Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro

Synaptic plasticity: from chimera states to synchronicity oscillations in multilayer neural networks

This research scrutinizes the simultaneous evolution of each layer within a multilayered complex neural network and elucidates the effect of synaptic plasticity on inter-layer dynamics. In the absence of synaptic plasticity, a predominant feedforward effect is observed, resulting in the manifestation of complete synchrony in deep networks, with each layer assuming a chimera state. A significant increase in the number of synchronized neurons is observed as the layers augment, culminating in complete synchronization in the deeper sections. The study categorizes the layers into three distinct parts: the initial layers (1-4) demonstrate the emergence of non-uniformity in the random firing of neurons; the middle layers (5-7) exhibit an amplification of this non-uniformity, forming a higher degree of synchronization; and the final layers (8-10) display a completely synchronized process. The introduction of synaptic plasticity disrupts this synchrony, inducing periodic oscillation characteristics across layers. The specificity of these oscillations is notably accentuated with increasing network depth. These insights shed light on the interplay between neural network complexity and synaptic plasticity in influencing synchronization dynamics, presenting avenues for enhanced neural network architectures and refined neuroscientific models. The findings underscore the imperative to delve deeper into the implications of synaptic plasticity on the structure and function of intricate multi-layer neural networks.

Between-area communication through the lens of within-area neuronal dynamics

A core problem in systems and circuits neuroscience is deciphering the origin of shared dynamics in neuronal activity: Do they emerge through local network interactions, or are they inherited from external sources? We explore this question with large-scale networks of spatially ordered spiking neuron models where a downstream network receives input from an upstream sender network. We show that linear measures of the communication between the sender and receiver networks can discriminate between emergent or inherited population dynamics. A match in the dimensionality of the sender and receiver population activities promotes faithful communication. In contrast, a nonlinear mapping between the sender to receiver activity, for example, through downstream emergent population-wide fluctuations, can impair linear communication. Our work exposes the benefits and limitations of linear measures when analyzing between-area communication in circuits with rich population-wide neuronal dynamics.

Early classification of Alzheimer's disease phenotype based on hippocampal electrophysiology in the TgF344-AD rat model

The hippocampus plays a vital role in navigation, learning, and memory, and is affected in Alzheimer's disease (AD). This study investigated the classification of AD-transgenic rats versus wild-type littermates using electrophysiological activity recorded from the hippocampus at an early, presymptomatic stage of the disease (6 months old) in the TgF344-AD rat model. The recorded signals were filtered into low frequency (LFP) and high frequency (spiking activity) signals, and machine learning classifiers were employed to identify the rat genotype (TG vs. WT). By analyzing specific frequency bands in the low frequency signals and calculating distance metrics between spike trains in the high frequency signals, accurate classification was achieved. Gamma band power emerged as a valuable signal for classification, and combining information from both low and high frequency signals improved the accuracy further. These findings provide valuable insights into the early stage effects of AD on different regions of the hippocampus.

Geometry of spiking patterns in early visual cortex: a topological data analytic approach

In the brain, spiking patterns live in a high-dimensional space of neurons and time. Thus, determining the intrinsic structure of this space presents a theoretical and experimental challenge. To address this challenge, we introduce a new framework for applying topological data analysis (TDA) to spike train data and use it to determine the geometry of spiking patterns in the visual cortex. Key to our approach is a parametrized family of distances based on the timing of spikes that quantifies the dissimilarity between neuronal responses. We applied TDA to visually driven single-unit and multiple single-unit spiking activity in macaque V1 and V2. TDA across timescales reveals a common geometry for spiking patterns in V1 and V2 which, among simple models, is most similar to that of a low-dimensional space endowed with Euclidean or hyperbolic geometry with modest curvature. Remarkably, the inferred geometry depends on timescale and is clearest for the timescales that are important for encoding contrast, orientation and spatial correlations.

Error correction and improved precision of spike timing in converging cortical networks

The brain propagates neuronal signals accurately and rapidly. Nevertheless, whether and how a pool of cortical neurons transmits an undistorted message to a target remains unclear. We apply optogenetic white noise signals to small assemblies of cortical pyramidal cells (PYRs) in freely moving mice. The directly activated PYRs exhibit a spike timing precision of several milliseconds. Instead of losing precision, interneurons driven via synaptic activation exhibit higher precision with respect to the white noise signal. Compared with directly activated PYRs, postsynaptic interneuron spike trains allow better signal reconstruction, demonstrating error correction. Data-driven modeling shows that nonlinear amplification of coincident spikes can generate error correction and improved precision. Over multiple applications of the same signal, postsynaptic interneuron spiking is most reliable at timescales ten times shorter than those of the presynaptic PYR, exhibiting temporal coding. Similar results are observed in hippocampal region CA1. Coincidence detection of convergent inputs enables messages to be precisely propagated between cortical PYRs and interneurons.

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PYR-to-interneuron spike transmission exhibits error correction and improved precision

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Interneuron precision is higher when a larger pool of presynaptic PYRs is recruited

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Error correction and improved precision are consistent with coincidence detection

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Interneurons activated by synaptic transmission act as temporal coders

State-dependent activity dynamics of hypothalamic stress effector neurons

The stress response necessitates an immediate boost in vital physiological functions from their homeostatic operation to an elevated emergency response. However, the neural mechanisms underlying this state-dependent change remain largely unknown. Using a combination of in vivo and ex vivo electrophysiology with computational modeling, we report that corticotropin releasing hormone (CRH) neurons in the paraventricular nucleus of the hypothalamus (PVN), the effector neurons of hormonal stress response, rapidly transition between distinct activity states through recurrent inhibition. Specifically, in vivo optrode recording shows that under non-stress conditions, CRH_PVN neurons often fire with rhythmic brief bursts (RB), which, somewhat counterintuitively, constrains firing rate due to long (~2 s) interburst intervals. Stressful stimuli rapidly switch RB to continuous single spiking (SS), permitting a large increase in firing rate. A spiking network model shows that recurrent inhibition can control this activity-state switch, and more broadly the gain of spiking responses to excitatory inputs. In biological CRH_PVN neurons ex vivo, the injection of whole-cell currents derived from our computational model recreates the in vivo-like switch between RB and SS, providing direct evidence that physiologically relevant network inputs enable state-dependent computation in single neurons. Together, we present a novel mechanism for state-dependent activity dynamics in CRH_PVN neurons.

