selectivity was higher in the FAF versus A1. We calculated the neuronal spectrotemporal receptive fields (STRFs) and spike-triggered averages (STAs) to predict responses to the communication calls and provide an explanation for the differences in call selectivity between the FAF and A1. In the A1, we found a high correlation between predicted and evoked responses. However, we did not generate reasonable STRFs in the FAF, and the prediction based on the STAs showed lower correlation coefficient than that of the A1. This suggests nonlinear response properties in the FAF that are stronger than the linear response properties in the A1. Stimulating with a call sequence increased call selectivity in the A1, but it remained unchanged in the FAF. These data are consistent with a role for the FAF in assessing distinctive acoustic features downstream of A1, similar to the role proposed for primate ventrolateral prefrontal cortex.NEW & NOTEWORTHY In this study, we examined the neuronal responses of a frontal cortical area in an echolocating bat to behaviorally relevant acoustic stimuli and compared them with those in the primary auditory cortex (A1). In contrast to the A1, neurons in the bat frontal auditory field are not frequency tuned but showed a higher selectivity for social signals such as communication calls. The results presented here indicate that the frontal auditory field may represent an additional processing center for behaviorally relevant sounds.

Robust Coding of Eye Position in Posterior Parietal Cortex despite Context-Dependent Tuning

Neurons in posterior parietal cortex (PPC) encode many aspects of the sensory world (e.g., scene structure), the posture of the body, and plans for action. For a downstream computation, however, only some of these dimensions are relevant; the rest are "nuisance variables" because their influence on neural activity changes with sensory and behavioral context, potentially corrupting the read-out of relevant information. Here we show that a key postural variable for vision (eye position) is represented robustly in male macaque PPC across a range of contexts, although the tuning of single neurons depended strongly on context. Contexts were defined by different stages of a visually guided reaching task, including (1) a visually sparse epoch, (2) a visually rich epoch, (3) a "go" epoch in which the reach was cued, and (4) during the reach itself. Eye position was constant within trials but varied across trials in a 3 × 3 grid spanning 24° × 24°. Using demixed principal component analysis of neural spike-counts, we found that the subspace of the population response encoding eye position is orthogonal to that encoding task context. Accordingly, a context-naive (fixed-parameter) decoder was nevertheless able to estimate eye position reliably across contexts. Errors were small given the sample size (∼1.78°) and would likely be even smaller with larger populations. Moreover, they were comparable to that of decoders that were optimized for each context. Our results suggest that population codes in PPC shield encoded signals from crosstalk to support robust sensorimotor transformations across contexts.SIGNIFICANCE STATEMENT Neurons in posterior parietal cortex (PPC) which are sensitive to gaze direction are thought to play a key role in spatial perception and behavior (e.g., reaching, navigation), and provide a potential substrate for brain-controlled prosthetics. Many, however, change their tuning under different sensory and behavioral contexts, raising the prospect that they provide unreliable representations of egocentric space. Here, we analyze the structure of encoding dimensions for gaze direction and context in PPC during different stages of a visually guided reaching task. We use demixed dimensionality reduction and decoding techniques to show that the coding of gaze direction in PPC is mostly invariant to context. This suggests that PPC can provide reliable spatial information across sensory and behavioral contexts.

Variability of neuronal responses in the posterior superior temporal sulcus predicts choice behavior during social interactions

Recent studies have shown that neural activity in a well-defined patch in the posterior superior temporal sulcus (the "gaze-following patch," GFP) of the primate brain is strongly modulated when the other's gaze attracts the observer's attention to locations/objects, the other is looking at. Changes of the mean discharge rate of neurons in the monkey GFP indicate that they are involved in two distinct computations: the allocation of spatial attention guided by the other's gaze vector and the suppression of gaze following if inappropriate in a given situation. Here, we asked if and how the discharge variability of neurons in the GFP is related to the task and if it carries information on behavioral performance. To this end, we calculated the Fano factor as a measure of across-trial discharge variability as a function of time. Our results show that all neurons exhibiting a task-related discharge-rate modulation also exhibit a stimulus onset-dependent drop in the Fano factor. Furthermore, the amplitude of the Fano factor reduction is modulated by task condition and the neuron's selectivity in this regard. We found that these effects are directly related to the monkeys' behavioral performance in that the Fano factor is predictive about upcoming correct or wrong decisions. Our results indicate that neuronal discharge variability as gauged by the Fano factor, hitherto primarily studied in the context of visual perception or motor control, is an informative measure also in studies of the neural underpinnings of complex social behavior.NEW & NOTEWORTHY Quenching of neural variability following stimulus onset is a widely accepted phenomenon. However, the relevance of quenching for the shaping of complex social behaviors remains to be explored. Here, we show that task selective neurons in the GFP exhibit a higher degree of variability quenching than their neighboring unselective neurons. Furthermore, we demonstrate that behavioral errors are not only associated with lower firing rates but also less variability quenching, suggesting that both facilitate optimal performance.

Prefrontal cortical activity predicts the occurrence of nonlocal hippocampal representations during spatial navigation

The receptive field of a neuron describes the regions of a stimulus space where the neuron is consistently active. Sparse spiking outside of the receptive field is often considered to be noise, rather than a reflection of information processing. Whether this characterization is accurate remains unclear. We therefore contrasted the sparse, temporally isolated spiking of hippocampal CA1 place cells to the consistent, temporally adjacent spiking seen within their spatial receptive fields ("place fields"). We found that isolated spikes, which occur during locomotion, are strongly phase coupled to hippocampal theta oscillations and transiently express coherent nonlocal spatial representations. Further, prefrontal cortical activity is coordinated with and can predict the occurrence of future isolated spiking events. Rather than local noise within the hippocampus, sparse, isolated place cell spiking reflects a coordinated cortical-hippocampal process consistent with the generation of nonlocal scenario representations during active navigation.

