Decoding stimulus variance from a distributional neural code of interspike intervals

Expectation violations enhance neuronal encoding of sensory information in mouse primary visual cortex

The response of cortical neurons to sensory stimuli is shaped both by past events (adaptation) and the expectation of future events (prediction). Here we employed a visual stimulus paradigm with different levels of predictability to characterise how expectation influences orientation selectivity in the primary visual cortex (V1) of male mice. We recorded neuronal activity using two-photon calcium imaging (GCaMP6f) while animals viewed sequences of grating stimuli which either varied randomly in their orientations or rotated predictably with occasional transitions to an unexpected orientation. For single neurons and the population, there was significant enhancement in the gain of orientation-selective responses to unexpected gratings. This gain-enhancement for unexpected stimuli was prominent in both awake and anaesthetised mice. We implemented a computational model to demonstrate how trial-to-trial variability in neuronal responses were best characterised when adaptation and expectation effects were combined.

Objective methods for matching neuropsychological patterns: Formulas and comparisons

INTRODUCTION

Objective neuropsychology test score pattern matching methods can help to identify data similarities and differences with comparison groups which can help the clinician in diagnosis and in identifying treatment options.

MATERIALS AND METHODS

The current study examines five methods of matching a data set: Correlation, Configuration, Kullback-Leibler (KL) Divergence, Pooled Effect Size (Cohen's d), and a new method called MNB (Meyers Neuropsychological Battery) Code. Thirty data sets diagnosed with Traumatic Brain Injury (TBI) were compared with four Comparison Group data sets consisting of TBI, Depression, Anxiety and Attention Deficit/Hyperactivity Disorder.

RESULTS

The Correlation Method was correct 90% (27/30) and Configuration was correct 86% (26/30). The KL Divergence was correct 76% (23/30) and the MNB Code was correct 73% (22/30). The Effect Size Method was correct 70% (21/30). When using a simple majority of all the matching methods, the classification rate was 90+ percent.

CONCLUSIONS

The results of this study demonstrate that there are statistical methods that can identify patterns of cognitive strengths and weaknesses. Multiple matching methods and a simple majority of agreement between the different comparisons suggests the best matching profile for diagnosis. In some cases, more than one pattern may be present.

Short-Term Visual Experience Leads to Potentiation of Spontaneous Activity in Mouse Superior Colliculus

Spontaneous activity in the brain maintains an internal structured pattern that reflects the external environment, which is essential for processing information and developing perception and cognition. An essential prerequisite of spontaneous activity for perception is the ability to reverberate external information, such as by potentiation. Yet its role in the processing of potentiation in mouse superior colliculus (SC) neurons is less studied. Here, we used electrophysiological recording, optogenetics, and drug infusion methods to investigate the mechanism of potentiation in SC neurons. We found that visual experience potentiated SC neurons several minutes later in different developmental stages, and the similarity between spontaneous and visually-evoked activity increased with age. Before eye-opening, activation of retinal ganglion cells that expressed ChR2 also induced the potentiation of spontaneous activity in the mouse SC. Potentiation was dependent on stimulus number and showed feature selectivity for direction and orientation. Optogenetic activation of parvalbumin neurons in the SC attenuated the potentiation induced by visual experience. Furthermore, potentiation in SC neurons was blocked by inhibiting the glutamate transporter GLT1. These results indicated that the potentiation induced by a visual stimulus might play a key role in shaping the internal representation of the environment, and serves as a carrier for short-term memory consolidation.

Clustering of Neural Activity: A Design Principle for Population Codes

We propose that correlations among neurons are generically strong enough to organize neural activity patterns into a discrete set of clusters, which can each be viewed as a population codeword. Our reasoning starts with the analysis of retinal ganglion cell data using maximum entropy models, showing that the population is robustly in a frustrated, marginally sub-critical, or glassy, state. This leads to an argument that neural populations in many other brain areas might share this structure. Next, we use latent variable models to show that this glassy state possesses well-defined clusters of neural activity. Clusters have three appealing properties: (i) clusters exhibit error correction, i.e., they are reproducibly elicited by the same stimulus despite variability at the level of constituent neurons; (ii) clusters encode qualitatively different visual features than their constituent neurons; and (iii) clusters can be learned by downstream neural circuits in an unsupervised fashion. We hypothesize that these properties give rise to a "learnable" neural code which the cortical hierarchy uses to extract increasingly complex features without supervision or reinforcement.

Locating the engram: Should we look for plastic synapses or information-storing molecules?

