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Cortical microcircuits exhibit complex recurrent architectures that possess dynamically rich properties. The neurons that make up these microcircuits communicate mainly via discrete spikes, and it is not clear how spikes give rise to dynamics that can be used to perform computationally challenging tasks. In contrast, continuous models of rate-coding neurons can be trained to perform complex tasks. Here, we present a simple framework to construct biologically realistic spiking recurrent neural networks (RNNs) capable of learning a wide range of tasks. Our framework involves training a continuous-variable rate RNN with important biophysical constraints and transferring the learned dynamics and constraints to a spiking RNN in a one-to-one manner. The proposed framework introduces only 1 additional parameter to establish the equivalence between rate and spiking RNN models. We also study other model parameters related to the rate and spiking networks to optimize the one-to-one mapping. By establishing a close relationship between rate and spiking models, we demonstrate that spiking RNNs could be constructed to achieve similar performance as their counterpart continuous rate networks.

Our understanding of neural population coding has been limited by a lack of analysis methods to characterize spiking data from large populations. The biggest challenge comes from the fact that the number of possible network activity patterns scales exponentially with the number of neurons recorded ([Formula: see text]). Here we introduce a new statistical method for characterizing neural population activity that requires semi-independent fitting of only as many parameters as the square of the number of neurons, requiring drastically smaller data sets and minimal computation time. The model works by matching the population rate (the number of neurons synchronously active) and the probability that each individual neuron fires given the population rate. We found that this model can accurately fit synthetic data from up to 1000 neurons. We also found that the model could rapidly decode visual stimuli from neural population data from macaque primary visual cortex about 65 ms after stimulus onset. Finally, we used the model to estimate the entropy of neural population activity in developing mouse somatosensory cortex and, surprisingly, found that it first increases, and then decreases during development. This statistical model opens new options for interrogating neural population data and can bolster the use of modern large-scale in vivo Ca[Formula: see text] and voltage imaging tools.

Inhibition-stabilized networks (ISNs) are neural architectures with strong positive feedback among pyramidal neurons balanced by strong negative feedback from inhibitory interneurons, a circuit element found in the hippocampus and the primary visual cortex. In their working regime, ISNs produce damped oscillations in the [Formula: see text]-range in response to inputs to the inhibitory population. In order to understand the properties of interconnected ISNs, we investigated periodic forcing of ISNs. We show that ISNs can be excited over a range of frequencies and derive properties of the resonance peaks. In particular, we studied the phase-locked solutions, the torus solutions, and the resonance peaks. Periodically forced ISNs respond with (possibly multistable) phase-locked activity, whereas networks with sustained intrinsic oscillations respond more dynamically to periodic inputs with tori. Hence, the dynamics are surprisingly rich, and phase effects alone do not adequately describe the network response. This strengthens the importance of phase-amplitude coupling as opposed to phase-phase coupling in providing multiple frequencies for multiplexing and routing information.

Many symptoms of nerve damage arise from ectopic spiking caused by hyperexcitability. Ectopic spiking can originate at the site of axonal damage and elsewhere within affected neurons. This raises the question of whether localized damage elicits cell-wide changes in excitability and/or if localized changes in excitability can drive abnormal spiking at remote locations. Computer modeling revealed an example of the latter involving afterdischarge (AD)--stimulus-evoked spiking that outlasts stimulation. We found that AD originating in a hyperexcitable region of axon could shift to the soma where it was maintained. This repositioning of ectopic spike initiation was independent of distance between the two sites but relied on the rate and number of ectopic spikes originating from the first site. Nonlinear dynamical analysis of a reduced model demonstrated that properties which rendered the axonal site prone to initiating AD discouraged it from maintaining AD, whereas the soma had the inverse properties thus enabling the two sites to interact cooperatively. A first phase of AD originating in the axon could, by providing sufficient drive to trigger somatic AD, give way to a second phase of AD originating in the soma such that spiking continued when axonal AD failed. Ectopic spikes originating from the soma during phase 2 AD propagated successfully through the defunct site of axonal spike initiation. This novel mechanism whereby ectopic spiking at one site facilitates ectopic spiking at another site is likely to contribute to the chronification of hyperexcitability in conditions such as neuropathic pain.

