Neural Avalanches at the Critical Point between Replay and Non-Replay of Spatiotemporal Patterns

We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between the activity of the network and the stored patterns. We find that, depending on the excitability of the network, different working regimes are possible. For high excitability, the dynamical attractors are stable, and a collective activity that replays one of the stored patterns emerges spontaneously, while for low excitability, no replay is induced. Between these two regimes, there is a critical region in which the dynamical attractors are unstable, and intermittent short replays are induced by noise. At the critical spiking threshold, the order parameter goes from zero to one, and its fluctuations are maximized, as expected for a phase transition (and as observed in recent experimental results in the brain). Notably, in this critical region, the avalanche size and duration distributions follow power laws. Critical exponents are consistent with a scaling relationship observed recently in neural avalanches measurements. In conclusion, our simple model suggests that avalanche power laws in cortical spontaneous activity may be the effect of a network at the critical point between the replay and non-replay of spatio-temporal patterns.     

Associative memory of phase-coded spatiotemporal patterns in leaky Integrate and Fire networks

We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at different time scales. Using an STDP-based learning process, we store in the connectivity several phase-coded spike patterns, and we find that, depending on the excitability of the network, different working regimes are possible, with transient or persistent replay activity induced by a brief signal. We introduce an order parameter to evaluate the similarity between stored and recalled phase-coded pattern, and measure the storage capacity. Modulation of spiking thresholds during replay changes the frequency of the collective oscillation or the number of spikes per cycle, keeping preserved the phases relationship. This allows a coding scheme in which phase, rate and frequency are dissociable. Robustness with respect to noise and heterogeneity of neurons parameters is studied, showing that, since dynamics is a retrieval process, neurons preserve stable precise phase relationship among units, keeping a unique frequency of oscillation, even in noisy conditions and with heterogeneity of internal parameters of the units.     

A fluctuation-driven mechanism for slow decision processes in reverberant networks

The spike activity of cells in some cortical areas has been found to be correlated with reaction times and behavioral responses during two-choice decision tasks. These experimental findings have motivated the study of biologically plausible winner-take-all network models, in which strong recurrent excitation and feedback inhibition allow the network to form a categorical choice upon stimulation. Choice formation corresponds in these models to the transition from the spontaneous state of the network to a state where neurons selective for one of the choices fire at a high rate and inhibit the activity of the other neurons. This transition has been traditionally induced by an increase in the external input that destabilizes the spontaneous state of the network and forces its relaxation to a decision state. Here we explore a different mechanism by which the system can undergo such transitions while keeping the spontaneous state stable, based on an escape induced by finite-size noise from the spontaneous state. This decision mechanism naturally arises for low stimulus strengths and leads to exponentially distributed decision times when the amount of noise in the system is small. Furthermore, we show using numerical simulations that mean decision times follow in this regime an exponential dependence on the amplitude of noise. The escape mechanism provides thus a dynamical basis for the wide range and variability of decision times observed experimentally.     

Querying hippocampal replay with subcortical inputs

During sleep, the hippocampus recapitulates neuronal patterns corresponding to behavioral trajectories during previous experiences. This hippocampal replay supports the formation of long-term memories. Yet, whether replay originates within the hippocampal circuitry or is initiated by extrahippocampal inputs is unknown. Here, I review recent findings regarding the organization of neuronal activity upstream to the hippocampus, in the head-direction (HD) and grid cell networks, and its relationship to replay. I argue that hippocampal activity at the onset of replay is under the influence of signals from primary spatial areas. In turn, hippocampal replay resets the HD network activity to select a new direction for the next replay event. This reciprocal interaction between the HD network and the hippocampus may be essential in grounding meaning to hippocampal activity, specifically by training decoders of hippocampal sequences. Neuronal dynamics in thalamo-hippocampal loops may thus be instrumental for memory processes during sleep.     

Synaptic efficacy shapes resource limitations in working memory

Working memory (WM) is limited in its temporal length and capacity. Classic conceptions of WM capacity assume the system possesses a finite number of slots, but recent evidence suggests WM may be a continuous resource. Resource models typically assume there is no hard upper bound on the number of items that can be stored, but WM fidelity decreases with the number of items. We analyze a neural field model of multi-item WM that associates each item with the location of a bump in a finite spatial domain, considering items that span a one-dimensional continuous feature space. Our analysis relates the neural architecture of the network to accumulated errors and capacity limitations arising during the delay period of a multi-item WM task. Networks with stronger synapses support wider bumps that interact more, whereas networks with weaker synapses support narrower bumps that are more susceptible to noise perturbations. There is an optimal synaptic strength that both limits bump interaction events and the effects of noise perturbations. This optimum shifts to weaker synapses as the number of items stored in the network is increased. Our model not only provides a circuit-based explanation for WM capacity, but also speaks to how capacity relates to the arrangement of stored items in a feature space.     

