Extracting functionally feedforward networks from a population of spiking neurons

Estimating null and potent modes of feedforward communication in a computational model of cortical activity

Communication across anatomical areas of the brain is key to both sensory and motor processes. Dimensionality reduction approaches have shown that the covariation of activity across cortical areas follows well-delimited patterns. Some of these patterns fall within the "potent space" of neural interactions and generate downstream responses; other patterns fall within the "null space" and prevent the feedforward propagation of synaptic inputs. Despite growing evidence for the role of null space activity in visual processing as well as preparatory motor control, a mechanistic understanding of its neural origins is lacking. Here, we developed a mean-rate model that allowed for the systematic control of feedforward propagation by potent and null modes of interaction. In this model, altering the number of null modes led to no systematic changes in firing rates, pairwise correlations, or mean synaptic strengths across areas, making it difficult to characterize feedforward communication with common measures of functional connectivity. A novel measure termed the null ratio captured the proportion of null modes relayed from one area to another. Applied to simultaneous recordings of primate cortical areas V1 and V2 during image viewing, the null ratio revealed that feedforward interactions have a broad null space that may reflect properties of visual stimuli.

New Types of Experiments Reveal that a Neuron Functions as Multiple Independent Threshold Units

Neurons are the computational elements that compose the brain and their fundamental principles of activity are known for decades. According to the long-lasting computational scheme, each neuron sums the incoming electrical signals via its dendrites and when the membrane potential reaches a certain threshold the neuron typically generates a spike to its axon. Here we present three types of experiments, using neuronal cultures, indicating that each neuron functions as a collection of independent threshold units. The neuron is anisotropically activated following the origin of the arriving signals to the membrane, via its dendritic trees. The first type of experiments demonstrates that a single neuron’s spike waveform typically varies as a function of the stimulation location. The second type reveals that spatial summation is absent for extracellular stimulations from different directions. The third type indicates that spatial summation and subtraction are not achieved when combining intra- and extra- cellular stimulations, as well as for nonlocal time interference, where the precise timings of the stimulations are irrelevant. Results call to re-examine neuronal functionalities beyond the traditional framework, and the advanced computational capabilities and dynamical properties of such complex systems.

Feedforward architectures driven by inhibitory interactions

Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward networks, activity is exclusively driven by excitatory neurons and the wiring patterns between them, while inhibitory neurons play only a stabilizing role for the network dynamics. Motivated by recent experimental discoveries of hippocampal circuitry, cortical circuitry, and the diversity of inhibitory neurons throughout the brain, here we illustrate that one can construct such networks even if the connectivity between the excitatory units in the system remains random. This is achieved by endowing inhibitory nodes with a more active role in the network. Our findings demonstrate that apparent feedforward activity can be caused by a much broader network-architectural basis than often assumed.

Psychedelics as Medicines: An Emerging New Paradigm

Scientific interest in serotonergic psychedelics (e.g., psilocybin and LSD; 5-HT_2A receptor agonists) has dramatically increased within the last decade. Clinical studies administering psychedelics with psychotherapy have shown preliminary evidence of robust efficacy in treating anxiety and depression, as well as addiction to tobacco and alcohol. Moreover, recent research has suggested that these compounds have potential efficacy against inflammatory diseases through novel mechanisms, with potential advantages over existing antiinflammatory agents. We propose that psychedelics exert therapeutic effects for psychiatric disorders by acutely destabilizing local brain network hubs and global network connectivity via amplification of neuronal avalanches, providing the occasion for brain network "resetting" after the acute effects have resolved. Antiinflammatory effects may hold promise for efficacy in treatment of inflammation-related nonpsychiatric as well as potentially for psychiatric disorders. Serotonergic psychedelics operate through unique mechanisms that show promising effects for a variety of intractable, debilitating, and lethal disorders, and should be rigorously researched.