Precisely timed action potentials related to stimuli and behavior have been observed in the cerebral cortex. However, information carried by the precise spike timing has to propagate through many cortical areas, and noise could disrupt millisecond precision during the transmission. Previous studies have demonstrated that only strong stimuli that evoke a large number of spikes with small dispersion of spike times can propagate through multilayer networks without degrading the temporal precision. Here we show that feedback projections can increase the number of spikes in spike volleys without degrading their temporal precision. Feedback also increased the range of spike volleys that can propagate through multilayer networks. Our work suggests that feedback projections could be responsible for the reliable propagation of information encoded in spike times through cortex, and thus could serve as an attentional mechanism to regulate the flow of information in the cortex. Feedback projections may also participate in generating spike synchronization that is engaged in cognitive behaviors by the same mechanisms described here for spike propagation.

The Hodgkin-Huxley studies of the action potential, published 60 years ago, are a central pillar of modern neuroscience research, ranging from molecular investigations of the structural basis of ion channel function to the computational implications at circuit level. In this Symposium Review, we aim to demonstrate the ongoing impact of Hodgkin's and Huxley's ideas. The Hodgkin-Huxley model established a framework in which to describe the structural and functional properties of ion channels, including the mechanisms of ion permeation, selectivity, and gating. At a cellular level, the model is used to understand the conditions that control both the rate and timing of action potentials, essential for neural encoding of information. Finally, the Hodgkin-Huxley formalism is central to computational neuroscience to understand both neuronal integration and circuit level information processing, and how these mechanisms might have evolved to minimize energy cost.

The response of a neuron to repeated somatic fluctuating current injections in vitro can elicit a reliable and precisely timed sequence of action potentials. The set of responses obtained across trials can also be interpreted as the response of an ensemble of similar neurons receiving the same input, with the precise spike times representing synchronous volleys that would be effective in driving postsynaptic neurons. To study the reproducibility of the output spike times for different conditions that might occur in vivo, we somatically injected aperiodic current waveforms into cortical neurons in vitro and systematically varied the amplitude and DC offset of the fluctuations. As the amplitude of the fluctuations was increased, reliability increased and the spike times remained stable over a wide range of values. However, at specific values called bifurcation points, large shifts in the spike times were obtained in response to small changes in the stimulus, resulting in multiple spike patterns that were revealed using an unsupervised classification method. Increasing the DC offset, which mimicked an overall increase in network background activity, also revealed bifurcation points and increased the reliability. Furthermore, the spike times shifted earlier with increasing offset. Although the reliability was reduced at bifurcation points, a theoretical analysis showed that the information about the stimulus time course was increased because each of the spike time patterns contained different information about the input.

Neurons rely on action potentials, or spikes, to relay information. Pathological changes in spike generation likely contribute to certain enigmatic features of neurological disease, like paroxysmal attacks of pain and muscle spasm. Paroxysmal symptoms are characterized by abrupt onset and short duration, and are associated with abnormal spiking although the exact pathophysiology remains unclear. To help decipher the biophysical basis for 'paroxysmal' spiking, we replicated afterdischarge (i.e. continued spiking after a brief stimulus) in a minimal conductance-based axon model. We then applied nonlinear dynamical analysis to explain the dynamical basis for initiation and termination of afterdischarge. A perturbation could abruptly switch the system between two (quasi-)stable attractor states: rest and repetitive spiking. This bistability was a consequence of slow positive feedback mediated by persistent inward current. Initiation of afterdischarge was explained by activation of the persistent inward current forcing the system to cross a saddle point that separates the basins of attraction associated with each attractor. Termination of afterdischarge was explained by the attractor associated with repetitive spiking being destroyed. This occurred when ultra-slow negative feedback, such as intracellular sodium accumulation, caused the saddle point and stable limit cycle to collide; in that regard, the active attractor is not truly stable when the slowest dynamics are taken into account. The model also explains other features of paroxysmal symptoms, including temporal summation and refractoriness.