The structures and functions of correlations in neural population codes

The collective activity of a population of neurons, beyond the properties of individual cells, is crucial for many brain functions. A fundamental question is how activity correlations between neurons affect how neural populations process information. Over the past 30 years, major progress has been made on how the levels and structures of correlations shape the encoding of information in population codes. Correlations influence population coding through the organization of pairwise-activity correlations with respect to the similarity of tuning of individual neurons, by their stimulus modulation and by the presence of higher-order correlations. Recent work has shown that correlations also profoundly shape other important functions performed by neural populations, including generating codes across multiple timescales and facilitating information transmission to, and readout by, downstream brain areas to guide behaviour. Here, we review this recent work and discuss how the structures of correlations can have opposite effects on the different functions of neural populations, thus creating trade-offs and constraints for the structure-function relationships of population codes. Further, we present ideas on how to combine large-scale simultaneous recordings of neural populations, computational models, analyses of behaviour, optogenetics and anatomy to unravel how the structures of correlations might be optimized to serve multiple functions.

Internally generated population activity in cortical networks hinders information transmission

How neuronal variability affects sensory coding is a central question in systems neuroscience, often with complex and model-dependent answers. Many studies explore population models with a parametric structure for response tuning and variability, preventing an analysis of how synaptic circuitry establishes neural codes. We study stimulus coding in networks of spiking neuron models with spatially ordered excitatory and inhibitory connectivity. The wiring structure is capable of producing rich population-wide shared neuronal variability that agrees with many features of recorded cortical activity. While both the spatial scales of feedforward and recurrent projections strongly affect noise correlations, only recurrent projections, and in particular inhibitory projections, can introduce correlations that limit the stimulus information available to a decoder. Using a spatial neural field model, we relate the recurrent circuit conditions for information limiting noise correlations to how recurrent excitation and inhibition can form spatiotemporal patterns of population-wide activity.

Does brain activity cause consciousness? A thought experiment

Rapid advances in neuroscience have provided remarkable breakthroughs in understanding the brain on many fronts. Although promising, the role of these advancements in solving the problem of consciousness is still unclear. Based on technologies conceivably within the grasp of modern neuroscience, we discuss a thought experiment in which neural activity, in the form of action potentials, is initially recorded from all the neurons in a participant's brain during a conscious experience and then played back into the same neurons. We consider whether this artificial replay can reconstitute a conscious experience. The possible outcomes of this experiment unravel hidden costs and pitfalls in understanding consciousness from the neurosciences' perspective and challenge the conventional wisdom that causally links action potentials and consciousness.

Multi-regional module-based signal transmission in mouse visual cortex

The visual cortex is hierarchically organized, yet the presence of extensive recurrent and parallel pathways make it challenging to decipher how signals flow between neuronal populations. Here, we tracked the flow of spiking activity recorded from six interconnected levels of the mouse visual hierarchy. By analyzing leading and lagging spike-timing relationships among pairs of simultaneously recorded neurons, we created a cellular-scale directed network graph. Using a module-detection algorithm to cluster neurons based on shared connectivity patterns, we uncovered two multi-regional communication modules distributed across the hierarchy. The direction of signal flow both between and within these modules, differences in layer and area distributions, and distinct temporal dynamics suggest that one module transmits feedforward sensory signals, whereas the other integrates inputs for recurrent processing. These results suggest that multi-regional functional modules may be a fundamental feature of organization beyond cortical areas that supports signal propagation across hierarchical recurrent networks.

Frequency Selectivity of Neural Circuits With Heterogeneous Discrete Transmission Delays

Neurons are connected to other neurons by axons and dendrites that conduct signals with finite velocities, resulting in delays between the firing of a neuron and the arrival of the resultant impulse at other neurons. Since delays greatly complicate the analytical treatment and interpretation of models, they are usually neglected or taken to be uniform, leading to a lack in the comprehension of the effects of delays in neural systems. This letter shows that heterogeneous transmission delays make small groups of neurons respond selectively to inputs with differing frequency spectra. By studying a single integrate-and-fire neuron receiving correlated time-shifted inputs, it is shown how the frequency response is linked to both the strengths and delay times of the afferent connections. The results show that incorporating delays alters the functioning of neural networks, and changes the effect that neural connections and synaptic strengths have.

Correlations enhance the behavioral readout of neural population activity in association cortex

Noise correlations (that is, trial-to-trial covariations in neural activity for a given stimulus) limit the stimulus information encoded by neural populations, leading to the widely held prediction that they impair perceptual discrimination behaviors. However, this prediction neglects the effects of correlations on information readout. We studied how correlations affect both encoding and readout of sensory information. We analyzed calcium imaging data from mouse posterior parietal cortex during two perceptual discrimination tasks. Correlations reduced the encoded stimulus information, but, seemingly paradoxically, were higher when mice made correct rather than incorrect choices. Single-trial behavioral choices depended not only on the stimulus information encoded by the whole population, but unexpectedly also on the consistency of information across neurons and time. Because correlations increased information consistency, they enhanced the conversion of sensory information into behavioral choices, overcoming their detrimental information-limiting effects. Thus, correlations in association cortex can benefit task performance even if they decrease sensory information.

A Functional Spiking Neural Network of Ultra Compact Neurons

We demonstrate that recently introduced ultra-compact neurons (UCN) with a minimal number of components can be interconnected to implement a functional spiking neural network. For concreteness we focus on the Jeffress model, which is a classic neuro-computational model proposed in the 40’s to explain the sound directionality detection by animals and humans. In addition, we introduce a long-axon neuron, whose architecture is inspired by the Hodgkin-Huxley axon delay-line and where the UCNs implement the nodes of Ranvier. We then interconnect two of those neurons to an output layer of UCNs, which detect coincidences between spikes propagating down the long-axons. This functional spiking neural neuron circuit with biological relevance is built from identical UCN blocks, which are simple enough to be made with off-the-shelf electronic components. Our work realizes a new, accessible and affordable physical model platform, where neuroscientists can construct arbitrary mid-size spiking neuronal networks in a lego-block like fashion that work in continuous time. This should enable them to address in a novel experimental manner fundamental questions about the nature of the neural code and to test predictions from mathematical models and algorithms of basic neurobiology research. The present work aims at opening a new experimental field of basic research in Spiking Neural Networks to a potentially large community, which is at the crossroads of neurobiology, dynamical systems, theoretical neuroscience, condensed matter physics, neuromorphic engineering, artificial intelligence, and complex systems.