Neuronal pattern separation of motion-relevant input in LIP activity

In various regions of the brain, neurons discriminate sensory stimuli by decreasing the similarity between ambiguous input patterns. Here, we examine whether this process of pattern separation may drive the rapid discrimination of visual motion stimuli in the lateral intraparietal area (LIP). Starting with a simple mean-rate population model that captures neuronal activity in LIP, we show that overlapping input patterns can be reformatted dynamically to give rise to separated patterns of neuronal activity. The population model predicts that a key ingredient of pattern separation is the presence of heterogeneity in the response of individual units. Furthermore, the model proposes that pattern separation relies on heterogeneity in the temporal dynamics of neural activity and not merely in the mean firing rates of individual neurons over time. We confirm these predictions in recordings of macaque LIP neurons and show that the accuracy of pattern separation is a strong predictor of behavioral performance. Overall, results propose that LIP relies on neuronal pattern separation to facilitate decision-relevant discrimination of sensory stimuli.NEW & NOTEWORTHY A new hypothesis is proposed on the role of the lateral intraparietal (LIP) region of cortex during rapid decision making. This hypothesis suggests that LIP alters the representation of ambiguous inputs to reduce their overlap, thus improving sensory discrimination. A combination of computational modeling, theoretical analysis, and electrophysiological data shows that the pattern separation hypothesis links neural activity to behavior and offers novel predictions on the role of LIP during sensory discrimination.

Feed-Forward Propagation of Temporal and Rate Information between Cortical Populations during Coherent Activation in Engineered In Vitro Networks

Transient propagation of information across neuronal assembles is thought to underlie many cognitive processes. However, the nature of the neural code that is embedded within these transmissions remains uncertain. Much of our understanding of how information is transmitted among these assemblies has been derived from computational models. While these models have been instrumental in understanding these processes they often make simplifying assumptions about the biophysical properties of neurons that may influence the nature and properties expressed. To address this issue we created an in vitro analog of a feed-forward network composed of two small populations (also referred to as assemblies or layers) of living dissociated rat cortical neurons. The populations were separated by, and communicated through, a microelectromechanical systems (MEMS) device containing a strip of microscale tunnels. Delayed culturing of one population in the first layer followed by the second a few days later induced the unidirectional growth of axons through the microtunnels resulting in a primarily feed-forward communication between these two small neural populations. In this study we systematically manipulated the number of tunnels that connected each layer and hence, the number of axons providing communication between those populations. We then assess the effect of reducing the number of tunnels has upon the properties of between-layer communication capacity and fidelity of neural transmission among spike trains transmitted across and within layers. We show evidence based on Victor-Purpura's and van Rossum's spike train similarity metrics supporting the presence of both rate and temporal information embedded within these transmissions whose fidelity increased during communication both between and within layers when the number of tunnels are increased. We also provide evidence reinforcing the role of synchronized activity upon transmission fidelity during the spontaneous synchronized network burst events that propagated between layers and highlight the potential applications of these MEMs devices as a tool for further investigation of structure and functional dynamics among neural populations.

Statistical Evaluation of Waveform Collapse Reveals Scale-Free Properties of Neuronal Avalanches

Neural avalanches are a prominent form of brain activity characterized by network-wide bursts whose statistics follow a power-law distribution with a slope near 3/2. Recent work suggests that avalanches of different durations can be rescaled and thus collapsed together. This collapse mirrors work in statistical physics where it is proposed to form a signature of systems evolving in a critical state. However, no rigorous statistical test has been proposed to examine the degree to which neuronal avalanches collapse together. Here, we describe a statistical test based on functional data analysis, where raw avalanches are first smoothed with a Fourier basis, then rescaled using a time-warping function. Finally, an F ratio test combined with a bootstrap permutation is employed to determine if avalanches collapse together in a statistically reliable fashion. To illustrate this approach, we recorded avalanches from cortical cultures on multielectrode arrays as in previous work. Analyses show that avalanches of various durations can be collapsed together in a statistically robust fashion. However, a principal components analysis revealed that the offset of avalanches resulted in marked variance in the time-warping function, thus arguing for limitations to the strict fractal nature of avalanche dynamics. We compared these results with those obtained from cultures treated with an AMPA/NMDA receptor antagonist (APV/DNQX), which yield a power-law of avalanche durations with a slope greater than 3/2. When collapsed together, these avalanches showed marked misalignments both at onset and offset time-points. In sum, the proposed statistical evaluation suggests the presence of scale-free avalanche waveforms and constitutes an avenue for examining critical dynamics in neuronal systems.