Relay neurons in dorsal thalamic nuclei can fire high-frequency bursts of action potentials that ride the crest of voltage-dependent transient (T-type) calcium currents [low-threshold spike (LTS)]. To explore potential nucleus-specific burst features, we compared the membrane properties of dorsal lateral geniculate nucleus (dLGN) and pulvinar nucleus relay neurons using in vitro whole-cell recording in juvenile and adult tree shrew (Tupaia) tissue slices. We injected current ramps of variable slope into neurons that were sufficiently hyperpolarized to de-inactivate T-type calcium channels. In a small percentage of juvenile pulvinar and dLGN neurons, an LTS could not be evoked. In the remaining juvenile neurons and in all adult dLGN neurons, a single LTS could be evoked by current ramps. However, in the adult pulvinar, current ramps evoked multiple LTSs in >70% of recorded neurons. Using immunohistochemistry, Western blot techniques, unbiased stereology, and confocal and electron microscopy, we found that pulvinar neurons expressed more T-type calcium channels (Ca(v) 3.2) and more small conductance potassium channels (SK2) than dLGN neurons and that the pulvinar nucleus contained a higher glia-to-neuron ratio than the dLGN. Hodgkin-Huxley-type compartmental models revealed that the distinct firing modes could be replicated by manipulating T-type calcium and SK2 channel density, distribution, and kinetics. The intrinsic properties of pulvinar neurons that promote burst firing in the adult may be relevant to the treatment of conditions that involve the adult onset of aberrant thalamocortical interactions.

Neurons in sensory systems convey information about physical stimuli in their spike trains. In vitro, single neurons respond precisely and reliably to the repeated injection of the same fluctuating current, producing regions of elevated firing rate, termed events. Analysis of these spike trains reveals that multiple distinct spike patterns can be identified as trial-to-trial correlations between spike times (Fellous, Tiesinga, Thomas, & Sejnowski, 2004 ). Finding events in data with realistic spiking statistics is challenging because events belonging to different spike patterns may overlap. We propose a method for finding spiking events that uses contextual information to disambiguate which pattern a trial belongs to. The procedure can be applied to spike trains of the same neuron across multiple trials to detect and separate responses obtained during different brain states. The procedure can also be applied to spike trains from multiple simultaneously recorded neurons in order to identify volleys of near-synchronous activity or to distinguish between excitatory and inhibitory neurons. The procedure was tested using artificial data as well as recordings in vitro in response to fluctuating current waveforms.

Independent component analysis (ICA) is a technique that can be used to extract the source signals from sets of signal mixtures where the sources themselves are unknown. The analysis of optical recordings of invertebrate neuronal networks with fast voltage-sensitive dyes could benefit greatly from ICA. These experiments can generate hundreds of voltage traces containing both redundant and mixed recordings of action potentials originating from unknown numbers of neurons. ICA can be used as a method for converting such complex data sets into single-neuron traces, but its accuracy for doing so has never been empirically evaluated. Here, we tested the accuracy of ICA for such blind source separation by simultaneously performing sharp electrode intracellular recording and fast voltage-sensitive dye imaging of neurons located in the central ganglia of Tritonia diomedea and Aplysia californica, using a 464-element photodiode array. After running ICA on the optical data sets, we found that in 34 of 34 cases the intracellularly recorded action potentials corresponded 100% to the spiking activity of one of the independent components returned by ICA. We also show that ICA can accurately sort action potentials into single neuron traces from a series of optical data files obtained at different times from the same preparation, allowing one to monitor the network participation of large numbers of individually identifiable neurons over several recording episodes. Our validation of the accuracy of ICA for extracting the neural activity of many individual neurons from noisy, mixed, and redundant optical recording data sets should enable the use of this powerful large-scale imaging approach for studies of invertebrate and suitable vertebrate neuronal networks.

Fast axonal conduction of action potentials in mammals relies on myelin insulation. Demyelination can cause slowed, blocked, desynchronized, or paradoxically excessive spiking that underlies the symptoms observed in demyelination diseases. The diversity and timing of such symptoms are poorly understood, often intermittent, and uncorrelated with disease progress. We modeled the effects of demyelination (and secondary remodeling) on intrinsic axonal excitability using Hodgkin-Huxley and reduced Morris-Lecar models. Simulations and analysis suggested a simple explanation for the breadth of symptoms and revealed that the ratio of sodium to leak conductance, g(Na)/g(L), acted as a four-way switch controlling excitability patterns that included spike failure, single spike transmission, afterdischarge, and spontaneous spiking. Failure occurred when this ratio fell below a threshold value. Afterdischarge occurred at g(Na)/g(L) just below the threshold for spontaneous spiking and required a slow inward current that allowed for two stable attractor states, one corresponding to quiescence and the other to repetitive spiking. A neuron prone to afterdischarge could function normally unless it was switched to its "pathological" attractor state; thus, although the underlying pathology may develop slowly by continuous changes in membrane conductances, a discontinuous change in axonal excitability can occur and lead to paroxysmal symptoms. We conclude that tonic and paroxysmal positive symptoms as well as negative symptoms may be a consequence of varying degrees of imbalance between g(Na) and g(L) after demyelination. The KCNK family of g(L) potassium channels may be an important target for new drugs to treat the symptoms of demyelination.