Spontaneous Activity of Neuronal Ensembles in Mouse Motor Cortex: Changes after GABAergic Blockade

The mouse motor cortex exhibits spontaneous activity in the form of temporal sequences of neuronal ensembles in vitro without the need of tissue stimulation. These neuronal ensembles are defined as groups of neurons with a strong correlation between its firing patterns, generating what appears to be a predetermined neural conduction mode that needs study. Each ensemble is commonly accompanied by one or more parvalbumin expressing neurons (PV+) or fast spiking interneurons. Many of these interneurons have functional connections between them, helping to form a circuit configuration similar to a small-world network. However, rich club metrics show that most connected neurons are neurons not expressing parvalbumin, mainly pyramidal neurons (PV-) suggesting feed-forward propagation through pyramidal cells. Ensembles with PV+ neurons are connected to these hubs. When ligand-gated fast GABAergic transmission is blocked, temporal sequences of ensembles collapse into a unique synchronous and recurrent ensemble, showing the need of inhibition for coding cortical spontaneous activity. This new ensemble has a duration and electrophysiological characteristics of brief recurrent interictal epileptiform discharges (IEDs) composed by the coactivity of both PV- and PV+ neurons, demonstrating that GABA transmission impedes its occurrence. Synchronous ensembles are clearly divided into two clusters one of them lasting longer and mainly composed by PV+ neurons. Because an ictal-like event was not recorded after several minutes of IEDs recording, it is inferred that an external stimulus and/or fast GABA transmission are necessary for its appearance, making this preparation ideal to study both the neuronal machinery to encode cortical spontaneous activity and its transformation into brief non-ictal epileptiform discharges.

Information filtering by coincidence detection of synchronous population output: analytical approaches to the coherence function of a two-stage neural system

Information about time-dependent sensory stimuli is encoded in the activity of neural populations; distinct aspects of the stimulus are read out by different types of neurons: while overall information is perceived by integrator cells, so-called coincidence detector cells are driven mainly by the synchronous activity in the population that encodes predominantly high-frequency content of the input signal (high-pass information filtering). Previously, an analytically accessible statistic called the partial synchronous output was introduced as a proxy for the coincidence detector cell's output in order to approximate its information transmission. In the first part of the current paper, we compare the information filtering properties (specifically, the coherence function) of this proxy to those of a simple coincidence detector neuron. We show that the latter's coherence function can indeed be well-approximated by the partial synchronous output with a time scale and threshold criterion that are related approximately linearly to the membrane time constant and firing threshold of the coincidence detector cell. In the second part of the paper, we propose an alternative theory for the spectral measures (including the coherence) of the coincidence detector cell that combines linear-response theory for shot-noise driven integrate-and-fire neurons with a novel perturbation ansatz for the spectra of spike-trains driven by colored noise. We demonstrate how the variability of the synaptic weights for connections from the population to the coincidence detector can shape the information transmission of the entire two-stage system.

Effects of network topologies on stochastic resonance in feedforward neural network

The effects of network topologies on signal propagation are studied in noisy feedforward neural network in detail, where the network topologies are modulated by changing both the in-degree and out-degree distributions of FFNs as identical, uniform and exponential respectively. Stochastic resonance appeared in three FFNs when the same external stimuli and noise are applied to the three different network topologies. It is found that optimal noise intensity decreases with the increase of network's layer index. Meanwhile, the Q index of FFN with identical distribution is higher than that of the other two FFNs, indicating that the synchronization between the neuronal firing activities and the external stimuli is more obvious in FFN with identical distribution. The optimal parameter regions for the time cycle of external stimuli and the noise intensity are found for three FFNs, in which the resonance is more easily induced when the parameters of stimuli are set in this region. Furthermore, the relationship between the in-degree, the average membrane potential and the resonance performance is studied at the neuronal level, where it is found that both the average membrane potentials and the Q indexes of neurons in FFN with identical degree distribution is more consistent with each other than that of the other two FFNs due to their network topologies. In summary, the simulations here indicate that the network topologies play essential roles in affecting the signal propagation of FFNs.

Portraits of communication in neuronal networks

The brain is organized as a network of highly specialized networks of spiking neurons. To exploit such a modular architecture for computation, the brain has to be able to regulate the flow of spiking activity between these specialized networks. In this Opinion article, we review various prominent mechanisms that may underlie communication between neuronal networks. We show that communication between neuronal networks can be understood as trajectories in a two-dimensional state space, spanned by the properties of the input. Thus, we propose a common framework to understand neuronal communication mediated by seemingly different mechanisms. We also suggest that the nesting of slow (for example, alpha-band and theta-band) oscillations and fast (gamma-band) oscillations can serve as an important control mechanism that allows or prevents spiking signals to be routed between specific networks. We argue that slow oscillations can modulate the time required to establish network resonance or entrainment and, thereby, regulate communication between neuronal networks.

Degeneracy in hippocampal physiology and plasticity

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis that point to the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross-interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding-homeostasis system in accomplishing its tasks in an input- and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals.

Propagation of temporal and rate signals in cultured multilayer networks

Analyses of idealized feedforward networks suggest that several conditions have to be satisfied in order for activity to propagate faithfully across layers. Verifying these concepts experimentally has been difficult owing to the vast number of variables that must be controlled. Here, we cultured cortical neurons in a chamber with sequentially connected compartments, optogenetically stimulated individual neurons in the first layer with high spatiotemporal resolution, and then monitored the subthreshold and suprathreshold potentials in subsequent layers. Brief stimuli delivered to the first layer evoked a short-latency transient response followed by sustained activity. Rate signals, carried by the sustained component, propagated reliably through 4 layers, unlike idealized feedforward networks, which tended strongly towards synchrony. Moreover, temporal jitter in the stimulus was transformed into a rate code and transmitted to the last layer. This novel mode of propagation occurred in the balanced excitatory-inhibitory regime and is mediated by NMDA-mediated receptors and recurrent activity.

