Reliability, synchrony and noise

Analysis of slow (theta) oscillations as a potential temporal reference frame for information coding in sensory cortices

While sensory neurons carry behaviorally relevant information in responses that often extend over hundreds of milliseconds, the key units of neural information likely consist of much shorter and temporally precise spike patterns. The mechanisms and temporal reference frames by which sensory networks partition responses into these shorter units of information remain unknown. One hypothesis holds that slow oscillations provide a network-intrinsic reference to temporally partitioned spike trains without exploiting the millisecond-precise alignment of spikes to sensory stimuli. We tested this hypothesis on neural responses recorded in visual and auditory cortices of macaque monkeys in response to natural stimuli. Comparing different schemes for response partitioning revealed that theta band oscillations provide a temporal reference that permits extracting significantly more information than can be obtained from spike counts, and sometimes almost as much information as obtained by partitioning spike trains using precisely stimulus-locked time bins. We further tested the robustness of these partitioning schemes to temporal uncertainty in the decoding process and to noise in the sensory input. This revealed that partitioning using an oscillatory reference provides greater robustness than partitioning using precisely stimulus-locked time bins. Overall, these results provide a computational proof of concept for the hypothesis that slow rhythmic network activity may serve as internal reference frame for information coding in sensory cortices and they foster the notion that slow oscillations serve as key elements for the computations underlying perception.

The shape of phase-resetting curves in oscillators with a saddle node on an invariant circle bifurcation

We introduce a simple two-dimensional model that extends the Poincaré oscillator so that the attracting limit cycle undergoes a saddle node bifurcation on an invariant circle (SNIC) for certain parameter values. Arbitrarily close to this bifurcation, the phase-resetting curve (PRC) continuously depends on parameters, where its shape can be not only primarily positive or primarily negative but also nearly sinusoidal. This example system shows that one must be careful inferring anything about the bifurcation structure of the oscillator from the shape of its PRC.

Noise-induced synchronization in small world networks of phase oscillators

A small-world (SW) network of similar phase oscillators, interacting according to the Kuramoto model, is studied numerically. It is shown that deterministic Kuramoto dynamics on SW networks has various stable stationary states. This can be attributed to the so-called defect patterns in an SW network, which it inherits from deformation of helical patterns in its regular parent. Turning on an uncorrelated random force causes vanishing of the defect patterns, hence increasing the synchronization among oscillators for moderate noise intensities. This phenomenon, called stochastic synchronization, is generally observed in some natural networks such as the brain neural network.

A biophysical signature of network affiliation and sensory processing in mitral cells

One defining characteristic of the mammalian brain is its neuronal diversity. For a given region, substructure, layer or even cell type, variability in neuronal morphology and connectivity persists. Although it is well known that such cellular properties vary considerably according to neuronal type, the substantial biophysical diversity of neurons of the same morphological class is typically averaged out and ignored. Here we show that the amplitude of hyperpolarization-evoked sag of membrane potential recorded in olfactory bulb mitral cells is an emergent, homotypic property of local networks and sensory information processing. Simultaneous whole-cell recordings from pairs of cells show that the amount of hyperpolarization-evoked sag potential and current (Ih) is stereotypic for mitral cells belonging to the same glomerular circuit. This is corroborated by a mosaic, glomerulus-based pattern of expression of the HCN2 (hyperpolarization-activated cyclic nucleotide-gated channel 2) subunit of the Ih channel. Furthermore, inter-glomerular differences in both membrane potential sag and HCN2 protein are diminished when sensory input to glomeruli is genetically and globally altered so that only one type of odorant receptor is universally expressed. Population diversity in this intrinsic property therefore reflects differential expression between local mitral cell networks processing distinct odour-related information.

Identifying type I excitability using dynamics of stochastic neural firing patterns

The stochastic firing patterns are simulated near saddle-node bifurcation on an invariant cycle corresponding to type I excitability in stochastic Morris-Lecar model. In absence of external periodic signal, the stochastic firing manifests continuous distribution in ISI histogram (ISIH), whose amplitude at first increases sharply and then decreases exponentially. In presence of the external periodic signal, stochastic firing patterns appear as two cases of integer multiple firing with multiple discrete peaks in ISIH. One manifests perfect exponential decay in all peaks and the other imperfect exponential decay except a lower first peak. These stochastic firing patterns simulated with or without external periodic signal can be demonstrated in the experiments on rat hippocampal CA1 pyramidal neurons. The exponential decay laws in the multiple peaks are also acquired using probability analysis method. The perfect decay law is determined by the independent characteristic within the firing while the imperfect decay law is from the inhibitory effect. In addition, the stochastic firing patterns corresponding to type I excitability are compared to those of type II excitability. The results not only reveal the dynamics of stochastic firing patterns with or without external signal corresponding to type I excitability, but also provide practical indicators to availably identify type I excitability.