Karl Lashley began the search for the engram nearly seventy years ago. In the time since, much has been learned but divisions remain. In the contemporary neurobiology of learning and memory, two profoundly different conceptions contend: the associative/connectionist (A/C) conception and the computational/representational (C/R) conception. Both theories ground themselves in the belief that the mind is emergent from the properties and processes of a material brain. Where these theories differ is in their description of what the neurobiological substrate of memory is and where it resides in the brain. The A/C theory of memory emphasizes the need to distinguish memory cognition from the memory engram and postulates that memory cognition is an emergent property of patterned neural activity routed through engram circuits. In this model, learning re-organizes synapse association strengths to guide future neural activity. Importantly, the version of the A/C theory advocated for here contends that synaptic change is not symbolic and, despite normally being necessary, is not sufficient for memory cognition. Instead, synaptic change provides the capacity and a blueprint for reinstating symbolic patterns of neural activity. Unlike the A/C theory, which posits that memory emerges at the circuit level, the C/R conception suggests that memory manifests at the level of intracellular molecular structures. In C/R theory, these intracellular structures are information-conveying and have properties compatible with the view that brain computation utilizes a read/write memory, functionally similar to that in a computer. New research has energized both sides and highlighted the need for new discussion. Both theories, the key questions each theory has yet to resolve and several potential paths forward are presented here.

Coding Principles in Adaptation

Adaptation is a common principle that recurs throughout the nervous system at all stages of processing. This principle manifests in a variety of phenomena, from spike frequency adaptation, to apparent changes in receptive fields with changes in stimulus statistics, to enhanced responses to unexpected stimuli. The ubiquity of adaptation leads naturally to the question: What purpose do these different types of adaptation serve? A diverse set of theories, often highly overlapping, has been proposed to explain the functional role of adaptive phenomena. In this review, we discuss several of these theoretical frameworks, highlighting relationships among them and clarifying distinctions. We summarize observations of the varied manifestations of adaptation, particularly as they relate to these theoretical frameworks, focusing throughout on the visual system and making connections to other sensory systems.

Temporal pattern separation in hippocampal neurons through multiplexed neural codes

Pattern separation is a central concept in current theories of episodic memory: this computation is thought to support our ability to avoid confusion between similar memories by transforming similar cortical input patterns of neural activity into dissimilar output patterns before their long-term storage in the hippocampus. Because there are many ways one can define patterns of neuronal activity and the similarity between them, pattern separation could in theory be achieved through multiple coding strategies. Using our recently developed assay that evaluates pattern separation in isolated tissue by controlling and recording the input and output spike trains of single hippocampal neurons, we explored neural codes through which pattern separation is performed by systematic testing of different similarity metrics and various time resolutions. We discovered that granule cells, the projection neurons of the dentate gyrus, can exhibit both pattern separation and its opposite computation, pattern convergence, depending on the neural code considered and the statistical structure of the input patterns. Pattern separation is favored when inputs are highly similar, and is achieved through spike time reorganization at short time scales (< 100 ms) as well as through variations in firing rate and burstiness at longer time scales. These multiplexed forms of pattern separation are network phenomena, notably controlled by GABAergic inhibition, that involve many celltypes with input-output transformations that participate in pattern separation to different extents and with complementary neural codes: a rate code for dentate fast-spiking interneurons, a burstiness code for hilar mossy cells and a synchrony code at long time scales for CA3 pyramidal cells. Therefore, the isolated hippocampal circuit itself is capable of performing temporal pattern separation using multiplexed coding strategies that might be essential to optimally disambiguate multimodal mnemonic representations.

Spike-timing-dependent ensemble encoding by non-classically responsive cortical neurons

Neurons recorded in behaving animals often do not discernibly respond to sensory input and are not overtly task-modulated. These non-classically responsive neurons are difficult to interpret and are typically neglected from analysis, confounding attempts to connect neural activity to perception and behavior. Here, we describe a trial-by-trial, spike-timing-based algorithm to reveal the coding capacities of these neurons in auditory and frontal cortex of behaving rats. Classically responsive and non-classically responsive cells contained significant information about sensory stimuli and behavioral decisions. Stimulus category was more accurately represented in frontal cortex than auditory cortex, via ensembles of non-classically responsive cells coordinating the behavioral meaning of spike timings on correct but not error trials. This unbiased approach allows the contribution of all recorded neurons – particularly those without obvious task-related, trial-averaged firing rate modulation – to be assessed for behavioral relevance on single trials.

Neurons encode information in the form of electrical signals called spikes. Certain neurons increase the rate at which they produce spikes under specific circumstances, e.g., whenever an animal hears a particular sound. These neurons are said to be 'classically responsive'. But not all neurons behave in this way. Others produce spikes at a variable rate that does not obviously relate to the animal's behavior. These neurons are said to be 'non-classically responsive'. They are often omitted from analyses, despite typically outnumbering their classically responsive counterparts. So, what are these neurons doing?

To find out, Insanally et al. trained rats to respond to sounds. The animals learned to poke their nose into a window whenever they heard a specific tone, and to avoid responding whenever they heard any other tone. As the rats performed the task, Insanally et al. recorded from neurons in two areas of the brain, the frontal cortex and the auditory cortex. A computer then analyzed the activity of individual neurons during each trial.

