Computation by ensemble synchronization in recurrent networks with synaptic depression

Shaping dynamical neural computations using spatiotemporal constraints

Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant multidisciplinary progress has been made in bridging the gap between how we understand biological versus artificial computation, including how insights gained from one can translate to the other. Research has revealed that neurobiology is a key determinant of brain network architecture, which gives rise to spatiotemporally constrained patterns of activity that underlie computation. Here, we discuss how neural systems use dynamics for computation, and claim that the biological constraints that shape brain networks may be leveraged to improve the implementation of artificial neural networks. To formalize this discussion, we consider a natural artificial analog of the brain that has been used extensively to model neural computation: the recurrent neural network (RNN). In both the brain and the RNN, we emphasize the common computational substrate atop which dynamics occur-the connectivity between neurons-and we explore the unique computational advantages offered by biophysical constraints such as resource efficiency, spatial embedding, and neurodevelopment.

Dynamics of spike transmission and suppression between principal cells and interneurons in the hippocampus and entorhinal cortex

Synaptic excitation and inhibition are essential for neuronal communication. However, the variables that regulate synaptic excitation and inhibition in the intact brain remain largely unknown. Here, we examined how spike transmission and suppression between principal cells (PCs) and interneurons (INTs) are modulated by activity history, brain state, cell type, and somatic distance between presynaptic and postsynaptic neurons by applying cross-correlogram analyses to datasets recorded from the dorsal hippocampus and medial entorhinal cortex (MEC) of 11 male behaving and sleeping Long Evans rats. The strength, temporal delay, and brain-state dependency of the spike transmission and suppression depended on the subregions/layers. The spike transmission probability of PC-INT excitatory pairs that showed short-term depression versus short-term facilitation was higher in CA1 and lower in CA3. Likewise, the intersomatic distance affected the proportion of PC-INT excitatory pairs that showed short-term depression and facilitation in the opposite manner in CA1 compared with CA3. The time constant of depression was longer, while that of facilitation was shorter in MEC than in CA1 and CA3. During sharp-wave ripples, spike transmission showed a larger gain in the MEC than in CA1 and CA3. The intersomatic distance affected the spike transmission gain during sharp-wave ripples differently in CA1 versus CA3. A subgroup of MEC layer 3 (EC3) INTs preferentially received excitatory inputs from and inhibited MEC layer 2 (EC2) PCs. The EC2 PC-EC3 INT excitatory pairs, most of which showed short-term depression, exhibited higher spike transmission probabilities than the EC2 PC-EC2 INT and EC3 PC-EC3 INT excitatory pairs. EC2 putative stellate cells exhibited stronger spike transmission to and received weaker spike suppression from EC3 INTs than EC2 putative pyramidal cells. This study provides detailed comparisons of monosynaptic interaction dynamics in the hippocampal-entorhinal loop, which may help to elucidate circuit operations.

Bimodular continuous attractor neural networks with static and moving stimuli

We investigated the dynamical behaviors of bimodular continuous attractor neural networks, each processing a modality of sensory input and interacting with each other. We found that when bumps coexist in both modules, the position of each bump is shifted towards the other input when the intermodular couplings are excitatory and is shifted away when inhibitory. When one intermodular coupling is excitatory while another is moderately inhibitory, temporally modulated population spikes can be generated. On further increase of the inhibitory coupling, momentary spikes will emerge. In the regime of bump coexistence, bump heights are primarily strengthened by excitatory intermodular couplings, but there is a lesser weakening effect due to a bump being displaced from the direct input. When bimodular networks serve as decoders of multisensory integration, we extend the Bayesian framework to show that excitatory and inhibitory couplings encode attractive and repulsive priors, respectively. At low disparity, the bump positions decode the posterior means in the Bayesian framework, whereas at high disparity, multiple steady states exist. In the regime of multiple steady states, the less stable state can be accessed if the input causing the more stable state arrives after a sufficiently long delay. When one input is moving, the bump in the corresponding module is pinned when the moving stimulus is weak, unpinned at intermediate stimulus strength, and tracks the input at strong stimulus strength, and the stimulus strengths for these transitions increase with the velocity of the moving stimulus. These results are important to understanding multisensory integration of static and dynamic stimuli.

Modelling novelty detection in the thalamocortical loop

In complex natural environments, sensory systems are constantly exposed to a large stream of inputs. Novel or rare stimuli, which are often associated with behaviorally important events, are typically processed differently than the steady sensory background, which has less relevance. Neural signatures of such differential processing, commonly referred to as novelty detection, have been identified on the level of EEG recordings as mismatch negativity (MMN) and on the level of single neurons as stimulus-specific adaptation (SSA). Here, we propose a multi-scale recurrent network with synaptic depression to explain how novelty detection can arise in the whisker-related part of the somatosensory thalamocortical loop. The "minimalistic" architecture and dynamics of the model presume that neurons in cortical layer 6 adapt, via synaptic depression, specifically to a frequently presented stimulus, resulting in reduced population activity in the corresponding cortical column when compared with the population activity evoked by a rare stimulus. This difference in population activity is then projected from the cortex to the thalamus and amplified through the interaction between neurons of the primary and reticular nuclei of the thalamus, resulting in rhythmic oscillations. These differentially activated thalamic oscillations are forwarded to cortical layer 4 as a late secondary response that is specific to rare stimuli that violate a particular stimulus pattern. Model results show a strong analogy between this late single neuron activity and EEG-based mismatch negativity in terms of their common sensitivity to presentation context and timescales of response latency, as observed experimentally. Our results indicate that adaptation in L6 can establish the thalamocortical dynamics that produce signatures of SSA and MMN and suggest a mechanistic model of novelty detection that could generalize to other sensory modalities.

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity patterns are propagating bursts of place-cell activities called hippocampal replay, which is critical for memory consolidation. The sudden and repeated occurrences of these burst states during ongoing neural activity suggest metastable neural circuit dynamics. As metastability has been attributed to noise and/or slow fatigue mechanisms, we propose a concise mesoscopic model which accounts for both. Crucially, our model is bottom-up: it is analytically derived from the dynamics of finite-size networks of Linear-Nonlinear Poisson neurons with short-term synaptic depression. As such, noise is explicitly linked to stochastic spiking and network size, and fatigue is explicitly linked to synaptic dynamics. To derive the mesoscopic model, we first consider a homogeneous spiking neural network and follow the temporal coarse-graining approach of Gillespie to obtain a "chemical Langevin equation", which can be naturally interpreted as a stochastic neural mass model. The Langevin equation is computationally inexpensive to simulate and enables a thorough study of metastable dynamics in classical setups (population spikes and Up-Down-states dynamics) by means of phase-plane analysis. An extension of the Langevin equation for small network sizes is also presented. The stochastic neural mass model constitutes the basic component of our mesoscopic model for replay. We show that the mesoscopic model faithfully captures the statistical structure of individual replayed trajectories in microscopic simulations and in previously reported experimental data. Moreover, compared to the deterministic Romani-Tsodyks model of place-cell dynamics, it exhibits a higher level of variability regarding order, direction and timing of replayed trajectories, which seems biologically more plausible and could be functionally desirable. This variability is the product of a new dynamical regime where metastability emerges from a complex interplay between finite-size fluctuations and local fatigue.