The brain contains an astonishing diversity of neurons, each expressing only one set of ion channels out of the billions of potential channel combinations. Simple organizing principles are required for us to make sense of this abundance of possibilities and wealth of related data. We suggest that energy minimization subject to functional constraints may be one such unifying principle. We compared the energy needed to produce action potentials singly and in trains for a wide range of channel densities and kinetic parameters and examined which combinations of parameters maximized spiking function while minimizing energetic cost. We confirmed these results for sodium channels using a dynamic current clamp in neocortical fast spiking interneurons. We find further evidence supporting this hypothesis in a wide range of other neurons from several species and conclude that the ion channels in these neurons minimize energy expenditure in their normal range of spiking.

Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.

Spike generation in cortical neurons depends on the interplay between diverse intrinsic conductances. The phase response curve (PRC) is a measure of the spike time shift caused by perturbations of the membrane potential as a function of the phase of the spike cycle of a neuron. Near the rheobase, purely positive (type I) phase-response curves are associated with an onset of repetitive firing through a saddle-node bifurcation, whereas biphasic (type II) phase-response curves point towards a transition based on a Hopf-Andronov bifurcation. In recordings from layer 2/3 pyramidal neurons in cortical slices, cholinergic action, consistent with down-regulation of slow voltage-dependent potassium currents such as the M-current, switched the PRC from type II to type I. This is the first report showing that cholinergic neuromodulation may cause a qualitative switch in the PRCs type implying a change in the fundamental dynamical mechanism of spike generation.

Pharmacologically isolated GABAergic irregular spiking and stuttering interneurons in the mouse visual cortex display highly irregular spike times, with high coefficients of variation approximately 0.9-3, in response to a depolarizing, constant current input. This is in marked contrast to cortical pyramidal cells, which spike quite regularly in response to the same current injection. We applied time-series analysis methods to show that the irregular behavior of the interneurons was not a consequence of low-dimensional, deterministic processes. These methods were also applied to the Hindmarsh and Rose neuronal model to confirm that the methods are adequate for the types of data under investigation. This result has important consequences for the origin of fluctuations observed in the cortex in vivo.

The membrane conductance of a pyramidal neuron in vivo is substantially increased by background synaptic input. Increased membrane conductance, or shunting, does not simply reduce neuronal excitability. Recordings from hippocampal pyramidal neurons using dynamic clamp revealed that adaptation caused complete cessation of spiking in the high conductance state, whereas repetitive spiking could persist despite adaptation in the low conductance state. This behavior was reproduced in a phase plane model and was explained by a shunting-induced increase in voltage threshold. The increase in threshold allows greater activation of the M current (I(M)) at subthreshold potentials and reduces the minimum adaptation required to stabilize the system; in contrast, activation of the afterhyperpolarization current is unaffected by the increase in threshold and therefore remains unable to stop repetitive spiking. The nonlinear interaction between shunting and I(M) has other important consequences. First, timing of spikes elicited by brief stimuli is more precise when background spikes elicited by sustained input are prohibited, as occurs exclusively with I(M)-mediated adaptation in the high conductance state. Second, activation of I(M) at subthreshold potentials, which is increased in the high conductance state, hyperpolarizes average membrane potential away from voltage threshold, allowing only large, rapid fluctuations to reach threshold and elicit spikes. These results suggest that the shift from a low to high conductance state in a pyramidal neuron is accompanied by a switch from encoding time-averaged input with firing rate to encoding transient inputs with precisely timed spikes, in effect, switching the operational mode from integration to coincidence detection.

When a cortical neuron is repeatedly injected with the same fluctuating current stimulus (frozen noise) the timing of the spikes is highly precise from trial to trial and the spike pattern appears to be unique. We show here that the same repeated stimulus can produce more than one reliable temporal pattern of spikes. A new method is introduced to find these patterns in raw multitrial data and is tested on surrogate data sets. Using it, multiple coexisting spike patterns were discovered in pyramidal cells recorded from rat prefrontal cortex in vitro, in data obtained in vivo from the middle temporal area of the monkey (Buracas et al., 1998) and from the cat lateral geniculate nucleus (Reinagel and Reid, 2002). The spike patterns lasted from a few tens of milliseconds in vitro to several seconds in vivo. We conclude that the prestimulus history of a neuron may influence the precise timing of the spikes in response to a stimulus over a wide range of time scales.

