Highly nonrandom features of synaptic connectivity in local cortical circuits

Dynamic systems approaches and levels of analysis in the nervous system

Various analyses are applied to physiological signals. While epistemological diversity is necessary to address effects at different levels, there is often a sense of competition between analyses rather than integration. This is evidenced by the differences in the criteria needed to claim understanding in different approaches. In the nervous system, neuronal analyses that attempt to explain network outputs in cellular and synaptic terms are rightly criticized as being insufficient to explain global effects, emergent or otherwise, while higher-level statistical and mathematical analyses can provide quantitative descriptions of outputs but can only hypothesize on their underlying mechanisms. The major gap in neuroscience is arguably our inability to translate what should be seen as complementary effects between levels. We thus ultimately need approaches that allow us to bridge between different spatial and temporal levels. Analytical approaches derived from critical phenomena in the physical sciences are increasingly being applied to physiological systems, including the nervous system, and claim to provide novel insight into physiological mechanisms and opportunities for their control. Analyses of criticality have suggested several important insights that should be considered in cellular analyses. However, there is a mismatch between lower-level neurophysiological approaches and statistical phenomenological analyses that assume that lower-level effects can be abstracted away, which means that these effects are unknown or inaccessible to experimentalists. As a result experimental designs often generate data that is insufficient for analyses of criticality. This review considers the relevance of insights from analyses of criticality to neuronal network analyses, and highlights that to move the analyses forward and close the gap between the theoretical and neurobiological levels, it is necessary to consider that effects at each level are complementary rather than in competition.

Altered network communication following a neuroprotective drug treatment

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

Network self-organization explains the statistics and dynamics of synaptic connection strengths in cortex

The information processing abilities of neural circuits arise from their synaptic connection patterns. Understanding the laws governing these connectivity patterns is essential for understanding brain function. The overall distribution of synaptic strengths of local excitatory connections in cortex and hippocampus is long-tailed, exhibiting a small number of synaptic connections of very large efficacy. At the same time, new synaptic connections are constantly being created and individual synaptic connection strengths show substantial fluctuations across time. It remains unclear through what mechanisms these properties of neural circuits arise and how they contribute to learning and memory. In this study we show that fundamental characteristics of excitatory synaptic connections in cortex and hippocampus can be explained as a consequence of self-organization in a recurrent network combining spike-timing-dependent plasticity (STDP), structural plasticity and different forms of homeostatic plasticity. In the network, associative synaptic plasticity in the form of STDP induces a rich-get-richer dynamics among synapses, while homeostatic mechanisms induce competition. Under distinctly different initial conditions, the ensuing self-organization produces long-tailed synaptic strength distributions matching experimental findings. We show that this self-organization can take place with a purely additive STDP mechanism and that multiplicative weight dynamics emerge as a consequence of network interactions. The observed patterns of fluctuation of synaptic strengths, including elimination and generation of synaptic connections and long-term persistence of strong connections, are consistent with the dynamics of dendritic spines found in rat hippocampus. Beyond this, the model predicts an approximately power-law scaling of the lifetimes of newly established synaptic connection strengths during development. Our results suggest that the combined action of multiple forms of neuronal plasticity plays an essential role in the formation and maintenance of cortical circuits.

The computations that brain circuits can perform depend on their wiring. While a wiring diagram is still out of reach for major brain structures such as the neocortex and hippocampus, data on the overall distribution of synaptic connection strengths and the temporal fluctuations of individual synapses have recently become available. Specifically, there exists a small population of very strong and stable synaptic connections, which may form the physiological substrate of life-long memories. This population coexists with a big and ever changing population of much smaller and strongly fluctuating synaptic connections. So far it has remained unclear how these properties of networks in neocortex and hippocampus arise. Here we present a computational model that explains these fundamental properties of neural circuits as a consequence of network self-organization resulting from the combined action of different forms of neuronal plasticity. This self-organization is driven by a rich-get-richer effect induced by an associative synaptic learning mechanism which is kept in check by several homeostatic plasticity mechanisms stabilizing the network. The model highlights the role of self-organization in the formation of brain circuits and parsimoniously explains a range of recent findings about their fundamental properties.

Computing complex visual features with retinal spike times

Neurons in sensory systems can represent information not only by their firing rate, but also by the precise timing of individual spikes. For example, certain retinal ganglion cells, first identified in the salamander, encode the spatial structure of a new image by their first-spike latencies. Here we explore how this temporal code can be used by downstream neural circuits for computing complex features of the image that are not available from the signals of individual ganglion cells. To this end, we feed the experimentally observed spike trains from a population of retinal ganglion cells to an integrate-and-fire model of post-synaptic integration. The synaptic weights of this integration are tuned according to the recently introduced tempotron learning rule. We find that this model neuron can perform complex visual detection tasks in a single synaptic stage that would require multiple stages for neurons operating instead on neural spike counts. Furthermore, the model computes rapidly, using only a single spike per afferent, and can signal its decision in turn by just a single spike. Extending these analyses to large ensembles of simulated retinal signals, we show that the model can detect the orientation of a visual pattern independent of its phase, an operation thought to be one of the primitives in early visual processing. We analyze how these computations work and compare the performance of this model to other schemes for reading out spike-timing information. These results demonstrate that the retina formats spatial information into temporal spike sequences in a way that favors computation in the time domain. Moreover, complex image analysis can be achieved already by a simple integrate-and-fire model neuron, emphasizing the power and plausibility of rapid neural computing with spike times.