Fluctuating inhibitory inputs promote reliable spiking at theta frequencies in hippocampal interneurons

Theta-frequency (4–12 Hz) rhythms in the hippocampus play important roles in learning and memory. CA1 interneurons located at the stratum lacunosum-moleculare and radiatum junction (LM/RAD) are thought to contribute to hippocampal theta population activities by rhythmically pacing pyramidal cells with inhibitory postsynaptic potentials. This implies that LM/RAD cells need to fire reliably at theta frequencies in vivo. To determine whether this could occur, we use biophysically based LM/RAD model cells and apply different cholinergic and synaptic inputs to simulate in vivo-like network environments. We assess spike reliabilities and spiking frequencies, identifying biophysical properties and network conditions that best promote reliable theta spiking. We find that synaptic background activities that feature large inhibitory, but not excitatory, fluctuations are essential. This suggests that strong inhibitory input to these cells is vital for them to be able to contribute to population theta activities. Furthermore, we find that Type I-like oscillator models produced by augmented persistent sodium currents (I_NaP) or diminished A-type potassium currents (I_A) enhance reliable spiking at lower theta frequencies. These Type I-like models are also the most responsive to large inhibitory fluctuations and can fire more reliably under such conditions. In previous work, we showed that I_NaP and I_A are largely responsible for establishing LM/RAD cells’ subthreshold activities. Taken together with this study, we see that while both these currents are important for subthreshold theta fluctuations and reliable theta spiking, they contribute in different ways – I_NaP to reliable theta spiking and subthreshold activity generation, and I_A to subthreshold activities at theta frequencies. This suggests that linking subthreshold and suprathreshold activities should be done with consideration of both in vivo contexts and biophysical specifics.

How does the brain solve visual object recognition?

Mounting evidence suggests that 'core object recognition,' the ability to rapidly recognize objects despite substantial appearance variation, is solved in the brain via a cascade of reflexive, largely feedforward computations that culminate in a powerful neuronal representation in the inferior temporal cortex. However, the algorithm that produces this solution remains poorly understood. Here we review evidence ranging from individual neurons and neuronal populations to behavior and computational models. We propose that understanding this algorithm will require using neuronal and psychophysical data to sift through many computational models, each based on building blocks of small, canonical subnetworks with a common functional goal.

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.

Spontaneous voltage oscillations and response dynamics of a Hodgkin-Huxley type model of sensory hair cells

We employ a Hodgkin-Huxley type model of basolateral ionic currents in bullfrog saccular hair cells to study the genesis of spontaneous voltage oscillations and their role in shaping the response of the hair cell to external mechanical stimuli. Consistent with recent experimental reports, we find that the spontaneous dynamics of the model can be categorized using conductance parameters of calcium activated potassium, inward rectifier potassium, and mechano-electrical transduction ionic currents. The model is demonstrated to exhibit a broad spectrum of autonomous rhythmic activity, including periodic and quasiperiodic oscillations with two independent frequencies as well as various regular and chaotic bursting patterns. Complex patterns of spontaneous oscillations in the model emerge at small values of the conductance of Ca(2+) activated potassium currents. These patterns are significantly affected by thermal fluctuations of the mechano-electrical transduction current. We show that self-sustained regular voltage oscillations lead to enhanced and sharply tuned sensitivity of the hair cell to weak mechanical periodic stimuli. While regimes of chaotic oscillations are argued to result in poor tuning to sinusoidal driving, chaotically oscillating cells do provide a high sensitivity to low-frequency variations of external stimuli.

Brain rhythms reveal a hierarchical network organization

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or "virtual brains", whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.

Virogenetic and optogenetic mechanisms to define potential therapeutic targets in psychiatric disorders

A continuously increasing body of knowledge shows that the brain is an extremely complex neural network and single neurons possess their own complicated interactive signaling pathways. Such complexity of the nervous system makes it increasingly difficult to investigate the functions of specific neural components such as genes, proteins, transcription factors, neurons and nuclei in the brain. Technically, it has been even more of a significant challenge to identify the molecular and cellular adaptations that are both sufficient and necessary to underlie behavioral functions in health and disease states. Defining such neural adaptations is a critical step to identify the potential therapeutic targets within the complex neural network that are beneficial to treat psychiatric disorders. Recently, the new development and extensive application of in vivo viral-mediated gene transfer (virogenetics) and optical manipulation of specific neurons or selective neural circuits in freely-moving animals (optogenetics) make it feasible, through loss- and gain-of-function approaches, to reliably define sufficient and necessary neuroadaptations in the behavioral models of psychiatric disorders, including drug addiction, depression, anxiety and bipolar disorders. In this article, we focus on recent studies that successfully employ these advanced virogenetic and optogenetic techniques as a powerful tool to identify potential targets in the brain, and to provide highly useful information in the development of novel therapeutic strategies for psychiatric disorders. This article is part of a Special Issue entitled 'Anxiety and Depression'.