Modulation of working memory duration by synaptic and astrocytic mechanisms

Short-term synaptic plasticity and modulations of the presynaptic vesicle release rate are key components of many working memory models. At the same time, an increasing number of studies suggests a potential role of astrocytes in modulating higher cognitive function such as WM through their influence on synaptic transmission. Which influence astrocytic signaling could have on the stability and duration of WM representations, however, is still unclear. Here, we introduce a slow, activity-dependent astrocytic regulation of the presynaptic release probability in a synaptic attractor model of WM. We compare and analyze simulations of a simple WM protocol in firing rate and spiking networks with and without astrocytic regulation, and underpin our observations with analyses of the phase space dynamics in the rate network. We find that the duration and stability of working memory representations are altered by astrocytic signaling and by noise. We show that astrocytic signaling modulates the mean duration of WM representations. Moreover, if the astrocytic regulation is strong, a slow presynaptic timescale introduces a ‘window of vulnerability’, during which WM representations are easily disruptable by noise before being stabilized. We identify two mechanisms through which noise from different sources in the network can either stabilize or destabilize WM representations. Our findings suggest that (i) astrocytic regulation can act as a crucial determinant for the duration of WM representations in synaptic attractor models of WM, and (ii) that astrocytic signaling could facilitate different mechanisms for volitional top-down control of WM representations and their duration.

The ability to form memories and recall them is one of the fascinating features of our brain. Working memory operates like a memory scratch pad storing ongoing information for further processing. Here, we present a computational model dissecting the influence of astrocytes on the stability and duration of working memories. We find that a long astrocytic time constant can influence the mean duration of working memory representations and generate a “window of vulnerability”, during which some memories are tagged for long-term survival while some are terminated. The fraction of memories in the survival and termination groups could be regulated by adjusting the strength of astrocytic feedback or its time constant. This indicates that astrocytic signaling can be viewed as a candidate mechanism for top-down control of working memory representations and their duration.

Ictal wavefront propagation in slices and simulations with conductance-based refractory density model

The mechanisms determining ictal discharge (ID) propagation are still not clear. In the present study, we aimed to examine these mechanisms in animal and mathematical models of epileptiform activity. Using double-patch and extracellular potassium ion concentration recordings in rat hippocampal-cortical slices, we observed that IDs moved at a speed of about 1 mm/s or less. The mechanisms of such slow propagation have been studied with a mathematical, conductance-based refractory density (CBRD) model that describes the GABA- and glutamatergic neuronal populations’ interactions and ion dynamics in brain tissue. The modeling study reveals two main factors triggerring IDs: (i) increased interneuronal activity leading to chloride ion accumulation and a consequent depolarizing GABAergic effect and (ii) the elevation of extracellular potassium ion concentration. The local synaptic transmission followed by local potassium ion extrusion and GABA receptor-mediated chloride ion accumulation underlies the ID wavefront’s propagation. In contrast, potassium ion diffusion in the extracellular space is slower and does not affect ID’s speed. The short discharges, constituting the ID, propagate much faster than the ID front. The accumulation of sodium ions inside neurons due to their hyperactivity and glutamatergic currents boosts the Na⁺/K⁺ pump, which terminates the ID. Knowledge of the mechanism of ID generation and propagation contributes to the development of new treatments against epilepsy.

During an epileptic seizure, neuronal excitation spreads across the brain tissue and is accompanied by significant changes in ionic concentrations. Ictal discharge front spreads at low speeds, less than 1 mm/s. Mechanisms underlying this phenomenon are not yet well understood. We study these mechanisms using electrophysiological recordings in brain slices and computer simulations. Our detailed biophysical model describing neuronal populations’ interaction, spatial propagation, and ionic dynamics reproduces the generation and propagation of spontaneously repeating ictal discharges. The simulations are consistent with our recordings of the electrical activity and the extracellular potassium ion concentration. We distinguished between the two alternative mechanisms of the ictal wavefront propagation: (i) the diffusion of potassium ions released from excited neurons, which depolarizes distant neurons and thus supports excitation, and (ii) the axonal spread of excitation followed by the local extracellular potassium ion accumulation that supports the excitation. Our simulations provide evidence in favor of the latter mechanism. Our experiment-based modeling contributes to a mathematical description of brain tissue functioning and potentially contributes to developing new treatments against epilepsy.

Nonlinear transient amplification in recurrent neural networks with short-term plasticity

To rapidly process information, neural circuits have to amplify specific activity patterns transiently. How the brain performs this nonlinear operation remains elusive. Hebbian assemblies are one possibility whereby strong recurrent excitatory connections boost neuronal activity. However, such Hebbian amplification is often associated with dynamical slowing of network dynamics, non-transient attractor states, and pathological run-away activity. Feedback inhibition can alleviate these effects but typically linearizes responses and reduces amplification gain. Here, we study nonlinear transient amplification (NTA), a plausible alternative mechanism that reconciles strong recurrent excitation with rapid amplification while avoiding the above issues. NTA has two distinct temporal phases. Initially, positive feedback excitation selectively amplifies inputs that exceed a critical threshold. Subsequently, short-term plasticity quenches the run-away dynamics into an inhibition-stabilized network state. By characterizing NTA in supralinear network models, we establish that the resulting onset transients are stimulus selective and well-suited for speedy information processing. Further, we find that excitatory-inhibitory co-tuning widens the parameter regime in which NTA is possible in the absence of persistent activity. In summary, NTA provides a parsimonious explanation for how excitatory-inhibitory co-tuning and short-term plasticity collaborate in recurrent networks to achieve transient amplification.