Soft-bound synaptic plasticity increases storage capacity

Accurate models of synaptic plasticity are essential to understand the adaptive properties of the nervous system and for realistic models of learning and memory. Experiments have shown that synaptic plasticity depends not only on pre- and post-synaptic activity patterns, but also on the strength of the connection itself. Namely, weaker synapses are more easily strengthened than already strong ones. This so called soft-bound plasticity automatically constrains the synaptic strengths. It is known that this has important consequences for the dynamics of plasticity and the synaptic weight distribution, but its impact on information storage is unknown. In this modeling study we introduce an information theoretic framework to analyse memory storage in an online learning setting. We show that soft-bound plasticity increases a variety of performance criteria by about 18% over hard-bound plasticity, and likely maximizes the storage capacity of synapses.

It is generally believed that our memories are stored in the synaptic connections between neurons. Numerous experimental studies have therefore examined when and how the synaptic connections change. In parallel, many computational studies have examined the properties of memory and synaptic plasticity, aiming to better understand human memory and allow for neural network models of the brain. However, the plasticity rules used in most studies are highly simplified and do not take into account the rich behaviour found in experiments. For instance, it has been observed in experiments that it is hard to make strong synapses even stronger. Here we show that this saturation of plasticity enhances the number of memories that can be stored and introduce a general framework to calculate information storage in online learning paradigms.

Efficient associative memory storage in cortical circuits of inhibitory and excitatory neurons

Many features of synaptic connectivity are ubiquitous among cortical systems. Cortical networks are dominated by excitatory neurons and synapses, are sparsely connected, and function with stereotypically distributed connection weights. We show that these basic structural and functional features of synaptic connectivity arise readily from the requirement of efficient associative memory storage. Our theory makes two fundamental predictions. First, we predict that, despite a large number of neuron classes, functional connections between potentially connected cells must be realized with <50% probability if the presynaptic cell is excitatory and >50% probability if the presynaptic cell is inhibitory. Second, we establish a unique relation between probability of connection and coefficient of variation in connection weights. These predictions are consistent with a dataset of 74 published experiments reporting connection probabilities and distributions of postsynaptic potential amplitudes in various cortical systems. What is more, our theory explains the shapes of the distributions obtained in these experiments.

The cell-type specific cortical microcircuit: relating structure and activity in a full-scale spiking network model

In the past decade, the cell-type specific connectivity and activity of local cortical networks have been characterized experimentally to some detail. In parallel, modeling has been established as a tool to relate network structure to activity dynamics. While available comprehensive connectivity maps ( Thomson, West, et al. 2002; Binzegger et al. 2004) have been used in various computational studies, prominent features of the simulated activity such as the spontaneous firing rates do not match the experimental findings. Here, we analyze the properties of these maps to compile an integrated connectivity map, which additionally incorporates insights on the specific selection of target types. Based on this integrated map, we build a full-scale spiking network model of the local cortical microcircuit. The simulated spontaneous activity is asynchronous irregular and cell-type specific firing rates are in agreement with in vivo recordings in awake animals, including the low rate of layer 2/3 excitatory cells. The interplay of excitation and inhibition captures the flow of activity through cortical layers after transient thalamic stimulation. In conclusion, the integration of a large body of the available connectivity data enables us to expose the dynamical consequences of the cortical microcircuitry.

Time scales of memory, learning, and plasticity

After only about 10 days would the storage capacity of our nervous system be reached if we stored every bit of input. The nervous system relies on at least two mechanisms that counteract this capacity limit: compression and forgetting. But the latter mechanism needs to know how long an entity should be stored: some memories are relevant only for the next few minutes, some are important even after the passage of several years. Psychology and physiology have found and described many different memory mechanisms, and these mechanisms indeed use different time scales. In this prospect we review these mechanisms with respect to their time scale and propose relations between mechanisms in learning and memory and their underlying physiological basis.

Motifs in health and disease: the promise of circuit interrogation by optogenetics

Identifying the dominant dynamical motifs in cortical circuits and determining their functional relevance is of the utmost importance to understand the underlying mechanisms of psychiatric diseases and to develop effective therapies. Optogenetics can be used to interrogate cortical circuits to determine the dominant motif and thereby identify the relevant biophysical time scales that set the oscillation frequency. We review how computational models of cortical networks can help guide optogenetics experiments. We focus our attention on the pyramidal interneuron gamma motif, which is comprised of reciprocally connected excitatory and inhibitory neurons, and determine how the different biophysical time scales of the circuit components are reflected in the resonance of the power in the local field potential at the frequency of stimulation as a function of that frequency. Cardin et al. [J.A. Cardin et al. (2009)Nature, 459, 663-667] find that periodic stimulation of inhibitory cells leads to a resonance at gamma frequencies (30-80 Hz), but that stimulation of excitatory cells does not lead to a resonance. We can account for these results when the pyramidal cells are endowed with an intrinsic frequency preference due to a slow hyperpolarizing current. Furthermore, when fast α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)-mediated excitatory currents are replaced by slow N-methyl-d-aspartate (NMDA)-mediated ones in inhibitory cells, the gamma frequency resonance is reduced; however, when the same replacement is made in excitatory cells, gamma oscillations are enhanced. The results are relevant to schizophrenia, because there is evidence that NMDA receptors on parvalbumin-positive cells are primarily affected and that the regulation of gamma oscillations is impaired.