Reliable Sequential Activation of Neural Assemblies by Single Pyramidal Cells in a Three-Layered Cortex

Recent studies reveal the occasional impact of single neurons on surround firing statistics and even simple behaviors. Exploiting the advantages of a simple cortex, we examined the influence of single pyramidal neurons on surrounding cortical circuits. Brief activation of single neurons triggered reliable sequences of firing in tens of other excitatory and inhibitory cortical neurons, reflecting cascading activity through local networks, as indicated by delayed yet precisely timed polysynaptic subthreshold potentials. The evoked patterns were specific to the pyramidal cell of origin, extended over hundreds of micrometers from their source, and unfolded over up to 200 ms. Simultaneous activation of pyramidal cell pairs indicated balanced control of population activity, preventing paroxysmal amplification. Single cortical pyramidal neurons can thus trigger reliable postsynaptic activity that can propagate in a reliable fashion through cortex, generating rapidly evolving and non-random firing sequences reminiscent of those observed in mammalian hippocampus during "replay" and in avian song circuits.

Characteristics of Waveform Shape in Parkinson's Disease Detected with Scalp Electroencephalography

Neural activity in the β frequency range (13-30 Hz) is excessively synchronized in Parkinson's disease (PD). Previous work using invasive intracranial recordings and non-invasive scalp electroencephalography (EEG) has shown that correlations between β phase and broad-band γ (>50 Hz) amplitude [i.e., phase amplitude coupling (PAC)] are elevated in PD, perhaps a reflection of this synchrony. Recently, it has also been shown, in invasive human recordings, that non-sinusoidal features of β oscillation shape also characterize PD. Here, we show that these features of β waveform shape also distinguish PD patients on and off medication using non-invasive recordings in a dataset of 15 PD patients with resting scalp EEG. Specifically, β oscillations over sensorimotor electrodes in PD patients off medication had greater sharpness asymmetry and steepness asymmetry than on medication (sign rank, p < 0.02, corrected). We also showed that β oscillations over sensorimotor cortex most often had a canonical shape, and that using this prototypical shape as an inclusion criteria increased the effect size of our findings. Together, our findings suggest that novel ways of measuring β synchrony that incorporate waveform shape could improve detection of PD pathophysiology in non-invasive recordings. Moreover, they motivate the consideration of waveform shape in future EEG studies.

Detection of Multiway Gamma Coordination Reveals How Frequency Mixing Shapes Neural Dynamics

A principle of communication technology, frequency mixing, describes how novel oscillations are generated when rhythmic inputs converge on a nonlinearly activating target. As expected given that neurons are nonlinear integrators, it was demonstrated that neuronal networks exhibit mixing in response to imposed oscillations of known frequencies. However, determining when mixing occurs in spontaneous conditions, where weaker or more variable rhythms prevail, has remained impractical. Here, we show that, by exploiting the predicted phase (rather than frequency) relationships between oscillations, the contributions of mixing can be readily identified, even in small samples of noisy data. Assessment of extracellular data using this approach revealed that frequency mixing is widely expressed in a state- and region-dependent manner and that oscillations emerging from mixing entrain unit activity. Frequency mixing is thus intrinsic to the structure of neural activity and contributes importantly to neural dynamics.

Modeling the Correlated Activity of Neural Populations: A Review

The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the importance of collective effects in populations of neurons, only in the past two decades has it become possible to record from many cells simultaneously using advanced experimental techniques with single-spike resolution and to relate these correlations to function and behavior. This review focuses on the modeling and inference approaches that have been recently developed to describe the correlated spiking activity of populations of neurons. We cover a variety of models describing correlations between pairs of neurons, as well as between larger groups, synchronous or delayed in time, with or without the explicit influence of the stimulus, and including or not latent variables. We discuss the advantages and drawbacks or each method, as well as the computational challenges related to their application to recordings of ever larger populations.

Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity

Many neurons possess dendrites enriched with sodium channels and are capable of generating action potentials. However, the role of dendritic sodium spikes remain unclear. Here, we study computational models of neurons to investigate the functional effects of dendritic spikes. In agreement with previous studies, we found that point neurons or neurons with passive dendrites increase their somatic firing rate in response to the correlation of synaptic bombardment for a wide range of input conditions, i.e. input firing rates, synaptic conductances, or refractory periods. However, neurons with active dendrites show the opposite behavior: for a wide range of conditions the firing rate decreases as a function of correlation. We found this property in three types of models of dendritic excitability: a Hodgkin-Huxley model of dendritic spikes, a model with integrate and fire dendrites, and a discrete-state dendritic model. We conclude that fast dendritic spikes confer much broader computational properties to neurons, sometimes opposite to that of point neurons.

Data-Driven Modeling of Cholinergic Modulation of Neural Microcircuits: Bridging Neurons, Synapses and Network Activity

Neuromodulators, such as acetylcholine (ACh), control information processing in neural microcircuits by regulating neuronal and synaptic physiology. Computational models and simulations enable predictions on the potential role of ACh in reconfiguring network activity. As a prelude into investigating how the cellular and synaptic effects of ACh collectively influence emergent network dynamics, we developed a data-driven framework incorporating phenomenological models of the physiology of cholinergic modulation of neocortical cells and synapses. The first-draft models were integrated into a biologically detailed tissue model of neocortical microcircuitry to investigate the effects of levels of ACh on diverse neuron types and synapses, and consequently on emergent network activity. Preliminary simulations from the framework, which was not tuned to reproduce any specific ACh-induced network effects, not only corroborate the long-standing notion that ACh desynchronizes spontaneous network activity, but also predict that a dose-dependent activation of ACh gives rise to a spectrum of neocortical network activity. We show that low levels of ACh, such as during non-rapid eye movement (nREM) sleep, drive microcircuit activity into slow oscillations and network synchrony, whereas high ACh concentrations, such as during wakefulness and REM sleep, govern fast oscillations and network asynchrony. In addition, spontaneous network activity modulated by ACh levels shape spike-time cross-correlations across distinct neuronal populations in strikingly different ways. These effects are likely due to the regulation of neurons and synapses caused by increasing levels of ACh, which enhances cellular excitability and decreases the efficacy of local synaptic transmission. We conclude by discussing future directions to refine the biological accuracy of the framework, which will extend its utility and foster the development of hypotheses to investigate the role of neuromodulators in neural information processing.