A Cerebellar Computational Mechanism for Delay Conditioning at Precise Time Intervals

The cerebellum is known to have an important role in sensing and execution of precise time intervals, but the mechanism by which arbitrary time intervals can be recognized and replicated with high precision is unknown. We propose a computational model in which precise time intervals can be identified from the pattern of individual spike activity in a population of parallel fibers in the cerebellar cortex. The model depends on the presence of repeatable sequences of spikes in response to conditioned stimulus input. We emulate granule cells using a population of Izhikevich neuron approximations driven by random but repeatable mossy fiber input. We emulate long-term depression (LTD) and long-term potentiation (LTP) synaptic plasticity at the parallel fiber to Purkinje cell synapse. We simulate a delay conditioning paradigm with a conditioned stimulus (CS) presented to the mossy fibers and an unconditioned stimulus (US) some time later issued to the Purkinje cells as a teaching signal. We show that Purkinje cells rapidly adapt to decrease firing probability following onset of the CS only at the interval for which the US had occurred. We suggest that detection of replicable spike patterns provides an accurate and easily learned timing structure that could be an important mechanism for behaviors that require identification and production of precise time intervals.

Trial-to-Trial Variability in Electrodermal Activity to Odor in Autism

Abnormal trial-to-trial variability (TTV) has been identified as a key feature of neural processing that is related to increased symptom severity in autism. The majority of studies evaluating TTV have focused on cortical processing. However, identifying whether similar atypicalities are evident in the peripheral nervous system will help isolate perturbed mechanisms in autism. The current study focuses on TTV in responses from the peripheral nervous system, specifically from electrodermal activity (EDA). We analyzed previously collected EDA data from 17 adults with autism and 19 neurotypical controls who viewed faces while being simultaneously exposed to fear (fear-induced sweat) and neutral odors. Average EDA peaks were significantly smaller and TTV was reduced in the autism group compared to controls, particularly during the fear odor condition. Amplitude and TTV were positively correlated in both groups, but the relationship was stronger in the control group. In addition, TTV was reduced in those with higher Autism Quotient scores but only for the individuals with autism. These findings confirm the existing results that atypical TTV is a key feature of autism and that it reflects symptom severity, although the smaller TTV in EDA contrasts with the previous findings of greater TTV in cortical responses. Identifying the relationship between cortical and peripheral TTV in autism is key for furthering our understanding of autism physiology. LAY SUMMARY: We compared the changes in electrodermal activity (EDA) to emotional faces over the course of repeated faces in adults with autism and their matched controls. The faces were accompanied by smelling fear-inducing odors. We found smaller and less variable responses to the faces in autism when smelling fear odors, suggesting that the peripheral nervous system may be more rigid. These findings were exaggerated in those who had more severe autism-related symptoms.

Fronto-Temporal Coupling Dynamics During Spontaneous Activity and Auditory Processing in the Bat Carollia perspicillata

Most mammals rely on the extraction of acoustic information from the environment in order to survive. However, the mechanisms that support sound representation in auditory neural networks involving sensory and association brain areas remain underexplored. In this study, we address the functional connectivity between an auditory region in frontal cortex (the frontal auditory field, FAF) and the auditory cortex (AC) in the bat Carollia perspicillata. The AC is a classic sensory area central for the processing of acoustic information. On the other hand, the FAF belongs to the frontal lobe, a brain region involved in the integration of sensory inputs, modulation of cognitive states, and in the coordination of behavioral outputs. The FAF-AC network was examined in terms of oscillatory coherence (local-field potentials, LFPs), and within an information theoretical framework linking FAF and AC spiking activity. We show that in the absence of acoustic stimulation, simultaneously recorded LFPs from FAF and AC are coherent in low frequencies (1-12 Hz). This "default" coupling was strongest in deep AC layers and was unaltered by acoustic stimulation. However, presenting auditory stimuli did trigger the emergence of coherent auditory-evoked gamma-band activity (>25 Hz) between the FAF and AC. In terms of spiking, our results suggest that FAF and AC engage in distinct coding strategies for representing artificial and natural sounds. Taken together, our findings shed light onto the neuronal coding strategies and functional coupling mechanisms that enable sound representation at the network level in the mammalian brain.

Fluctuations in Human Corticospinal Activity Prior to Grasp

Neuronal firing rate variability prior to movement onset contributes to trial-to-trial variability in primate behavior. However, in humans, whether similar mechanisms contribute to trial-to-trial behavioral variability remains unknown. We investigated the time-course of trial-to-trial variability in corticospinal excitability (CSE) using transcranial magnetic stimulation (TMS) during a self-paced reach-to-grasp task. We hypothesized that CSE variability will be modulated prior to the initiation of reach and that such a modulation would explain trial-to-trial behavioral variability. Able-bodied individuals were visually cued to plan their grip force before exertion of either 30% or 5% of their maximum pinch force capacity on an object. TMS was delivered at six time points (0.5, 0.75, 1, 1.1, 1.2, and 1.3 s) following a visual cue that instructed the force level. We first modeled the relation between CSE magnitude and its variability at rest (n = 12) to study the component of CSE variability pertaining to the task but not related to changes in CSE magnitude (n = 12). We found an increase in CSE variability from 1.2 to 1.3 s following the visual cue at 30% but not at 5% of force. This effect was temporally dissociated from the decrease in CSE magnitude that was observed from 0.5 to 0.75 s following the cue. Importantly, the increase in CSE variability explained at least ∼40% of inter-individual differences in trial-to-trial variability in time to peak force rate. These results were found to be repeatable across studies and robust to different analysis methods. Our findings suggest that the neural mechanisms underlying modulation in CSE variability and CSE magnitude are distinct. Notably, the extent of modulation in variability in corticospinal system prior to grasp within individuals may explain their trial-to-trial behavioral variability.