From functional architecture to functional connectomics

"Receptive Fields, Binocular Interaction and Functional Architecture in the Cat's Visual Cortex" by Hubel and Wiesel (1962) reported several important discoveries: orientation columns, the distinct structures of simple and complex receptive fields, and binocular integration. But perhaps the paper's greatest influence came from the concept of functional architecture (the complex relationship between in vivo physiology and the spatial arrangement of neurons) and several models of functionally specific connectivity. They thus identified two distinct concepts, topographic specificity and functional specificity, which together with cell-type specificity constitute the major determinants of nonrandom cortical connectivity. Orientation columns are iconic examples of topographic specificity, whereby axons within a column connect with cells of a single orientation preference. Hubel and Wiesel also saw the need for functional specificity at a finer scale in their model of thalamic inputs to simple cells, verified in the 1990s. The difficult but potentially more important question of functional specificity between cortical neurons is only now becoming tractable with new experimental techniques.

Sequencing the connectome

Recasting the study of neural circuitry as a problem of high-throughput DNA sequencing instead of microscopy holds the potential to increase efficiency by orders of magnitude.

Connectivity determines the function of neural circuits. Historically, circuit mapping has usually been viewed as a problem of microscopy, but no current method can achieve high-throughput mapping of entire circuits with single neuron precision. Here we describe a novel approach to determining connectivity. We propose BOINC (“barcoding of individual neuronal connections”), a method for converting the problem of connectivity into a form that can be read out by high-throughput DNA sequencing. The appeal of using sequencing is that its scale—sequencing billions of nucleotides per day is now routine—is a natural match to the complexity of neural circuits. An inexpensive high-throughput technique for establishing circuit connectivity at single neuron resolution could transform neuroscience research.

Neuronal circuits underlying persistent representations despite time varying activity

BACKGROUND

Our brains are capable of remarkably stable stimulus representations despite time-varying neural activity. For instance, during delay periods in working memory tasks, while stimuli are represented in working memory, neurons in the prefrontal cortex, thought to support the memory representation, exhibit time-varying neuronal activity. Since neuronal activity encodes the stimulus, its time-varying dynamics appears to be paradoxical and incompatible with stable network stimulus representations. Indeed, this finding raises a fundamental question: can stable representations only be encoded with stable neural activity, or, its corollary, is every change in activity a sign of change in stimulus representation?

RESULTS

Here we explain how different time-varying representations offered by individual neurons can be woven together to form a coherent, time-invariant, representation. Motivated by two ubiquitous features of the neocortex-redundancy of neural representation and sparse intracortical connections-we derive a network architecture that resolves the apparent contradiction between representation stability and changing neural activity. Unexpectedly, this network architecture exhibits many structural properties that have been measured in cortical sensory areas. In particular, we can account for few-neuron motifs, synapse weight distribution, and the relations between neuronal functional properties and connection probability.

CONCLUSIONS

We show that the intuition regarding network stimulus representation, typically derived from considering single neurons, may be misleading and that time-varying activity of distributed representation in cortical circuits does not necessarily imply that the network explicitly encodes time-varying properties.

Communication and wiring in the cortical connectome

In cerebral cortex, the huge mass of axonal wiring that carries information between near and distant neurons is thought to provide the neural substrate for cognitive and perceptual function. The goal of mapping the connectivity of cortical axons at different spatial scales, the cortical connectome, is to trace the paths of information flow in cerebral cortex. To appreciate the relationship between the connectome and cortical function, we need to discover the nature and purpose of the wiring principles underlying cortical connectivity. A popular explanation has been that axonal length is strictly minimized both within and between cortical regions. In contrast, we have hypothesized the existence of a multi-scale principle of cortical wiring where to optimize communication there is a trade-off between spatial (construction) and temporal (routing) costs. Here, using recent evidence concerning cortical spatial networks we critically evaluate this hypothesis at neuron, local circuit, and pathway scales. We report three main conclusions. First, the axonal and dendritic arbor morphology of single neocortical neurons may be governed by a similar wiring principle, one that balances the conservation of cellular material and conduction delay. Second, the same principle may be observed for fiber tracts connecting cortical regions. Third, the absence of sufficient local circuit data currently prohibits any meaningful assessment of the hypothesis at this scale of cortical organization. To avoid neglecting neuron and microcircuit levels of cortical organization, the connectome framework should incorporate more morphological description. In addition, structural analyses of temporal cost for cortical circuits should take account of both axonal conduction and neuronal integration delays, which appear mostly of the same order of magnitude. We conclude the hypothesized trade-off between spatial and temporal costs may potentially offer a powerful explanation for cortical wiring patterns.