As expected, the firing rate of non-classically responsive cells did not relate to the animals' behavior. But the timing of this firing did. The interval between spikes contained information about which tone the animals had heard and/or how they had responded. The cells worked together in groups to encode this information. Over the course of each trial, every neuron in the group varied the interval between its spikes. Eventually, the group reached a consensus, with all neurons using the same interval to represent information relevant to the task. Groups of neurons in the frontal cortex encoded more information about the category of the tone than those in the auditory cortex.

By including all neurons – both classically and non-classically responsive – this model offers a more comprehensive view of how neural activity relates to behavior. This may in turn help us understand the variable and complex neural activity seen in people with sensory and cognitive disorders.

Circuit Polarity Effect of Cortical Connectivity, Activity, and Memory

Experimental constraints have traditionally implied separate studies of different cortical functions, such as memory and sensory-motor control. Yet certain cortical modalities, while repeatedly observed and reported, have not been clearly identified with one cortical function or another. Specifically, while neuronal membrane and synapse polarities with respect to a certain potential value have been attracting considerable interest in recent years, the purposes of such polarities have largely remained a subject for speculation and debate. Formally identifying these polarities as on-off neuronal polarity gates, we analytically show that cortical circuit structure, behavior, and memory are all governed by the combined potent effect of these gates, which we collectively term circuit polarity. Employing widely accepted and biologically validated firing rate and plasticity paradigms, we show that circuit polarity is mathematically embedded in the corresponding models. Moreover, we show that the firing rate dynamics implied by these models are driven by ongoing circuit polarity gating dynamics. Furthermore, circuit polarity is shown to segregate cortical circuits into internally synchronous, externally asynchronous subcircuits, defining their firing rate modes in accordance with different cortical tasks. In contrast to the Hebbian paradigm, which is shown to be susceptible to mutual neuronal interference in the face of asynchrony, circuit polarity is shown to block such interference. Noting convergence of synaptic weights, we show that circuit polarity holds the key to cortical memory, having a segregated capacity linear in the number of neurons. While memory concealment is implied by complete neuronal silencing, memory is restored by reactivating the original circuit polarity. Finally, we show that incomplete deterioration or restoration of circuit polarity results in memory modification, which may be associated with partial or false recall, or novel innovation.

A Hierarchy of Time Scales for Discriminating and Classifying the Temporal Shape of Sound in Three Auditory Cortical Fields

Auditory cortex is essential for mammals, including rodents, to detect temporal "shape" cues in the sound envelope but it remains unclear how different cortical fields may contribute to this ability (Lomber and Malhotra, 2008; Threlkeld et al., 2008). Previously, we found that precise spiking patterns provide a potential neural code for temporal shape cues in the sound envelope in the primary auditory (A1), and ventral auditory field (VAF) and caudal suprarhinal auditory field (cSRAF) of the rat (Lee et al., 2016). Here, we extend these findings and characterize the time course of the temporally precise output of auditory cortical neurons in male rats. A pairwise sound discrimination index and a Naive Bayesian classifier are used to determine how these spiking patterns could provide brain signals for behavioral discrimination and classification of sounds. We find response durations and optimal time constants for discriminating sound envelope shape increase in rank order with: A1 < VAF < cSRAF. Accordingly, sustained spiking is more prominent and results in more robust sound discrimination in non-primary cortex versus A1. Spike-timing patterns classify 10 different sound envelope shape sequences and there is a twofold increase in maximal performance when pooling output across the neuron population indicating a robust distributed neural code in all three cortical fields. Together, these results support the idea that temporally precise spiking patterns from primary and non-primary auditory cortical fields provide the necessary signals for animals to discriminate and classify a large range of temporal shapes in the sound envelope.SIGNIFICANCE STATEMENT Functional hierarchies in the visual cortices support the concept that classification of visual objects requires successive cortical stages of processing including a progressive increase in classical receptive field size. The present study is significant as it supports the idea that a similar progression exists in auditory cortices in the time domain. We demonstrate for the first time that three cortices provide temporal spiking patterns for robust temporal envelope shape discrimination but only the ventral non-primary cortices do so on long time scales. This study raises the possibility that primary and non-primary cortices provide unique temporal spiking patterns and time scales for perception of sound envelope shape.

Targeting alpha-band oscillations in a cortical model with amplitude-modulated high-frequency transcranial electric stimulation