Repertoires of Spike Avalanches Are Modulated by Behavior and Novelty

Neuronal avalanches measured as consecutive bouts of thresholded field potentials represent a statistical signature that the brain operates near a critical point. In theory, criticality optimizes stimulus sensitivity, information transmission, computational capability and mnemonic repertoires size. Field potential avalanches recorded via multielectrode arrays from cortical slice cultures are repeatable spatiotemporal activity patterns. It remains unclear whether avalanches of action potentials observed in forebrain regions of freely-behaving rats also form recursive repertoires, and whether these have any behavioral relevance. Here, we show that spike avalanches, recorded from hippocampus (HP) and sensory neocortex of freely-behaving rats, constitute distinct families of recursive spatiotemporal patterns. A significant number of those patterns were specific to a behavioral state. Although avalanches produced during sleep were mostly similar to others that occurred during waking, the repertoire of patterns recruited during sleep differed significantly from that of waking. More importantly, exposure to novel objects increased the rate at which new patterns arose, also leading to changes in post-exposure repertoires, which were significantly different from those before the exposure. A significant number of families occurred exclusively during periods of whisker contact with objects, but few were associated with specific objects. Altogether, the results provide original evidence linking behavior and criticality at the spike level: spike avalanches form repertoires that emerge in waking, recur during sleep, are diversified by novelty and contribute to object representation.

Burst predicting neurons survive an in vitro glutamate injury model of cerebral ischemia

Neuronal activity in vitro exhibits network bursts characterized by brief periods of increased spike rates. Recent work shows that a subpopulation of neurons reliably predicts the occurrence of network bursts. Here, we examined the role of burst predictors in cultures undergoing an in vitro model of cerebral ischemia. Dissociated primary cortical neurons were plated on multielectrode arrays and spontaneous activity was recorded at 17 days in vitro (DIV). This activity was characterized by neuronal avalanches where burst statistics followed a power law. We identified burst predictors as channels that consistently fired immediately prior to network bursts. The timing of these predictors relative to bursts followed a skewed distribution that differed sharply from a null model based on branching ratio. A portion of cultures were subjected to an excitotoxic insult (DIV 18). Propidium iodine and fluorescence imaging confirmed cell death in these cultures. While the insult did not alter the distribution of avalanches, it resulted in alterations in overall spike rates. Burst predictors, however, maintained baseline levels of activity. The resilience of burst predictors following excitotoxic insult suggests a key role of these units in maintaining network activity following injury, with implications for the selective effects of ischemia in the brain.

Functional Clusters, Hubs, and Communities in the Cortical Microconnectome

Although relationships between networks of different scales have been observed in macroscopic brain studies, relationships between structures of different scales in networks of neurons are unknown. To address this, we recorded from up to 500 neurons simultaneously from slice cultures of rodent somatosensory cortex. We then measured directed effective networks with transfer entropy, previously validated in simulated cortical networks. These effective networks enabled us to evaluate distinctive nonrandom structures of connectivity at 2 different scales. We have 4 main findings. First, at the scale of 3-6 neurons (clusters), we found that high numbers of connections occurred significantly more often than expected by chance. Second, the distribution of the number of connections per neuron (degree distribution) had a long tail, indicating that the network contained distinctively high-degree neurons, or hubs. Third, at the scale of tens to hundreds of neurons, we typically found 2-3 significantly large communities. Finally, we demonstrated that communities were relatively more robust than clusters against shuffling of connections. We conclude the microconnectome of the cortex has specific organization at different scales, as revealed by differences in robustness. We suggest that this information will help us to understand how the microconnectome is robust against damage.

Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state

Spontaneous fluctuations in neuronal activity emerge at many spatial and temporal scales in cortex. Population measures found these fluctuations to organize as scale-invariant neuronal avalanches, suggesting cortical dynamics to be critical. Macroscopic dynamics, though, depend on physiological states and are ambiguous as to their cellular composition, spatiotemporal origin, and contributions from synaptic input or action potential (AP) output. Here, we study spontaneous firing in pyramidal neurons (PNs) from rat superficial cortical layers in vivo and in vitro using 2-photon imaging. As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level. In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition. This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity.

DOI:http://dx.doi.org/10.7554/eLife.07224.001

Even when we are not engaged in any specific task, the brain shows coordinated patterns of spontaneous activity that can be monitored using electrodes placed on the scalp. This resting activity shapes the way that the brain responds to subsequent stimuli. Changes in resting activity patterns are seen in various neurological and psychiatric disorders, as well as in healthy individuals following sleep deprivation.

The brain's outer layer is known as the cortex. On a large scale, when monitoring many thousands of neurons, resting activity in the cortex demonstrates propagation in the brain in an organized manner. Specifically, resting activity was found to organize as so-called neuronal avalanches, in which large bursts of neuronal activity are grouped with medium-sized and smaller bursts in a very characteristic order. In fact, the sizes of these bursts—that is, the number of neurons that fire—are found to be scale-invariant, that is, the ratio of large bursts to medium-sized bursts is the same as that of medium-sized to small bursts. Such scale-invariance suggests that neuronal bursts are not independent of one another. However, it is largely unclear how neuronal avalanches arise from individual neurons, which fire simply in a noisy, irregular manner.

Bellay, Klaus et al. have now provided insights into this process by examining patterns of firing of a particular type of neuron—known as a pyramidal cell—in the cortex of rats as they recover from anesthesia. As the animals awaken, the firing of individual pyramidal cells in the cortex becomes even more irregular than under anesthesia. However, by considering the activity of a group of these neurons, Bellay, Klaus et al. realized that it is this more irregular firing that gives rise to neuronal avalanches, and that this occurs only when the animals are awake. Further experiments on individual pyramidal cells grown in the laboratory confirmed that neuronal avalanches emerge spontaneously from the irregular firing of individual neurons. These avalanches depend on there being a balance between two types of activity among the cells: ‘excitatory’ activity that causes other neurons to fire, and ‘inhibitory’ activity that prevents neuronal firing.

Given that resting activity influences the brain's responses to the outside world, the origins of neuronal avalanches are likely to provide clues about the way the brain processes information. Future experiments should also examine the possibility that the emergence of neuronal avalanches marks the transition from unconsciousness to wakefulness within the brain.

DOI:http://dx.doi.org/10.7554/eLife.07224.002

Large-scale, high-resolution multielectrode-array recording depicts functional network differences of cortical and hippocampal cultures

Understanding the detailed circuitry of functioning neuronal networks is one of the major goals of neuroscience. Recent improvements in neuronal recording techniques have made it possible to record the spiking activity from hundreds of neurons simultaneously with sub-millisecond temporal resolution. Here we used a 512-channel multielectrode array system to record the activity from hundreds of neurons in organotypic cultures of cortico-hippocampal brain slices from mice. To probe the network structure, we employed a wavelet transform of the cross-correlogram to categorize the functional connectivity in different frequency ranges. With this method we directly compare, for the first time, in any preparation, the neuronal network structures of cortex and hippocampus, on the scale of hundreds of neurons, with sub-millisecond time resolution. Among the three frequency ranges that we investigated, the lower two frequency ranges (gamma (30–80 Hz) and beta (12–30 Hz) range) showed similar network structure between cortex and hippocampus, but there were many significant differences between these structures in the high frequency range (100–1000 Hz). The high frequency networks in cortex showed short tailed degree-distributions, shorter decay length of connectivity density, smaller clustering coefficients, and positive assortativity. Our results suggest that our method can characterize frequency dependent differences of network architecture from different brain regions. Crucially, because these differences between brain regions require millisecond temporal scales to be observed and characterized, these results underscore the importance of high temporal resolution recordings for the understanding of functional networks in neuronal systems.