Similarity of visual selectivity among clonally related neurons in visual cortex

Neurons in rodent visual cortex are organized in a salt-and-pepper fashion for orientation selectivity, but it is still unknown how this functional architecture develops. A recent study reported that the progeny of single cortical progenitor cells are preferentially connected in the postnatal cortex. If these neurons acquire similar selectivity through their connections, a salt-and-pepper organization may be generated, because neurons derived from different progenitors are intermingled in rodents. Here we investigated whether clonally related cells have similar preferred orientation by using a transgenic mouse, which labels all the progeny of single cortical progenitor cells. We found that preferred orientations of clonally related cells are similar to each other, suggesting that cell lineage is involved in the development of response selectivity of neurons in the cortex. However, not all clonally related cells share response selectivity, suggesting that cell lineage is not the only determinant of response selectivity.

Harnessing plasticity to understand learning and treat disease

A large body of evidence suggests that neural plasticity contributes to learning and disease. Recent studies suggest that cortical map plasticity is typically a transient phase that improves learning by increasing the pool of task-relevant responses. Here, I discuss a new perspective on neural plasticity and suggest how plasticity might be targeted to reset dysfunctional circuits. Specifically, a new model is proposed in which map expansion provides a form of replication with variation that supports a Darwinian mechanism to select the most behaviorally useful circuits. Precisely targeted neural plasticity provides a new avenue for the treatment of neurological and psychiatric disorders and is a powerful tool to test the neural mechanisms of learning and memory.

Slow dynamics and high variability in balanced cortical networks with clustered connections

Anatomical studies demonstrate that excitatory connections in cortex are not uniformly distributed across a network but instead exhibit clustering into groups of highly connected neurons. The implications of clustering for cortical activity are unclear. We studied the effect of clustered excitatory connections on the dynamics of neuronal networks that exhibited high spike time variability owing to a balance between excitation and inhibition. Even modest clustering substantially changed the behavior of these networks, introducing slow dynamics during which clusters of neurons transiently increased or decreased their firing rate. Consequently, neurons exhibited both fast spiking variability and slow firing rate fluctuations. A simplified model shows how stimuli bias networks toward particular activity states, thereby reducing firing rate variability as observed experimentally in many cortical areas. Our model thus relates cortical architecture to the reported variability in spontaneous and evoked spiking activity.

Mnemonic representations of transient stimuli and temporal sequences in the rodent hippocampus in vitro

A primary function of the brain is to store and retrieve information. Except for working memory, where extracellular recordings demonstrate persistent discharges during delay-response tasks, it has been difficult to link memories with changes in individual neurons or specific synaptic connections. Here, we demonstrate that transient stimuli are reliably encoded in the ongoing activity of brain tissue in vitro. We found that the patterns of synaptic input onto dentate hilar neurons predict which of four pathways were stimulated with an accuracy of 76% and performed significantly better than chance for >15 s. Dentate gyrus neurons also could accurately encode temporal sequences using population representations that were robust to variation in sequence interval. These results demonstrate direct neural encoding of temporal sequences in the spontaneous activity of brain tissue and suggest a novel local circuit mechanism that may contribute to diverse forms of short-term memory.

Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Unraveling the general organizing principles of connectivity in neural circuits is a crucial step towards understanding brain function. However, even the simpler task of assessing the global excitatory connectivity of a culture in vitro, where neurons form self-organized networks in absence of external stimuli, remains challenging. Neuronal cultures undergo spontaneous switching between episodes of synchronous bursting and quieter inter-burst periods. We introduce here a novel algorithm which aims at inferring the connectivity of neuronal cultures from calcium fluorescence recordings of their network dynamics. To achieve this goal, we develop a suitable generalization of Transfer Entropy, an information-theoretic measure of causal influences between time series. Unlike previous algorithmic approaches to reconstruction, Transfer Entropy is data-driven and does not rely on specific assumptions about neuronal firing statistics or network topology. We generate simulated calcium signals from networks with controlled ground-truth topology and purely excitatory interactions and show that, by restricting the analysis to inter-bursts periods, Transfer Entropy robustly achieves a good reconstruction performance for disparate network connectivities. Finally, we apply our method to real data and find evidence of non-random features in cultured networks, such as the existence of highly connected hub excitatory neurons and of an elevated (but not extreme) level of clustering.

Differential wiring of layer 2/3 neurons drives sparse and reliable firing during neocortical development

Sensory information is transmitted with high fidelity across multiple synapses until it reaches the neocortex. There, individual neurons exhibit enormous variability in responses. The source of this diversity in output has been debated. Using transgenic mice expressing the green fluorescent protein coupled to the activity-dependent gene c-fos, we identified neurons with a history of elevated activity in vivo. Focusing on layer 4 to layer 2/3 connections, a site of strong excitatory drive at an initial stage of cortical processing, we find that fluorescently tagged neurons receive significantly greater excitatory and reduced inhibitory input compared with neighboring, unlabeled cells. Differential wiring of layer 2/3 neurons arises early in development and requires sensory input to be established. Stronger connection strength is not associated with evidence for recent synaptic plasticity, suggesting that these more active ensembles may not be generated over short time scales. Paired recordings show fosGFP+ neurons spike at lower stimulus thresholds than neighboring, fosGFP- neurons. These data indicate that differences in circuit construction can underlie response heterogeneity amongst neocortical neurons.

Does spike-timing-dependent synaptic plasticity couple or decouple neurons firing in synchrony?