Non-invasive brain stimulation to target specific network activity patterns, e.g. transcranial alternating current stimulation (tACS), has become an essential tool to understand the causal role of neuronal oscillations in cognition and behavior. However, conventional sinusoidal tACS limits the ability to record neuronal activity during stimulation and lacks spatial focality. One particularly promising new tACS stimulation paradigm uses amplitude-modulated (AM) high-frequency waveforms (AM-tACS) with a slow signal envelope that may overcome the limitations. Moreover. AM-tACS using high-frequency carrier signals is more tolerable than conventional tACS, e.g. in terms of skin irritation and occurrence of phosphenes, when applied at the same current intensities (e.g. 1-2 mA). Yet, the fundamental mechanism of neuronal target-engagement by AM-tACS waveforms has remained unknown. We used a computational model of cortex to investigate how AM-tACS modulates endogenous oscillations and compared the target engagement mechanism to the case of conventional (unmodulated) low-frequency tACS. Analysis of stimulation amplitude and frequency indicated that cortical oscillations were phase-locked to the envelope of the AM stimulation signal, which thus exhibits the same target engagement mechanism as conventional (unmodulated) low frequency tACS. However, in the computational model substantially higher current intensities were needed for AM-tACS than for low-frequency (unmodulated) tACS waveforms to achieve pronounced phase synchronization. Our analysis of the carrier frequency suggests that there might be a trade-off between the use of high-frequency carriers and the stimulation amplitude required for successful entrainment. Together, our computational simulations support the use of slow-envelope high frequency carrier AM waveforms as a tool for noninvasive modulation of brain oscillations. More empirical data will be needed to identify the optimal stimulation parameters and to evaluate tolerability and safety of both, AM- and conventional tACS.

Temporal pairwise spike correlations fully capture single-neuron information

To crack the neural code and read out the information neural spikes convey, it is essential to understand how the information is coded and how much of it is available for decoding. To this end, it is indispensable to derive from first principles a minimal set of spike features containing the complete information content of a neuron. Here we present such a complete set of coding features. We show that temporal pairwise spike correlations fully determine the information conveyed by a single spiking neuron with finite temporal memory and stationary spike statistics. We reveal that interspike interval temporal correlations, which are often neglected, can significantly change the total information. Our findings provide a conceptual link between numerous disparate observations and recommend shifting the focus of future studies from addressing firing rates to addressing pairwise spike correlation functions as the primary determinants of neural information.

Developmental metaplasticity in neural circuit codes of firing and structure

Firing-rate dynamics have been hypothesized to mediate inter-neural information transfer in the brain. While the Hebbian paradigm, relating learning and memory to firing activity, has put synaptic efficacy variation at the center of cortical plasticity, we suggest that the external expression of plasticity by changes in the firing-rate dynamics represents a more general notion of plasticity. Hypothesizing that time constants of plasticity and firing dynamics increase with age, and employing the filtering property of the neuron, we obtain the elementary code of global attractors associated with the firing-rate dynamics in each developmental stage. We define a neural circuit connectivity code as an indivisible set of circuit structures generated by membrane and synapse activation and silencing. Synchronous firing patterns under parameter uniformity, and asynchronous circuit firing are shown to be driven, respectively, by membrane and synapse silencing and reactivation, and maintained by the neuronal filtering property. Analytic, graphical and simulation representation of the discrete iteration maps and of the global attractor codes of neural firing rate are found to be consistent with previous empirical neurobiological findings, which have lacked, however, a specific correspondence between firing modes, time constants, circuit connectivity and cortical developmental stages.

Computational Classification Approach to Profile Neuron Subtypes from Brain Activity Mapping Data

The analysis of cell type-specific activity patterns during behaviors is important for better understanding of how neural circuits generate cognition, but has not been well explored from in vivo neurophysiological datasets. Here, we describe a computational approach to uncover distinct cell subpopulations from in vivo neural spike datasets. This method, termed “inter-spike-interval classification-analysis” (ISICA), is comprised of four major steps: spike pattern feature-extraction, pre-clustering analysis, clustering classification, and unbiased classification-dimensionality selection. By using two key features of spike dynamic - namely, gamma distribution shape factors and a coefficient of variation of inter-spike interval - we show that this ISICA method provides invariant classification for dopaminergic neurons or CA1 pyramidal cell subtypes regardless of the brain states from which spike data were collected. Moreover, we show that these ISICA-classified neuron subtypes underlie distinct physiological functions. We demonstrate that the uncovered dopaminergic neuron subtypes encoded distinct aspects of fearful experiences such as valence or value, whereas distinct hippocampal CA1 pyramidal cells responded differentially to ketamine-induced anesthesia. This ISICA method should be useful to better data mining of large-scale in vivo neural datasets, leading to novel insights into circuit dynamics associated with cognitions.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation.

Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states.

Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods.

Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

A neural mechanism for time-window separation resolves ambiguity of adaptive coding

The senses of animals are confronted with changing environments and different contexts. Neural adaptation is one important tool to adjust sensitivity to varying intensity ranges. For instance, in a quiet night outdoors, our hearing is more sensitive than when we are confronted with the plurality of sounds in a large city during the day. However, adaptation also removes available information on absolute sound levels and may thus cause ambiguity. Experimental data on the trade-off between benefits and loss through adaptation is scarce and very few mechanisms have been proposed to resolve it. We present an example where adaptation is beneficial for one task—namely, the reliable encoding of the pattern of an acoustic signal—but detrimental for another—the localization of the same acoustic stimulus. With a combination of neurophysiological data, modeling, and behavioral tests, we show that adaptation in the periphery of the auditory pathway of grasshoppers enables intensity-invariant coding of amplitude modulations, but at the same time, degrades information available for sound localization. We demonstrate how focusing the response of localization neurons to the onset of relevant signals separates processing of localization and pattern information temporally. In this way, the ambiguity of adaptive coding can be circumvented and both absolute and relative levels can be processed using the same set of peripheral neurons.