Modified synaptic dynamics predict neural activity patterns in an auditory field within the frontal cortex

Frontal areas of the mammalian cortex are thought to be important for cognitive control and complex behaviour. These areas have been studied mostly in humans, non-human primates and rodents. In this article, we present a quantitative characterization of response properties of a frontal auditory area responsive to sound in the brain of Carollia perspicillata, the frontal auditory field (FAF). Bats are highly vocal animals, and they constitute an important experimental model for studying the auditory system. We combined electrophysiology experiments and computational simulations to compare the response properties of auditory neurons found in the bat FAF and auditory cortex (AC) to simple sounds (pure tones). Anatomical studies have shown that the latter provides feedforward inputs to the former. Our results show that bat FAF neurons are responsive to sounds, and however, when compared to AC neurons, they presented sparser, less precise spiking and longer-lasting responses. Based on the results of an integrate-and-fire neuronal model, we suggest that slow, subthreshold, synaptic dynamics can account for the activity pattern of neurons in the FAF. These properties reflect the general function of the frontal cortex and likely result from its connections with multiple brain regions, including cortico-cortical projections from the AC to the FAF.

Increased Intra-Subject Variability of Reaction Times and Single-Trial Event-Related Potential Components in Children With Autism Spectrum Disorder

Autism spectrum disorder (ASD) is an increasingly common neurodevelopmental disorder that affects 1 in 59 children. The cognitive profiles of individuals with ASD are varied, and the neurophysiological underpinnings of these developmental difficulties are unclear. While many studies have focused on overall group differences in the amplitude or latency of event related potential (ERP) responses, recent research suggests that increased intra-subject neural variability may also be a reliable indicator of atypical brain function in ASD. This study aimed to identify behavioral and neural variability responses during an emotional inhibitory control task in children with ASD compared to typically developing (TD) children. Children with ASD showed increased variability in response to both inhibitory and emotional stimuli, evidenced by greater reaction time variability and single-trial ERP variability of N200 and N170 amplitudes and/or latencies compared to TD children. These results suggest that the physiological basis of ASD may be more accurately explained by increased intra-subject variability, in addition to characteristic increases or decreases in the amplitude or latency of neural responses. Autism Res 2020, 13:221-229. © 2019 International Society for Autism Research, Wiley Periodicals, Inc. LAY SUMMARY: The cognitive functions including memory, attention, executive functions, and perception, of individuals with ASD are varied, and the physiological underpinnings of these profiles are unclear. In this study, children with ASD showed increased intra-subject neural and behavioral variability in response to an emotional inhibitory control task compared to typically developing children. These results suggest that the physiological basis of ASD may also be explained by increased behavioral and neural variability in people with ASD, rather than simply characteristic increases or decreases in averaged brain responses.

Cortical reliability amid noise and chaos

Typical responses of cortical neurons to identical sensory stimuli appear highly variable. It has thus been proposed that the cortex primarily uses a rate code. However, other studies have argued for spike-time coding under certain conditions. The potential role of spike-time coding is directly limited by the internally generated variability of cortical circuits, which remains largely unexplored. Here, we quantify this internally generated variability using a biophysical model of rat neocortical microcircuitry with biologically realistic noise sources. We find that stochastic neurotransmitter release is a critical component of internally generated variability, causing rapidly diverging, chaotic recurrent network dynamics. Surprisingly, the same nonlinear recurrent network dynamics can transiently overcome the chaos in response to weak feed-forward thalamocortical inputs, and support reliable spike times with millisecond precision. Our model shows that the noisy and chaotic network dynamics of recurrent cortical microcircuitry are compatible with stimulus-evoked, millisecond spike-time reliability, resolving a long-standing debate.

Dynamics of motor cortical activity during naturalistic feeding behavior

OBJECTIVE

The orofacial primary motor cortex (MIo) plays a critical role in controlling tongue and jaw movements during oral motor functions, such as chewing, swallowing and speech. However, the neural mechanisms of MIo during naturalistic feeding are still poorly understood. There is a strong need for a systematic study of motor cortical dynamics during feeding behavior.

APPROACH

To investigate the neural dynamics and variability of MIo neuronal activity during naturalistic feeding, we used chronically implanted micro-electrode arrays to simultaneously recorded ensembles of neuronal activity in the MIo of two monkeys (Macaca mulatta) while eating various types of food. We developed a Bayesian nonparametric latent variable model to reveal latent structures of neuronal population activity of the MIo and identify the complex mapping between MIo ensemble spike activity and high-dimensional kinematics.

MAIN RESULTS

Rhythmic neuronal firing patterns and oscillatory dynamics are evident in single-unit activity. At the population level, we uncovered the neural dynamics of rhythmic chewing, and quantified the neural variability at multiple timescales (complete feeding sequences, chewing sequence stages, chewing gape cycle phases) across food types. Our approach accommodates time-warping of chewing sequences and automatic model selection, and maps the latent states to chewing behaviors at fine timescales.

SIGNIFICANCE

Our work shows that neural representations of MIo ensembles display spatiotemporal patterns in chewing gape cycles at different chew sequence stages, and these patterns vary in a stage-dependent manner. Unsupervised learning and decoding analysis may reveal the link between complex MIo spatiotemporal patterns and chewing kinematics.