A robust model of Stimulus-Specific Adaptation validated on neuromorphic hardware

Stimulus-Specific Adaptation (SSA) to repetitive stimulation is a phenomenon that has been observed across many different species and in several brain sensory areas. It has been proposed as a computational mechanism, responsible for separating behaviorally relevant information from the continuous stream of sensory information. Although SSA can be induced and measured reliably in a wide variety of conditions, the network details and intracellular mechanisms giving rise to SSA still remain unclear. Recent computational studies proposed that SSA could be associated with a fast and synchronous neuronal firing phenomenon called Population Spikes (PS). Here, we test this hypothesis using a mean-field rate model and corroborate it using a neuromorphic hardware. As the neuromorphic circuits used in this study operate in real-time with biologically realistic time constants, they can reproduce the same dynamics observed in biological systems, together with the exploration of different connectivity schemes, with complete control of the system parameter settings. Besides, the hardware permits the iteration of multiple experiments over many trials, for extended amounts of time and without losing the networks and individual neural processes being studied. Following this "neuromorphic engineering" approach, we therefore study the PS hypothesis in a biophysically inspired recurrent networks of spiking neurons and evaluate the role of different linear and non-linear dynamic computational primitives such as spike-frequency adaptation or short-term depression (STD). We compare both the theoretical mean-field model of SSA and PS to previously obtained experimental results in the area of novelty detection and observe its behavior on its neuromorphic physical equivalent model. We show how the approach proposed can be extended to other computational neuroscience modelling efforts for understanding high-level phenomena in mechanistic models.

A simple model of epileptic seizure propagation: Potassium diffusion versus axo-dendritic spread

The mechanisms of epileptic discharge generation and spread are not yet fully known. A recently proposed simple biophysical model of interictal and ictal discharges, Epileptor-2, reproduces well the main features of neuronal excitation and ionic dynamics during discharge generation. In order to distinguish between two hypothesized mechanisms of discharge propagation, we extend the model to the case of two-dimensional propagation along the cortical neural tissue. The first mechanism is based on extracellular potassium diffusion, and the second is the propagation of spikes and postsynaptic signals along axons and dendrites. Our simulations show that potassium diffusion is too slow to reproduce an experimentally observed speed of ictal wavefront propagation (tenths of mm/s). By contrast, the synaptic mechanism predicts well the speed and synchronization of the pre-ictal bursts before the ictal front and the afterdischarges in the ictal core. Though this fact diminishes the role of diffusion and electrodiffusion, the model nevertheless highlights the role of potassium extrusion during neuronal excitation, which provides a positive feedback that changes at the ictal wavefront the balance of excitation versus inhibition in favor of excitation. This finding may help to find a target for a treatment to prevent seizure propagation.

Unstructured network topology begets order-based representation by privileged neurons

How spiking activity reverberates through neuronal networks, how evoked and spontaneous activity interacts and blends, and how the combined activities represent external stimulation are pivotal questions in neuroscience. We simulated minimal models of unstructured spiking networks in silico, asking whether and how gentle external stimulation might be subsequently reflected in spontaneous activity fluctuations. Consistent with earlier findings in silico and in vitro, we observe a privileged subpopulation of 'pioneer neurons' that, by their firing order, reliably encode previous external stimulation. We also confirm that pioneer neurons are 'sensitive' in that they are recruited by small fluctuations of population activity. We show that order-based representations rely on a 'chain' of pioneer neurons with different degrees of sensitivity and thus constitute an emergent property of collective dynamics. The forming of such representations is greatly favoured by a broadly heterogeneous connection topology-a broad 'middle class' in degree of connectedness. In conclusion, we offer a minimal model for the representational role of pioneer neurons, as observed experimentally in vitro. In addition, we show that broadly heterogeneous connectivity enhances the representational capacity of unstructured networks.

Mechanisms underlying sharpening of visual response dynamics with familiarity

Experience-dependent modifications of synaptic connections are thought to change patterns of network activities and stimulus tuning with learning. However, only a few studies explored how synaptic plasticity shapes the response dynamics of cortical circuits. Here, we investigated the mechanism underlying sharpening of both stimulus selectivity and response dynamics with familiarity observed in monkey inferotemporal cortex. Broadening the distribution of activities and stronger oscillations in the response dynamics after learning provide evidence for synaptic plasticity in recurrent connections modifying the strength of positive feedback. Its interplay with slow negative feedback via firing rate adaptation is critical in sharpening response dynamics. Analysis of changes in temporal patterns also enables us to disentangle recurrent and feedforward synaptic plasticity and provides a measure for the strengths of recurrent synaptic plasticity. Overall, this work highlights the importance of analyzing changes in dynamics as well as network patterns to further reveal the mechanisms of visual learning.

Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges

Despite big experimental data on the phenomena and mechanisms of the generation of ictal and interictal discharges (IDs and IIDs), mathematical models that can describe the synaptic interactions of neurons and the ionic dynamics in biophysical detail are not well-established. Based on experimental recordings of combined hippocampal-entorhinal cortex slices from rats in a high-potassium and a low-magnesium solution containing 4-aminopyridine as well as previous observations of similar experimental models, this type of mathematical model has been developed. The model describes neuronal excitation through the application of the conductance-based refractory density approach for three neuronal populations: two populations of glutamatergic neurons with hyperpolarizing and depolarizing GABAergic synapses and one GABAergic population. The ionic dynamics account for the contributions of voltage-gated and synaptic channels, active and passive transporters, and diffusion. The relatively slow dynamics of potassium, chloride, and sodium ion concentrations determine the transitions from pure GABAergic IIDs to IDs and GABA-glutamatergic IIDs. The model reproduces different types of IIDs, including those initiated by interneurons; repetitive IDs; tonic and bursting modes of an ID composed of clustered IID-like events. The simulations revealed contributions from different ionic channels to the ion concentration dynamics before and during ID generation. The proposed model is a step forward to an optimal mathematical description of the mechanisms of epileptic discharges.

Dynamic Communications Between GABAA Switch, Local Connectivity, and Synapses During Cortical Development: A Computational Study

Several factors regulate cortical development, such as changes in local connectivity and the influences of dynamical synapses. In this study, we simulated various factors affecting the regulation of neural network activity during cortical development. Previous studies have shown that during early cortical development, the reversal potential of GABA_A shifts from depolarizing to hyperpolarizing. Here we provide the first integrative computational model to simulate the combined effects of these factors in a unified framework (building on our prior work: Khalil et al., 2017a,b). In the current study, we extend our model to monitor firing activity in response to the excitatory action of GABA_A. Precisely, we created a Spiking Neural Network model that included certain biophysical parameters for lateral connectivity (distance between adjacent neurons) and nearby local connectivity (complex connections involving those between neuronal groups). We simulated different network scenarios (for immature and mature conditions) based on these biophysical parameters. Then, we implemented two forms of Short-term synaptic plasticity (depression and facilitation). Each form has two distinct kinds according to its synaptic time constant value. Finally, in both sets of networks, we compared firing rate activity responses before and after simulating dynamical synapses. Based on simulation results, we found that the modulation effect of dynamical synapses for evaluating and shaping the firing activity of the neural network is strongly dependent on the physiological state of GABA_A. Moreover, the STP mechanism acts differently in every network scenario, mirroring the crucial modulating roles of these critical parameters during cortical development. Clinical implications for pathological alterations of GABAergic signaling in neurological and psychiatric disorders are discussed.