Storage of a temporal pattern sequence in a network

Learning of single patterns and a temporal pattern sequence in a network when the coupling coefficients between the network elements change their values according to a definite coupling function is described. In contrast to technical systems (e.g. film, tape) where temporal sequences are often encoded in the storage location, the network stores information only by changing the values of the coupling coefficients. A network of 100 elements was simulated on an UNIVAC 1100/80 computer. Eight single patterns and a sequence of these patterns were offered at the input of the network. After the learning process the network reproduces every stored pattern as an output signal when only parts of it are fed in. The activity, that is the sum of all output signals, is regulated by an external control signal. By setting that control signal to a suitable value the network is able to reproduce the stored pattern sequence starting from any arbitrary pattern. Lowering the external control signal during that process causes the network to hold the last presented pattern until the external control signal is changed again. It is speculated that the coupling function implemented in the simulation may be anaogous to a characteristic describing the chemical process of cooperative binding.Supported by DFG (Ha 381/9 and Ha 381/11)     

A Signature of Attractor Dynamics in the CA3 Region of the Hippocampus

The notion of attractor networks is the leading hypothesis for how associative memories are stored and recalled. A defining anatomical feature of such networks is excitatory recurrent connections. These “attract” the firing pattern of the network to a stored pattern, even when the external input is incomplete (pattern completion). The CA3 region of the hippocampus has been postulated to be such an attractor network; however, the experimental evidence has been ambiguous, leading to the suggestion that CA3 is not an attractor network. In order to resolve this controversy and to better understand how CA3 functions, we simulated CA3 and its input structures. In our simulation, we could reproduce critical experimental results and establish the criteria for identifying attractor properties. Notably, under conditions in which there is continuous input, the output should be “attracted” to a stored pattern. However, contrary to previous expectations, as a pattern is gradually “morphed” from one stored pattern to another, a sharp transition between output patterns is not expected. The observed firing patterns of CA3 meet these criteria and can be quantitatively accounted for by our model. Notably, as morphing proceeds, the activity pattern in the dentate gyrus changes; in contrast, the activity pattern in the downstream CA3 network is attracted to a stored pattern and thus undergoes little change. We furthermore show that other aspects of the observed firing patterns can be explained by learning that occurs during behavioral testing. The CA3 thus displays both the learning and recall signatures of an attractor network. These observations, taken together with existing anatomical and behavioral evidence, make the strong case that CA3 constructs associative memories based on attractor dynamics.     

Towards the virtual brain: network modeling of the intact and the damaged brain

Neurocomputational models of large-scale brain dynamics utilizing realistic connectivity matrices have advanced our understanding of the operational network principles in the brain. In particular, spontaneous or resting state activity has been studied on various scales of spatial and temporal organization including those that relate to physiological, encephalographic and hemodynamic data. In this article we focus on the brain from the perspective of a dynamic network and discuss the role of its network constituents in shaping brain dynamics. These constituents include the brain's structural connectivity, the population dynamics of its network nodes and the time delays involved in signal transmission. In addition, no discussion of brain dynamics would be complete without considering noise and stochastic effects. In fact, there is mounting evidence that the interaction between noise and dynamics plays an important functional role in shaping key brain processes. In particular, we discuss a unifying theoretical framework that explains how structured spatio-temporal resting state patterns emerge from noise driven explorations of unstable or stable oscillatory states. Embracing this perspective, we explore the consequences of network manipulations to understand some of the brain's dysfunctions, as well as network effects that offer new insights into routes towards therapy, recovery and brain repair. These collective insights will be at the core of a new computational environment, the Virtual Brain, which will allow flexible incorporation of empirical data constraining the brain models to integrate, unify and predict network responses to incipient pathological processes.     

Representing Representation: Integration between the Temporal Lobe and the Posterior Cingulate Influences the Content and Form of Spontaneous Thought

When not engaged in the moment, we often spontaneously represent people, places and events that are not present in the environment. Although this capacity has been linked to the default mode network (DMN), it remains unclear how interactions between the nodes of this network give rise to particular mental experiences during spontaneous thought. One hypothesis is that the core of the DMN integrates information from medial and lateral temporal lobe memory systems, which represent different aspects of knowledge. Individual differences in the connectivity between temporal lobe regions and the default mode network core would then predict differences in the content and form of people’s spontaneous thoughts. This study tested this hypothesis by examining the relationship between seed-based functional connectivity and the contents of spontaneous thought recorded in a laboratory study several days later. Variations in connectivity from both medial and lateral temporal lobe regions was associated with different patterns of spontaneous thought and these effects converged on an overlapping region in the posterior cingulate cortex. We propose that the posterior core of the DMN acts as a representational hub that integrates information represented in medial and lateral temporal lobe and this process is important in determining the content and form of spontaneous thought.     

Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.     

Stochastic emergence of repeating cortical motifs in spontaneous membrane potential fluctuations in vivo

It was recently discovered that subthreshold membrane potential fluctuations of cortical neurons can precisely repeat during spontaneous activity, seconds to minutes apart, both in brain slices and in anesthetized animals. These repeats, also called cortical motifs, were suggested to reflect a replay of sequential neuronal firing patterns. We searched for motifs in spontaneous activity, recorded from the rat barrel cortex and from the cat striate cortex of anesthetized animals, and found numerous repeating patterns of high similarity and repetition rates. To test their significance, various statistics were compared between physiological data and three different types of stochastic surrogate data that preserve dynamical characteristics of the recorded data. We found no evidence for the existence of deterministically generated cortical motifs. Rather, the stochastic properties of cortical motifs suggest that they appear by chance, as a result of the constraints imposed by the coarse dynamics of subthreshold ongoing activity.     

A Model of Visuospatial Working Memory in Prefrontal Cortex: Recurrent Network and Cellular Bistability

We report a computer simulation of the visuospatial delayed-response experiments of Funahashi et al. (1989), using a firing-rate model that combines intrinsic cellular bistability with the recurrent local network architecture of the neocortex. In our model, the visuospatial working memory is stored in the form of a continuum of network activity profiles that coexist with a spontaneous activity state. These neuronal firing patterns provide a population code for the cue position in a graded manner. We show that neuronal persistent activity and tuning curves of delay-period activity (memory fields) can be generated by an excitatory feedback circuit and recurrent synaptic inhibition. However, if the memory fields are constructed solely by network mechanisms, noise may induce a random drift over time in the encoded cue position, so that the working memory storage becomes unreliable. Furthermore, a distraction stimulus presented during the delay period produces a systematic shift in the encoded cue position. We found that the working memory performance can be rendered robust against noise and distraction stimuli if single neurons are endowed with cellular bistability (presumably due to intrinsic ion channel mechanisms) that is conditional and realized only with sustained synaptic inputs from the recurrent network. We discuss how cellular bistability at the single cell level may be detected by analysis of spike trains recorded during delay-period activity and how local modulation of intrinsic cell properties and/or synaptic transmission can alter the memory fields of individual neurons in the prefrontal cortex.     

Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5-10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.     

Variable threshold as a model for selective attention, (de)sensitization,and anesthesia in associative neural networks

We study the influence of a variable neuronal threshold on fixed points and convergence rates of an associative neural network in the presence of noise. We allow a random distribution in the activity levels of the patterns stored, and a modification to the standard Hebbian learning rule is proposed for this purpose. There is a threshold at which the retrieval ability, including the average final overlap and the convergence rate, is optimized for patterns with a particular activity level at a given noise level. This type of selective attention to one class of patterns with a certain activity level may be obtained at the cost of reducing the retrieval ability of the network for patterns with different activity levels. The effects of a constant threshold independent of noise, time, and pattern are discussed. For high-(low-) activity patterns, the average final overlap is shown to be increased at high noise levels and decreased at low noise levels by a negative (positive) constant threshold, whereas a positive (negative) threshold always reduces the final average overlap. When the magnitude of the constant threshold exceeds a critical value, there is no retrieval. Rates of convergence towards the stored pattern with negative (positive) thresholds are greater than those with positive (negative) thresholds. These results are related to (de)sensitization and anesthesia. For certain threshold values and patterns with certain activity levels, hysteresis appears in the plot of the average final overlap versus the noise level, even for first order interactions. We make the analogy between the pattern-dependent neuronal threshold proposed in the present paper and the task-related modulation in neuronal excitability determined by cognitive factors, such as the attentional state of a higher animal. A constant threshold is associated with overall changes in neuronal excitability caused, e.g., by various drugs and physical injuries. Neurophysiological evidence of a dynamically variable neuronal threshold, such as accommodation and potentiation, is presented.     

Noise induced complexity: patterns and collective phenomena in a small-world neuronal network

The effects of noise on patterns and collective phenomena are studied in a small-world neuronal network with the dynamics of each neuron being described by a two-dimensional Rulkov map neuron. It is shown that for intermediate noise levels, noise-induced ordered patterns emerge spatially, which supports the spatiotemporal coherence resonance. However, the inherent long range couplings of small-world networks can effectively disrupt the internal spatial scale of the media at small fraction of long-range couplings. The temporal order, characterized by the autocorrelation of a firing rate function, can be greatly enhanced by the introduction of small-world connectivity. There exists an optimal fraction of randomly rewired links, where the temporal order and synchronization can be optimized.     