Long-Term Activity Dynamics of Single Neurons and Networks

The firing rate of neuronal spiking in vitro and in vivo significantly varies over extended timescales, characterized by long-memory processes and complex statistics, and appears in spontaneous as well as evoked activity upon repeated stimulus presentation. These variations in response features and their statistics, in face of repeated instances of a given physical input, are ubiquitous in all levels of brain-behavior organization. They are expressed in single neuron and network response variability but even appear in variations of subjective percepts or psychophysical choices and have been described as stemming from history-dependent, stochastic, or rate-determined processes.But what are the sources underlying these temporally rich variations in firing rate? Are they determined by interactions of the nervous system as a whole, or do isolated, single neurons or neuronal networks already express these fluctuations independent of higher levels? These questions motivated the application of a method that allows for controlled and specific long-term activation of a single neuron or neuronal network, isolated from higher levels of cortical organization.This chapter highlights the research done in cultured cortical networks to study (1) the inherent non-stationarity of neuronal network activity, (2) single neuron response fluctuations and underlying processes, and (3) the interface layer between network and single cell, the non-stationary efficacy of the ensemble of synapses impinging onto the observed neuron.

STDP Allows Close-to-Optimal Spatiotemporal Spike Pattern Detection by Single Coincidence Detector Neurons

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Repeating spike patterns exist and are informative. Can a single cell do the readout?

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We show how a leaky integrate-and-fire (LIF) can do this readout optimally.

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The optimal membrane time constant is short, possibly much shorter than the pattern.

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Spike-timing-dependent plasticity (STDP) can turn a neuron into an optimal detector.

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These results may explain how humans can learn repeating visual or auditory sequences.

Repeating spatiotemporal spike patterns exist and carry information. How this information is extracted by downstream neurons is unclear. Here we theoretically investigate to what extent a single cell could detect a given spike pattern and what the optimal parameters to do so are, in particular the membrane time constant τ. Using a leaky integrate-and-fire (LIF) neuron with homogeneous Poisson input, we computed this optimum analytically. We found that a relatively small τ (at most a few tens of ms) is usually optimal, even when the pattern is much longer. This is somewhat counter-intuitive as the resulting detector ignores most of the pattern, due to its fast memory decay. Next, we wondered if spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimum. We simulated a LIF equipped with additive STDP, and repeatedly exposed it to a given input spike pattern. As in previous studies, the LIF progressively became selective to the repeating pattern with no supervision, even when the pattern was embedded in Poisson activity. Here we show that, using certain STDP parameters, the resulting pattern detector is optimal. These mechanisms may explain how humans learn repeating sensory sequences. Long sequences could be recognized thanks to coincidence detectors working at a much shorter timescale. This is consistent with the fact that recognition is still possible if a sound sequence is compressed, played backward, or scrambled using 10-ms bins. Coincidence detection is a simple yet powerful mechanism, which could be the main function of neurons in the brain.

Optimal Localist and Distributed Coding of Spatiotemporal Spike Patterns Through STDP and Coincidence Detection

Repeating spatiotemporal spike patterns exist and carry information. Here we investigated how a single spiking neuron can optimally respond to one given pattern (localist coding), or to either one of several patterns (distributed coding, i.e., the neuron's response is ambiguous but the identity of the pattern could be inferred from the response of multiple neurons), but not to random inputs. To do so, we extended a theory developed in a previous paper (Masquelier, 2017), which was limited to localist coding. More specifically, we computed analytically the signal-to-noise ratio (SNR) of a multi-pattern-detector neuron, using a threshold-free leaky integrate-and-fire (LIF) neuron model with non-plastic unitary synapses and homogeneous Poisson inputs. Surprisingly, when increasing the number of patterns, the SNR decreases slowly, and remains acceptable for several tens of independent patterns. In addition, we investigated whether spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimal SNR. To this aim, we simulated a LIF equipped with STDP, and repeatedly exposed it to multiple input spike patterns, embedded in equally dense Poisson spike trains. The LIF progressively became selective to every repeating pattern with no supervision, and stopped discharging during the Poisson spike trains. Furthermore, tuning certain STDP parameters, the resulting pattern detectors were optimal. Tens of independent patterns could be learned by a single neuron using a low adaptive threshold, in contrast with previous studies, in which higher thresholds led to localist coding only. Taken together these results suggest that coincidence detection and STDP are powerful mechanisms, fully compatible with distributed coding. Yet we acknowledge that our theory is limited to single neurons, and thus also applies to feed-forward networks, but not to recurrent ones.

Winnerless competition in clustered balanced networks: inhibitory assemblies do the trick

Balanced networks are a frequently employed basic model for neuronal networks in the mammalian neocortex. Large numbers of excitatory and inhibitory neurons are recurrently connected so that the numerous positive and negative inputs that each neuron receives cancel out on average. Neuronal firing is therefore driven by fluctuations in the input and resembles the irregular and asynchronous activity observed in cortical in vivo data. Recently, the balanced network model has been extended to accommodate clusters of strongly interconnected excitatory neurons in order to explain persistent activity in working memory-related tasks. This clustered topology introduces multistability and winnerless competition between attractors and can capture the high trial-to-trial variability and its reduction during stimulation that has been found experimentally. In this prospect article, we review the mean field description of balanced networks of binary neurons and apply the theory to clustered networks. We show that the stable fixed points of networks with clustered excitatory connectivity tend quickly towards firing rate saturation, which is generally inconsistent with experimental data. To remedy this shortcoming, we then present a novel perspective on networks with locally balanced clusters of both excitatory and inhibitory neuron populations. This approach allows for true multistability and moderate firing rates in activated clusters over a wide range of parameters. Our findings are supported by mean field theory and numerical network simulations. Finally, we discuss possible applications of the concept of joint excitatory and inhibitory clustering in future cortical network modelling studies.