Spatial propagation of interictal discharges along the cortex

Interictal discharges (IIDs) accompany epileptic seizures and highlight the mechanisms of pathological activity. The propagation of IIDs along the neural tissue is not well understood. To simulate IID propagation, this study proposes a new mathematical model that uses the conductance-based refractory density approach for glutamatergic and GABAergic neuronal populations. The mathematical model is found to be consistent with experimental double-patch registrations in the 4-aminopyridine in vitro model of epilepsy. In slices, the spontaneous activity of interneurons leads to their synchronization by means of the depolarizing GABAmediated response, thus initiating IIDs. Modeling reveals a clustering of interneuronal synchronization followed by IIDs with activity fronts that propagate along the cortex. The GABA-mediated depolarization either remains to be subthreshold for the principal neurons and thus results in pure GABAergic IIDs (IID1s) or leads to glutamatergic excitation, thus resulting in another type of IIDs (IID2s). In both the model and experiment, IIDs propagate as waves, with constant activity profiles and velocity. The speed of IIDs is of the order of tens of mm/s and is larger for IID2s than for IID1s (40 and 20 mm/s, respectively). The simulations, consistent with experimental observations, show that the wavelike propagation of IIDs initiated by interneurons is determined by local synaptic connectivity under the conditions of depolarizing GABA.

Seizure-Induced Potentiation of AMPA Receptor-Mediated Synaptic Transmission in the Entorhinal Cortex

Excessive excitation is considered one of the key mechanisms underlying epileptic seizures. We investigated changes in the evoked postsynaptic responses of medial entorhinal cortex (ERC) pyramidal neurons by seizure-like events (SLEs), using the modified 4-aminopyridine (4-AP) model of epileptiform activity. Rat brain slices were perfused with pro-epileptic solution contained 4-AP and elevated potassium and reduced magnesium concentration. We demonstrated that 15-min robust epileptiform activity in slices leads to an increase in the amplitude of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR)-mediated component of the evoked response, as well as an increase in the polysynaptic γ-aminobutyric acid (GABA) and N-methyl-D-aspartate (NMDA) receptor-mediated components. The increase in AMPA-mediated postsynaptic conductance depends on NMDA receptor activation. It persists for at least 15 min after the cessation of SLEs and is partly attributed to the inclusion of calcium-permeable AMPA receptors in the postsynaptic membrane. The mathematical modeling of the evoked responses using the conductance-based refractory density (CBRD) approach indicated that such augmentation of the AMPA receptor function and depolarization by GABA receptors results in prolonged firing that explains the increase in polysynaptic components, which contribute to overall network excitability. Taken together, our data suggest that AMPA receptor enhancement could be a critical determinant of sustained status epilepticus (SE).

Modeling driver cells in developing neuronal networks

Spontaneous emergence of synchronized population activity is a characteristic feature of developing brain circuits. Recent experiments in the developing neo-cortex showed the existence of driver cells able to impact the synchronization dynamics when single-handedly stimulated. We have developed a spiking network model capable to reproduce the experimental results, thus identifying two classes of driver cells: functional hubs and low functionally connected (LC) neurons. The functional hubs arranged in a clique orchestrated the synchronization build-up, while the LC drivers were lately or not at all recruited in the synchronization process. Notwithstanding, they were able to alter the network state when stimulated by modifying the temporal activation of the functional clique or even its composition. LC drivers can lead either to higher population synchrony or even to the arrest of population dynamics, upon stimulation. Noticeably, some LC driver can display both effects depending on the received stimulus. We show that in the model the presence of inhibitory neurons together with the assumption that younger cells are more excitable and less connected is crucial for the emergence of LC drivers. These results provide a further understanding of the structural-functional mechanisms underlying synchronized firings in developing circuits possibly related to the coordinated activity of cell assemblies in the adult brain.

Minimal model of interictal and ictal discharges "Epileptor-2"

Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures.

In pathological conditions of epilepsy, the functioning of the neural network crucially depends on the ionic concentrations inside and outside neurons. A number of factors that affect neuronal activity is large. That is why the development of a minimal model that reproduces typical seizures could structure further experimental and analytical studies of the pathological mechanisms. Here, on a base of known biophysical models, we present a simple population-type model that includes only four principal variables, the extracellular potassium concentration, the intracellular sodium concentration, the membrane potential and the synaptic resource diminishing due to short-term synaptic depression. A simple modeled neuron is used as an observer of the population activity. We validate the model assumptions with in vitro experiments. Our model reproduces ictal and interictal events, where the latter result in bursts of spikes in single neurons, and the former represent the cluster of spike bursts. Mathematical analysis reveals that the bursts are spontaneous large-amplitude oscillations, which may cluster after a saddle-node on invariant circle bifurcation in the pro-epileptic conditions. Our consideration has significant bearing in understanding pathological neuronal network dynamics.

AMPAR-mediated Interictal Discharges in Neurons of Entorhinal Cortex: Experiment and Model

The mechanisms of interictal discharges (IID) were studied under the conditions of the 4-aminopyridine model of spontaneous epileptiform activity in surviving rat brain slice preparations. Addition of the agents blocking GABA and NMDA receptors failed to inhibit IID generation in the entorhinal cortex. A mathematical model of IID has been developed on the basis of the excitatory neuron interaction mediated by the AMPA receptor. Short-term synaptic depression and slow afterspike-hyperpolarization are the key factors required to terminate a single IID. The IID shape-determining factors have been identified. The experimental and model IID features correspond to each other.

Phase-locking and bistability in neuronal networks with synaptic depression

We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris-Lecar neuron models.

The effects of dynamical synapses on firing rate activity: a spiking neural network model

Accumulating evidence relates the fine-tuning of synaptic maturation and regulation of neural network activity to several key factors, including GABA_A signaling and a lateral spread length between neighboring neurons (i.e., local connectivity). Furthermore, a number of studies consider short-term synaptic plasticity (STP) as an essential element in the instant modification of synaptic efficacy in the neuronal network and in modulating responses to sustained ranges of external Poisson input frequency (IF). Nevertheless, evaluating the firing activity in response to the dynamical interaction between STP (triggered by ranges of IF) and these key parameters in vitro remains elusive. Therefore, we designed a spiking neural network (SNN) model in which we incorporated the following parameters: local density of arbor essences and a lateral spread length between neighboring neurons. We also created several network scenarios based on these key parameters. Then, we implemented two classes of STP: (1) short-term synaptic depression (STD) and (2) short-term synaptic facilitation (STF). Each class has two differential forms based on the parametric value of its synaptic time constant (either for depressing or facilitating synapses). Lastly, we compared the neural firing responses before and after the treatment with STP. We found that dynamical synapses (STP) have a critical differential role on evaluating and modulating the firing rate activity in each network scenario. Moreover, we investigated the impact of changing the balance between excitation (E) and inhibition (I) on stabilizing this firing activity.