Voltage fluctuations in neurons: signal or noise?

Noise and variability are fundamental companions to ion channels and synapses and thus inescapable elements of brain function. The overriding unresolved issue is to what extent noise distorts and limits signaling on one hand and at the same time constitutes a crucial and fundamental enrichment that allows and facilitates complex adaptive behavior in an unpredictable world. Here we review the growing experimental evidence that functional network activity is associated with intense fluctuations in membrane potential and spike timing. We trace origins and consequences of noise and variability. Finally, we discuss noise-free neuronal signaling and detrimental and beneficial forms of noise in large-scale functional neural networks. Evidence that noise and variability in some cases go hand in hand with behavioral variability and increase behavioral choice, richness, and adaptability opens new avenues for future studies.

GABA neuron alterations, cortical circuit dysfunction and cognitive deficits in schizophrenia

Schizophrenia is a brain disorder associated with cognitive deficits that severely affect the patients' capacity for daily functioning. Whereas our understanding of its pathophysiology is limited, postmortem studies suggest that schizophrenia is associated with deficits of GABA-mediated synaptic transmission. A major role of GABA-mediated transmission may be producing synchronized network oscillations which are currently hypothesized to be essential for normal cognitive function. Therefore, cognitive deficits in schizophrenia may result from a GABA synapse dysfunction that disturbs neural synchrony. Here, we highlight recent studies further suggesting alterations of GABA transmission and network oscillations in schizophrenia. We also review current models for the mechanisms of GABA-mediated synchronization of neural activity, focusing on parvalbumin-positive GABA neurons, which are altered in schizophrenia and whose function has been strongly linked to the production of neural synchrony. Alterations of GABA signaling that impair gamma oscillations and, as a result, cognitive function suggest paths for novel therapeutic interventions.

Physiological Signal Variability in hMT+ Reflects Performance on a Direction Discrimination Task

Our ability to perceive visual motion is critically dependent on the human motion complex (hMT+) in the dorsal visual stream. Extensive electrophysiological research in the monkey equivalent of this region has demonstrated how neuronal populations code for properties such as speed and direction, and that neurometric functions relate to psychometric functions within the individual monkey. In humans, the physiological correlates of inter-individual perceptual differences are still largely unknown. To address this question, we used functional magnetic resonance imaging (fMRI) while participants viewed translational motion in different directions, and we measured thresholds for direction discrimination of moving stimuli in a separate psychophysics experiment. After determining hMT+ in each participant with a functional localizer, we were able to decode the different directions of visual motion from it using pattern classification (PC). We also characterized the variability of fMRI signal in hMT+ during stimulus and rest periods with a generative model. Relating perceptual performance to physiology, individual direction discrimination thresholds were significantly correlated with the variability measure in hMT+, but not with PC accuracies. Individual differences in PC accuracy were driven by non-physiological sources of noise, such as head-movement, which makes this method a poor tool to investigate inter-individual differences. In contrast, variability analysis of the fMRI signal was robust to non-physiological noise, and variability characteristics in hMT+ correlated with psychophysical thresholds in the individual participants. Higher levels of fMRI signal variability compared to rest correlated with lower discrimination thresholds. This result is in line with theories on stochastic resonance in the context of neuronal populations, which suggest that endogenous or exogenous noise can increase the sensitivity of neuronal populations to incoming signals.

Optimal phase response curves for stochastic synchronization of limit-cycle oscillators by common Poisson noise

We consider optimization of phase response curves for stochastic synchronization of noninteracting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional shape for sufficiently weak signals is sinusoidal, but can differ for stronger signals. By solving the Euler-Lagrange equation associated with the minimization of the Lyapunov exponent characterizing synchronization efficiency, the optimal phase response curve is obtained. We show that the optimal shape mutates from a sinusoid to a sawtooth as the constraint on its squared amplitude is varied.

Finding the event structure of neuronal spike trains

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.

Connectional parameters determine multisensory processing in a spiking network model of multisensory convergence

For the brain to synthesize information from different sensory modalities, connections from different sensory systems must converge onto individual neurons. However, despite being the definitive, first step in the multisensory process, little is known about multisensory convergence at the neuronal level. This lack of knowledge may be due to the difficulty for biological experiments to manipulate and test the connectional parameters that define convergence. Therefore, the present study used a computational network of spiking neurons to measure the influence of convergence from two separate projection areas on the responses of neurons in a convergent area. Systematic changes in the proportion of extrinsic projections, the proportion of intrinsic connections, or the amount of local inhibitory contacts affected the multisensory properties of neurons in the convergent area by influencing (1) the proportion of multisensory neurons generated, (2) the proportion of neurons that generate integrated multisensory responses, and (3) the magnitude of multisensory integration. These simulations provide insight into the connectional parameters of convergence that contribute to the generation of populations of multisensory neurons in different neural regions as well as indicate that the simple effect of multisensory convergence is sufficient to generate multisensory properties like those of biological multisensory neurons.