Scale-free and economical features of functional connectivity in neuronal networks

A form of activity that is highly studied in cultured cortical networks is the neuronal avalanche, characterized by bursts whose distribution follows a power law. While the statistics of neuronal avalanches are well characterized, much less is known about the neuronal interactions from which they arise. We examined statistical dependencies between pairs of cells in spontaneously active cultures of cortical neurons using an information measure of transfer entropy. We show that the distribution of transfer entropy follows a power law with a slope near 3/2. Using graph-theoretic approaches of weighted networks, we demonstrate that this power law maximizes a measure of global economy that accounts for both the efficiency of neuronal interactions as well as the overall traffic in the network. Finally, we describe a pairwise Poisson model that captures the statistics of information transfer in a population of spiking neurons. Using this model, we show that avalanches can occur in systems with weak pairwise interactions, and that strong pairwise interactions can arise without avalanches, suggesting that these two measures capture distinct properties of brain dynamics.

Scale-invariant neuronal avalanche dynamics and the cut-off in size distributions

Identification of cortical dynamics strongly benefits from the simultaneous recording of as many neurons as possible. Yet current technologies provide only incomplete access to the mammalian cortex from which adequate conclusions about dynamics need to be derived. Here, we identify constraints introduced by sub-sampling with a limited number of electrodes, i.e. spatial 'windowing', for well-characterized critical dynamics-neuronal avalanches. The local field potential (LFP) was recorded from premotor and prefrontal cortices in two awake macaque monkeys during rest using chronically implanted 96-microelectrode arrays. Negative deflections in the LFP (nLFP) were identified on the full as well as compact sub-regions of the array quantified by the number of electrodes N (10-95), i.e., the window size. Spatiotemporal nLFP clusters organized as neuronal avalanches, i.e., the probability in cluster size, p(s), invariably followed a power law with exponent -1.5 up to N, beyond which p(s) declined more steeply producing a 'cut-off' that varied with N and the LFP filter parameters. Clusters of size s≤N consisted mainly of nLFPs from unique, non-repeated cortical sites, emerged from local propagation between nearby sites, and carried spatial information about cluster organization. In contrast, clusters of size s>N were dominated by repeated site activations and carried little spatial information, reflecting greatly distorted sampling conditions. Our findings were confirmed in a neuron-electrode network model. Thus, avalanche analysis needs to be constrained to the size of the observation window to reveal the underlying scale-invariant organization produced by locally unfolding, predominantly feed-forward neuronal cascades.

Maximum likelihood estimators for truncated and censored power-law distributions show how neuronal avalanches may be misevaluated

The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.

Altered network communication following a neuroprotective drug treatment

Preconditioning is defined as a range of stimuli that allow cells to withstand subsequent anaerobic and other deleterious conditions. While cell protection under preconditioning is well established, this paper investigates the influence of neuroprotective preconditioning drugs, 4-aminopyridine and bicuculline (4-AP/bic), on synaptic communication across a broad network of in vitro rat cortical neurons. Using a permutation test, we evaluated cross-correlations of extracellular spiking activity across all pairs of recording electrodes on a 64-channel multielectrode array. The resulting functional connectivity maps were analyzed in terms of their graph-theoretic properties. A small-world effect was found, characterized by a functional network with high clustering coefficient and short average path length. Twenty-four hours after exposure to 4-AP/bic, small-world properties were comparable to control cultures that were not treated with the drug. Four hours following drug washout, however, the density of functional connections increased, while path length decreased and clustering coefficient increased. These alterations in functional connectivity were maintained at four days post-washout, suggesting that 4-AP/bic preconditioning leads to long-term effects on functional networks of cortical neurons. Because of their influence on communication efficiency in neuronal networks, alterations in small-world properties hold implications for information processing in brain systems. The observed relationship between density, path length, and clustering coefficient is captured by a phenomenological model where connections are added randomly within a spatially-embedded network. Taken together, results provide information regarding functional consequences of drug therapies that are overlooked in traditional viability studies and present the first investigation of functional networks under neuroprotective preconditioning.