Developmental Emergence of Sparse Coding: A Dynamic Systems Approach

During neocortical development, network activity undergoes a dramatic transition from largely synchronized, so-called cluster activity, to a relatively sparse pattern around the time of eye-opening in rodents. Biophysical mechanisms underlying this sparsification phenomenon remain poorly understood. Here, we present a dynamic systems modeling study of a developing neural network that provides the first mechanistic insights into sparsification. We find that the rest state of immature networks is strongly affected by the dynamics of a transient, unstable state hidden in their firing activities, allowing these networks to either be silent or generate large cluster activity. We address how, and which, specific developmental changes in neuronal and synaptic parameters drive sparsification. We also reveal how these changes refine the information processing capabilities of an in vivo developing network, mainly by showing a developmental reduction in the instability of network’s firing activity, an effective availability of inhibition-stabilized states, and an emergence of spontaneous attractors and state transition mechanisms. Furthermore, we demonstrate the key role of GABAergic transmission and depressing glutamatergic synapses in governing the spatiotemporal evolution of cluster activity. These results, by providing a strong link between experimental observations and model behavior, suggest how adult sparse coding networks may emerge developmentally.

Computational model of interictal discharges triggered by interneurons

Interictal discharges (IIDs) are abnormal waveforms registered in the periods before or between seizures. IIDs that are initiated by GABAergic interneurons have not been mathematically modeled yet. In the present study, a mathematical model that describes the mechanisms of these discharges is proposed. The model is based on the experimental recordings of IIDs in pyramidal neurons of the rat entorhinal cortex and estimations of synaptic conductances during IIDs. IIDs were induced in cortico-hippocampal slices by applying an extracellular solution with 4-aminopyridine, high potassium, and low magnesium concentrations. Two different types of IIDs initiated by interneurons were observed. The first type of IID (IID1) was pure GABAergic. The second type of IID (IID2) was induced by GABAergic excitation and maintained by recurrent interactions of both GABA- and glutamatergic neuronal populations. The model employed the conductance-based refractory density (CBRD) approach, which accurately approximates the firing rate of a population of similar Hodgkin-Huxley-like neurons. The model of coupled excitatory and inhibitory populations includes AMPA, NMDA, and GABA-receptor-mediated synapses and gap junctions. These neurons receive both arbitrary deterministic input and individual colored Gaussian noise. Both types of IIDs were successfully reproduced in the model by setting two different depolarized levels for GABA-mediated current reversal potential. It was revealed that short-term synaptic depression is a crucial factor in ceasing each of the discharges, and it also determines their durations and frequencies.

Stimulus-specific adaptation in a recurrent network model of primary auditory cortex

Stimulus-specific adaptation (SSA) occurs when neurons decrease their responses to frequently-presented (standard) stimuli but not, or not as much, to other, rare (deviant) stimuli. SSA is present in all mammalian species in which it has been tested as well as in birds. SSA confers short-term memory to neuronal responses, and may lie upstream of the generation of mismatch negativity (MMN), an important human event-related potential. Previously published models of SSA mostly rely on synaptic depression of the feedforward, thalamocortical input. Here we study SSA in a recurrent neural network model of primary auditory cortex. When the recurrent, intracortical synapses display synaptic depression, the network generates population spikes (PSs). SSA occurs in this network when deviants elicit a PS but standards do not, and we demarcate the regions in parameter space that allow SSA. While SSA based on PSs does not require feedforward depression, we identify feedforward depression as a mechanism for expanding the range of parameters that support SSA. We provide predictions for experiments that could help differentiate between SSA due to synaptic depression of feedforward connections and SSA due to synaptic depression of recurrent connections. Similar to experimental data, the magnitude of SSA in the model depends on the frequency difference between deviant and standard, probability of the deviant, inter-stimulus interval and input amplitude. In contrast to models based on feedforward depression, our model shows true deviance sensitivity as found in experiments.

A Unified Dynamic Model for Learning, Replay, and Sharp-Wave/Ripples

Hippocampal activity is fundamental for episodic memory formation and consolidation. During phases of rest and sleep, it exhibits sharp-wave/ripple (SPW/R) complexes, which are short episodes of increased activity with superimposed high-frequency oscillations. Simultaneously, spike sequences reflecting previous behavior, such as traversed trajectories in space, are replayed. Whereas these phenomena are thought to be crucial for the formation and consolidation of episodic memory, their neurophysiological mechanisms are not well understood. Here we present a unified model showing how experience may be stored and thereafter replayed in association with SPW/Rs. We propose that replay and SPW/Rs are tightly interconnected as they mutually generate and support each other. The underlying mechanism is based on the nonlinear dendritic computation attributable to dendritic sodium spikes that have been prominently found in the hippocampal regions CA1 and CA3, where SPW/Rs and replay are also generated. Besides assigning SPW/Rs a crucial role for replay and thus memory processing, the proposed mechanism also explains their characteristic features, such as the oscillation frequency and the overall wave form. The results shed a new light on the dynamical aspects of hippocampal circuit learning.

SIGNIFICANCE STATEMENT

During phases of rest and sleep, the hippocampus, the "memory center" of the brain, generates intermittent patterns of strongly increased overall activity with high-frequency oscillations, the so-called sharp-wave/ripples. We investigate their role in learning and memory processing. They occur together with replay of activity sequences reflecting previous behavior. Developing a unifying computational model, we propose that both phenomena are tightly linked, by mutually generating and supporting each other. The underlying mechanism depends on nonlinear amplification of synchronous inputs that has been prominently found in the hippocampus. Besides assigning sharp-wave/ripples a crucial role for replay generation and thus memory processing, the proposed mechanism also explains their characteristic features, such as the oscillation frequency and the overall wave form.

Rich spectrum of neural field dynamics in the presence of short-term synaptic depression

In continuous attractor neural networks (CANNs), spatially continuous information such as orientation, head direction, and spatial location is represented by Gaussian-like tuning curves that can be displaced continuously in the space of the preferred stimuli of the neurons. We investigate how short-term synaptic depression (STD) can reshape the intrinsic dynamics of the CANN model and its responses to a single static input. In particular, CANNs with STD can support various complex firing patterns and chaotic behaviors. These chaotic behaviors have the potential to encode various stimuli in the neuronal system.