Spike synchronization is thought to have a constructive role for feature integration, attention, associative learning, and the formation of bidirectionally connected Hebbian cell assemblies. By contrast, theoretical studies on spike-timing-dependent plasticity (STDP) report an inherently decoupling influence of spike synchronization on synaptic connections of coactivated neurons. For example, bidirectional synaptic connections as found in cortical areas could be reproduced only by assuming realistic models of STDP and rate coding. We resolve this conflict by theoretical analysis and simulation of various simple and realistic STDP models that provide a more complete characterization of conditions when STDP leads to either coupling or decoupling of neurons firing in synchrony. In particular, we show that STDP consistently couples synchronized neurons if key model parameters are matched to physiological data: First, synaptic potentiation must be significantly stronger than synaptic depression for small (positive or negative) time lags between presynaptic and postsynaptic spikes. Second, spike synchronization must be sufficiently imprecise, for example, within a time window of 5-10 ms instead of 1 ms. Third, axonal propagation delays should not be much larger than dendritic delays. Under these assumptions synchronized neurons will be strongly coupled leading to a dominance of bidirectional synaptic connections even for simple STDP models and low mean firing rates at the level of spontaneous activity.

Neuronal communication: firing spikes with spikes

Spikes of single cortical neurons can exert powerful effects even though most cortical synapses are too weak to fire postsynaptic neurons. A recent study combining single-cell stimulation with population imaging has visualized in vivo postsynaptic firing in genetically identified target cells. The results confirm predictions from in vitro work and might help to understand how the brain reads single-neuron activity.

Building blocks of self-sustained activity in a simple deterministic model of excitable neural networks

Understanding the interplay of topology and dynamics of excitable neural networks is one of the major challenges in computational neuroscience. Here we employ a simple deterministic excitable model to explore how network-wide activation patterns are shaped by network architecture. Our observables are co-activation patterns, together with the average activity of the network and the periodicities in the excitation density. Our main results are: (1) the dependence of the correlation between the adjacency matrix and the instantaneous (zero time delay) co-activation matrix on global network features (clustering, modularity, scale-free degree distribution), (2) a correlation between the average activity and the amount of small cycles in the graph, and (3) a microscopic understanding of the contributions by 3-node and 4-node cycles to sustained activity.

Information storage, loop motifs, and clustered structure in complex networks

We use a standard discrete-time linear Gaussian model to analyze the information storage capability of individual nodes in complex networks, given the network structure and link weights. In particular, we investigate the role of two- and three-node motifs in contributing to local information storage. We show analytically that directed feedback and feedforward loop motifs are the dominant contributors to information storage capability, with their weighted motif counts locally positively correlated to storage capability. We also reveal the direct local relationship between clustering coefficient(s) and information storage. These results explain the dynamical importance of clustered structure and offer an explanation for the prevalence of these motifs in biological and artificial networks.

Stability of synchronization clusters and seizurability in temporal lobe epilepsy

PURPOSE

Identification of critical areas in presurgical evaluations of patients with temporal lobe epilepsy is the most important step prior to resection. According to the "epileptic focus model", localization of seizure onset zones is the main task to be accomplished. Nevertheless, a significant minority of epileptic patients continue to experience seizures after surgery (even when the focus is correctly located), an observation that is difficult to explain under this approach. However, if attention is shifted from a specific cortical location toward the network properties themselves, then the epileptic network model does allow us to explain unsuccessful surgical outcomes.

METHODS

The intraoperative electrocorticography records of 20 patients with temporal lobe epilepsy were analyzed in search of interictal synchronization clusters. Synchronization was analyzed, and the stability of highly synchronized areas was quantified. Surrogate data were constructed and used to statistically validate the results. Our results show the existence of highly localized and stable synchronization areas in both the lateral and the mesial areas of the temporal lobe ipsilateral to the clinical seizures. Synchronization areas seem to play a central role in the capacity of the epileptic network to generate clinical seizures. Resection of stable synchronization areas is associated with elimination of seizures; nonresection of synchronization clusters is associated with the persistence of seizures after surgery.

DISCUSSION

We suggest that synchronization clusters and their stability play a central role in the epileptic network, favoring seizure onset and propagation. We further speculate that the stability distribution of these synchronization areas would differentiate normal from pathologic cases.

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.

Excitatory neuronal connectivity in the barrel cortex

Neocortical areas are believed to be organized into vertical modules, the cortical columns, and the horizontal layers 1–6. In the somatosensory barrel cortex these columns are defined by the readily discernible barrel structure in layer 4. Information processing in the neocortex occurs along vertical and horizontal axes, thereby linking individual barrel-related columns via axons running through the different cortical layers of the barrel cortex. Long-range signaling occurs within the neocortical layers but also through axons projecting through the white matter to other neocortical areas and subcortical brain regions. Because of the ease of identification of barrel-related columns, the rodent barrel cortex has become a prototypical system to study the interactions between different neuronal connections within a sensory cortical area and between this area and other cortical as well subcortical regions. Such interactions will be discussed specifically for the feed-forward and feedback loops between the somatosensory and the somatomotor cortices as well as the different thalamic nuclei. In addition, recent advances concerning the morphological characteristics of excitatory neurons and their impact on the synaptic connectivity patterns and signaling properties of neuronal microcircuits in the whisker-related somatosensory cortex will be reviewed. In this context, their relationship between the structural properties of barrel-related columns and their function as a module in vertical synaptic signaling in the whisker-related cortical areas will be discussed.