Neuronal data, computational modeling, and behavioral experiments reveal how the conflict between sensory adaptation and sound localization is resolved in the grasshopper auditory system, allowing processing of both absolute and relative sound levels.

Smell, vision, hearing—virtually all of our senses adapt their sensitivity to cope with the varying environment. Adaptation removes information about absolute stimulus intensity available to the brain, as this information is usually of little relevance for sensory representation. For some tasks, however, knowledge of absolute stimulus intensities is essential. How sensory pathways cope with this conflict remains an open question. We addressed this question in the grasshopper auditory system, in which comparison of absolute intensities of conspecific calls at both ears is crucial for mate localization. We recorded activity from three levels in the auditory pathway, showing that adaptation in the peripheral auditory system indeed removes information about absolute intensities. We discovered that strong negative feedback restricts coding of sound direction in the central auditory system to the very beginning of a stimulus, when peripheral adaptation has not yet acted. By using a computational model, we show that this central mechanism enables localization of the sound source over a wide range of stimulus intensities and that its time course is well matched to the time course of peripheral adaptation. In a final step, we confirmed predictions from our model in behavioral experiments on sound localization.

Analysis of interspike interval of dorsal horn neurons evoked by different needle manipulations at ST36

OBJECTIVES

Previous research has suggested that different manual acupuncture (MA) manipulations may have different physiological effects. Recent studies have demonstrated that neural electrical signals are generated or changed when acupuncture is administered. In order to explore the effects of different MA manipulations on the neural system, an experiment was designed to record the discharges of wide dynamic range (WDR) neurons in the spinal dorsal horn evoked by MA at different frequencies (0.5, 1, 2 and 3 Hz) at ST36.

METHODS

Microelectrode extracellular recordings were used to record the discharges of WDR neurons evoked by different MA manipulations. Approximate firing rate and coefficient of variation of interspike interval (ISI) were used to extract the characteristic parameters of the neural electrical signals after spike sorting, and the neural coding of the evoked discharges by different MA manipulations was obtained.

RESULTS

Our results indicated that the neuronal firing rate and time sequences of ISI showed distinct clustering properties for different MA manipulations, which could distinguish them effectively.

CONCLUSIONS

The combination of firing rate and ISI codes carries information about the acupuncture stimulus frequency. Different MA manipulations appear to change the neural coding of electrical signals in the spinal dorsal horn through WDR neurons.

Global attractor alphabet of neural firing modes

The elementary set, or alphabet, of neural firing modes is derived from the widely accepted conductance-based rectified firing-rate model. The firing dynamics of interacting neurons are shown to be governed by a multidimensional bilinear threshold discrete iteration map. The parameter-dependent global attractors of the map morph into 12 attractor types. Consistent with the dynamic modes observed in biological neuronal firing, the global attractor alphabet is highly visual and intuitive in the scalar, single-neuron case. As synapse permeability varies from high depression to high potentiation, the global attractor type varies from chaotic to multiplexed, oscillatory, fixed, and saturated. As membrane permeability decreases, the global attractor transforms from active to passive state. Under the same activation, learning and retrieval end at the same global attractor. The bilinear threshold structure of the multidimensional map associated with interacting neurons generalizes the global attractor alphabet of neuronal firing modes to multineuron systems. Selective positive or negative activation and neural interaction yield combinatorial revelation and concealment of stored neuronal global attractors.

Spike-based probabilistic inference in analog graphical models using interspike-interval coding

Temporal spike codes play a crucial role in neural information processing. In particular, there is strong experimental evidence that interspike intervals (ISIs) are used for stimulus representation in neural systems. However, very few algorithmic principles exploit the benefits of such temporal codes for probabilistic inference of stimuli or decisions. Here, we describe and rigorously prove the functional properties of a spike-based processor that uses ISI distributions to perform probabilistic inference. The abstract processor architecture serves as a building block for more concrete, neural implementations of the belief-propagation (BP) algorithm in arbitrary graphical models (e.g., Bayesian networks and factor graphs). The distributed nature of graphical models matches well with the architectural and functional constraints imposed by biology. In our model, ISI distributions represent the BP messages exchanged between factor nodes, leading to the interpretation of a single spike as a random sample that follows such a distribution. We verify the abstract processor model by numerical simulation in full graphs, and demonstrate that it can be applied even in the presence of analog variables. As a particular example, we also show results of a concrete, neural implementation of the processor, although in principle our approach is more flexible and allows different neurobiological interpretations. Furthermore, electrophysiological data from area LIP during behavioral experiments are assessed in light of ISI coding, leading to concrete testable, quantitative predictions and a more accurate description of these data compared to hitherto existing models.