Spontaneous motion on two-dimensional continuous attractors

Attractor models are simplified models used to describe the dynamics of firing rate profiles of a pool of neurons. The firing rate profile, or the neuronal activity, is thought to carry information. Continuous attractor neural networks (CANNs) describe the neural processing of continuous information such as object position, object orientation, and direction of object motion. Recently it was found that in one-dimensional CANNs, short-term synaptic depression can destabilize bump-shaped neuronal attractor activity profiles. In this article, we study two-dimensional CANNs with short-term synaptic depression and spike frequency adaptation. We found that the dynamics of CANNs with short-term synaptic depression and CANNs with spike frequency adaptation are qualitatively similar. We also found that in both kinds of CANNs, the perturbative approach can be used to predict phase diagrams, dynamical variables, and speed of spontaneous motion.

Clique of functional hubs orchestrates population bursts in developmentally regulated neural networks

It has recently been discovered that single neuron stimulation can impact network dynamics in immature and adult neuronal circuits. Here we report a novel mechanism which can explain in neuronal circuits, at an early stage of development, the peculiar role played by a few specific neurons in promoting/arresting the population activity. For this purpose, we consider a standard neuronal network model, with short-term synaptic plasticity, whose population activity is characterized by bursting behavior. The addition of developmentally inspired constraints and correlations in the distribution of the neuronal connectivities and excitabilities leads to the emergence of functional hub neurons, whose stimulation/deletion is critical for the network activity. Functional hubs form a clique, where a precise sequential activation of the neurons is essential to ignite collective events without any need for a specific topological architecture. Unsupervised time-lagged firings of supra-threshold cells, in connection with coordinated entrainments of near-threshold neurons, are the key ingredients to orchestrate population activity.

To which extent a single neuron can influence brain circuits/networks dynamics? Why only a few neurons display such a strong power? These open questions are inspired by recent experimental observations in developing and adult neuronal circuits, as well as by classical debates within the framework of the single neuron doctrine. In this work we identify and present a mechanism which can explain in neuronal circuits, at some early stage of their development, how and why only a few specific neurons can exhibit such power. For this purpose, we consider a standard neuronal network model whose population activity is characterized by bursting behavior. The introduction of a distribution of correlated neuronal excitabilities and degrees, inspired by the simultaneous presence of younger and older neurons in the network, leads to the emergence of functional hub neurons. These critical cells, whenever perturbed, are capable of suppressing network synchronization. Notably, we show that their strong influence on the population dynamics is not related to their structural properties, but to their operational and structural integration into a clique. These results highlight how network-wide effects can be induced by single neurons without any need for a specific topological architecture.

Cellular adaptation facilitates sparse and reliable coding in sensory pathways

Most neurons in peripheral sensory pathways initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. It is unclear how this phenomenon affects stimulus coding in the later stages of sensory processing. Here, we show that a temporally sparse and reliable stimulus representation develops naturally in sequential stages of a sensory network with adapting neurons. As a modeling framework we employ a mean-field approach together with an adaptive population density treatment, accompanied by numerical simulations of spiking neural networks. We find that cellular adaptation plays a critical role in the dynamic reduction of the trial-by-trial variability of cortical spike responses by transiently suppressing self-generated fast fluctuations in the cortical balanced network. This provides an explanation for a widespread cortical phenomenon by a simple mechanism. We further show that in the insect olfactory system cellular adaptation is sufficient to explain the emergence of the temporally sparse and reliable stimulus representation in the mushroom body. Our results reveal a generic, biophysically plausible mechanism that can explain the emergence of a temporally sparse and reliable stimulus representation within a sequential processing architecture.

Resolution enhancement in neural networks with dynamical synapses

Conventionally, information is represented by spike rates in the neural system. Here, we consider the ability of temporally modulated activities in neuronal networks to carry information extra to spike rates. These temporal modulations, commonly known as population spikes, are due to the presence of synaptic depression in a neuronal network model. We discuss its relevance to an experiment on transparent motions in macaque monkeys by Treue et al. in 2000. They found that if the moving directions of objects are too close, the firing rate profile will be very similar to that with one direction. As the difference in the moving directions of objects is large enough, the neuronal system would respond in such a way that the network enhances the resolution in the moving directions of the objects. In this paper, we propose that this behavior can be reproduced by neural networks with dynamical synapses when there are multiple external inputs. We will demonstrate how resolution enhancement can be achieved, and discuss the conditions under which temporally modulated activities are able to enhance information processing performances in general.

Synaptic depression and slow oscillatory activity in a biophysical network model of the cerebral cortex

Short-term synaptic depression (STD) is a form of synaptic plasticity that has a large impact on network computations. Experimental results suggest that STD is modulated by cortical activity, decreasing with activity in the network and increasing during silent states. Here, we explored different activity-modulation protocols in a biophysical network model for which the model displayed less STD when the network was active than when it was silent, in agreement with experimental results. Furthermore, we studied how trains of synaptic potentials had lesser decay during periods of activity (UP states) than during silent periods (DOWN states), providing new experimental predictions. We next tackled the inverse question of what is the impact of modifying STD parameters on the emergent activity of the network, a question difficult to answer experimentally. We found that synaptic depression of cortical connections had a critical role to determine the regime of rhythmic cortical activity. While low STD resulted in an emergent rhythmic activity with short UP states and long DOWN states, increasing STD resulted in longer and more frequent UP states interleaved with short silent periods. A still higher synaptic depression set the network into a non-oscillatory firing regime where DOWN states no longer occurred. The speed of propagation of UP states along the network was not found to be modulated by STD during the oscillatory regime; it remained relatively stable over a range of values of STD. Overall, we found that the mutual interactions between synaptic depression and ongoing network activity are critical to determine the mechanisms that modulate cortical emergent patterns.

Population spikes in cortical networks during different functional states

Brain computational challenges vary between behavioral states. Engaged animals react according to incoming sensory information, while in relaxed and sleeping states consolidation of the learned information is believed to take place. Different states are characterized by different forms of cortical activity. We study a possible neuronal mechanism for generating these diverse dynamics and suggest their possible functional significance. Previous studies demonstrated that brief synchronized increase in a neural firing [Population Spikes (PS)] can be generated in homogenous recurrent neural networks with short-term synaptic depression (STD). Here we consider more realistic networks with clustered architecture. We show that the level of synchronization in neural activity can be controlled smoothly by network parameters. The network shifts from asynchronous activity to a regime in which clusters synchronized separately, then, the synchronization between the clusters increases gradually to fully synchronized state. We examine the effects of different synchrony levels on the transmission of information by the network. We find that the regime of intermediate synchronization is preferential for the flow of information between sparsely connected areas. Based on these results, we suggest that the regime of intermediate synchronization corresponds to engaged behavioral state of the animal, while global synchronization is exhibited during relaxed and sleeping states.