Local field potentials of subthalamic nucleus contain electrophysiological footprints of motor subtypes of Parkinson's disease

Although motor subtypes of Parkinson's disease (PD), such as tremor dominant (TD) and postural instability and gait difficulty (PIGD), have been defined based on symptoms since the mid-1990s, no underlying neural correlates of these clinical subtypes have yet been identified. Very limited data exist regarding the electrophysiological abnormalities within the subthalamic nucleus (STN) that likely accompany the symptom severity or the phenotype of PD. Here, we show that activity in subbands of local field potentials (LFPs) recorded with multiple microelectrodes from subterritories of STN provide distinguishing neurophysiological information about the motor subtypes of PD. We studied 24 patients with PD and found distinct patterns between TD (n = 13) and PIGD (n = 11) groups in high-frequency oscillations (HFOs) and their nonlinear interactions with beta band in the superior and inferior regions of the STN. Particularly, in the superior region of STN, the power of the slow HFO (sHFO) (200-260 Hz) and the coupling of its amplitude with beta-band phase were significantly stronger in the TD group. The inferior region of STN exhibited fast HFOs (fHFOs) (260-450 Hz), which have a significantly higher center frequency in the PIGD group. The cross-frequency coupling between fHFOs and beta band in the inferior region of STN was significantly stronger in the PIGD group. Our results indicate that the spatiospectral dynamics of STN-LFPs can be used as an objective method to distinguish these two motor subtypes of PD. These observations might lead to the development of sensing and stimulation strategies targeting the subterritories of STN for the personalization of deep-brain stimulation (DBS).

Epileptic pilocarpine-treated rats exhibit aberrant hippocampal EPSP-spike potentiation but retain long-term potentiation

Hippocampal neuron plasticity is strongly associated with learning, memory, and cognition. In addition to modification of synaptic function and connectivity, the capacity of hippocampal neurons to undergo plasticity involves the ability to change nonsynaptic excitability. This includes altering the probability that EPSPs will generate action potentials (E‐S plasticity). Epilepsy is a prevalent neurological disorder commonly associated with neuronal hyperexcitability and cognitive dysfunction. We examined E‐S plasticity in chronically epileptic Sprague–Dawley rats 3–10 weeks after pilocarpine‐induced status epilepticus. CA1 neurons in hippocampal slices were assayed by whole‐cell current clamp to measure EPSPs evoked by Schaffer collateral stimulation. Using a weak spike‐timing‐dependent protocol to induce plasticity, we found robust E‐S potentiation in conjunction with weak long‐term potentiation (LTP) in saline‐treated rats. In pilocarpine‐treated rats, a similar degree of LTP was found, but E‐S potentiation was reduced. Additionally, the degree of E‐S potentiation was not correlated with the degree of LTP for either group, suggesting that they independently contribute to neuronal plasticity. E‐S potentiation also differed from LTP in that E‐S plasticity could be induced solely from action potentials generated by postsynaptic current injection. The calcium chelating agent BAPTA in the intracellular solution blocked LTP and E‐S potentiation, revealing the calcium dependence of both processes. These findings suggest that LTP and E‐S potentiation have overlapping but nonidentical mechanisms of inducing neuronal plasticity that may independently contribute to cognitive disruptions observed in the chronic epileptic state.

Transmission of temporally correlated spike trains through synapses with short-term depression

Short-term synaptic depression, caused by depletion of releasable neurotransmitter, modulates the strength of neuronal connections in a history-dependent manner. Quantifying the statistics of synaptic transmission requires stochastic models that link probabilistic neurotransmitter release with presynaptic spike-train statistics. Common approaches are to model the presynaptic spike train as either regular or a memory-less Poisson process: few analytical results are available that describe depressing synapses when the afferent spike train has more complex, temporally correlated statistics such as bursts. Here we present a series of analytical results—from vesicle release-site occupancy statistics, via neurotransmitter release, to the post-synaptic voltage mean and variance—for depressing synapses driven by correlated presynaptic spike trains. The class of presynaptic drive considered is that fully characterised by the inter-spike-interval distribution and encompasses a broad range of models used for neuronal circuit and network analyses, such as integrate-and-fire models with a complete post-spike reset and receiving sufficiently short-time correlated drive. We further demonstrate that the derived post-synaptic voltage mean and variance allow for a simple and accurate approximation of the firing rate of the post-synaptic neuron, using the exponential integrate-and-fire model as an example. These results extend the level of biological detail included in models of synaptic transmission and will allow for the incorporation of more complex and physiologically relevant firing patterns into future studies of neuronal networks.

Synapses between neurons transmit signals with strengths that vary with the history of their activity, over scales from milliseconds to decades. Short-term changes in synaptic strength modulate and sculpt ongoing neuronal activity, whereas long-term changes underpin memory formation. Here we focus on changes of strength over timescales of less than a second caused by transitory depletion of the neurotransmitters that carry signals across the synapse. Neurotransmitters are stored in small vesicles that release their contents, with a certain probability, when the presynaptic neuron is active. Once a vesicle has been used it is replenished after a variable delay. There is therefore a complex interaction between the pattern of incoming signals to the synapse and the probablistic release and restock of packaged neurotransmitter. Here we extend existing models to examine how correlated synaptic activity is transmitted through synapses and affects the voltage fluctuations and firing rate of the target neuron. Our results provide a framework that will allow for the inclusion of biophysically realistic synaptic behaviour in studies of neuronal circuits.