We combined in vitro intracellular recording from prefrontal cortical neurons with simulated synaptic activity of a layer 5 prefrontal microcircuit using a dynamic clamp. During simulated in vivo background conditions, the cell responded to a brief depolarization with a sequence of spikes that outlasted the depolarization, mimicking the activity of a cell recorded during the delay period of a working memory task in the behaving monkey. The onset of sustained activity depended on the number of action potentials elicited by the cue-like depolarization. Too few spikes failed to provide enough NMDA drive to elicit sustained reverberations; too many spikes activated a slow intrinsic hyperpolarization current that prevented spiking; an intermediate number of spikes produced sustained activity. When high dopamine levels were simulated by depolarizing the cell and by increasing the amount of NMDA current, the cell exhibited spontaneous 'up-states' that terminated by the activation of a slow intrinsic hyperpolarizing current. The firing rate during the delay period could be effectively modulated by the standard deviation of the inhibitory background synaptic noise without significant changes in the background firing rate before cue onset. These results suggest that the balance between fast feedback inhibition and slower AMPA and NMDA feedback excitation is critical in initiating persistent activity and that the maintenance of persistent activity may be regulated by the amount of correlated background inhibition.

Synchronously spiking neurons have been observed in the cerebral cortex and the hippocampus. In computer models, synchronous spike volleys may be propagated across appropriately connected neuron populations. However, it is unclear how the appropriate synaptic connectivity is set up during development and maintained during adult learning. We performed computer simulations to investigate the influence of temporally asymmetric Hebbian synaptic plasticity on the propagation of spike volleys. In addition to feedforward connections, recurrent connections were included between and within neuron populations and spike transmission delays varied due to axonal, synaptic and dendritic transmission. We found that repeated presentations of input volleys decreased the synaptic conductances of intragroup and feedback connections while synaptic conductances of feedforward connections with short delays became stronger than those of connections with longer delays. These adaptations led to the synchronization of spike volleys as they propagated across neuron populations. The findings suggests that temporally asymmetric Hebbian learning may enhance synchronized spiking within small populations of neurons in cortical and hippocampal areas and familiar stimuli may produce synchronized spike volleys that are rapidly propagated across neural tissue.

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus. High reliability characterizes neurons that can support a spike-time code, unlike neurons with discharges forming a renewal process (such as a Poisson process). These two classes of responses cannot be distinguished using measures based on the spike-time histogram, but they can be identified by the attractor dynamics of spike trains, as shown here using a new method for calculating the attractor reliability. We applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro. These spike trains did not form a renewal process and had a higher reliability compared to renewal-like processes with the same spike-time histogram.

Calmodulin-dependent kinase II (CaMKII) has long been known to play an important role in learning and memory as well as long term potentiation (LTP). More recently it has been suggested that it might be involved in the time averaging of synaptic signals, which can then lead to the high precision of information stored at a single synapse. However, the role of the scaffolding molecule, neurogranin (Ng), in governing the dynamics of CaMKII is not yet fully understood. In this work, we adopt a rule-based modeling approach through the Monte Carlo method to study the effect of Ca2+ signals on the dynamics of CaMKII phosphorylation in the postsynaptic density (PSD). Calcium surges are observed in synaptic spines during an EPSP and back-propagating action potential due to the opening of NMDA receptors and voltage dependent calcium channels. Using agent-based models, we computationally investigate the dynamics of phosphorylation of CaMKII monomers and dodecameric holoenzymes. The scaffolding molecule, Ng, when present in significant concentration, limits the availability of free calmodulin (CaM), the protein which activates CaMKII in the presence of calcium. We show that Ng plays an important modulatory role in CaMKII phosphorylation following a surge of high calcium concentration. We find a non-intuitive dependence of this effect on CaM concentration that results from the different affinities of CaM for CaMKII depending on the number of calcium ions bound to the former. It has been shown previously that in the absence of phosphatase, CaMKII monomers integrate over Ca2+ signals of certain frequencies through autophosphorylation (Pepke et al, Plos Comp. Bio., 2010). We also study the effect of multiple calcium spikes on CaMKII holoenzyme autophosphorylation, and show that in the presence of phosphatase, CaMKII behaves as a leaky integrator of calcium signals, a result that has been recently observed in vivo. Our models predict that the parameters of this leaky integrator are finely tuned through the interactions of Ng, CaM, CaMKII, and PP1, providing a mechanism to precisely control the sensitivity of synapses to calcium signals. Author Summary not valid for PLOS ONE submissions.