Dynamics of the semantic priming shift: behavioral experiments and cortical network model

Multiple semantic priming processes between several related and/or unrelated words are at work during the processing of sequences of words. Multiple priming generates rich dynamics of effects depending on the relationship between the target word and the first and/or second prime previously presented. The experimental literature suggests that during the on-line processing of the primes, the activation can shift from associates to the first prime to associates to the second prime. Though the semantic priming shift is central to the on-line and rapid updating of word meanings in the working memory, its precise dynamics are still poorly understood and it is still a challenge to model how it functions in the cerebral cortex. Four multiple priming experiments are proposed that cross-manipulate delays and association strength between the primes and the target. Results show for the first time that association strength determines complex dynamics of the semantic priming shift, ranging from an absence of a shift to a complete shift. A cortical network model of spike frequency adaptive neuron populations is proposed to account for the non-continuous evolution of the priming shift over time. It allows linking the dynamics of the priming shift assessed at the behavioral level to the non-linear dynamics of the firing rates of neurons populations.

Dynamical synapses enhance neural information processing: gracefulness, accuracy, and mobility

Experimental data have revealed that neuronal connection efficacy exhibits two forms of short-term plasticity: short-term depression (STD) and short-term facilitation (STF). They have time constants residing between fast neural signaling and rapid learning and may serve as substrates for neural systems manipulating temporal information on relevant timescales. This study investigates the impact of STD and STF on the dynamics of continuous attractor neural networks and their potential roles in neural information processing. We find that STD endows the network with slow-decaying plateau behaviors: the network that is initially being stimulated to an active state decays to a silent state very slowly on the timescale of STD rather than on that of neuralsignaling. This provides a mechanism for neural systems to hold sensory memory easily and shut off persistent activities gracefully. With STF, we find that the network can hold a memory trace of external inputs in the facilitated neuronal interactions, which provides a way to stabilize the network response to noisy inputs, leading to improved accuracy in population decoding. Furthermore, we find that STD increases the mobility of the network states. The increased mobility enhances the tracking performance of the network in response to time-varying stimuli, leading to anticipative neural responses. In general, we find that STD and STP tend to have opposite effects on network dynamics and complementary computational advantages, suggesting that the brain may employ a strategy of weighting them differentially depending on the computational purpose.

Short-term plasticity optimizes synaptic information transmission

Short-term synaptic plasticity (STP) is widely thought to play an important role in information processing. This major function of STP has recently been challenged, however, by several computational studies indicating that transmission of information by dynamic synapses is broadband, i.e., frequency independent. Here we developed an analytical approach to quantify time- and rate-dependent synaptic information transfer during arbitrary spike trains using a realistic model of synaptic dynamics in excitatory hippocampal synapses. We found that STP indeed increases information transfer in a wide range of input rates, which corresponds well to the naturally occurring spike frequencies at these synapses. This increased information transfer is observed both during Poisson-distributed spike trains with a constant rate and during naturalistic spike trains recorded in hippocampal place cells in exploring rodents. Interestingly, we found that the presence of STP in low release probability excitatory synapses leads to optimization of information transfer specifically for short high-frequency bursts, which are indeed commonly observed in many excitatory hippocampal neurons. In contrast, more reliable high release probability synapses that express dominant short-term depression are predicted to have optimal information transmission for single spikes rather than bursts. This prediction is verified in analyses of experimental recordings from high release probability inhibitory synapses in mouse hippocampal slices and fits well with the observation that inhibitory hippocampal interneurons do not commonly fire spike bursts. We conclude that STP indeed contributes significantly to synaptic information transfer and may serve to maximize information transfer for specific firing patterns of the corresponding neurons.

LTS and FS inhibitory interneurons, short-term synaptic plasticity, and cortical circuit dynamics

Somatostatin-expressing, low threshold-spiking (LTS) cells and fast-spiking (FS) cells are two common subtypes of inhibitory neocortical interneuron. Excitatory synapses from regular-spiking (RS) pyramidal neurons to LTS cells strongly facilitate when activated repetitively, whereas RS-to-FS synapses depress. This suggests that LTS neurons may be especially relevant at high rate regimes and protect cortical circuits against over-excitation and seizures. However, the inhibitory synapses from LTS cells usually depress, which may reduce their effectiveness at high rates. We ask: by which mechanisms and at what firing rates do LTS neurons control the activity of cortical circuits responding to thalamic input, and how is control by LTS neurons different from that of FS neurons? We study rate models of circuits that include RS cells and LTS and FS inhibitory cells with short-term synaptic plasticity. LTS neurons shift the RS firing-rate vs. current curve to the right at high rates and reduce its slope at low rates; the LTS effect is delayed and prolonged. FS neurons always shift the curve to the right and affect RS firing transiently. In an RS-LTS-FS network, FS neurons reach a quiescent state if they receive weak input, LTS neurons are quiescent if RS neurons receive weak input, and both FS and RS populations are active if they both receive large inputs. In general, FS neurons tend to follow the spiking of RS neurons much more closely than LTS neurons. A novel type of facilitation-induced slow oscillations is observed above the LTS firing threshold with a frequency determined by the time scale of recovery from facilitation. To conclude, contrary to earlier proposals, LTS neurons affect the transient and steady state responses of cortical circuits over a range of firing rates, not only during the high rate regime; LTS neurons protect against over-activation about as well as FS neurons.

The brain consists of circuits of neurons that signal to one another via synapses. There are two classes of neurons: excitatory cells, which cause other neurons to become more active, and inhibitory neurons, which cause other neurons to become less active. It is thought that the activity of excitatory neurons is kept in check largely by inhibitory neurons; when such an inhibitory “brake” fails, a seizure can result. Inhibitory neurons of the low-threshold spiking (LTS) subtype can potentially fulfill this braking, or anticonvulsant, role because the synaptic input to these neurons facilitates, i.e., those neurons are active when excitatory neurons are strongly active. Using a computational model we show that, because the synaptic output of LTS neurons onto excitatory neurons depresses (decreases with activity), the ability of LTS neurons to prevent strong cortical activity and seizures is not qualitatively larger than that of inhibitory neurons of another subtype, the fast-spiking (FS) cells. Furthermore, short-term (∼one second) changes in the strength of synapses to and from LTS interneurons allow them to shape the behavior of cortical circuits even at modest rates of activity, and an RS-LTS-FS circuit is capable of producing slow oscillations, on the time scale of these short-term changes.