Effects of multiplicative power law neural noise in visual information processing

The human visual system is intrinsically noisy. The benefits of internal noise as part of visual code are controversial. Here the information-theoretic properties of multiplicative (i.e. signal-dependent) neural noise are investigated. A quasi-linear communication channel model is presented. The model shows that multiplicative power law neural noise promotes the minimum information transfer after efficient coding. It is demonstrated that Weber's law and the human contrast sensitivity function arise on the basis of minimum transfer of information and power law neural noise. The implications of minimum information transfer in self-organized neural networks and weakly coupled neurons are discussed.

Stochastic resonance modulates neural synchronization within and between cortical sources

Neural synchronization is a mechanism whereby functionally specific brain regions establish transient networks for perception, cognition, and action. Direct addition of weak noise (fast random fluctuations) to various neural systems enhances synchronization through the mechanism of stochastic resonance (SR). Moreover, SR also occurs in human perception, cognition, and action. Perception, cognition, and action are closely correlated with, and may depend upon, synchronized oscillations within specialized brain networks. We tested the hypothesis that SR-mediated neural synchronization occurs within and between functionally relevant brain areas and thus could be responsible for behavioral SR. We measured the 40-Hz transient response of the human auditory cortex to brief pure tones. This response arises when the ongoing, random-phase, 40-Hz activity of a group of tuned neurons in the auditory cortex becomes synchronized in response to the onset of an above-threshold sound at its "preferred" frequency. We presented a stream of near-threshold standard sounds in various levels of added broadband noise and measured subjects' 40-Hz response to the standards in a deviant-detection paradigm using high-density EEG. We used independent component analysis and dipole fitting to locate neural sources of the 40-Hz response in bilateral auditory cortex, left posterior cingulate cortex and left superior frontal gyrus. We found that added noise enhanced the 40-Hz response in all these areas. Moreover, added noise also increased the synchronization between these regions in alpha and gamma frequency bands both during and after the 40-Hz response. Our results demonstrate neural SR in several functionally specific brain regions, including areas not traditionally thought to contribute to the auditory 40-Hz transient response. In addition, we demonstrated SR in the synchronization between these brain regions. Thus, both intra- and inter-regional synchronization of neural activity are facilitated by the addition of moderate amounts of random noise. Because the noise levels in the brain fluctuate with arousal system activity, particularly across sleep-wake cycles, optimal neural noise levels, and thus SR, could be involved in optimizing the formation of task-relevant brain networks at several scales under normal conditions.

Phase-response curves and synchronized neural networks

We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases. (ii) Reduced models for PRC-based analysis can be formally related to more realistic models. (iii) Spike-rate adaptation limits PRC-based analysis but does not invalidate it. (iv) The dependence of PRCs on synaptic location emphasizes the importance of improving methods of synaptic stimulation. (v) New methods can distinguish between oscillations that derive from mutual connections and those arising from common drive. (vi) It is helpful to assume linear summation of effects of synaptic inputs; experiments with trains of inputs call this assumption into question. (vii) Relatively subtle changes in network structure can invalidate PRC-based predictions. (viii) Heterogeneity in the preferred frequencies of component neurons does not invalidate PRC analysis, but can annihilate synchronous activity.

Desynchronization of neocortical networks by asynchronous release of GABA at autaptic and synaptic contacts from fast-spiking interneurons

Networks of specific inhibitory interneurons regulate principal cell firing in several forms of neocortical activity. Fast-spiking (FS) interneurons are potently self-inhibited by GABAergic autaptic transmission, allowing them to precisely control their own firing dynamics and timing. Here we show that in FS interneurons, high-frequency trains of action potentials can generate a delayed and prolonged GABAergic self-inhibition due to sustained asynchronous release at FS-cell autapses. Asynchronous release of GABA is simultaneously recorded in connected pyramidal (P) neurons. Asynchronous and synchronous autaptic release show differential presynaptic Ca(2+) sensitivity, suggesting that they rely on different Ca(2+) sensors and/or involve distinct pools of vesicles. In addition, asynchronous release is modulated by the endogenous Ca(2+) buffer parvalbumin. Functionally, asynchronous release decreases FS-cell spike reliability and reduces the ability of P neurons to integrate incoming stimuli into precise firing. Since each FS cell contacts many P neurons, asynchronous release from a single interneuron may desynchronize a large portion of the local network and disrupt cortical information processing.

Analysis and modeling of ensemble recordings from respiratory pre-motor neurons indicate changes in functional network architecture after acute hypoxia

We have combined neurophysiologic recording, statistical analysis, and computational modeling to investigate the dynamics of the respiratory network in the brainstem. Using a multielectrode array, we recorded ensembles of respiratory neurons in perfused in situ rat preparations that produce spontaneous breathing patterns, focusing on inspiratory pre-motor neurons. We compared firing rates and neuronal synchronization among these neurons before and after a brief hypoxic stimulus. We observed a significant decrease in the number of spikes after stimulation, in part due to a transient slowing of the respiratory pattern. However, the median interspike interval did not change, suggesting that the firing threshold of the neurons was not affected but rather the synaptic input was. A bootstrap analysis of synchrony between spike trains revealed that both before and after brief hypoxia, up to 45% (but typically less than 5%) of coincident spikes across neuronal pairs was not explained by chance. Most likely, this synchrony resulted from common synaptic input to the pre-motor population, an example of stochastic synchronization. After brief hypoxia most pairs were less synchronized, although some were more, suggesting that the respiratory network was transiently “rewired” after the stimulus. To investigate this hypothesis, we created a simple computational model with feed-forward divergent connections along the inspiratory pathway. Assuming that (1) the number of divergent projections was not the same for all presynaptic cells, but rather spanned a wide range and (2) that the stimulus increased inhibition at the top of the network; this model reproduced the reduction in firing rate and bootstrap-corrected synchrony subsequent to hypoxic stimulation observed in our experimental data.

Synchronization of uncoupled oscillators by common gamma impulses: From phase locking to noise-induced synchronization

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by the Poisson random impulses, but their difference has not been fully quantified. Here, we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between the regular periodic and the random Poisson impulses. Their dynamics are characterized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.

Intrinsic biophysical diversity decorrelates neuronal firing while increasing information content

While examples of variation and diversity exist throughout the nervous system, their importance remains a source of debate. Even neurons of the same molecular type show notable intrinsic differences. Largely unknown however is the degree to which these differences impair or assist neural coding. When outputs from a single type of neuron were examined - the mitral cells of the mouse olfactory bulb - to identical stimuli, we found that each cell's spiking response was dictated by its unique biophysical fingerprint. By exploiting this intrinsic heterogeneity, diverse populations coded for 2-fold more information than their homogeneous counterparts. Additionally, biophysical variability alone reduced pairwise output spike correlations to low levels. Our results demonstrate that intrinsic neuronal diversity serves an important role in neural coding and is not simply the result of biological imprecision.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

Real-time simulation of biologically realistic stochastic neurons in VLSI

Neuronal variability has been thought to play an important role in the brain. As the variability mainly comes from the uncertainty in biophysical mechanisms, stochastic neuron models have been proposed for studying how neurons compute with noise. However, most papers are limited to simulating stochastic neurons in a digital computer. The speed and the efficiency are thus limited especially when a large neuronal network is of concern. This brief explores the feasibility of simulating the stochastic behavior of biological neurons in a very large scale integrated (VLSI) system, which implements a programmable and configurable Hodgkin-Huxley model. By simply injecting noise to the VLSI neuron, various stochastic behaviors observed in biological neurons are reproduced realistically in VLSI. The noise-induced variability is further shown to enhance the signal modulation of a neuron. These results point toward the development of analog VLSI systems for exploring the stochastic behaviors of biological neuronal networks in large scale.

The temporal structures and functional significance of scale-free brain activity

Scale-free dynamics, with a power spectrum following P proportional to f(-beta), are an intrinsic feature of many complex processes in nature. In neural systems, scale-free activity is often neglected in electrophysiological research. Here, we investigate scale-free dynamics in human brain and show that it contains extensive nested frequencies, with the phase of lower frequencies modulating the amplitude of higher frequencies in an upward progression across the frequency spectrum. The functional significance of scale-free brain activity is indicated by task performance modulation and regional variation, with beta being larger in default network and visual cortex and smaller in hippocampus and cerebellum. The precise patterns of nested frequencies in the brain differ from other scale-free dynamics in nature, such as earth seismic waves and stock market fluctuations, suggesting system-specific generative mechanisms. Our findings reveal robust temporal structures and behavioral significance of scale-free brain activity and should motivate future study on its physiological mechanisms and cognitive implications.

Stochastic cellular automata model of neural networks

We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers, and spontaneous activity. This model has a complex phase diagram with self-organized active neural states, hybrid phase transitions, and a rich array of behaviors. We show that if spontaneous activity (noise) reaches a threshold level then global neural oscillations emerge. Stochastic resonance is a precursor of this dynamical phase transition. These oscillations are an intrinsic property of even small groups of 50 neurons.

Priming of hippocampal population bursts by individual perisomatic-targeting interneurons

Hippocampal population bursts ("sharp wave-ripples") occur during rest and slow-wave sleep and are thought to be important for memory consolidation. The cellular mechanisms involved are incompletely understood. Here we investigated the cellular mechanisms underlying the initiation of sharp waves using a hippocampal slice model. To this end, we used a combination of field recordings with planar multielectrode arrays and whole-cell patch-clamp recordings of individual anatomically identified pyramidal neurons and interneurons. We found that GABA(A) receptor-mediated inhibition is necessary for sharp wave generation. Moreover, the activity of individual perisomatic-targeting interneurons can both suppress, and subsequently enhance, the local generation of sharp waves. Finally, we show that this is achieved by the tight control of local excitation and inhibition by perisomatic-targeting interneurons. These results suggest that perisomatic-targeting interneurons assist in selecting the subset of pyramidal neurons that initiate each hippocampal sharp wave-ripple.

Epilepsy as a dynamic disease: a tutorial of the past with an eye to the future

How can clinical epileptologists and computational neuroscientists learn to function together within the confines of interdisciplinary teams to develop new and more effective treatment strategies for epilepsy? Here we introduce epileptologists to the way modelers think about epilepsy as a dynamic disease. Not only is there terminology to be learned, but also it is necessary to identify those areas where clinical input might be expected to have the greatest impact. It is concluded that both groups have major roles to play in educating, evaluating, and shaping the direction of the efforts of each other.

The effect of noise on CaMKII activation in a dendritic spine during LTP induction

Activation of calcium-calmodulin dependent protein kinase II (CaMKII) during induction of long-term potentiation (LTP) is a series of complicated stochastic processes that are affected by noise. There are two main sources of noise affecting CaMKII activation within a dendritic spine. One is the noise associated with stochastic opening of N-methyl-d-aspartate (NMDA) receptor channels and the other is the noise associated with the stochastic reaction-diffusion kinetics leading to CaMKII activation. Many models have been developed to simulate CaMKII activation, but there is no fully stochastic model that studies the effect of noise on CaMKII activation. Here we construct a fully stochastic model to study these effects. Our results show that noise has important effects on CaMKII activation variability, with the effect from stochastic opening of NMDA receptor channels being 5-10 times more significant than that from stochastic reactions involving CaMKII. In addition, CaMKII activation levels and the variability of activation are greatly affected by small changes in NMDA receptor channel number at the synapse. One reason LTP induction protocols may require tetanic or repeated burst stimulation is that there is a need to overcome inherent variability to provide sufficiently large calcium signals through NMDA receptor channels; with meaningful physiological stimuli, noise may allow the calcium signal to exceed threshold for CaMKII activation when it might not do so otherwise.

How synchronization protects from noise

The functional role of synchronization has attracted much interest and debate: in particular, synchronization may allow distant sites in the brain to communicate and cooperate with each other, and therefore may play a role in temporal binding, in attention or in sensory-motor integration mechanisms. In this article, we study another role for synchronization: the so-called “collective enhancement of precision”. We argue, in a full nonlinear dynamical context, that synchronization may help protect interconnected neurons from the influence of random perturbations—intrinsic neuronal noise—which affect all neurons in the nervous system. More precisely, our main contribution is a mathematical proof that, under specific, quantified conditions, the impact of noise on individual interconnected systems and on their spatial mean can essentially be cancelled through synchronization. This property then allows reliable computations to be carried out even in the presence of significant noise (as experimentally found e.g., in retinal ganglion cells in primates). This in turn is key to obtaining meaningful downstream signals, whether in terms of precisely-timed interaction (temporal coding), population coding, or frequency coding. Similar concepts may be applicable to questions of noise and variability in systems biology.

Synchronization phenomena are pervasive in biology, creating collective behavior out of local interactions between neurons, cells, or animals. On the other hand, many of these systems function in the presence of large amounts of noise or disturbances, making one wonder how meaningful behavior can arise in these highly perturbed conditions. In this paper we show mathematically, in a general context, that synchronization is actually a means to protect interconnected systems from effects of noise and disturbances. One possible mechanism for synchronization is that the systems jointly create and then share a common signal, such as a mean electrical field or a global chemical concentration, which in turn makes each system directly connected to all others. Conversely, extracting meaningful information from average measurements over populations of cells (as commonly used for instance in electro-encephalography, or more recently in brain-machine interfaces) may require the presence of synchronization mechanisms similar to those we describe.