Sleep-Dependent Reactivation of Ensembles in Motor Cortex Promotes Skill Consolidation

Despite many prior studies demonstrating offline behavioral gains in motor skills after sleep, the underlying neural mechanisms remain poorly understood. To investigate the neurophysiological basis for offline gains, we performed single-unit recordings in motor cortex as rats learned a skilled upper-limb task. We found that sleep improved movement speed with preservation of accuracy. These offline improvements were linked to both replay of task-related ensembles during non-rapid eye movement (NREM) sleep and temporal shifts that more tightly bound motor cortical ensembles to movements; such offline gains and temporal shifts were not evident with sleep restriction. Interestingly, replay was linked to the coincidence of slow-wave events and bursts of spindle activity. Neurons that experienced the most consistent replay also underwent the most significant temporal shift and binding to the motor task. Significantly, replay and the associated performance gains after sleep only occurred when animals first learned the skill; continued practice during later stages of learning (i.e., after motor kinematics had stabilized) did not show evidence of replay. Our results highlight how replay of synchronous neural activity during sleep mediates large-scale neural plasticity and stabilizes kinematics during early motor learning.     

On how network architecture determines the dominant patterns of spontaneous neural activity

In the absence of sensory stimulation, neocortical circuits display complex patterns of neural activity. These patterns are thought to reflect relevant properties of the network, including anatomical features like its modularity. It is also assumed that the synaptic connections of the network constrain the repertoire of emergent, spontaneous patterns. Although the link between network architecture and network activity has been extensively investigated in the last few years from different perspectives, our understanding of the relationship between the network connectivity and the structure of its spontaneous activity is still incomplete. Using a general mathematical model of neural dynamics we have studied the link between spontaneous activity and the underlying network architecture. In particular, here we show mathematically how the synaptic connections between neurons determine the repertoire of spatial patterns displayed in the spontaneous activity. To test our theoretical result, we have also used the model to simulate spontaneous activity of a neural network, whose architecture is inspired by the patchy organization of horizontal connections between cortical columns in the neocortex of primates and other mammals. The dominant spatial patterns of the spontaneous activity, calculated as its principal components, coincide remarkably well with those patterns predicted from the network connectivity using our theory. The equivalence between the concept of dominant pattern and the concept of attractor of the network dynamics is also demonstrated. This in turn suggests new ways of investigating encoding and storage capabilities of neural networks.     

Spatiotemporal pattern formation in two-dimensional neural circuits: roles of refractoriness and noise

Refractoriness is one of the most fundamental states of neural firing activity, in which neurons that have just fired are unable to produce another spike, regardless of the strength of afferent stimuli. Another essential and unavoidable feature of neural systems is the existence of noise. To study the role of these essential factors in spatiotemporal pattern formation in neural systems, a spatially expended neural network model is constructed, with the dynamics of its individual neurons capturing the three most essential states of the neural firing behavior: firing, refractory and resting, and the network topology consistent with the widely observed center-surround coupling manner in the real brain. By changing the refractory period with and without noise in a systematic way in the network, it is shown numerically and analytically that without refractoriness, or when the refractory period is smaller than a certain value, the collective activity pattern of the system consists of localized, oscillating patterns. However, when the refractory period is greater than a certain value, crescent-shaped, localized propagating patterns emerge in the presence of noise. It is further illustrated that the formation of the dynamical spiking patterns is due to a symmetry breaking mechanism, refractoriness-induced symmetry breaking; that is generated by the interplay of noise and refractoriness in the network model. This refractoriness-induced symmetry breaking provides a novel perspective on the emergence of localized, spiking wave patterns or spike timing sequences as ubiquitously observed in real neural systems; it therefore suggests that refractoriness may benefit neural systems in their temporal information processing, rather than limiting the performance of neurons, as has been conventionally thought. Our results also highlight the importance of considering noise in studying spatially extended neural systems, where it may facilitate the formation of spatiotemporal order.     

A network capable of reading the temporal codes in the olfactory discrimination of insects]

Recent work on the insect olfactory system has shown that its mushroom bodies (one of its major components) are involved in the fine discrimination of odours and that the temporal organisation of spike discharges plays a fundamental role. We propose here a model of a network that is able to decode the temporal patterns which characterise an odour. This model has three fundamental properties that seem to exist in all mushroom bodies of insects studied so far: a) long lasting inhibitions with rebounds, able to facilitate delayed spike generation; b) synaptic plasticity, which allows the network to learn to recognise temporal patterns; c) above all a large interconnection, which allows this network to recognise intervals of various duration. This model thus appears suited to identify combinations of temporal patterns in the dendrites of Kenyon cells (the principal cells in the calyces of the mushroom bodies). Moreover, the mushroom bodies integrate multimodal inputs, suggesting that the detection of temporal patterns may be extended to the detection of a complex environment, combining in particular olfactive and visual inputs.