The diverse functions of short-term plasticity components in synaptic computations

Short-term plasticity (STP) comprises several rapid synaptic processes that operate on millisecond-to-minute timescales and modulate synaptic efficacy in an activity-dependent manner. Facilitation and augmentation are two major STP components in central synapses that work to enhance synaptic strength, while various forms of short-term depression work to decrease it. These multiple components of STP interact to perform a variety of synaptic computations. Using a modeling approach in excitatory hippocampal synapses, we recently described the contributions of individual STP components to synaptic operations. In this mini-review, we summarize the recent findings that revealed a wide palette of functions that STP components play in neural operations and discuss their roles in information processing, working memory and decision making.

Vectorized algorithms for spiking neural network simulation

High-level languages (Matlab, Python) are popular in neuroscience because they are flexible and accelerate development. However, for simulating spiking neural networks, the cost of interpretation is a bottleneck. We describe a set of algorithms to simulate large spiking neural networks efficiently with high-level languages using vector-based operations. These algorithms constitute the core of Brian, a spiking neural network simulator written in the Python language. Vectorized simulation makes it possible to combine the flexibility of high-level languages with the computational efficiency usually associated with compiled languages.

Neurophysiological and computational principles of cortical rhythms in cognition

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

A physiologically based model for temporal envelope encoding in human primary auditory cortex

Communication sounds exhibit temporal envelope fluctuations in the low frequency range (<70 Hz) and human speech has prominent 2-16 Hz modulations with a maximum at 3-4 Hz. Here, we propose a new phenomenological model of the human auditory pathway (from cochlea to primary auditory cortex) to simulate responses to amplitude-modulated white noise. To validate the model, performance was estimated by quantifying temporal modulation transfer functions (TMTFs). Previous models considered either the lower stages of the auditory system (up to the inferior colliculus) or only the thalamocortical loop. The present model, divided in two stages, is based on anatomical and physiological findings and includes the entire auditory pathway. The first stage, from the outer ear to the colliculus, incorporates inhibitory interneurons in the cochlear nucleus to increase performance at high stimuli levels. The second stage takes into account the anatomical connections of the thalamocortical system and includes the fast and slow excitatory and inhibitory currents. After optimizing the parameters of the model to reproduce the diversity of TMTFs obtained from human subjects, a patient-specific model was derived and the parameters were optimized to effectively reproduce both spontaneous activity and the oscillatory part of the evoked response.

Adaptive integration in the visual cortex by depressing recurrent cortical circuits

Neurons in the visual cortex receive a large amount of input from recurrent connections, yet the functional role of these connections remains unclear. Here we explore networks with strong recurrence in a computational model and show that short-term depression of the synapses in the recurrent loops implements an adaptive filter. This allows the visual system to respond reliably to deteriorated stimuli yet quickly to high-quality stimuli. For low-contrast stimuli, the model predicts long response latencies, whereas latencies are short for high-contrast stimuli. This is consistent with physiological data showing that in higher visual areas, latencies can increase more than 100 ms at low contrast compared to high contrast. Moreover, when presented with briefly flashed stimuli, the model predicts stereotypical responses that outlast the stimulus, again consistent with physiological findings. The adaptive properties of the model suggest that the abundant recurrent connections found in visual cortex serve to adapt the network's time constant in accordance with the stimulus and normalizes neuronal signals such that processing is as fast as possible while maintaining reliability.

Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation

We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the rate of background synaptic inputs, we show how noise can provide a mechanism for increasing the robustness of rhythmic bursting and the range of burst frequencies. By exploiting a separation of time scales we also show how the system dynamics can be reduced to low-dimensional mean field equations in the limit N --> infinity. Analysis of the bifurcation structure of the mean field equations provides insights into the dynamical mechanisms for initiating and terminating the bursts.

Synaptic theory of working memory

It is usually assumed that enhanced spiking activity in the form of persistent reverberation for several seconds is the neural correlate of working memory. Here, we propose that working memory is sustained by calcium-mediated synaptic facilitation in the recurrent connections of neocortical networks. In this account, the presynaptic residual calcium is used as a buffer that is loaded, refreshed, and read out by spiking activity. Because of the long time constants of calcium kinetics, the refresh rate can be low, resulting in a mechanism that is metabolically efficient and robust. The duration and stability of working memory can be regulated by modulating the spontaneous activity in the network.

Processing of sounds by population spikes in a model of primary auditory cortex

We propose a model of the primary auditory cortex (A1), in which each iso-frequency column is represented by a recurrent neural network with short-term synaptic depression. Such networks can emit Population Spikes, in which most of the neurons fire synchronously for a short time period. Different columns are interconnected in a way that reflects the tonotopic map in A1, and population spikes can propagate along the map from one column to the next, in a temporally precise manner that depends on the specific input presented to the network. The network, therefore, processes incoming sounds by precise sequences of population spikes that are embedded in a continuous asynchronous activity, with both of these response components carrying information about the inputs and interacting with each other. With these basic characteristics, the model can account for a wide range of experimental findings. We reproduce neuronal frequency tuning curves, whose width depends on the strength of the intracortical inhibitory and excitatory connections. Non-simultaneous two-tone stimuli show forward masking depending on their temporal separation, as well as on the duration of the first stimulus. The model also exhibits non-linear suppressive interactions between sub-threshold tones and broad-band noise inputs, similar to the hypersensitive locking suppression recently demonstrated in auditory cortex. We derive several predictions from the model. In particular, we predict that spontaneous activity in primary auditory cortex gates the temporally locked responses of A1 neurons to auditory stimuli. Spontaneous activity could, therefore, be a mechanism for rapid and reversible modulation of cortical processing.

Modeling the primary auditory cortex using dynamic synapses: can synaptic plasticity explain the temporal tuning?

The molecular mechanisms underlying the temporal plasticity (temporal tuning) of cortical cells remain controversial. Experimental observations indicate that the neuronal responses at the primary auditory cortex are affected by behavioral learning. In this paper, we present a minimal feed-forward model of the primary auditory cortex, based on the dynamic synapse and the leaky integrate-and-fire neuron models, in order to search for the origin of the observed plasticity. We demonstrate that the frequency response of the model is markedly modified by regulating the contribution of synaptic facilitation to the short-term dynamics of synapses (U(1)). Consequently, we propose that the variation of this parameter may be responsible for primary auditory cortex enhancement achieved by behavioral training. Based on our model, we assume that the contribution of facilitation arises from the amount of Ca(2+) influx each time an action potential arrives at the nerve terminal. Regardless of what really leads to the long-term variation of Ca(2+) influx, we suggest that this process is responsible for the temporal tuning of responses observed in experimental studies. We believe that measurement of the long-term variation of Ca(2+) influx at the pre-synaptic area of the cortical cells in auditory learning trials would be the first step to validate our hypothesis.