Complex dynamics in recurrent cortical networks based on spatially realistic connectivities

Most studies on the dynamics of recurrent cortical networks are either based on purely random wiring or neighborhood couplings. Neuronal cortical connectivity, however, shows a complex spatial pattern composed of local and remote patchy connections. We ask to what extent such geometric traits influence the “idle” dynamics of two-dimensional (2d) cortical network models composed of conductance-based integrate-and-fire (iaf) neurons. In contrast to the typical 1 mm² used in most studies, we employ an enlarged spatial set-up of 25 mm² to provide for long-range connections. Our models range from purely random to distance-dependent connectivities including patchy projections, i.e., spatially clustered synapses. Analyzing the characteristic measures for synchronicity and regularity in neuronal spiking, we explore and compare the phase spaces and activity patterns of our simulation results. Depending on the input parameters, different dynamical states appear, similar to the known synchronous regular “SR” or asynchronous irregular “AI” firing in random networks. Our structured networks, however, exhibit shifted and sharper transitions, as well as more complex activity patterns. Distance-dependent connectivity structures induce a spatio-temporal spread of activity, e.g., propagating waves, that random networks cannot account for. Spatially and temporally restricted activity injections reveal that a high amount of local coupling induces rather unstable AI dynamics. We find that the amount of local versus long-range connections is an important parameter, whereas the structurally advantageous wiring cost optimization of patchy networks has little bearing on the phase space.

Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links

The connectivity of complex networks and functional implications has been attracting much interest in many physical, biological and social systems. However, the significance of the weight distributions of network links remains largely unknown except for uniformly- or Gaussian-weighted links. Here, we show analytically and numerically, that recurrent neural networks can robustly generate internal noise optimal for spike transmission between neurons with the help of a long-tailed distribution in the weights of recurrent connections. The structure of spontaneous activity in such networks involves weak-dense connections that redistribute excitatory activity over the network as noise sources to optimally enhance the responses of individual neurons to input at sparse-strong connections, thus opening multiple signal transmission pathways. Electrophysiological experiments confirm the importance of a highly broad connectivity spectrum supported by the model. Our results identify a simple network mechanism for internal noise generation by highly inhomogeneous connection strengths supporting both stability and optimal communication.

Persistence and storage of activity patterns in spiking recurrent cortical networks: modulation of sigmoid signals by after-hyperpolarization currents and acetylcholine

Many cortical networks contain recurrent architectures that transform input patterns before storing them in short-term memory (STM). Theorems in the 1970's showed how feedback signal functions in rate-based recurrent on-center off-surround networks control this process. A sigmoid signal function induces a quenching threshold below which inputs are suppressed as noise and above which they are contrast-enhanced before pattern storage. This article describes how changes in feedback signaling, neuromodulation, and recurrent connectivity may alter pattern processing in recurrent on-center off-surround networks of spiking neurons. In spiking neurons, fast, medium, and slow after-hyperpolarization (AHP) currents control sigmoid signal threshold and slope. Modulation of AHP currents by acetylcholine (ACh) can change sigmoid shape and, with it, network dynamics. For example, decreasing signal function threshold and increasing slope can lengthen the persistence of a partially contrast-enhanced pattern, increase the number of active cells stored in STM, or, if connectivity is distance-dependent, cause cell activities to cluster. These results clarify how cholinergic modulation by the basal forebrain may alter the vigilance of category learning circuits, and thus their sensitivity to predictive mismatches, thereby controlling whether learned categories code concrete or abstract features, as predicted by Adaptive Resonance Theory. The analysis includes global, distance-dependent, and interneuron-mediated circuits. With an appropriate degree of recurrent excitation and inhibition, spiking networks maintain a partially contrast-enhanced pattern for 800 ms or longer after stimuli offset, then resolve to no stored pattern, or to winner-take-all (WTA) stored patterns with one or multiple winners. Strengthening inhibition prolongs a partially contrast-enhanced pattern by slowing the transition to stability, while strengthening excitation causes more winners when the network stabilizes.

Dissection of cortical microcircuits by single-neuron stimulation in vivo

BACKGROUND

A fundamental process underlying all brain functions is the propagation of spiking activity in networks of excitatory and inhibitory neurons. In the neocortex, although functional connections between pairs of neurons have been studied extensively in brain slices, they remain poorly characterized in vivo, where the high background activity, global brain states, and neuromodulation can powerfully influence synaptic transmission. To understand how spikes are transmitted in cortical circuits in vivo, we used two-photon calcium imaging to monitor ensemble activity and targeted patching to stimulate a single neuron in mouse visual cortex.

RESULTS

Burst spiking of a single pyramidal neuron can drive spiking activity in both excitatory and inhibitory neurons within a ∼100 μm radius. For inhibitory neurons, ∼30% of the somatostatin interneurons fire reliably in response to a presynaptic burst of ≥5 spikes. In contrast, parvalbumin interneurons showed no detectable responses to single-neuron stimulation, but their spiking is highly correlated with the local network activity.