Dethroning the Fano Factor: A Flexible, Model-Based Approach to Partitioning Neural Variability

Neurons in many brain areas exhibit high trial-to-trial variability, with spike counts that are overdispersed relative to a Poisson distribution. Recent work (Goris, Movshon, & Simoncelli, 2014 ) has proposed to explain this variability in terms of a multiplicative interaction between a stochastic gain variable and a stimulus-dependent Poisson firing rate, which produces quadratic relationships between spike count mean and variance. Here we examine this quadratic assumption and propose a more flexible family of models that can account for a more diverse set of mean-variance relationships. Our model contains additive gaussian noise that is transformed nonlinearly to produce a Poisson spike rate. Different choices of the nonlinear function can give rise to qualitatively different mean-variance relationships, ranging from sublinear to linear to quadratic. Intriguingly, a rectified squaring nonlinearity produces a linear mean-variance function, corresponding to responses with a constant Fano factor. We describe a computationally efficient method for fitting this model to data and demonstrate that a majority of neurons in a V1 population are better described by a model with a nonquadratic relationship between mean and variance. Finally, we demonstrate a practical use of our model via an application to Bayesian adaptive stimulus selection in closed-loop neurophysiology experiments, which shows that accounting for overdispersion can lead to dramatic improvements in adaptive tuning curve estimation.

The HTM Spatial Pooler-A Neocortical Algorithm for Online Sparse Distributed Coding

Hierarchical temporal memory (HTM) provides a theoretical framework that models several key computational principles of the neocortex. In this paper, we analyze an important component of HTM, the HTM spatial pooler (SP). The SP models how neurons learn feedforward connections and form efficient representations of the input. It converts arbitrary binary input patterns into sparse distributed representations (SDRs) using a combination of competitive Hebbian learning rules and homeostatic excitability control. We describe a number of key properties of the SP, including fast adaptation to changing input statistics, improved noise robustness through learning, efficient use of cells, and robustness to cell death. In order to quantify these properties we develop a set of metrics that can be directly computed from the SP outputs. We show how the properties are met using these metrics and targeted artificial simulations. We then demonstrate the value of the SP in a complete end-to-end real-world HTM system. We discuss the relationship with neuroscience and previous studies of sparse coding. The HTM spatial pooler represents a neurally inspired algorithm for learning sparse representations from noisy data streams in an online fashion.

Neural Code-Neural Self-information Theory on How Cell-Assembly Code Rises from Spike Time and Neuronal Variability

A major stumbling block to cracking the real-time neural code is neuronal variability - neurons discharge spikes with enormous variability not only across trials within the same experiments but also in resting states. Such variability is widely regarded as a noise which is often deliberately averaged out during data analyses. In contrast to such a dogma, we put forth the Neural Self-Information Theory that neural coding is operated based on the self-information principle under which variability in the time durations of inter-spike-intervals (ISI), or neuronal silence durations, is self-tagged with discrete information. As the self-information processor, each ISI carries a certain amount of information based on its variability-probability distribution; higher-probability ISIs which reflect the balanced excitation-inhibition ground state convey minimal information, whereas lower-probability ISIs which signify rare-occurrence surprisals in the form of extremely transient or prolonged silence carry most information. These variable silence durations are naturally coupled with intracellular biochemical cascades, energy equilibrium and dynamic regulation of protein and gene expression levels. As such, this silence variability-based self-information code is completely intrinsic to the neurons themselves, with no need for outside observers to set any reference point as typically used in the rate code, population code and temporal code models. Moreover, temporally coordinated ISI surprisals across cell population can inherently give rise to robust real-time cell-assembly codes which can be readily sensed by the downstream neural clique assemblies. One immediate utility of this self-information code is a general decoding strategy to uncover a variety of cell-assembly patterns underlying external and internal categorical or continuous variables in an unbiased manner.

Variability of Neuronal Responses: Types and Functional Significance in Neuroplasticity and Neural Darwinism

HIGHLIGHTS We suggest classifying variability of neuronal responses as follows: false (associated with a lack of knowledge about the influential factors), "genuine harmful" (noise), "genuine neutral" (synonyms, repeats), and "genuine useful" (the basis of neuroplasticity and learning).The genuine neutral variability is considered in terms of the phenomenon of degeneracy.Of particular importance is the genuine useful variability that is considered as a potential basis for neuroplasticity and learning. This type of variability is considered in terms of the neural Darwinism theory. In many cases, neural signals detected under the same external experimental conditions significantly change from trial to trial. The variability phenomenon, which complicates extraction of reproducible results and is ignored in many studies by averaging, has attracted attention of researchers in recent years. In this paper, we classify possible types of variability based on its functional significance and describe features of each type. We describe the key adaptive significance of variability at the neural network level and the degeneracy phenomenon that may be important for learning processes in connection with the principle of neuronal group selection.

The structure function as new integral measure of spatial and temporal properties of multichannel EEG

The first-order temporal structure functions (SFs), i.e., the first-order statistical moment of absolute increments of scaled multichannel resting state EEG signals in healthy children and teenagers over a wide range of temporal separation (time lags) are computed. Our research shows that the sill level (asymptote) of the SF is mainly defined by a determinant of EEG correlation matrix reflecting the EEG spatial structure. The temporal structure of EEG is found to be characterized by power-law scaling or statistical-scale invariance over time scales less than 0.028 s and at least by two dominant frequencies differing by less than 0.3 Hz. These frequencies define the oscillation behavior of the SF and are mainly distributed within the range of 7.5-12.0 Hz. In this paper, we propose the combined Bessel and exponential model that fits well the empirical SF. It provides a good fit with the mean relative error fitting of 2.8 % over the time lag range of 1 s, using a sampling interval of 4 ms, for all cases under analysis. We also show that the hyper gamma distribution (HGD) fits to the empirical probability density functions (PDFs) of absolute increments of scaled multichannel resting state EEG signals at any given time lag. It means that only two parameters (sample mean of absolute increments and relevant coefficient of variation) may approximately define the empirical PDFs for a given number of channels. A three-dimensional feature vector constructed from the shape and scale parameters of the HGD and the sill level may be used to estimate the closeness of the real EEG to the "random" EEG characterized by the absence of temporal and spatial correlation.