Information transmission using non-poisson regular firing

In many cortical areas, neural spike trains do not follow a Poisson process. In this study, we investigate a possible benefit of non-Poisson spiking for information transmission by studying the minimal rate fluctuation that can be detected by a Bayesian estimator. The idea is that an inhomogeneous Poisson process may make it difficult for downstream decoders to resolve subtle changes in rate fluctuation, but by using a more regular non-Poisson process, the nervous system can make rate fluctuations easier to detect. We evaluate the degree to which regular firing reduces the rate fluctuation detection threshold. We find that the threshold for detection is reduced in proportion to the coefficient of variation of interspike intervals.

The effect of neural noise on spike time precision in a detailed CA3 neuron model

Experimental and computational studies emphasize the role of the millisecond precision of neuronal spike times as an important coding mechanism for transmitting and representing information in the central nervous system. We investigate the spike time precision of a multicompartmental pyramidal neuron model of the CA3 region of the hippocampus under the influence of various sources of neuronal noise. We describe differences in the contribution to noise originating from voltage-gated ion channels, synaptic vesicle release, and vesicle quantal size. We analyze the effect of interspike intervals and the voltage course preceding the firing of spikes on the spike-timing jitter. The main finding of this study is the ranking of different noise sources according to their contribution to spike time precision. The most influential is synaptic vesicle release noise, causing the spike jitter to vary from 1 ms to 7 ms of a mean value 2.5 ms. Of second importance was the noise incurred by vesicle quantal size variation causing the spike time jitter to vary from 0.03 ms to 0.6 ms. Least influential was the voltage-gated channel noise generating spike jitter from 0.02 ms to 0.15 ms.

Spike-interval triggered averaging reveals a quasi-periodic spiking alternative for stochastic resonance in catfish electroreceptors

Catfish detect and identify invisible prey by sensing their ultra-weak electric fields with electroreceptors. Any neuron that deals with small-amplitude input has to overcome sensitivity limitations arising from inherent threshold non-linearities in spike-generation mechanisms. Many sensory cells solve this issue with stochastic resonance, in which a moderate amount of intrinsic noise causes irregular spontaneous spiking activity with a probability that is modulated by the input signal. Here we show that catfish electroreceptors have adopted a fundamentally different strategy. Using a reverse correlation technique in which we take spike interval durations into account, we show that the electroreceptors generate a supra-threshold bias current that results in quasi-periodically produced spikes. In this regime stimuli modulate the interval between successive spikes rather than the instantaneous probability for a spike. This alternative for stochastic resonance combines threshold-free sensitivity for weak stimuli with similar sensitivity for excitations and inhibitions based on single interspike intervals.

Noninvertibility, chaotic coding, and chaotic multiplexity of synaptically modulated neural firing

Widely accepted neural firing and synaptic potentiation rules specify a cross-dependence of the two processes, which, evolving on different timescales, have been separated for analytic purposes, concealing essential dynamics. Here, the morphology of the firing rates process, modulated by synaptic potentiation, is shown to be described by a discrete iteration map in the form of a thresholded polynomial. Given initial synaptic weights, a firing activity is triggered by conductance. Elementary dynamic modes are defined by fixed points, cycles, and saddles of the map, building blocks of the underlying firing code. Showing parameter-dependent multiplicity of real polynomial roots, the map is proved to be noninvertible. The incidence of chaos is then implied by the parameter-dependent existence of snap-back repellers. The highly patterned geometric and statistical structures of the associated chaotic attractors suggest that these attractors are an integral part of the neural code. It further suggests the chaotic attractor as a natural mechanism for statistical encoding and temporal multiplexing of neural information. The analytic findings are supported by simulation.

Cortical dynamics during naturalistic sensory stimulations: experiments and models

We report the results of our experimental and theoretical investigations of the neural response dynamics in primary visual cortex (V1) during naturalistic visual stimulation. We recorded Local Field Potentials (LFPs) and spiking activity from V1 of anaesthetized macaques during binocular presentation of Hollywood color movies. We analyzed these recordings with information theoretic methods, and found that visual information was encoded mainly by two bands of LFP responses: the network fluctuations measured by the phase and power of low-frequency (less than 12 Hz) LFPs; and fast gamma-range (50-100 Hz) oscillations. Both the power and phase of low frequency LFPs carried information largely complementary to that carried by spikes, whereas gamma range oscillations carried information largely redundant to that of spikes. To interpret these results within a quantitative theoretical framework, we then simulated a sparsely connected recurrent network of excitatory and inhibitory neurons receiving slowly varying naturalistic inputs, and we determined how the LFPs generated by the network encoded information about the inputs. We found that this simulated recurrent network reproduced well the experimentally observed dependency of LFP information upon frequency. This network encoded the overall strength of the input into the power of gamma-range oscillations generated by inhibitory-excitatory neural interactions, and encoded slow variations in the input by entraining the network LFP at the corresponding frequency. This dynamical behavior accounted quantitatively for the independent information carried by high and low frequency LFPs, and for the experimentally observed cross-frequency coupling between phase of slow LFPs and the power of gamma LFPs. We also present new results showing that the model's dynamics also accounted for the extra visual information that the low-frequency LFP phase of spike firing carries beyond that carried by spike rates. Overall, our results suggest biological mechanisms by which cortex can multiplex information about naturalistic sensory environments.