CONCLUSIONS

Our results demonstrate the feasibility of mapping functional connectivity at cellular resolution in vivo and reveal distinct operations of two major inhibitory circuits, one detecting single-neuron spike bursts and the other reflecting distributed network activity.

Heterogeneity and independency of unitary synaptic outputs from hippocampal CA3 pyramidal cells

The variation of individual synaptic transmission impacts the dynamics of complex neural circuits. We performed whole-cell recordings from monosynaptically connected hippocampal neurons in rat organotypic slice cultures using a synapse mapping method. The amplitude of unitary excitatory postsynaptic current (uEPSC) varied from trial to trial and was independent of the physical distance between cell pairs. To investigate the source of the transmission variability, we obtained patch-clamp recordings from intact axons. Axonal action potentials (APs) were reliably transmitted throughout the axonal arbour and showed modest changes in width. In contrast, calcium imaging from presynaptic boutons revealed that the amplitude of AP-evoked calcium transients exhibited large variations both among different boutons at a given trial and among trials in a given bouton. These results suggest that a factor contributing to the uEPSC fluctuations is the variability in calcium dynamics at presynaptic terminals. Finally, we acquired triple whole-cell recordings from divergent circuit motifs with one presynaptic neuron projecting to two postsynaptic neurons. Consistent with the independency of calcium dynamics among axonal boutons, a series of uEPSC fluctuations was not correlated between the two postsynaptic cells, indicating that different synapses even from the same neuron act independently.We conclude that the intra-bouton and inter-bouton variability in AP-induced calcium dynamics determine the heterogeneity and independency of uEPSCs.

Default activity patterns at the neocortical microcircuit level

Even in absence of sensory stimuli cortical networks exhibit complex, self-organized activity patterns. While the function of those spontaneous patterns of activation remains poorly understood, recent studies both in vivo and in vitro have demonstrated that neocortical neurons activate in a surprisingly similar sequential order both spontaneously and following input into cortex. For example, neurons that tend to fire earlier within spontaneous bursts of activity also fire earlier than other neurons in response to sensory stimuli. These “default patterns” can last hundreds of milliseconds and are strongly conserved under a variety of conditions. In this paper, we will review recent evidence for these default patterns at the local cortical level. We speculate that cortical architecture imposes common constraints on spontaneous and evoked activity flow, which result in the similarity of the patterns.

Universal critical dynamics in high resolution neuronal avalanche data

The tasks of neural computation are remarkably diverse. To function optimally, neuronal networks have been hypothesized to operate near a nonequilibrium critical point. However, experimental evidence for critical dynamics has been inconclusive. Here, we show that the dynamics of cultured cortical networks are critical. We analyze neuronal network data collected at the individual neuron level using the framework of nonequilibrium phase transitions. Among the most striking predictions confirmed is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function. We also show that the data have three additional features predicted by critical phenomena: approximate power law distributions of avalanche sizes and durations, samples in subcritical and supercritical phases, and scaling laws between anomalous exponents.

An improved test for detecting multiplicative homeostatic synaptic scaling

Homeostatic scaling of synaptic strengths is essential for maintenance of network "gain", but also poses a risk of losing the distinctions among relative synaptic weights, which are possibly cellular correlates of memory storage. Multiplicative scaling of all synapses has been proposed as a mechanism that would preserve the relative weights among them, because they would all be proportionately adjusted. It is crucial for this hypothesis that all synapses be affected identically, but whether or not this actually occurs is difficult to determine directly. Mathematical tests for multiplicative synaptic scaling are presently carried out on distributions of miniature synaptic current amplitudes, but the accuracy of the test procedure has not been fully validated. We now show that the existence of an amplitude threshold for empirical detection of miniature synaptic currents limits the use of the most common method for detecting multiplicative changes. Our new method circumvents the problem by discarding the potentially distorting subthreshold values after computational scaling. This new method should be useful in assessing the underlying neurophysiological nature of a homeostatic synaptic scaling transformation, and therefore in evaluating its functional significance.

Population coding in sparsely connected networks of noisy neurons

This study examines the relationship between population coding and spatial connection statistics in networks of noisy neurons. Encoding of sensory information in the neocortex is thought to require coordinated neural populations, because individual cortical neurons respond to a wide range of stimuli, and exhibit highly variable spiking in response to repeated stimuli. Population coding is rooted in network structure, because cortical neurons receive information only from other neurons, and because the information they encode must be decoded by other neurons, if it is to affect behavior. However, population coding theory has often ignored network structure, or assumed discrete, fully connected populations (in contrast with the sparsely connected, continuous sheet of the cortex). In this study, we modeled a sheet of cortical neurons with sparse, primarily local connections, and found that a network with this structure could encode multiple internal state variables with high signal-to-noise ratio. However, we were unable to create high-fidelity networks by instantiating connections at random according to spatial connection probabilities. In our models, high-fidelity networks required additional structure, with higher cluster factors and correlations between the inputs to nearby neurons.