Children with developmental coordination disorder (DCD) can adapt to perceptible and subliminal rhythm changes but are more variable

Children with DCD demonstrate impairments in bimanual finger tapping during self-paced tapping and tapping in synchrony to different frequencies. In this study, we investigated the ability of children with DCD to adapt motorically to perceptible or subliminal changes of the auditory stimuli without a change in frequency, and compared their performance to typically developing controls (TDC). Nineteen children with DCD between ages 6-11years (mean age±SD=114±21months) and 17 TDC (mean age±SD=113±21months) participated in this study. Auditory perceptual threshold was established. Children initially tapped bimanually to an antiphase beat and then to either a perceptible change in rhythm or to gradual subliminal changes in rhythm. Children with DCD were able to perceive changes in rhythm similar to TDC. They were also able to adapt to both perceptible and subliminal changes in rhythms similar to their age- and gender- matched TDC. However, these children were significantly more variable compared with TDC in all phasing conditions. The results suggest that the performance impairments in bilateral tapping are not a result of poor conscious or sub-conscious perception of the auditory cue. The increased motor variability may be associated with cerebellar dysfunction but further behavioral and neurophysiological studies are needed.

Inferring Cortical Variability from Local Field Potentials

The responses of sensory neurons can be quite different to repeated presentations of the same stimulus. Here, we demonstrate a direct link between the trial-to-trial variability of cortical neuron responses and network activity that is reflected in local field potentials (LFPs). Spikes and LFPs were recorded with a multielectrode array from the middle temporal (MT) area of the visual cortex of macaques during the presentation of continuous optic flow stimuli. A maximum likelihood-based modeling framework was used to predict single-neuron spiking responses using the stimulus, the LFPs, and the activity of other recorded neurons. MT neuron responses were strongly linked to gamma oscillations (maximum at 40 Hz) as well as to lower-frequency delta oscillations (1-4 Hz), with consistent phase preferences across neurons. The predicted modulation associated with the LFP was largely complementary to that driven by visual stimulation, as well as the activity of other neurons, and accounted for nearly half of the trial-to-trial variability in the spiking responses. Moreover, the LFP model predictions accurately captured the temporal structure of noise correlations between pairs of simultaneously recorded neurons, and explained the variation in correlation magnitudes observed across the population. These results therefore identify signatures of network activity related to the variability of cortical neuron responses, and suggest their central role in sensory cortical function.

SIGNIFICANCE STATEMENT

The function of sensory neurons is nearly always cast in terms of representing sensory stimuli. However, recordings from visual cortex in awake animals show that a large fraction of neural activity is not predictable from the stimulus. We show that this variability is predictable given the simultaneously recorded measures of network activity, local field potentials. A model that combines elements of these signals with the stimulus processing of the neuron can predict neural responses dramatically better than current models, and can predict the structure of correlations across the cortical population. In identifying ways to understand stimulus processing in the context of ongoing network activity, this work thus provides a foundation to understand the role of sensory cortex in combining sensory and cognitive variables.

Spike Pattern Structure Influences Synaptic Efficacy Variability under STDP and Synaptic Homeostasis. II: Spike Shuffling Methods on LIF Networks

Synapses may undergo variable changes during plasticity because of the variability of spike patterns such as temporal stochasticity and spatial randomness. Here, we call the variability of synaptic weight changes during plasticity to be efficacy variability. In this paper, we investigate how four aspects of spike pattern statistics (i.e., synchronous firing, burstiness/regularity, heterogeneity of rates and heterogeneity of cross-correlations) influence the efficacy variability under pair-wise additive spike-timing dependent plasticity (STDP) and synaptic homeostasis (the mean strength of plastic synapses into a neuron is bounded), by implementing spike shuffling methods onto spike patterns self-organized by a network of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons. With the increase of the decay time scale of the inhibitory synaptic currents, the LIF network undergoes a transition from asynchronous state to weak synchronous state and then to synchronous bursting state. We first shuffle these spike patterns using a variety of methods, each designed to evidently change a specific pattern statistics; and then investigate the change of efficacy variability of the synapses under STDP and synaptic homeostasis, when the neurons in the network fire according to the spike patterns before and after being treated by a shuffling method. In this way, we can understand how the change of pattern statistics may cause the change of efficacy variability. Our results are consistent with those of our previous study which implements spike-generating models on converging motifs. We also find that burstiness/regularity is important to determine the efficacy variability under asynchronous states, while heterogeneity of cross-correlations is the main factor to cause efficacy variability when the network moves into synchronous bursting states (the states observed in epilepsy).

Microsaccades enable efficient synchrony-based coding in the retina: a simulation study

It is now reasonably well established that microsaccades (MS) enhance visual perception, although the underlying neuronal mechanisms are unclear. Here, using numerical simulations, we show that MSs enable efficient synchrony-based coding among the primate retinal ganglion cells (RGC). First, using a jerking contrast edge as stimulus, we demonstrate a qualitative change in the RGC responses: synchronous firing, with a precision in the 10 ms range, only occurs at high speed and high contrast. MSs appear to be sufficiently fast to be able reach the synchronous regime. Conversely, the other kinds of fixational eye movements known as tremor and drift both hardly synchronize RGCs because of a too weak amplitude and a too slow speed respectively. Then, under natural image stimulation, we find that each MS causes certain RGCs to fire synchronously, namely those whose receptive fields contain contrast edges after the MS. The emitted synchronous spike volley thus rapidly transmits the most salient edges of the stimulus, which often constitute the most crucial information. We demonstrate that the readout could be done rapidly by simple coincidence-detector neurons without knowledge of the MS landing time, and that the required connectivity could emerge spontaneously with spike timing-dependent plasticity.