Distribution of interspike intervals estimated from multiple spike trains observed in a short time window

Several nonparametric estimators of the probability distribution of interspike intervals are introduced. The methods are suitable for simultaneous spike trains observed in a time window of length comparable with the mean interspike interval. This reflects the situation in which a high number of input spike trains converge to a single cortical neuron that has to react in a relatively short time. The simulation study is performed to compare the estimators. For that purpose, several types of stationary point processes are considered as the models of neuronal activity. The methods permit one to estimate the distribution of interspike intervals even if practically none of them are observed. The Kaplan-Meier estimator seems to be the most flexible and reliable among all studied methods, but no direct conclusions as to how real neurons work can be deduced from it.

Biophysical information representation in temporally correlated spike trains

Spike trains commonly exhibit interspike interval (ISI) correlations caused by spike-activated adaptation currents. Here we investigate how the dynamics of adaptation currents can represent spike pattern information generated from stimulus inputs. By analyzing dynamical models of stimulus-driven single neurons, we show that the activation states of the correlation-inducing adaptation current are themselves statistically independent from spike to spike. This paradoxical finding suggests a biophysically plausible means of information representation. We show that adaptation independence is elicited by input levels that produce regular, non-Poisson spiking. This adaptation-independent regime is advantageous for sensory processing because it does not require sensory inferences on the basis of multivariate conditional probabilities, reducing the computational cost of decoding. Furthermore, if the kinetics of postsynaptic activation are similar to the adaptation, the activation state information can be communicated postsynaptically with no information loss, leading to an experimental prediction that simple synaptic kinetics can decorrelate the correlated ISI sequence. The adaptation-independence regime may underly efficient weak signal detection by sensory afferents that are known to exhibit intrinsic correlated spiking, thus efficiently encoding stimulus information at the limit of physical resolution.

Linear and Nonlinear Contributions to the Visual Sensitivity of Neurons in Primate Lateral Geniculate Nucleus

Several parallel pathways convey retinal signals to the visual cortex of primates. The signals of the parvocellular (P) and magnocellular (M) pathways are well characterized; the properties of other rarely encountered cell types are distinctive in many ways, but it is not clear that they can provide signals with the same fidelity. Here we study this by characterizing the temporal receptive field of neurons in the lateral geniculate nucleus of anesthetized marmosets. For each neuron, we measured the response to a flickering uniform field, and, from this, estimated the linear and nonlinear receptive fields using spike-triggered average (STA) and spike-triggered covariance (STC) analyses. As expected the response of most P-cells was dominated by the STA, but the response of most M-cells required additional nonlinear components, and these usually acted to suppress cell responses. The STC analysis showed stronger suppressive axes in suppressed-by-contrast cells, and both suppressive and excitatory axes in on-off cells. Together, the STA and the STC analyses form a model of the temporal response to a large uniform field: under this model, the information that was provided by suppressed-by-contrast cells or on-off cells approached that provided by the P- and M-cells. However, whereas P- and M-cells provided more information about luminance, the nonlinear cells provided more information about the contrast energy. This suggests that the nonlinear cells provide complimentary signals to those of P- and M-cells, with reasonably high fidelity, and may play an important role in normal visual processing.

Encoding of temporal information by timing, rate, and place in cat auditory cortex

A central goal in auditory neuroscience is to understand the neural coding of species-specific communication and human speech sounds. Low-rate repetitive sounds are elemental features of communication sounds, and core auditory cortical regions have been implicated in processing these information-bearing elements. Repetitive sounds could be encoded by at least three neural response properties: 1) the event-locked spike-timing precision, 2) the mean firing rate, and 3) the interspike interval (ISI). To determine how well these response aspects capture information about the repetition rate stimulus, we measured local group responses of cortical neurons in cat anterior auditory field (AAF) to click trains and calculated their mutual information based on these different codes. ISIs of the multiunit responses carried substantially higher information about low repetition rates than either spike-timing precision or firing rate. Combining firing rate and ISI codes was synergistic and captured modestly more repetition information. Spatial distribution analyses showed distinct local clustering properties for each encoding scheme for repetition information indicative of a place code. Diversity in local processing emphasis and distribution of different repetition rate codes across AAF may give rise to concurrent feed-forward processing streams that contribute differently to higher-order sound analysis.

Sensory neural codes using multiplexed temporal scales

Determining how neuronal activity represents sensory information is central for understanding perception. Recent work shows that neural responses at different timescales can encode different stimulus attributes, resulting in a temporal multiplexing of sensory information. Multiplexing increases the encoding capacity of neural responses, enables disambiguation of stimuli that cannot be discriminated at a single response timescale, and makes sensory representations stable to the presence of variability in the sensory world. Thus, as we discuss here, temporal multiplexing could be a key strategy used by the brain to form an information-rich and stable representation of the environment.