Coupling regularizes individual units in noisy populations

The regularity of a noisy system can modulate in various ways. It is well known that coupling in a population can lower the variability of the entire network; the collective activity is more regular. Here, we show that diffusive (reciprocal) coupling of two simple Ornstein-Uhlenbeck (O-U) processes can regularize the individual, even when it is coupled to a noisier process. In cellular networks, the regularity of individual cells is important when a select few play a significant role. The regularizing effect of coupling surprisingly applies also to general nonlinear noisy oscillators. However, unlike with the O-U process, coupling-induced regularity is robust to different kinds of coupling. With two coupled noisy oscillators, we derive an asymptotic formula assuming weak noise and coupling for the variance of the period (i.e., spike times) that accurately captures this effect. Moreover, we find that reciprocal coupling can regularize the individual period of higher dimensional oscillators such as the Morris-Lecar and Brusselator models, even when coupled to noisier oscillators. Coupling can have a counterintuitive and beneficial effect on noisy systems. These results have implications for the role of connectivity with noisy oscillators and the modulation of variability of individual oscillators.

Electrical coupling promotes fidelity of responses in the networks of model neurons

We consider an integrate-and-fire element subject to randomly perturbed synaptic input and an electrically coupled ensemble of such elements. The latter is interpreted as either a model of electrically coupled population of neurons or a multicompartment model of a dendrite. Random fluctuations blur the input signal and cause false responses in the system dynamics. For instance, under the influence of noise, the system may respond with an action potential to a subthreshold stimulus. We show that the responses of the elements within the network are more reliable than the responses of the same elements in isolation. Specifically, we show that the variances of the stochastic processes generated by the coupled model can be made arbitrarily small (i.e., the network responses can be made arbitrarily accurate) by increasing the number of elements in the network and the strength of electrical coupling. Our results suggest that the organization of cells in electrically coupled groups on the network level, or the dendritic morphology on the cellular level, may be involved in the filtering noise and therefore may play an important role in the information processing mechanisms operating on the network or cellular level respectively.

Reliable and precise neuronal firing during sensory plasticity in superficial layers of primary somatosensory cortex

Neocortical neurons show astonishing variation in the presence and timing of action potentials across stimulus trials, a phenomenon whose function and significance has been the subject of great interest. Here we present data showing that this response variability can be significantly reduced by altered sensory experience. Removal of all but one whisker from the side of the mouse face results in the rapid (within 24 h) potentiation of mean firing rates within the cortical representation of the spared whisker in young postnatal animals (postnatal days 13-16). Analysis of single-unit responses from whisker-spared animals shows that this potentiation can be attributed to an enhancement of trial-to-trial reliability (i.e., reduced response failures), as well as an increase in the mean number of spikes evoked within a successful trial. Changes were confined to superficial layers 2/3 and were not observed in the input layer of the cortex, layer 4. In addition to these changes in firing rates, we also observed profound changes in the precise timing of sensory-evoked responses. Trial-to-trial temporal precision was enhanced and the absolute latency of responses was reduced after single-whisker experience. Enhanced spike-timing precision and trial-to-trial reliability could also be triggered in adolescent animals with longer periods (7 d) of single-whisker experience. These experiments provide a quantitative analysis of how sensory experience can enhance both reliability and temporal precision in neocortical neurons and provide a framework for testing specific hypotheses about the role of response variability in cortical function and the molecular mechanisms underlying this phenomenon.

From the top down: flexible reading of a fragmented odor map

Animals that depend on smell for communication and survival extract multiple pieces of information from a single complex odor. Mice can collect information on sex, genotype, health and dietary status from urine scent marks, a stimulus made up of hundreds of molecules. This ability is all the more remarkable considering that natural odors are encountered against varying olfactory backgrounds; the olfactory system must therefore provide some mechanism for extracting the most relevant information. Here we discuss recent data indicating that the readout of olfactory input by mitral cells in the olfactory bulb can be modified by behavioral context. We speculate that the olfactory cortex plays a key role in tuning the readout of olfactory information from the olfactory bulb.

How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains

Functional interactions between neurons in vivo are often quantified by cross-correlation functions (CCFs) between their spike trains. It is therefore essential to understand quantitatively how CCFs are shaped by different factors, such as connectivity, synaptic parameters, and background activity. Here, we study the CCF between two neurons using analytical calculations and numerical simulations. We quantify the role of synaptic parameters, such as peak conductance, decay time, and reversal potential, and analyze how various patterns of connectivity influence CCF shapes. In particular, we find that the symmetry of the CCF distinguishes in general, but not always, the case of shared inputs between two neurons from the case in which they are directly synaptically connected. We systematically examine the influence of background synaptic inputs from the surrounding network that set the baseline firing statistics of the neurons and modulate their response properties. We find that variations in the background noise modify the amplitude of the cross-correlation function as strongly as variations of synaptic strength. In particular, we show that the postsynaptic neuron spiking regularity has a pronounced influence on CCF amplitude. This suggests an efficient and flexible mechanism for modulating functional interactions.

Calcium-activated SK channels influence voltage-gated ion channels to determine the precision of firing in globus pallidus neurons

Globus pallidus (GP) neurons fire rhythmically in the absence of synaptic input, suggesting that they may encode their inputs as changes in the phase of their rhythmic firing. Action potential afterhyperpolarization (AHP) enhances precision of firing by ensuring that the ion channels recover from inactivation by the same amount on each cycle. Voltage-clamp experiments in slices showed that the longest component of the GP neuron's AHP is blocked by apamin, a selective antagonist of calcium-activated SK channels. Application of 100 nm apamin also disrupted the precision of firing in perforated-patch and cell-attached recordings. SK channel blockade caused a small depolarization in spike threshold and made it more variable, but there was no reduction in the maximal rate of rise during an action potential. Thus, the firing irregularity was not caused solely by a reduction in voltage-gated Na(+) channel availability. Subthreshold voltage ramps triggered a large outward current that was sensitive to the initial holding potential and had properties similar to the A-type K(+) current in GP neurons. In numerical simulations, the availability of both Na(+) and A-type K(+) channels during autonomous firing were reduced when SK channels were removed, and a nearly equal reduction in Na(+) and K(+) subthreshold-activated ion channel availability produced a large decrease in the neuron's slope conductance near threshold. This change made the neuron more sensitive to intrinsically generated noise. In vivo, this change would also enhance the sensitivity of GP neurons to small synaptic inputs.

Stochastic phase reduction for a general class of noisy limit cycle oscillators

We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit cycle. The equation naturally includes previously proposed and mutually exclusive phase equations as special cases. The validity of the theory is numerically confirmed. Using the method, we reveal how noise and its correlation time affect limit cycle oscillations.

Ideal observer analysis of signal quality in retinal circuits

The function of the retina is crucial, for it must encode visual signals so the brain can detect objects in the visual world. However, the biological mechanisms of the retina add noise to the visual signal and therefore reduce its quality and capacity to inform about the world. Because an organism's survival depends on its ability to unambiguously detect visual stimuli in the presence of noise, its retinal circuits must have evolved to maximize signal quality, suggesting that each retinal circuit has a specific functional role. Here we explain how an ideal observer can measure signal quality to determine the functional roles of retinal circuits. In a visual discrimination task the ideal observer can measure from a neural response the increment threshold, the number of distinguishable response levels, and the neural code, which are fundamental measures of signal quality relevant to behavior. It can compare the signal quality in stimulus and response to determine the optimal stimulus, and can measure the specific loss of signal quality by a neuron's receptive field for non-optimal stimuli. Taking into account noise correlations, the ideal observer can track the signal-to-noise ratio available from one stage to the next, allowing one to determine each stage's role in preserving signal quality. A comparison between the ideal performance of the photon flux absorbed from the stimulus and actual performance of a retinal ganglion cell shows that in daylight a ganglion cell and its presynaptic circuit loses a factor of approximately 10-fold in contrast sensitivity, suggesting specific signal-processing roles for synaptic connections and other neural circuit elements. The ideal observer is a powerful tool for characterizing signal processing in single neurons and arrays along a neural pathway.

What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations--e.g., random noise--cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being "suboptimal". Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the "neural code". Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise--via stochastic resonance or otherwise--than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing "noise benefits", and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.

Relationship between spontaneous and evoked spike-time correlations in primate visual cortex

Coincident spikes have been implicated in vision-related processes such as feature binding, gain modulation, and long-distance communication. The source of these spike-time correlations is unknown. Although several studies have proposed that cortical spikes are correlated based on stimulus structure, others have suggested that spike-time correlations reflect ongoing cortical activity present even in the absence of a coherent visual stimulus. To examine this issue, we collected single-unit recordings from primary visual cortex (V1) of the anesthetized and paralyzed prosimian bush baby using a 100-electrode array. Spike-time correlations for pairs of cells were compared under three conditions: a moving grating at the cells' preferred orientation, an equiluminant blank screen, and a dark condition with eyes covered. The amplitudes, lags, and widths of cross-correlation histograms (CCHs) were strongly correlated between these conditions although for the blank stimulus and dark condition, the CCHs were broader with peaks lower in amplitude. In both preferred stimulus and blank conditions, the CCH amplitudes were greater when the cells within the pair had overlapping receptive fields and preferred similar orientations rather than nonoverlapping receptive fields and different orientations. These data suggest that spike-time correlations present in evoked activity are generated by mechanisms common to those operating in spontaneous conditions.