Flexible models for spike count data with both over- and under- dispersion

A key observation in systems neuroscience is that neural responses vary, even in controlled settings where stimuli are held constant. Many statistical models assume that trial-to-trial spike count variability is Poisson, but there is considerable evidence that neurons can be substantially more or less variable than Poisson depending on the stimuli, attentional state, and brain area. Here we examine a set of spike count models based on the Conway-Maxwell-Poisson (COM-Poisson) distribution that can flexibly account for both over- and under-dispersion in spike count data. We illustrate applications of this noise model for Bayesian estimation of tuning curves and peri-stimulus time histograms. We find that COM-Poisson models with group/observation-level dispersion, where spike count variability is a function of time or stimulus, produce more accurate descriptions of spike counts compared to Poisson models as well as negative-binomial models often used as alternatives. Since dispersion is one determinant of parameter standard errors, COM-Poisson models are also likely to yield more accurate model comparison. More generally, these methods provide a useful, model-based framework for inferring both the mean and variability of neural responses.

Learning of Precise Spike Times with Homeostatic Membrane Potential Dependent Synaptic Plasticity

Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there is no known biologically plausible implementation of this comparison. Here, we propose a simple and local unsupervised synaptic plasticity mechanism that is derived from the requirement of a balanced membrane potential. Since the relevant signal for synaptic change is the postsynaptic voltage rather than spike times, we call the plasticity rule Membrane Potential Dependent Plasticity (MPDP). Combining our plasticity mechanism with spike after-hyperpolarization causes a sensitivity of synaptic change to pre- and postsynaptic spike times which can reproduce Hebbian spike timing dependent plasticity for inhibitory synapses as was found in experiments. In addition, the sensitivity of MPDP to the time course of the voltage when generating a spike allows MPDP to distinguish between weak (spurious) and strong (teacher) spikes, which therefore provides a neuronal basis for the comparison of actual and target activity. For spatio-temporal input spike patterns our conceptually simple plasticity rule achieves a surprisingly high storage capacity for spike associations. The sensitivity of the MPDP to the subthreshold membrane potential during training allows robust memory retrieval after learning even in the presence of activity corrupted by noise. We propose that MPDP represents a biophysically plausible mechanism to learn temporal target activity patterns.

Where's the Noise? Key Features of Spontaneous Activity and Neural Variability Arise through Learning in a Deterministic Network

Even in the absence of sensory stimulation the brain is spontaneously active. This background “noise” seems to be the dominant cause of the notoriously high trial-to-trial variability of neural recordings. Recent experimental observations have extended our knowledge of trial-to-trial variability and spontaneous activity in several directions: 1. Trial-to-trial variability systematically decreases following the onset of a sensory stimulus or the start of a motor act. 2. Spontaneous activity states in sensory cortex outline the region of evoked sensory responses. 3. Across development, spontaneous activity aligns itself with typical evoked activity patterns. 4. The spontaneous brain activity prior to the presentation of an ambiguous stimulus predicts how the stimulus will be interpreted. At present it is unclear how these observations relate to each other and how they arise in cortical circuits. Here we demonstrate that all of these phenomena can be accounted for by a deterministic self-organizing recurrent neural network model (SORN), which learns a predictive model of its sensory environment. The SORN comprises recurrently coupled populations of excitatory and inhibitory threshold units and learns via a combination of spike-timing dependent plasticity (STDP) and homeostatic plasticity mechanisms. Similar to balanced network architectures, units in the network show irregular activity and variable responses to inputs. Additionally, however, the SORN exhibits sequence learning abilities matching recent findings from visual cortex and the network’s spontaneous activity reproduces the experimental findings mentioned above. Intriguingly, the network’s behaviour is reminiscent of sampling-based probabilistic inference, suggesting that correlates of sampling-based inference can develop from the interaction of STDP and homeostasis in deterministic networks. We conclude that key observations on spontaneous brain activity and the variability of neural responses can be accounted for by a simple deterministic recurrent neural network which learns a predictive model of its sensory environment via a combination of generic neural plasticity mechanisms.

Neural recordings seem very noisy. If the exact same stimulus is shown to an animal multiple times, the neural response will vary substantially. In fact, the activity of a single neuron shows many features of a random process. Furthermore, the spontaneous activity occurring in the absence of any sensory stimulus, which is usually considered a kind of background noise, often has a magnitude comparable to the activity evoked by stimulus presentation and interacts with sensory inputs in interesting ways. Here we show that the key features of neural variability and spontaneous activity can all be accounted for by a simple and completely deterministic neural network learning a predictive model of its sensory inputs. The network’s deterministic dynamics give rise to structured but variable responses matching key experimental findings obtained in different mammalian species with different recording techniques. Our results suggest that the notorious variability of neural recordings and the complex features of spontaneous brain activity could reflect the dynamics of a largely deterministic but highly adaptive network learning a predictive model of its sensory environment.

Philosophy of the Spike: Rate-Based vs. Spike-Based Theories of the Brain

Does the brain use a firing rate code or a spike timing code? Considering this controversial question from an epistemological perspective, I argue that progress has been hampered by its problematic phrasing. It takes the perspective of an external observer looking at whether those two observables vary with stimuli, and thereby misses the relevant question: which one has a causal role in neural activity? When rephrased in a more meaningful way, the rate-based view appears as an ad hoc methodological postulate, one that is practical but with virtually no empirical or theoretical support.