Sensitivity of firing rate to input fluctuations depends on time scale separation between fast and slow variables in single neurons

Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f-I curve. We introduce a novel classification of neurons into Types A, B-, and B+ according to how f-I curves are modulated by input fluctuations. In Type A neurons, the f-I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B- neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple "energy barrier" model.

Timescales of inference in visual adaptation

Adaptation is a hallmark of sensory function. Adapting optimally requires matching the dynamics of adaptation to those of changes in the stimulus distribution. Here we show that the dynamics of adaptation in the responses of mouse retinal ganglion cells depend on stimulus history. We hypothesized that the accumulation of evidence for a change in the stimulus distribution controls the dynamics of adaptation, and developed a model for adaptation as an ongoing inference problem. Guided by predictions of this model, we found that the dynamics of adaptation depend on the discriminability of the change in stimulus distribution and that the retina exploits information contained in properties of the stimulus beyond the mean and variance to adapt more quickly when possible.

Fractional differentiation by neocortical pyramidal neurons

Neural systems adapt to changes in stimulus statistics. However, it is not known how stimuli with complex temporal dynamics drive the dynamics of adaptation and the resulting firing rate. For single neurons, it has often been assumed that adaptation has a single time scale. We found that single rat neocortical pyramidal neurons adapt with a time scale that depends on the time scale of changes in stimulus statistics. This multiple time scale adaptation is consistent with fractional order differentiation, such that the neuron's firing rate is a fractional derivative of slowly varying stimulus parameters. Biophysically, even though neuronal fractional differentiation effectively yields adaptation with many time scales, we found that its implementation required only a few properly balanced known adaptive mechanisms. Fractional differentiation provides single neurons with a fundamental and general computation that can contribute to efficient information processing, stimulus anticipation and frequency-independent phase shifts of oscillatory neuronal firing.

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate versus current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.

Many neurons are known to achieve a wide dynamic range by adaptively changing their computational input/output function according to the input statistics. These adaptive changes can be very rapid, and it has been suggested that a component of this adaptation could be purely input-driven: even a fixed neural system can show apparent adaptive behavior since inputs with different statistics interact with the nonlinearity of the system in different ways. In this paper, we show how a single neuron's intrinsic computational function can dictate such input-driven changes in its response to varying input statistics, which begets a relationship between two different characterizations of neural function—in terms of mean firing rate and in terms of generating precise spike timing. We then apply our results to two biophysically defined model neurons, which have significantly different response patterns to inputs with various statistics. Our model of intrinsic adaptation explains their behaviors well. Contrary to the picture that neurons carry out a stereotyped computation on their inputs, our results show that even in the simplest cases they have simple yet effective mechanisms by which they can adapt to their input. Adaptation to stimulus statistics, therefore, is built into the most basic single neuron computations.

Distinct mechanisms mediate visual detection and identification

A core organizing principle for studies of the brain is that distinct neural pathways mediate distinct behavioral tasks [1, 2]. When two related tasks are mediated by a common pathway, studies of one are likely to generalize to the other. Here, we test whether performance on two laboratory tasks that model object detection and identification are mediated by common mechanisms of visual adaptation. Although both tasks rely on the luminance pattern in images, their demands on visual processing are quite different. Object detection requires discriminating image luminance differences associated with the light reflected from adjacent objects. To encode these differences reliably, neurons adapt their limited dynamic range to prevailing viewing conditions [3-6]. Object identification, on the other hand, demands a fixed response to light reflected from an object independent of illumination [7]. We compared performance in discrimination and identification tasks for simulated surfaces. In striking contrast to studies with less structured contexts, we found clear evidence that distinct processes mediate judgments in the two tasks. These results challenge models that account for perceived lightness entirely through the action of image-encoding mechanisms.

Interval coding. I. Burst interspike intervals as indicators of stimulus intensity

Short interspike intervals such as those that occur during burst firing are hypothesized to be distinct features of the neural code. Although a number of correlations between the occurrence of burst events and aspects of the stimulus have been identified, the relationship between burst characteristics and information transfer is uncertain. Pyramidal cells in the electrosensory lobe of the weakly electric fish, Apteronotus leptorhynchus, respond to dynamic broadband electrosensory stimuli with bursts and isolated spikes. In the present study, we mimic synaptic input during sensory stimulation by direct stimulation of electrosensory pyramidal cells with broadband current in vitro. The pyramidal cells respond to this stimulus with burst interspike intervals (ISIs) that are reliably and precisely correlated with the intensity of stimulus upstrokes. We found burst ISIs must differ by a minimum of 2 ms to discriminate, with low error, differences in stimulus intensity. Based on these results, we define and quantify a candidate interval code for the processing of sensory input. Finally, we demonstrate that interval coding is restricted to short ISIs such as those generated in burst events and that the proposed interval code is distinct from rate and timing codes.