A leading theory holds that neurodevelopmental brain disorders arise from imbalances in excitatory and inhibitory (E/I) brain circuitry. However, it is unclear whether this one-dimensional model is rich enough to capture the multiple neural circuit alterations underlying brain disorders. Here, we combined computational simulations with analysis of in vivo two-photon Ca2+ imaging data from somatosensory cortex of Fmr1 knock-out (KO) mice, a model of Fragile-X Syndrome, to test the E/I imbalance theory. We found that: (1) The E/I imbalance model cannot account for joint alterations in the observed neural firing rates and correlations; (2) Neural circuit function is vastly more sensitive to changes in some cellular components over others; (3) The direction of circuit alterations in Fmr1 KO mice changes across development. These findings suggest that the basic E/I imbalance model should be updated to higher dimensional models that can better capture the multidimensional computational functions of neural circuits.

N-methyl-D-aspartate receptor (NMDAR) hypofunction in parvalbumin-expressing (PV+) inhibitory neurons (INs) may contribute to symptoms in patients with schizophrenia (SZ). This hypothesis was inspired by studies in humans involving NMDAR antagonists that trigger SZ symptoms. Animal models of SZ using neuropharmacology and genetic knockouts have successfully replicated some of the key observations in human subjects involving alteration of gamma band oscillations (GBO) observed in electroencephalography and magnetoencephalography signals. However, it remains to be seen if NMDAR hypofunction in PV+ neurons is fundamental to the phenotype observed in these models. In this review, we discuss some of the key computational models of GBO and their predictions in the context of NMDAR hypofunction in INs. While PV+ INs have been the main focus of SZ studies in animal models, we also discuss the implications of NMDAR hypofunction in other types of INs using computational models for GBO modulation in the visual cortex.

Perceptual learning has been used to probe the mechanisms of cortical plasticity in the adult brain. Feedback projections are ubiquitous in the cortex, but little is known about their role in cortical plasticity. Here we explore the hypothesis that learning visual orientation discrimination involves learning-dependent plasticity of top-down feedback inputs from higher cortical areas, serving a different function from plasticity due to changes in recurrent connections within a cortical area. In a Hodgkin-Huxley-based spiking neural network model of visual cortex, we show that modulation of feedback inputs to V1 from higher cortical areas results in shunting inhibition in V1 neurons, which changes the response properties of V1 neurons. The orientation selectivity of V1 neurons is enhanced without changing orientation preference, preserving the topographic organizations in V1. These results provide new insights to the mechanisms of plasticity in the adult brain, reconciling apparently inconsistent experiments and providing a new hypothesis for a functional role of the feedback connections.

Episodic-like memory is thought to be supported by attractor dynamics in the hippocampus. A possible neural substrate for this memory mechanism is rate remapping, in which the spatial map of place cells encodes contextual information through firing rate variability. To test whether memories are stored as multimodal attractors in populations of place cells, recent experiments morphed one familiar context into another while observing the responses of CA3 cell ensembles. Average population activity in CA3 was reported to transition gradually rather than abruptly from one familiar context to the next, suggesting a lack of attractive forces associated with the two stored representations. On the other hand, individual CA3 cells showed a mix of gradual and abrupt transitions at different points along the morph sequence, and some displayed hysteresis which is a signature of attractor dynamics. To understand whether these seemingly conflicting results are commensurate with attractor network theory, we developed a neural network model of the CA3 with attractors for both position and discrete contexts. We found that for memories stored in overlapping neural ensembles within a single spatial map, position-dependent context attractors made transitions at different points along the morph sequence. Smooth transition curves arose from averaging across the population, while a heterogeneous set of responses was observed on the single unit level. In contrast, orthogonal memories led to abrupt and coherent transitions on both population and single unit levels as experimentally observed when remapping between two independent spatial maps. Strong recurrent feedback entailed a hysteretic effect on the network which diminished with the amount of overlap in the stored memories. These results suggest that context-dependent memory can be supported by overlapping local attractors within a spatial map of CA3 place cells. Similar mechanisms for context-dependent memory may also be found in other regions of the cerebral cortex.