Single synaptic inputs drive high-precision action potentials in parvalbumin expressing GABA-ergic cortical neurons in vivo

A defining feature of cortical layer 2/3 excitatory neurons is their sparse activity, often firing in singlets of action potentials. Local inhibitory neurons are thought to play a major role in regulating sparseness, but which cell types are recruited by single excitatory synaptic inputs is unknown. Using multiple, targeted, in vivo whole-cell recordings, we show that single _uEPSPs have little effect on the firing rates of excitatory neurons and somatostatin-expressing GABA-ergic inhibitory neurons but evoke precisely timed action potentials in parvalbumin-expressing inhibitory neurons. Despite a _uEPSP decay time of 7.8 ms, the evoked action potentials were almost completely restricted to the _uEPSP rising phase (~0.5 ms). Evoked parvalbumin-expressing neuron action potentials go on to inhibit the local excitatory network, thus providing a pathway for single spike evoked disynaptic inhibition which may enforce sparse and precisely timed cortical signaling.

Mutual Information and Information Gating in Synfire Chains

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains—SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

Effects of topologies on signal propagation in feedforward networks

We systematically investigate the effects of topologies on signal propagation in feedforward networks (FFNs) based on the FitzHugh-Nagumo neuron model. FFNs with different topological structures are constructed with same number of both in-degrees and out-degrees in each layer and given the same input signal. The propagation of firing patterns and firing rates are found to be affected by the distribution of neuron connections in the FFNs. Synchronous firing patterns emerge in the later layers of FFNs with identical, uniform, and exponential degree distributions, but the number of synchronous spike trains in the output layers of the three topologies obviously differs from one another. The firing rates in the output layers of the three FFNs can be ordered from high to low according to their topological structures as exponential, uniform, and identical distributions, respectively. Interestingly, the sequence of spiking regularity in the output layers of the three FFNs is consistent with the firing rates, but their firing synchronization is in the opposite order. In summary, the node degree is an important factor that can dramatically influence the neuronal network activity.

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.

Long Synfire Chains Emerge by Spike-Timing Dependent Plasticity Modulated by Population Activity

Sequences of precisely timed neuronal activity are observed in many brain areas in various species. Synfire chains are a well-established model that can explain such sequences. However, it is unknown under which conditions synfire chains can develop in initially unstructured networks by self-organization. This work shows that with spike-timing dependent plasticity (STDP), modulated by global population activity, long synfire chains emerge in sparse random networks. The learning rule fosters neurons to participate multiple times in the chain or in multiple chains. Such reuse of neurons has been experimentally observed and is necessary for high capacity. Sparse networks prevent the chains from being short and cyclic and show that the formation of specific synapses is not essential for chain formation. Analysis of the learning rule in a simple network of binary threshold neurons reveals the asymptotically optimal length of the emerging chains. The theoretical results generalize to simulated networks of conductance-based leaky integrate-and-fire (LIF) neurons. As an application of the emerged chain, we propose a one-shot memory for sequences of precisely timed neuronal activity.

Linking structure and activity in nonlinear spiking networks

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks’ spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities—including those of different cell types—combine with connectivity to shape population activity and function.

Neuronal networks, like many biological systems, exhibit variable activity. This activity is shaped by both the underlying biology of the component neurons and the structure of their interactions. How can we combine knowledge of these two things—that is, models of individual neurons and of their interactions—to predict the statistics of single- and multi-neuron activity? Current approaches rely on linearizing neural activity around a stationary state. In the face of neural nonlinearities, however, these linear methods can fail to predict spiking statistics and even fail to correctly predict whether activity is stable or pathological. Here, we show how to calculate any spike train cumulant in a broad class of models, while systematically accounting for nonlinear effects. We then study a fundamental effect of nonlinear input-rate transfer–coupling between different orders of spiking statistic–and how this depends on single-neuron and network properties.

Mechanisms underlying a thalamocortical transformation during active tactile sensation

During active somatosensation, neural signals expected from movement of the sensors are suppressed in the cortex, whereas information related to touch is enhanced. This tactile suppression underlies low-noise encoding of relevant tactile features and the brain’s ability to make fine tactile discriminations. Layer (L) 4 excitatory neurons in the barrel cortex, the major target of the somatosensory thalamus (VPM), respond to touch, but have low spike rates and low sensitivity to the movement of whiskers. Most neurons in VPM respond to touch and also show an increase in spike rate with whisker movement. Therefore, signals related to self-movement are suppressed in L4. Fast-spiking (FS) interneurons in L4 show similar dynamics to VPM neurons. Stimulation of halorhodopsin in FS interneurons causes a reduction in FS neuron activity and an increase in L4 excitatory neuron activity. This decrease of activity of L4 FS neurons contradicts the "paradoxical effect" predicted in networks stabilized by inhibition and in strongly-coupled networks. To explain these observations, we constructed a model of the L4 circuit, with connectivity constrained by in vitro measurements. The model explores the various synaptic conductance strengths for which L4 FS neurons actively suppress baseline and movement-related activity in layer 4 excitatory neurons. Feedforward inhibition, in concert with recurrent intracortical circuitry, produces tactile suppression. Synaptic delays in feedforward inhibition allow transmission of temporally brief volleys of activity associated with touch. Our model provides a mechanistic explanation of a behavior-related computation implemented by the thalamocortical circuit.

We study how information is transformed between connected brain areas: the thalamus, the gateway to the cortex, and layer 4 (L4) in cortex, which is the first station to process sensory input from the thalamus. When mice perform an active object localization task with their whiskers, thalamic neurons and inhibitory fast-spiking (FS) interneurons in L4 encode whisker movement and touch, whereas L4 excitatory neurons respond almost exclusively to touch. To explain these observations, we constructed a computational model based on measured circuit parameters. The model reveals that without touch, when thalamic activity varies slowly, strong inhibition from FS neurons prevents activity in L4 excitatory neurons. Brief and strong touch-induced thalamic activity excites both excitatory and FS neurons in L4. FS neurons inhibit excitatory neurons with a delay of approximately 1 ms relative to ascending excitation, allowing L4 excitatory neurons to spike. Our results demonstrate that cortical circuits exploit synaptic delays for fast computations. Similar mechanisms likely also operate for rapid stimuli in the visual and auditory systems.