Low-noise encoding of active touch by layer 4 in the somatosensory cortex

Cortical spike trains often appear noisy, with the timing and number of spikes varying across repetitions of stimuli. Spiking variability can arise from internal (behavioral state, unreliable neurons, or chaotic dynamics in neural circuits) and external (uncontrolled behavior or sensory stimuli) sources. The amount of irreducible internal noise in spike trains, an important constraint on models of cortical networks, has been difficult to estimate, since behavior and brain state must be precisely controlled or tracked. We recorded from excitatory barrel cortex neurons in layer 4 during active behavior, where mice control tactile input through learned whisker movements. Touch was the dominant sensorimotor feature, with >70% spikes occurring in millisecond timescale epochs after touch onset. The variance of touch responses was smaller than expected from Poisson processes, often reaching the theoretical minimum. Layer 4 spike trains thus reflect the millisecond-timescale structure of tactile input with little noise.

Hippocampal Synaptic Expansion Induced by Spatial Experience in Rats Correlates with Improved Information Processing in the Hippocampus

Spatial water maze (WM) overtraining induces hippocampal mossy fiber (MF) expansion, and it has been suggested that spatial pattern separation depends on the MF pathway. We hypothesized that WM experience inducing MF expansion in rats would improve spatial pattern separation in the hippocampal network. We first tested this by using the the delayed non-matching to place task (DNMP), in animals that had been previously trained on the water maze (WM) and found that these animals, as well as animals treated as swim controls (SC), performed better than home cage control animals the DNMP task. The "catFISH" imaging method provided neurophysiological evidence that hippocampal pattern separation improved in animals treated as SC, and this improvement was even clearer in animals that experienced the WM training. Moreover, these behavioral treatments also enhance network reliability and improve partial pattern separation in CA1 and pattern completion in CA3. By measuring the area occupied by synaptophysin staining in both the stratum oriens and the stratun lucidum of the distal CA3, we found evidence of structural synaptic plasticity that likely includes MF expansion. Finally, the measures of hippocampal network coding obtained with catFISH correlate significantly with the increased density of synaptophysin staining, strongly suggesting that structural synaptic plasticity in the hippocampus induced by the WM and SC experience is related to the improvement of spatial information processing in the hippocampus.

Ambiguity and nonidentifiability in the statistical analysis of neural codes

Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, "Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?" For another example, "How much of a neuron's observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?" However, a neuron's theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.

Understanding Neural Population Coding: Information Theoretic Insights from the Auditory System

In recent years, our research in computational neuroscience has focused on understanding how populations of neurons encode naturalistic stimuli. In particular, we focused on how populations of neurons use the time domain to encode sensory information. In this focused review, we summarize this recent work from our laboratory. We focus in particular on the mathematical methods that we developed for the quantification of how information is encoded by populations of neurons and on how we used these methods to investigate the encoding of complex naturalistic sounds in auditory cortex. We review how these methods revealed a complementary role of low frequency oscillations and millisecond precise spike patterns in encoding complex sounds and in making these representations robust to imprecise knowledge about the timing of the external stimulus. Further, we discuss challenges in extending this work to understand how large populations of neurons encode sensory information. Overall, this previous work provides analytical tools and conceptual understanding necessary to study the principles of how neural populations reflect sensory inputs and achieve a stable representation despite many uncertainties in the environment.

Self-consistent determination of the spike-train power spectrum in a neural network with sparse connectivity

A major source of random variability in cortical networks is the quasi-random arrival of presynaptic action potentials from many other cells. In network studies as well as in the study of the response properties of single cells embedded in a network, synaptic background input is often approximated by Poissonian spike trains. However, the output statistics of the cells is in most cases far from being Poisson. This is inconsistent with the assumption of similar spike-train statistics for pre- and postsynaptic cells in a recurrent network. Here we tackle this problem for the popular class of integrate-and-fire neurons and study a self-consistent statistics of input and output spectra of neural spike trains. Instead of actually using a large network, we use an iterative scheme, in which we simulate a single neuron over several generations. In each of these generations, the neuron is stimulated with surrogate stochastic input that has a similar statistics as the output of the previous generation. For the surrogate input, we employ two distinct approximations: (i) a superposition of renewal spike trains with the same interspike interval density as observed in the previous generation and (ii) a Gaussian current with a power spectrum proportional to that observed in the previous generation. For input parameters that correspond to balanced input in the network, both the renewal and the Gaussian iteration procedure converge quickly and yield comparable results for the self-consistent spike-train power spectrum. We compare our results to large-scale simulations of a random sparsely connected network of leaky integrate-and-fire neurons (Brunel, 2000) and show that in the asynchronous regime close to a state of balanced synaptic input from the network, our iterative schemes provide an excellent approximations to the autocorrelation of spike trains in the recurrent network.

Algorithms of causal inference for the analysis of effective connectivity among brain regions

In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC^*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity.

Can we identify non-stationary dynamics of trial-to-trial variability?

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings.

Oscillations can reconcile slowly changing stimuli with short neuronal integration and STDP timescales

Oscillatory brain activity has been widely reported experimentally, yet its functional roles, if any, are still under debate. In this review we argue two things: firstly, thanks to oscillations, even slowly changing stimuli can be encoded in precise relative spike times, decodable by downstream "coincidence detector" neurons in a feedforward manner. Secondly, the required connectivity to do so can spontaneously emerge with spike timing-dependent plasticity (STDP), in an unsupervised manner. The key here is that a common oscillatory drive enables neurons to remain under a fluctuation-driven regime. In this regime spike time jitter does not accumulate and can thus be lower than the intrinsic timescales of stimulus fluctuations, which leads to so-called "temporal encoding". Furthermore, the oscillatory drive formats the spikes in discrete oversampling volleys, and the relative spike times between neurons indicate the eventual differences in their activation levels. The oversampling accelerates the STDP-based learning for downstream neurons. After learning, readout only takes one oscillatory cycle. Finally, we also discuss experimental evidence, and the question of how the theory is complementary to the so-called "communication through coherence" theory.

Reading spike timing without a clock: intrinsic decoding of spike trains

The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter's computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns.