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Titanium oxynitride (TiO x N y ) thin films are fabricated using reactive magnetron sputtering. The mechanism of their growth formation is explained, and their optical properties are presented. The films grown when the level of residual oxygen in the background vacuum was between 5 nTorr to 20 nTorr exhibit double epsilon-near-Zero (2-ENZ) behavior with ENZ1 and ENZ2 wavelengths tunable in the 700-850 and 1100-1350 nm spectral ranges, respectively. Samples fabricated when the level of residual oxygen in the background vacuum was above 2 × 10 -8 Torr exhibit nonmetallic behavior, while the layers deposited when the level of residual oxygen in the background vacuum was below 5 × 10 -9 Torr show metallic behavior with a single ENZ value. The double ENZ phenomenon is related to the level of residual oxygen in the background vacuum and is attributed to the mixture of TiN and TiO x N y and TiO x phases in the films. Varying the partial pressure of nitrogen during the deposition can further control the amount of TiN, TiO x , and TiO x N y compounds in the films and, therefore, tune the screened plasma wavelengths. A good approximation of the ellipsometric behavior is achieved with Maxwell-Garnett theory for a composite film formed by a mixture of TiO 2 and TiN phases suggesting that double ENZ TiO x N y films are formed by inclusions of TiN within a TiO 2 matrix. These oxynitride compounds could be considered as new materials exhibiting double ENZ in the visible and near-IR spectral ranges. Materials with ENZ properties are advantageous for designing the enhanced nonlinear optical response, metasurfaces, and nonreciprocal behavior.

Many studies use population analysis approaches, such as dimensionality reduction, to characterize the activity of large groups of neurons. To date, these methods have treated each neuron equally, without taking into account whether neurons are excitatory or inhibitory. We studied population activity structure as a function of neuron type by applying factor analysis to spontaneous activity from spiking networks with balanced excitation and inhibition. Throughout the study, we characterized population activity structure by measuring its dimensionality and the percentage of overall activity variance that is shared among neurons. First, by sampling only excitatory or only inhibitory neurons, we found that the activity structures of these two populations in balanced networks are measurably different. We also found that the population activity structure is dependent on the ratio of excitatory to inhibitory neurons sampled. Finally we classified neurons from extracellular recordings in the primary visual cortex of anesthetized macaques as putative excitatory or inhibitory using waveform classification, and found similarities with the neuron type-specific population activity structure of a balanced network with excitatory clustering. These results imply that knowledge of neuron type is important, and allows for stronger statistical tests, when interpreting population activity structure.

The circuit mechanisms behind shared neural variability (noise correlation) and its dependence on neural state are poorly understood. Visual attention is well-suited to constrain cortical models of response variability because attention both increases firing rates and their stimulus sensitivity, as well as decreases noise correlations. We provide a novel analysis of population recordings in rhesus primate visual area V4 showing that a single biophysical mechanism may underlie these diverse neural correlates of attention. We explore model cortical networks where top-down mediated increases in excitability, distributed across excitatory and inhibitory targets, capture the key neuronal correlates of attention. Our models predict that top-down signals primarily affect inhibitory neurons, whereas excitatory neurons are more sensitive to stimulus specific bottom-up inputs. Accounting for trial variability in models of state dependent modulation of neuronal activity is a critical step in building a mechanistic theory of neuronal cognition.

The stochastic nature of neuronal response has lead to conjectures about the impact of input fluctuations on the neural coding. For the most part, low pass membrane integration and spike threshold dynamics have been the primary features assumed in the transfer from synaptic input to output spiking. Phasic neurons are a common, but understudied, neuron class that are characterized by a subthreshold negative feedback that suppresses spike train responses to low frequency signals. Past work has shown that when a low frequency signal is accompanied by moderate intensity broadband noise, phasic neurons spike trains are well locked to the signal. We extend these results with a simple, reduced model of phasic activity that demonstrates that a non-Markovian spike train structure caused by the negative feedback produces a noise-enhanced coding. Further, this enhancement is sensitive to the timescales, as opposed to the intensity, of a driving signal. Reduced hazard function models show that noise-enhanced phasic codes are both novel and separate from classical stochastic resonance reported in non-phasic neurons. The general features of our theory suggest that noise-enhanced codes in excitable systems with subthreshold negative feedback are a particularly rich framework to study.

Shared neural variability is ubiquitous in cortical populations. While this variability is presumed to arise from overlapping synaptic input, its precise relationship to local circuit architecture remains unclear. We combine computational models and in vivo recordings to study the relationship between the spatial structure of connectivity and correlated variability in neural circuits. Extending the theory of networks with balanced excitation and inhibition, we find that spatially localized lateral projections promote weakly correlated spiking, but broader lateral projections produce a distinctive spatial correlation structure: nearby neuron pairs are positively correlated, pairs at intermediate distances are negatively correlated and distant pairs are weakly correlated. This non-monotonic dependence of correlation on distance is revealed in a new analysis of recordings from superficial layers of macaque primary visual cortex. Our findings show that incorporating distance-dependent connectivity improves the extent to which balanced network theory can explain correlated neural variability., Competing Interests: The authors declare no competing financial interests.

Recent studies have applied dimensionality reduction methods to understand how the multi-dimensional structure of neural population activity gives rise to brain function. It is unclear, however, how the results obtained from dimensionality reduction generalize to recordings with larger numbers of neurons and trials or how these results relate to the underlying network structure. We address these questions by applying factor analysis to recordings in the visual cortex of non-human primates and to spiking network models that self-generate irregular activity through a balance of excitation and inhibition. We compared the scaling trends of two key outputs of dimensionality reduction-shared dimensionality and percent shared variance-with neuron and trial count. We found that the scaling properties of networks with non-clustered and clustered connectivity differed, and that the in vivo recordings were more consistent with the clustered network. Furthermore, recordings from tens of neurons were sufficient to identify the dominant modes of shared variability that generalize to larger portions of the network. These findings can help guide the interpretation of dimensionality reduction outputs in regimes of limited neuron and trial sampling and help relate these outputs to the underlying network structure., Competing Interests: The authors have declared that no competing interests exist.

Recent anatomical and functional characterization of cortical inhibitory interneurons has highlighted the diverse computations supported by different subtypes of interneurons. However, most theoretical models of cortex do not feature multiple classes of interneurons and rather assume a single homogeneous population. We study the dynamics of recurrent excitatory-inhibitory model cortical networks with parvalbumin (PV)-, somatostatin (SOM)-, and vasointestinal peptide-expressing (VIP) interneurons, with connectivity properties motivated by experimental recordings from mouse primary visual cortex. Our theory describes conditions under which the activity of such networks is stable and how perturbations of distinct neuronal subtypes recruit changes in activity through recurrent synaptic projections. We apply these conclusions to study the roles of each interneuron subtype in disinhibition, surround suppression, and subtractive or divisive modulation of orientation tuning curves. Our calculations and simulations determine the architectural and stimulus tuning conditions under which cortical activity consistent with experiment is possible. They also lead to novel predictions concerning connectivity and network dynamics that can be tested via optogenetic manipulations. Our work demonstrates that recurrent inhibitory dynamics must be taken into account to fully understand many properties of cortical dynamics observed in experiments., (Copyright © 2016 the American Physiological Society.)

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

Insulin replacement therapy is essential in type 1 diabetic individuals and is required in ~40- 50% of type 2 diabetics during their lifetime. Prior attempts at beta cell regeneration have relied upon pancreatic injury to induce beta cell proliferation, dedifferentiation and activation of the embryonic pathway, or stem cell replacement. We report an alternative method to transform adult non-stem (somatic) cells into pancreatic beta cells. The Cellular Networking, Integration and Processing (CNIP) approach targets cellular mechanisms involved in pancreatic function in the organ's adult state and utilizes a synergistic mechanism that integrates three important levels of cellular regulation to induce beta cell formation: (i) glucose metabolism, (ii) membrane receptor function, and (iii) gene transcription. The aim of the present study was to induce pancreatic beta cell formation in vivo in adult animals without stem cells and without dedifferentiating cells to recapitulate the embryonic pathway as previously published (1-3). Our results employing CNIP demonstrate that: (i) insulin secreting cells can be generated in adult pancreatic tissue in vivo and circumvent the problem of generating endocrine (glucagon and somatostatin) cells that exert deleterious effects on glucose homeostasis, and (ii) longterm normalization of glucose tolerance and insulin secretion can be achieved in a wild type diabetic mouse model. The CNIP cocktail has the potential to be used as a preventative or therapeutic treatment or cure for both type 1 and type 2 diabetes.

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

The architecture of cortex is flexible, permitting neuronal networks to store recent sensory experiences as specific synaptic connectivity patterns. However, it is unclear how these patterns are maintained in the face of the high spike time variability associated with cortex. Here we demonstrate, using a large-scale cortical network model, that realistic synaptic plasticity rules coupled with homeostatic mechanisms lead to the formation of neuronal assemblies that reflect previously experienced stimuli. Further, reverberation of past evoked states in spontaneous spiking activity stabilizes, rather than erases, this learned architecture. Spontaneous and evoked spiking activity contains a signature of learned assembly structures, leading to testable predictions about the effect of recent sensory experience on spike train statistics. Our work outlines requirements for synaptic plasticity rules capable of modifying spontaneous dynamics and shows that this modification is beneficial for stability of learned network architectures.

Low-threshold M currents are mediated by the Kv7 family of potassium channels. Kv7 channels are important regulators of spiking activity, having a direct influence on the firing rate, spike time variability, and filter properties of neurons. How Kv7 channels affect the joint spiking activity of populations of neurons is an important and open area of study. Using a combination of computational simulations and analytic calculations, we show that the activation of Kv7 conductances reduces the covariability between spike trains of pairs of neurons driven by common inputs. This reduction is beyond that explained by the lowering of firing rates and involves an active cancellation of common fluctuations in the membrane potentials of the cell pair. Our theory shows that the excess covariance reduction is due to a Kv7-induced shift from low-pass to band-pass filtering of the single neuron spike train response. Dysfunction of Kv7 conductances is related to a number of neurological diseases characterized by both elevated firing rates and increased network-wide correlations. We show how changes in the activation or strength of Kv7 conductances give rise to excess correlations that cannot be compensated for by synaptic scaling or homeostatic modulation of passive membrane properties. In contrast, modulation of Kv7 activation parameters consistent with pharmacological treatments for certain hyperactivity disorders can restore normal firing rates and spiking correlations. Our results provide key insights into how regulation of a ubiquitous potassium channel class can control the coordination of population spiking activity., (Copyright © 2014 the American Physiological Society.)

A signature feature of cortical spike trains is their trial-to-trial variability. This variability is large in the spontaneous state and is reduced when cortex is driven by a stimulus or task. Models of recurrent cortical networks with unstructured, yet balanced, excitation and inhibition generate variability consistent with evoked conditions. However, these models produce spike trains which lack the long timescale fluctuations and large variability exhibited during spontaneous cortical dynamics. We propose that global network architectures which support a large number of stable states (attractor networks) allow balanced networks to capture key features of neural variability in both spontaneous and evoked conditions. We illustrate this using balanced spiking networks with clustered assembly, feedforward chain, and ring structures. By assuming that global network structure is related to stimulus preference, we show that signal correlations are related to the magnitude of correlations in the spontaneous state. Finally, we contrast the impact of stimulation on the trial-to-trial variability in attractor networks with that of strongly coupled spiking networks with chaotic firing rate instabilities, recently investigated by Ostojic (2014). We find that only attractor networks replicate an experimentally observed stimulus-induced quenching of trial-to-trial variability. In total, the comparison of the trial-variable dynamics of single neurons or neuron pairs during spontaneous and evoked activity can be a window into the global structure of balanced cortical networks.

High frequency deep brain stimulation (DBS) of the subthalamic nucleus (STN) is a widely used treatment for Parkinson's disease, but its effects on neural activity in basal ganglia circuits are not fully understood. DBS increases the excitation of STN efferents yet decouples STN spiking patterns from the spiking patterns of STN synaptic targets. We propose that this apparent paradox is resolved by recent studies showing an increased rate of axonal and synaptic failures in STN projections during DBS. To investigate this hypothesis, we combine in vitro and in vivo recordings to derive a computational model of axonal and synaptic failure during DBS. Our model shows that these failures induce a short term depression that suppresses the synaptic transfer of firing rate oscillations, synchrony and rate-coded information from STN to its synaptic targets. In particular, our computational model reproduces the widely reported suppression of parkinsonian β oscillations and synchrony during DBS. Our results support the idea that short term depression is a therapeutic mechanism of STN DBS that works as a functional lesion by decoupling the somatic spiking patterns of STN neurons from spiking activity in basal ganglia output nuclei., (© 2013.)

A neural correlate of parametric working memory is a stimulus-specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural activity, linking network architecture and parametric working memory. Cortical neurons receive noisy input fluctuations that cause persistent activity to diffusively wander about the network, degrading memory over time. We explore how cortical architecture that supports parametric working memory affects the diffusion of persistent neural activity. Studying both a spiking network and a simplified potential well model, we show that spatially heterogeneous excitatory coupling stabilizes a discrete number of persistent states, reducing the diffusion of persistent activity over the network. However, heterogeneous coupling also coarse-grains the stimulus representation space, limiting the storage capacity of parametric working memory. The storage errors due to coarse-graining and diffusion trade off so that information transfer between the initial and recalled stimulus is optimized at a fixed network heterogeneity. For sufficiently long delay times, the optimal number of attractors is less than the number of possible stimuli, suggesting that memory networks can under-represent stimulus space to optimize performance. Our results clearly demonstrate the combined effects of network architecture and stochastic fluctuations on parametric memory storage.

Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations.

Anatomical studies demonstrate that excitatory connections in cortex are not uniformly distributed across a network but instead exhibit clustering into groups of highly connected neurons. The implications of clustering for cortical activity are unclear. We studied the effect of clustered excitatory connections on the dynamics of neuronal networks that exhibited high spike time variability owing to a balance between excitation and inhibition. Even modest clustering substantially changed the behavior of these networks, introducing slow dynamics during which clusters of neurons transiently increased or decreased their firing rate. Consequently, neurons exhibited both fast spiking variability and slow firing rate fluctuations. A simplified model shows how stimuli bias networks toward particular activity states, thereby reducing firing rate variability as observed experimentally in many cortical areas. Our model thus relates cortical architecture to the reported variability in spontaneous and evoked spiking activity.

Homeostatic mechanisms maintain homogeneous neuronal behavior among neurons that exhibit substantial variability in the expression levels of their ionic conductances. In contrast, the mechanisms, which generate heterogeneous neuronal behavior across a neuronal population, remain poorly understood. We addressed this problem in the dorsal cochlear nucleus, where principal neurons exist in two qualitatively distinct states: spontaneously active or not spontaneously active. Our studies reveal that distinct activity states are generated by the differential levels of a Ba(2+)-sensitive, inwardly rectifying potassium conductance (K(ir)). Variability in K(ir) maximal conductance causes variations in the resting membrane potential (RMP). Low K(ir) conductance depolarizes RMP to voltages above the threshold for activating subthreshold-persistent sodium channels (Na(p)). Once Na(p) channels are activated, the RMP becomes unstable, and spontaneous firing is triggered. Our results provide a biophysical mechanism for generating neural heterogeneity, which may play a role in the encoding of sensory information.

Neural activity that persists long after stimulus presentation is a biological correlate of short-term memory. Variability in spiking activity causes persistent states to drift over time, ultimately degrading memory. Models of short-term memory often assume that the input fluctuations to neural populations are independent across cells, a feature that attenuates population-level variability and stabilizes persistent activity. However, this assumption is at odds with experimental recordings from pairs of cortical neurons showing that both the input currents and output spike trains are correlated. It remains unclear how correlated variability affects the stability of persistent activity and the performance of cognitive tasks that it supports. We consider the stochastic long-timescale attractor dynamics of pairs of mutually inhibitory populations of spiking neurons. In these networks, persistent activity was less variable when correlated variability was globally distributed across both populations compared with the case when correlations were locally distributed only within each population. Using a reduced firing rate model with a continuum of persistent states, we show that, when input fluctuations are correlated across both populations, they drive firing rate fluctuations orthogonal to the persistent state attractor, thereby causing minimal stochastic drift. Using these insights, we establish that distributing correlated fluctuations globally as opposed to locally improves network's performance on a two-interval, delayed response discrimination task. Our work shows that the correlation structure of input fluctuations to a network is an important factor when determining long-timescale, persistent population spiking activity.

The responses of cortical neurons are highly variable across repeated presentations of a stimulus. Understanding this variability is critical for theories of both sensory and motor processing, since response variance affects the accuracy of neural codes. Despite this influence, the cellular and circuit mechanisms that shape the trial-to-trial variability of population responses remain poorly understood. We used a combination of experimental and computational techniques to uncover the mechanisms underlying response variability of populations of pyramidal (E) cells in layer 2/3 of rat whisker barrel cortex. Spike trains recorded from pairs of E-cells during either spontaneous activity or whisker deflected responses show similarly low levels of spiking co-variability, despite large differences in network activation between the two states. We developed network models that show how spike threshold non-linearities dilute E-cell spiking co-variability during spontaneous activity and low velocity whisker deflections. In contrast, during high velocity whisker deflections, cancelation mechanisms mediated by feedforward inhibition maintain low E-cell pairwise co-variability. Thus, the combination of these two mechanisms ensure low E-cell population variability over a wide range of whisker deflection velocities. Finally, we show how this active decorrelation of population variability leads to a drastic increase in the population information about whisker velocity. The prevalence of spiking non-linearities and feedforward inhibition in the nervous system suggests that the mechanisms for low network variability presented in our study may generalize throughout the brain.

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short (≈ 10 ms) timescales while simultaneously reducing correlations at long (≈ 100 ms) timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs.

Depletion of synaptic neurotransmitter vesicles induces a form of short term depression in synapses throughout the nervous system. This plasticity affects how synapses filter presynaptic spike trains. The filtering properties of short term depression are often studied using a deterministic synapse model that predicts the mean synaptic response to a presynaptic spike train, but ignores variability introduced by the probabilistic nature of vesicle release and stochasticity in synaptic recovery time. We show that this additional variability has important consequences for the synaptic filtering of presynaptic information. In particular, a synapse model with stochastic vesicle dynamics suppresses information encoded at lower frequencies more than information encoded at higher frequencies, while a model that ignores this stochasticity transfers information encoded at any frequency equally well. This distinction between the two models persists even when large numbers of synaptic contacts are considered. Our study provides strong evidence that the stochastic nature neurotransmitter vesicle dynamics must be considered when analyzing the information flow across a synapse.

Spike trains from neurons in the basal ganglia of parkinsonian primates show increased pairwise correlations, oscillatory activity, and burst rate compared to those from neurons recorded during normal brain activity. However, it is not known how these changes affect the behavior of downstream thalamic neurons. To understand how patterns of basal ganglia population activity may affect thalamic spike statistics, we study pairs of model thalamocortical (TC) relay neurons receiving correlated inhibitory input from the internal segment of the globus pallidus (GPi), a primary output nucleus of the basal ganglia. We observe that the strength of correlations of TC neuron spike trains increases with the GPi correlation level, and bursty firing patterns such as those seen in the parkinsonian GPi allow for stronger transfer of correlations than do firing patterns found under normal conditions. We also show that the T-current in the TC neurons does not significantly affect correlation transfer, despite its pronounced effects on spiking. Oscillatory firing patterns in GPi are shown to affect the timescale at which correlations are best transferred through the system. To explain this last result, we analytically compute the spike count correlation coefficient for oscillatory cases in a reduced point process model. Our analysis indicates that the dependence of the timescale of correlation transfer is robust to different levels of input spike and rate correlations and arises due to differences in instantaneous spike correlations, even when the long timescale rhythmic modulations of neurons are identical. Overall, these results show that parkinsonian firing patterns in GPi do affect the transfer of correlations to the thalamus.

Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states.

Neurons respond to sensory stimuli by altering the rate and temporal pattern of action potentials. These spike trains both encode and propagate information that guides behavior. Local inhibitory networks can affect the information encoded and propagated by neurons by altering correlations between different spike trains. Correlations introduce redundancy that can reduce encoding but also facilitate propagation of activity to downstream targets. Given this trade-off, how can networks maximize both encoding and propagation efficacy? Here, we examine this problem by measuring the effects of olfactory bulb inhibition on the pairwise statistics of mitral cell spiking. We evoked spiking activity in the olfactory bulb in vitro and measured how lateral inhibition shapes correlations across timescales. We show that inhibitory circuits simultaneously increase fast correlation (i.e., synchrony increases) and decrease slow correlation (i.e., firing rates become less similar). Further, we use computational models to show the benefits of fast correlation/slow decorrelation in the context of odor coding. Olfactory bulb inhibition enhances population-level discrimination of similar inputs, while improving propagation of mitral cell activity to cortex. Our findings represent a targeted strategy by which a network can optimize the correlation structure of its output in a dynamic, activity-dependent manner. This trade-off is not specific to the olfactory system, but rather our work highlights mechanisms by which neurons can simultaneously accomplish multiple, and sometimes competing, aspects of sensory processing.

Proper pattern organization and reorganization are central problems facing many biological networks which thrive in fluctuating environments. However, in many cases the mechanisms that organize system activity oppose those that support behavioral flexibility. Thus, a balance between pattern organization and pattern flexibility is critically important for overall biological fitness. We study this balance in the foraging strategies of ant colonies exploiting food in dynamic environments. We present discrete time and space simulations of colony activity that uses a pheromone-based recruitment strategy biasing foraging towards a food source. After food relocation, the pheromone must evaporate sufficiently before foraging can shift colony attention to a new food source. The amount of food consumed within the dynamic environment depends non-monotonically on the pheromone evaporation time constant-with maximal consumption occurring at a time constant which balances trail formation and trail flexibility. A deterministic, 'mean field' model of pheromone and foragers on trails mimics our colony simulations. This reduced framework captures the essence of the flexibility-organization balance, and relates optimal pheromone evaporation to the timescale of the dynamic environment. We expect that the principles exposed in our study will generalize and motivate novel analysis across a broad range systems biology., (2010 Elsevier Ltd. All rights reserved.)

Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal's rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism.

Phasic neurons, which do not fire repetitively to steady depolarization, are found at various stages of the auditory system. Phasic neurons are commonly described as band-pass filters because they do not respond to low-frequency inputs even when the amplitude is large. However, we show that phasic neurons can encode low-frequency inputs when noise is present. With a low-threshold potassium current (I(KLT)), a phasic neuron model responds to rising and falling phases of a subthreshold low-frequency signal with white noise. When the white noise was low-pass filtered, the phasic model also responded to the signal's trough but still not to the peak. In contrast, a tonic neuron model fired mostly to the signal's peak. To test the model predictions, whole cell slice recordings were obtained in the medial (MSO) and lateral (LSO) superior olivary neurons in gerbil from postnatal day 10 (P10) to 22. The phasic MSO neurons with strong I(KLT), mostly from gerbils aged P17 or older, showed firing patterns consistent with the preceding predictions. Moreover, injecting a virtual I(KLT) into weak-phasic MSO and tonic LSO neurons with putative weak or no I(KLT) (from gerbils younger than P17) shifted the neural response from the signal's peak to the rising phase. These findings advance our knowledge about how noise gates the signal pathway and how phasic neurons encode slow envelopes of sounds with high-frequency carriers.

The magnitude of correlations between stimulus-driven responses of pairs of neurons can itself be stimulus dependent. We examine how this dependence affects the information carried by neural populations about the stimuli that drive them. Stimulus-dependent changes in correlations can both carry information directly and modulate the information separately carried by the firing rates and variances. We use Fisher information to quantify these effects and show that, although stimulus-dependent correlations often carry little information directly, their modulatory effects on the overall information can be large. In particular, if the stimulus dependence is such that correlations increase with stimulus-induced firing rates, this can significantly enhance the information of the population when the structure of correlations is determined solely by the stimulus. However, in the presence of additional strong spatial decay of correlations, such stimulus dependence may have a negative impact. Opposite relationships hold when correlations decrease with firing rates.