Precise spike times carry information and are important for synaptic plasticity. Synchronizing oscillations such as gamma bursts could coordinate spike times, thus regulating information transmission in the cortex. Oscillations are driven by inhibitory neurons and are modulated by sensory stimuli and behavioral states. How their power and frequency are regulated is an open question. Using a model cortical circuit, we propose a regulatory mechanism that depends on the activity balance of monosynaptic and disynaptic pathways to inhibitory neurons: Monosynaptic input causes more powerful oscillations whereas disynaptic input increases the frequency of oscillations. The balance of stimulation to the two pathways modulates the overall distribution of spikes, with stronger disynaptic stimulation (e.g., preferred stimuli inside visual receptive fields) producing high firing rates and weak oscillations; in contrast, stronger monosynaptic stimulation (e.g., suppressive contextual stimulation from outside visual receptive fields) generates low firing rates and strong oscillatory regulation of spike timing, as observed in alert cortex processing complex natural stimuli. By accounting for otherwise paradoxical experimental findings, our results demonstrate how the frequency and power of oscillations, and hence spike times, can be modulated by both sensory input and behavioral context, with powerful oscillations signifying a cortical state under inhibitory control in which spikes are sparse and spike timing is precise.

The goal of the 79th Cold Spring Harbor Symposia on Quantitative Biology on Cognition held on May 28-June 2, 2014 was to survey recent advances in cognitive neuroscience and assess future prospects. The symposium succeeded beyond the dreams of the organizers and the participants were treated to an extraordinarily rich feast of 58 long talks, six short talks, and 137 posters. Equally important to the success of the symposium was the perfect setting for informal scientific exchange between 260 participants generously provided by the Cold Spring Harbor Laboratory. The sense that emerged from the symposium was that a threshold had been crossed and a new era in the study of cognition was underway. My attempt here will be to capture that sense of awakening, to trace the strands that gave rise to it, and to access its implications for future discoveries.

Chemical synapses exhibit a diverse array of internal mechanisms that affect the dynamics of transmission efficacy. Many of these processes, such as release of neurotransmitter and vesicle recycling, depend strongly on activity-dependent influx and accumulation of Ca2+. To model how each of these processes may affect the processing of information in neural circuits, and how their dysfunction may lead to disease states, requires a computationally efficient modelling framework, capable of generating accurate phenomenology without incurring a heavy computational cost per synapse. Constructing a phenomenologically realistic model requires the precise characterization of the timing and probability of neurotransmitter release. Difficulties arise in that functional forms of instantaneous release rate can be difficult to extract from noisy data without running many thousands of trials, and in biophysical synapses, facilitation of per-vesicle release probability is confounded by depletion. To overcome this, we obtained traces of free Ca2+ concentration in response to various action potential stimulus trains from a molecular MCell model of a hippocampal Schaffer collateral axon. Ca2+ sensors were placed at varying distance from a voltage-dependent calcium channel (VDCC) cluster, and Ca2+ was buffered by calbindin. Then, using the calcium traces to drive deterministic state vector models of synaptotagmin 1 and 7 (Syt-1/7), which respectively mediate synchronous and asynchronous release in excitatory hippocampal synapses, we obtained high-resolution profiles of instantaneous release rate, to which we applied functional fits. Synchronous vesicle release occurred predominantly within half a micron of the source of spike-evoked Ca2+ influx, while asynchronous release occurred more consistently at all distances. Both fast and slow mechanisms exhibited multi-exponential release rate curves, whose magnitudes decayed exponentially with distance from the Ca2+ source. Profile parameters facilitate on different time scales according to a single, general facilitation function. These functional descriptions lay the groundwork for efficient mesoscale modelling of vesicular release dynamics. Author summary: Most information transmission between neurons in the brain occurs via release of neurotransmitter from synaptic vesicles. In response to a presynaptic spike, calcium influx at the active zone of a synapse can trigger the release of neurotransmitter with a certain probability. These stochastic release events may occur immediately after a spike or with some delay. As calcium accumulates from one spike to the next, the probability of release may increase (facilitate) for subsequent spikes. This process, known as short-term plasticity, transforms the spiking code to a release code, underlying much of the brain's information processing. In this paper, we use an accurate, detailed model of presynaptic molecular physiology to characterize these processes at high precision in response to various spike trains. We then apply model reduction to the results to obtain a phenomenological model of release timing, probability, and facilitation, which can perform as accurately as the molecular model but with far less computational cost. This mesoscale model of spike-evoked release and facilitation helps to bridge the gap between microscale molecular dynamics and macroscale information processing in neural circuits. It can thus benefit large scale modelling of neural circuits, biologically inspired machine learning models, and the design of neuromorphic chips. [ABSTRACT FROM AUTHOR]