A Model of Fast Hebbian Spike Latency Normalization

Hebbian changes of excitatory synapses are driven by and enhance correlations between pre- and postsynaptic neuronal activations, forming a positive feedback loop that can lead to instability in simulated neural networks. Because Hebbian learning may occur on time scales of seconds to minutes, it is conjectured that some form of fast stabilization of neural firing is necessary to avoid runaway of excitation, but both the theoretical underpinning and the biological implementation for such homeostatic mechanism are to be fully investigated. Supported by analytical and computational arguments, we show that a Hebbian spike-timing-dependent metaplasticity rule, accounts for inherently-stable, quick tuning of the total input weight of a single neuron in the general scenario of asynchronous neural firing characterized by UP and DOWN states of activity.

Nonsinusoidal Beta Oscillations Reflect Cortical Pathophysiology in Parkinson's Disease

Oscillations in neural activity play a critical role in neural computation and communication. There is intriguing new evidence that the nonsinusoidal features of the oscillatory waveforms may inform underlying physiological and pathophysiological characteristics. Time-domain waveform analysis approaches stand in contrast to traditional Fourier-based methods, which alter or destroy subtle waveform features. Recently, it has been shown that the waveform features of oscillatory beta (13-30 Hz) events, a prominent motor cortical oscillation, may reflect near-synchronous excitatory synaptic inputs onto cortical pyramidal neurons. Here we analyze data from invasive human primary motor cortex (M1) recordings from patients with Parkinson's disease (PD) implanted with a deep brain stimulator (DBS) to test the hypothesis that the beta waveform becomes less sharp with DBS, suggesting that M1 input synchrony may be decreased. We find that, in PD, M1 beta oscillations have sharp, asymmetric, nonsinusoidal features, specifically asymmetries in the ratio between the sharpness of the beta peaks compared with the troughs. This waveform feature is nearly perfectly correlated with beta-high gamma phase-amplitude coupling (r = 0.94), a neural index previously shown to track PD-related motor deficit. Our results suggest that the pathophysiological beta generator is altered by DBS, smoothing out the beta waveform. This has implications not only for the interpretation of the physiological mechanism by which DBS reduces PD-related motor symptoms, but more broadly for our analytic toolkit in general. That is, the often-overlooked time-domain features of oscillatory waveforms may carry critical physiological information about neural processes and dynamics.SIGNIFICANCE STATEMENT To better understand the neural basis of cognition and disease, we need to understand how groups of neurons interact to communicate with one another. For example, there is evidence that parkinsonian bradykinesia and rigidity may arise from an oversynchronization of afferents to the motor cortex, and that these symptoms are treatable using deep brain stimulation. Here we show that the waveform shape of beta (13-30 Hz) oscillations, which may reflect input synchrony onto the cortex, is altered by deep brain stimulation. This suggests that mechanistic inferences regarding physiological and pathophysiological neural communication may be made from the temporal dynamics of oscillatory waveform shape.

Systems-based analysis of dendritic nonlinearities reveals temporal feature extraction in mouse L5 cortical neurons

What do dendritic nonlinearities tell a neuron about signals injected into the dendrite? Linear and nonlinear dendritic components affect how time-varying inputs are transformed into action potentials (APs), but the relative contribution of each component is unclear. We developed a novel systems-identification approach to isolate the nonlinear response of layer 5 pyramidal neuron dendrites in mouse prefrontal cortex in response to dendritic current injections. We then quantified the nonlinear component and its effect on the soma, using functional models composed of linear filters and static nonlinearities. Both noise and waveform current injections revealed linear and nonlinear components in the dendritic response. The nonlinear component consisted of fast Na⁺ spikes that varied in amplitude 10-fold in a single neuron. A functional model reproduced the timing and amplitude of the dendritic spikes and revealed that they were selective to a preferred input dynamic (~4.5 ms rise time). The selectivity of the dendritic spikes became wider in the presence of additive noise, which was also predicted by the functional model. A second functional model revealed that the dendritic spikes were weakly boosted before being linearly integrated at the soma. For both our noise and waveform dendritic input, somatic APs were dependent on the somatic integration of the stimulus, followed a subset of large dendritic spikes, and were selective to the same input dynamics preferred by the dendrites. Our results suggest that the amplitude of fast dendritic spikes conveys information about high-frequency features in the dendritic input, which is then combined with low-frequency somatic integration.NEW & NOTEWORTHY The nonlinear response of layer 5 mouse pyramidal dendrites was isolated with a novel systems-based approach. In response to dendritic current injections, the nonlinear component contained mostly fast, variable-amplitude, Na⁺ spikes. A functional model accounted for the timing and amplitude of the dendritic spikes and revealed that dendritic spikes are selective to a preferred input dynamic, which was verified experimentally. Thus, fast dendritic nonlinearities behave as high-frequency feature detectors that influence somatic action potentials.

Multichannel activity propagation across an engineered axon network

OBJECTIVE

Although substantial progress has been made in mapping the connections of the brain, less is known about how this organization translates into brain function. In particular, the massive interconnectivity of the brain has made it difficult to specifically examine data transmission between two nodes of the connectome, a central component of the 'neural code.' Here, we investigated the propagation of multiple streams of asynchronous neuronal activity across an isolated in vitro 'connectome unit.'

APPROACH

We used the novel technique of axon stretch growth to create a model of a long-range cortico-cortical network, a modular system consisting of paired nodes of cortical neurons connected by axon tracts. Using optical stimulation and multi-electrode array recording techniques, we explored how input patterns are represented by cortical networks, how these representations shift as they are transmitted between cortical nodes and perturbed by external conditions, and how well the downstream node distinguishes different patterns.

MAIN RESULTS

Stimulus representations included direct, synaptic, and multiplexed responses that grew in complexity as the distance between the stimulation source and recorded neuron increased. These representations collapsed into patterns with lower information content at higher stimulation frequencies. With internodal activity propagation, a hierarchy of network pathways, including latent circuits, was revealed using glutamatergic blockade. As stimulus channels were added, divergent, non-linear effects were observed in local versus distant network layers. Pairwise difference analysis of neuronal responses suggested that neuronal ensembles generally outperformed individual cells in discriminating input patterns.

SIGNIFICANCE

Our data illuminate the complexity of spiking activity propagation in cortical networks in vitro, which is characterized by the transformation of an input into myriad outputs over several network layers. These results provide insight into how the brain potentially processes information and generates the neural code and could guide the development of clinical therapies based on multichannel brain stimulation.

Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.

Simultaneous analysis of large-scale neural populations is necessary to understand coding principles of neurons because they concertedly process information. Methods of thermodynamics and statistical mechanics are useful to understand collective phenomena of the interacting elements, and they have been successfully used to understand diverse activity of neurons. However, most analysis methods assume stationary data, in which activity rates of neurons and their correlations are constant over time. This assumption is easily violated in the data recorded from awake animals. Neural correlations likely organize dynamically during behavior and cognition, and this may be independent from the modulated activity rates of individual neurons. Recently several methods were proposed to simultaneously estimate dynamics of neural interactions. However, these methods are applicable to up to about 10 neurons. Here by combining multiple analytic approximation methods, we made it possible to estimate time-varying interactions of much larger neural populations. The method allows us to trace dynamic macroscopic properties of neural circuitries such as sparseness, entropy, and sensitivity. Using these statistics, researchers can now quantify to what extent neurons are correlated or de-correlated, and test if neural systems are susceptible within a specific behavioral period.

Patterns of synchrony for feed-forward and auto-regulation feed-forward neural networks

We consider feed-forward and auto-regulation feed-forward neural (weighted) coupled cell networks. In feed-forward neural networks, cells are arranged in layers such that the cells of the first layer have empty input set and cells of each other layer receive only inputs from cells of the previous layer. An auto-regulation feed-forward neural coupled cell network is a feed-forward neural network where additionally some cells of the first layer have auto-regulation, that is, they have a self-loop. Given a network structure, a robust pattern of synchrony is a space defined in terms of equalities of cell coordinates that is flow-invariant for any coupled cell system (with additive input structure) associated with the network. In this paper, we describe the robust patterns of synchrony for feed-forward and auto-regulation feed-forward neural networks. Regarding feed-forward neural networks, we show that only cells in the same layer can synchronize. On the other hand, in the presence of auto-regulation, we prove that cells in different layers can synchronize in a robust way and we give a characterization of the possible patterns of synchrony that can occur for auto-regulation feed-forward neural networks.

Propagation of Collective Temporal Regularity in Noisy Hierarchical Networks

Neuronal communication between different brain areas is achieved in terms of spikes. Consequently, spike-time regularity is closely related to many cognitive tasks and timing precision of neural information processing. A recent experiment on primate parietal cortex reports that spike-time regularity increases consistently from primary sensory to higher cortical regions. This observation conflicts with the influential view that spikes in the neocortex are fundamentally irregular. To uncover the underlying network mechanism, we construct a multilayered feedforward neural information transmission pathway and investigate how spike-time regularity evolves across subsequent layers. Numerical results reveal that despite the obviously irregular spiking patterns in previous several layers, neurons in downstream layers can generate rather regular spikes, which depends on the network topology. In particular, we find that collective temporal regularity in deeper layers exhibits resonance-like behavior with respect to both synaptic connection probability and synaptic weight, i.e., the optimal topology parameter maximizes the spike-timing regularity. Furthermore, it is demonstrated that synaptic properties, including inhibition, synaptic transient dynamics, and plasticity, have significant impacts on spike-timing regularity propagation. The emergence of the increasingly regular spiking (RS) patterns in higher parietal regions can, thus, be viewed as a natural consequence of spiking activity propagation between different brain areas. Finally, we validate an important function served by increased RS: promoting reliable propagation of spike-rate signals across downstream layers.

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.

Shaping Neural Circuits by High Order Synaptic Interactions

Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected in previous theoretical treatments, and can be described as a sum over contributions from structural motifs. These interactions can have a pivotal influence on the connectivity patterns that emerge under the influence of STDP. In particular, we consider two highly ordered forms of structure: wide synfire chains, in which groups of neurons project to each other sequentially, and self connected assemblies. We show that high order synaptic interactions can enable the formation of both structures, depending on the form of the STDP function and the time course of synaptic currents. Furthermore, within a certain regime of biophysical parameters, emergence of the ordered connectivity occurs robustly and autonomously in a stochastic network of spiking neurons, without a need to expose the neural network to structured inputs during learning.

Plasticity between neural connections plays a key role in our ability to process and store information. One of the fundamental questions on plasticity, is the extent to which local processes, affecting individual synapses, are responsible for large scale structures of neural connectivity. Here we focus on two types of structures: synfire chains and self connected assemblies. These structures are often proposed as forms of neural connectivity that can support brain functions such as memory and generation of motor activity. We show that an important plasticity mechanism, spike timing dependent plasticity, can lead to autonomous emergence of these large scale structures in the brain: in contrast to previous theoretical proposals, we show that the emergence can occur autonomously even if instructive signals are not fed into the neural network while its form is shaped by synaptic plasticity.

Emergence of Narrowband High Frequency Oscillations from Asynchronous, Uncoupled Neural Firing

Previous experimental studies have demonstrated the emergence of narrowband local field potential oscillations during epileptic seizures in which the underlying neural activity appears to be completely asynchronous. We derive a mathematical model explaining how this counterintuitive phenomenon may occur, showing that a population of independent, completely asynchronous neurons may produce narrowband oscillations if each neuron fires quasi-periodically, without requiring any intrinsic oscillatory cells or feedback inhibition. This quasi-periodicity can occur through cells with similar frequency-current ([Formula: see text]-[Formula: see text]) curves receiving a similar, high amount of uncorrelated synaptic noise. Thus, this source of oscillatory behavior is distinct from the usual cases (pacemaker cells entraining a network, or oscillations being an inherent property of the network structure), as it requires no oscillatory drive nor any specific network or cellular properties other than cells that repetitively fire with continual stimulus. We also deduce bounds on the degree of variability in neural spike-timing which will permit the emergence of such oscillations, both for action potential- and postsynaptic potential-dominated LFPs. These results suggest that even an uncoupled network may generate collective rhythms, implying that the breakdown of inhibition and high synaptic input often observed during epileptic seizures may generate narrowband oscillations. We propose that this mechanism may explain why so many disparate epileptic and normal brain mechanisms can produce similar high frequency oscillations.