The joint influence of recurrent feedback and noise on gain control in a network of globally coupled spiking leaky integrate-and-fire neurons is studied theoretically and numerically. The context of our work is the origin of divisive versus subtractive gain control, as mixtures of these effects are seen in a variety of experimental systems. We focus on changes in the slope of the mean firing frequency-versus-input bias (f-I) curve when the gain control signal to the cells comes from the cells' output spikes. Feedback spikes are modeled as alpha functions that produce an additive current in the current balance equation. For generality, they occur after a fixed minimum delay. We show that purely divisive gain control, i.e. changes in the slope of the f-I curve, arises naturally with this additive negative or positive feedback, due to a linearizing actions of feedback. Negative feedback alone lowers the gain, accounting in particular for gain changes in weakly electric fish upon pharmacological opening of the feedback loop as reported by Bastian (J Neurosci 6:553-562, 1986). When negative feedback is sufficiently strong it further causes oscillatory firing patterns which produce irregularities in the f-I curve. Small positive feedback alone increases the gain, but larger amounts cause abrupt jumps to higher firing frequencies. On the other hand, noise alone in open loop linearizes the f-I curve around threshold, and produces mixtures of divisive and subtractive gain control. With both noise and feedback, the combined gain control schemes produce a primarily divisive gain control shift, indicating the robustness of feedback gain control in stochastic networks. Similar results are found when the "input" parameter is the contrast of a time-varying signal rather than the bias current. Theoretical results are derived relating the slope of the f-I curve to feedback gain and noise strength. Good agreement with simulation results are found for inhibitory and excitatory feedback. Finally, divisive feedback is also found for conductance-based feedback (shunting or excitatory) with and without noise.

The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses--thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.

Pyramidal cells of the apteronotid ELL have been shown to display a characteristic mechanism of burst discharge, which has been shown to play an important role in sensory coding. This form of bursting depends on a reciprocal dendro-somatic interaction, in which discharge of a somatic spike causes a dendritic spike, which in turn contributes a dendro-somatic current flow to create a depolarizing afterpotential (DAP) in the soma. We review here our recent work showing how the timing of this DAP influences the somatic firing dynamics, and how the degree of inactivation of dendritic Na(+) currents can cause an increased delay between somatic and dendritic spikes. This ultimately allows the DAP to become more effective at increasing the excitability of the somatic spike generating mechanism. Further, this delay between dendritic and somatic spiking can be regulated by strongly hyperpolarizing GABA(B) mediated dendritic inhibition, allowing the burst dynamics to fall under synaptic regulation. In contrast, a weaker, shunting inhibition due to GABA(A) mediated dendritic inhibition can regulate the dendritic spike waveform to decrease the dendro-somatic current flow and the resulting DAP. We therefore show that the qualitative behaviour of an individual cell can depend on the degree of synaptic input, and the exact timing of events across the spatial extent of the neuron. Thus, our results serve to illustrate the complex dynamics that can be observed in cells with significant dendritic arborisation, a nearly ubiquitous adaptation amongst principal neurons.

We study how pairs of neurons transfer correlated input currents into correlated spikes. Over rapid time scales, correlation transfer increases with both spike time variability and rate; the dependence on variability disappears at large time scales. This persists for a nonlinear membrane model and for heterogeneous cell pairs, but strong nonmonotonicities follow from refractory effects. We present consequences for population coding and for the encoding of time-varying stimuli.

Neurons in the auditory brain stem encode signals with exceptional temporal precision. A low-threshold potassium current, IKLT, present in many auditory brain stem structures and thought to enhance temporal encoding, facilitates spike selection of rapid input current transients through an associated dynamic gate. Whether the dynamic nature of IKLT interacts with the timescales in spectrally rich input to influence spike encoding remains unclear. We examine the general influence of IKLT on spike encoding of stochastic stimuli using a pattern classification analysis between spike responses from a ventral cochlear nucleus (VCN) model containing IKLT, and the same model with the IKLT dynamics removed. The influence of IKLT on spike encoding depended on the spectral content of the current stimulus such that maximal IKLT influence occurred for stimuli with power concentrated at frequencies low enough (<500 Hz) to allow IKLT activation. Further, broadband stimuli significantly decreased the influence of IKLT on spike encoding, suggesting that broadband stimuli are not well suited for investigating the influence of some dynamic membrane nonlinearities. Finally, pattern classification on spike responses was performed for physiologically realistic conductance stimuli created from various sounds filtered through an auditory nerve (AN) model. Regardless of the sound, the synaptic input arriving at VCN had similar low-pass power spectra, which led to a large influence of IKLT on spike encoding, suggesting that the subthreshold dynamics of IKLT plays a significant role in shaping the response of real auditory brain stem neurons.

Selective attention is an important filter for complex environments where distractions compete with signals. Attention increases both the gamma-band power of cortical local field potentials and the spike-field coherence within the receptive field of an attended object. However, the mechanisms by which gamma-band activity enhances, if at all, the encoding of input signals are not well understood. We propose that gamma oscillations induce binomial-like spike-count statistics across noisy neural populations. Using simplified models of spiking neurons, we show how the discrimination of static signals based on the population spike-count response is improved with gamma induced binomial statistics. These results give an important mechanistic link between the neural correlates of attention and the discrimination tasks where attention is known to enhance performance. Further, they show how a rhythmicity of spike responses can enhance coding schemes that are not temporally sensitive.

Populations of neurons in the retina, olfactory system, visual and somatosensory thalamus, and several cortical regions show temporal correlation between the discharge times of their action potentials (spike trains). Correlated firing has been linked to stimulus encoding, attention, stimulus discrimination, and motor behaviour. Nevertheless, the mechanisms underlying correlated spiking are poorly understood, and its coding implications are still debated. It is not clear, for instance, whether correlations between the discharges of two neurons are determined solely by the correlation between their afferent currents, or whether they also depend on the mean and variance of the input. We addressed this question by computing the spike train correlation coefficient of unconnected pairs of in vitro cortical neurons receiving correlated inputs. Notably, even when the input correlation remained fixed, the spike train output correlation increased with the firing rate, but was largely independent of spike train variability. With a combination of analytical techniques and numerical simulations using 'integrate-and-fire' neuron models we show that this relationship between output correlation and firing rate is robust to input heterogeneities. Finally, this overlooked relationship is replicated by a standard threshold-linear model, demonstrating the universality of the result. This connection between the rate and correlation of spiking activity links two fundamental features of the neural code.

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.

The rich temporal structure of neural spike trains provides multiple dimensions to code dynamic stimuli. Popular examples are spike trains from sensory cells where bursts and isolated spikes can serve distinct coding roles. In contrast to analyses of neural coding, the cellular mechanics of burst mechanisms are typically elucidated from the neural response to static input. Bridging the mechanics of bursting with coding of dynamic stimuli is an important step in establishing theories of neural coding. Electrosensory lateral line lobe (ELL) pyramidal neurons respond to static inputs with a complex dendrite-dependent burst mechanism. Here we show that in response to dynamic broadband stimuli, these bursts lack some of the electrophysiological characteristics observed in response to static inputs. A simple leaky integrate-and-fire (LIF)-style model with a dendrite-dependent depolarizing afterpotential (DAP) is sufficient to match both the output statistics and coding performance of experimental spike trains. We use this model to investigate a simplification of interval coding where the burst interspike interval (ISI) codes for the scale of a canonical upstroke rather than a multidimensional stimulus feature. Using this stimulus reduction, we compute a quantization of the burst ISIs and the upstroke scale to show that the mutual information rate of the interval code is maximized at a moderate DAP amplitude. The combination of a reduced description of ELL pyramidal cell bursting and a simplification of the interval code increases the generality of ELL burst codes to other sensory modalities.

We review mathematical aspects of biophysical dynamics, signal transduction and network architecture that have been used to uncover functionally significant relations between the dynamics of single neurons and the networks they compose. We focus on examples that combine insights from these three areas to expand our understanding of systems neuroscience. These range from single neuron coding to models of decision making and electrosensory discrimination by networks and populations and also coincidence detection in pairs of dendrites and dynamics of large networks of excitable dendritic spines. We conclude by describing some of the challenges that lie ahead as the applied mathematics community seeks to provide the tools which will ultimately underpin systems neuroscience.

We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.

A network of leaky integrate-and-fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied. We calculate the spectral statistics of the network (power spectrum of the population activity, cross spectrum between spike trains of different neurons) as well as of a single neuron (power spectrum of spike train, cross spectrum between external noise and spike train) within the network. As shown by comparison with numerical simulations, our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise. By means of our analytical results we discuss the quality of the correlation-induced oscillation in a large network as a function of the transmission delay and the internal noise intensity. It is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay (i.e., the delay period is longer than any other time scale in the system). For a neuron with a strong intrinsic frequency, the oscillation becomes strongly anharmonic in the case of a long delay time. We also discuss briefly the kind of synchrony introduced by the feedback-induced oscillation.

Multiplicative gain control is a vital component of many theoretical analyses of neural computations, conferring the ability to scale neuronal firing rate in response to synaptic inputs. Many theories of gain control in single cells have used precisely balanced noisy inputs. Such noisy inputs can degrade signal processing. We demonstrate a deterministic method for the control of gain without the use of noise. We show that a depolarizing afterpotential (DAP), arising from active dendritic spike backpropagation, leads to a multiplicative increase in gain. Reduction of DAP amplitude by dendritic inhibition dilutes the multiplicative effect, allowing for divisive scaling of the firing rate. In contrast, somatic inhibition acts in a subtractive manner, allowing spatially distinct inhibitory inputs to perform distinct computations. The simplicity of this mechanism and the ubiquity of its elementary components suggest that many cell types have the potential to display a dendritic division of neuronal output.

Oscillatory and synchronized neural activities are commonly found in the brain, and evidence suggests that many of them are caused by global feedback. Their mechanisms and roles in information processing have been discussed often using purely feedforward networks or recurrent networks with constant inputs. On the other hand, real recurrent neural networks are abundant and continually receive information-rich inputs from the outside environment or other parts of the brain. We examine how feedforward networks of spiking neurons with delayed global feedback process information about temporally changing inputs. We show that the network behavior is more synchronous as well as more correlated with and phase-locked to the stimulus when the stimulus frequency is resonant with the inherent frequency of the neuron or that of the network oscillation generated by the feedback architecture. The two eigenmodes have distinct dynamical characteristics, which are supported by numerical simulations and by analytical arguments based on frequency response and bifurcation theory. This distinction is similar to the class I versus class II classification of single neurons according to the bifurcation from quiescence to periodic firing, and the two modes depend differently on system parameters. These two mechanisms may be associated with different types of information processing.

We present results from a novel experimental paradigm to investigate the influence of spatial correlations of stimuli on electrosensory neural network dynamics. Further, a new theoretical analysis for the dynamics of a model network of stochastic leaky integrate-and-fire neurons with delayed feedback is proposed. Experiment and theory for this system both establish that spatial correlations induce a network oscillation, the strength of which is proportional to the degree of stimulus correlation at constant total stimulus power., (Copyright 2004 The American Physical Society)

Burst firing is commonly observed in many sensory systems and is proposed to transmit information reliably. Although a number of biophysical burst mechanisms have been identified, the relationship between burst dynamics and information transfer is uncertain. Electrosensory pyramidal cells have a well defined backpropagation-dependent burst mechanism. We used in vivo, in vitro, and modeling approaches to investigate pyramidal cell responses to mimics of behaviorally relevant sensory input. We found that within a given spike train, bursts are biased toward low-frequency events while isolated spikes simultaneously code for the entire frequency range. We also demonstrated that burst dynamics are essential for optimal feature detection but are not required for stimulus estimation. We conclude that burst and spike dynamics can segregate a single spike train into two parallel and complementary streams of information transfer.

We introduce the concept of "type I burst excitability", which is a generalization of the "normal" excitability that is well-known in cardiac and neural systems. We demonstrate this type of burst excitability in a specific model system, a pyramidal cell from the electrosensory lateral line lobe of the weakly electric fish Apteronotus leptorhynchus. As depolarizing current is increased, a saddle-node bifurcation of periodic orbits occurs, which separates tonic and burst activity. This bifurcation is responsible for the excitable nature of the system, and is the basis for the "type I" designation. We verify the existence of this transition from in vitro recordings of a number of actual pyramidal cells. A scaling relationship between the magnitude and duration of a current pulse required to induce a burst is derived. We also observe this type of burst excitability and the scaling relationships in a multicompartmental model that is driven by realistic stochastic synaptic inputs mimicking sensory input. We conclude by discussing the relevance of burst excitability to communication between weakly electric fish.

Animals have developed stereotyped communication calls to which specific sensory neurons are well tuned. These communication calls must be discriminated from environmental signals such as those produced by prey. Sensory systems might have evolved neural circuitry to encode both categories. In weakly electric fish, prey and communication signals differ in their spatial extent and frequency content. Here we show that stimuli of different spatial extents mimicking prey and communication signals cause a switch in the frequency tuning and spike-timing precision of electrosensory pyramidal neurons, resulting in the selective and optimal encoding of both stimulus categories. As in other sensory systems, pyramidal neurons respond only to stimuli located within a restricted region of space known as the classical receptive field (CRF). In some systems, stimulation outside the CRF but within a non-classical receptive field (nCRF) can modulate the neural response to CRF stimulation even though nCRF stimulation alone fails to elicit responses. We show that pyramidal neurons possess a nCRF and that it can modulate the response to CRF stimuli to induce this neurobiological switch in frequency tuning.

Na+-dependent spikes initiate in the soma or axon hillock region and actively backpropagate into the dendritic arbor of many central neurons. Inward currents underlying spike discharge are offset by outward K+ currents that repolarize a spike and establish a refractory period to temporarily prevent spike discharge. We show in a sensory neuron that somatic and dendritic K+ channels differentially control burst discharge by regulating the extent to which backpropagating dendritic spikes can re-excite the soma. During repetitive discharge a progressive broadening of dendritic spikes promotes a dynamic increase in dendritic spike refractory period. A leaky integrate-and-fire model shows that spike bursts are terminated when a decreasing somatic interspike interval and an increasing dendritic spike refractory period synergistically act to block backpropagation. The time required for the somatic interspike interval to intersect with dendritic refractory period determines burst frequency, a time that is regulated by somatic and dendritic spike repolarization. Thus, K+ channels involved in spike repolarization can efficiently control the pattern of spike output by establishing a soma-dendritic interaction that invokes dynamic shifts in dendritic spike properties.

Stimulus-induced oscillations occur in visual, olfactory and somatosensory systems. Several experimental and theoretical studies have shown how such oscillations can be generated by inhibitory connections between neurons. But the effects of realistic spatiotemporal sensory input on oscillatory network dynamics and the overall functional roles of such oscillations in sensory processing are poorly understood. Weakly electric fish must detect electric field modulations produced by both prey (spatially localized) and communication (spatially diffuse) signals. Here we show, through in vivo recordings, that sensory pyramidal neurons in these animals produce an oscillatory response to communication-like stimuli, but not to prey-like stimuli. On the basis of well-characterized circuitry, we construct a network model of pyramidal neurons that predicts that diffuse delayed inhibitory feedback is required to achieve oscillatory behaviour only in response to communication-like stimuli. This prediction is experimentally verified by reversible blockade of feedback inhibition that removes oscillatory behaviour in the presence of communication-like stimuli. Our results show that a sensory system can use inhibitory feedback as a mechanism to 'toggle' between oscillatory and non-oscillatory firing states, each associated with a naturalistic stimulus.