Recurrent neural network (RNN) models trained to perform cognitive tasks are a useful computational tool for understanding how cortical circuits execute complex computations. However, these models are often composed of units that interact with one another using continuous signals and overlook parameters intrinsic to spiking neurons. Here, we developed a method to directly train not only synaptic-related variables but also membrane-related parameters of a spiking RNN model. Training our model on a wide range of cognitive tasks resulted in diverse yet task-specific synaptic and membrane parameters. We also show that fast membrane time constants and slow synaptic decay dynamics naturally emerge from our model when it is trained on tasks associated with working memory (WM). Further dissecting the optimized parameters revealed that fast membrane properties are important for encoding stimuli, and slow synaptic dynamics are needed for WM maintenance. This approach offers a unique window into how connectivity patterns and intrinsic neuronal properties contribute to complex dynamics in neural populations. [ABSTRACT FROM AUTHOR]

Reliable timing of cortical spikes in response to visual events is crucial in representing visual inputs to the brain. Spikes in the primary visual cortex (VI) need to occur at the same time within a repeated visual stimulus. Two classical mechanisms are employed by the cortex to enhance reliable timing. First, cortical neurons respond reliably to a restricted set of stimuli through their preference for certain patterns of membrane potential due to their intrinsic properties. Second, intracortical networking of excitatory and inhibitory neurons induces lateral inhibition that, through the timing and strength of IPSCs and EPSCs, produces sparse and reliably timed cortical neuron spike trains to be transmitted downstream. Here, we describe a third mechanism that, through preferential thalamocortical synaptic connectivity, enhances the trial-to-trial timing precision of cortical spikes in the presence of spike train variability within each trial that is introduced between LGN neurons in the retino-thalamic pathway. Applying experimentally recorded LGN spike trains from the anesthetized cat to a detailed model of a spiny stellate VI neuron, we found that output spike timing precision improved with increasing numbers of convergent LGN inputs. The improvement was consistent with the predicted proportionality of II Jn for n LGN source neurons. We also found connectivity configurations that maximize reliability and that generate VI cell output spike trains quantitatively similar to the experimental recordings. Our findings suggest a general principle, namely intra-trial variability among converging inputs, that increases stimulus response precision and is widely applicable to synaptically connected spiking neurons. [ABSTRACT FROM AUTHOR]

Relay neurons in dorsal thalamic nuclei can fire high-frequency bursts of action potentials that ride the crest of voltage-dependent transient (T-type) calcium currents [low-threshold spike (LTS)]. To explore potential nucleus-specific burst features, we compared the membrane properties of dorsal lateral geniculate nucleus (dLGN) and pulvinar nucleus relay neurons using in vitro whole-cell recording in juvenile and adult tree shrew (Tupaia) tissue slices. We injected current ramps of variable slope into neurons that were sufficiently hyperpolarized to de-inactivate T-type calcium channels. In a small percentage of juvenile pulvinar and dLGN neurons, an LTS could not be evoked. In the remaining juvenile neurons and in all adult dLGN neurons, a single LTS could be evoked by current ramps. However, in the adult pulvinar, current ramps evoked multiple LTSs in >70% of recorded neurons. Using immunohistochemistry, Western blot techniques, unbiased stereology, and confocal and electron microscopy, we found that pulvinar neurons expressed more T-type calcium channels (Cav 3.2) and more small conductance potassium channels (SK2) than dLGN neurons and that the pulvinar nucleus contained a higher glia-to-neuron ratio than the dLGN. Hodgkin-Huxley-type compartmental models revealed that the distinct firing modes could be replicated by manipulating T-type calcium and SK2 channel density, distribution, and kinetics. The intrinsic properties of pulvinar neurons that promote burst firing in the adult may be relevant to the treatment of conditions that involve the adult onset of aberrant thalamocortical interactions. [ABSTRACT FROM AUTHOR]