Computational modeling of epilepsy for an experimental neurologist

Computational modeling can be a powerful tool for an experimentalist, providing a rigorous mathematical model of the system you are studying. This can be valuable in testing your hypotheses and developing experimental protocols prior to experimenting. This paper reviews models of seizures and epilepsy at different scales, including cellular, network, cortical region, and brain scales by looking at how they have been used in conjunction with experimental data. At each scale, models with different levels of abstraction, the extraction of physiological detail, are presented. Varying levels of detail are necessary in different situations. Physiologically realistic models are valuable surrogates for experimental systems because, unlike in an experiment, every parameter can be changed and every variable can be observed. Abstract models are useful in determining essential parameters of a system, allowing the experimentalist to extract principles that explain the relationship between mechanisms and the behavior of the system. Modeling is becoming easier with the emergence of platforms dedicated to neuronal modeling and databases of models that can be downloaded. Modeling will never be a replacement for animal and clinical experiments, but it should be a starting point in designing experiments and understanding their results.

Experimental evidence for sparse firing in the neocortex

The advent of unbiased recording and imaging techniques to evaluate firing activity across neocortical neurons has revealed substantial heterogeneity in response properties in vivo, and that a minority of neurons are responsible for the majority of spikes. Despite the computational advantages to sparsely firing populations, experimental data defining the fraction of responsive neurons and the range of firing rates have not been synthesized. Here we review data about the distribution of activity across neuronal populations in primary sensory cortex. Overall, the firing output of granular and infragranular layers is highest. Although subthreshold activity across supragranular neurons is decidedly non-sparse, spikes are much less frequent and some cells are silent. Superficial layers of the cortex may employ specific cell and circuit mechanisms to increase sparseness.

The conundrum of functional brain networks: small-world efficiency or fractal modularity

The human brain has been studied at multiple scales, from neurons, circuits, areas with well-defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology. Here, we provide more details on the use of network science tools to elaborate on this behavior. We indicate the importance of using percolation theory to highlight the modular character of the functional brain network. These modules present a fractal, self-similar topology, identified through fractal network methods. When we lower the threshold of correlations to include weaker ties, the network as a whole assumes a small-world character. These weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs.

Clonally related visual cortical neurons show similar stimulus feature selectivity

A fundamental feature of the mammalian neocortex is its columnar organization¹. In the visual cortex, functional columns consisting of neurons with similar orientation preference have been characterized extensively^2-4, but how these columns are constructed during development remains unclear⁵. The ‘radial unit hypothesis’⁶ posits that the ontogenetic columns formed by clonally related neurons migrating along the same radial glial fiber during corticogenesis⁷ provide the basis for functional columns in adult neocortex¹. However, direct correspondence between the ontogenetic and functional columns has not been demonstrated⁸. Here we show that, despite the lack of discernible orientation map in mouse visual cortex^4,9,10, sister neurons in the same radial clone exhibit similar orientation preference. Using a retroviral vector encoding green fluorescent protein (GFP) to label radial clones of excitatory neurons and in vivo two-photon calcium imaging to measure the neuronal response properties, we found that sister neurons preferred similar orientations, while nearby non-sisters showed no such relationship. Interestingly, disruption of gap junction coupling by viral expression of a dominant-negative mutant of Cx26 or by daily administration of a gap junction blocker carbenoxolone (CBX) during the first postnatal week greatly diminished the functional similarity between sister neurons, suggesting that the maturation of ontogenetic into functional columns requires intercellular communication through gap junctions. Together with the recent finding of preferential excitatory connections among sister neurons¹¹, our results support the radial unit hypothesis and unify the ontogenetic and functional columns in the visual cortex.

Non-additive coupling enables propagation of synchronous spiking activity in purely random networks

Despite the current debate about the computational role of experimentally observed precise spike patterns it is still theoretically unclear under which conditions and how they may emerge in neural circuits. Here, we study spiking neural networks with non-additive dendritic interactions that were recently uncovered in single-neuron experiments. We show that supra-additive dendritic interactions enable the persistent propagation of synchronous activity already in purely random networks without superimposed structures and explain the mechanism underlying it. This study adds a novel perspective on the dynamics of networks with nonlinear interactions in general and presents a new viable mechanism for the occurrence of patterns of precisely timed spikes in recurrent networks.

Molecular codes for neuronal individuality and cell assembly in the brain

The brain contains an enormous, but finite, number of neurons. The ability of this limited number of neurons to produce nearly limitless neural information over a lifetime is typically explained by combinatorial explosion; that is, by the exponential amplification of each neuron's contribution through its incorporation into "cell assemblies" and neural networks. In development, each neuron expresses diverse cellular recognition molecules that permit the formation of the appropriate neural cell assemblies to elicit various brain functions. The mechanism for generating neuronal assemblies and networks must involve molecular codes that give neurons individuality and allow them to recognize one another and join appropriate networks. The extensive molecular diversity of cell-surface proteins on neurons is likely to contribute to their individual identities. The clustered protocadherins (Pcdh) is a large subfamily within the diverse cadherin superfamily. The clustered Pcdh genes are encoded in tandem by three gene clusters, and are present in all known vertebrate genomes. The set of clustered Pcdh genes is expressed in a random and combinatorial manner in each neuron. In addition, cis-tetramers composed of heteromultimeric clustered Pcdh isoforms represent selective binding units for cell-cell interactions. Here I present the mathematical probabilities for neuronal individuality based on the random and combinatorial expression of clustered Pcdh isoforms and their formation of cis-tetramers in each neuron. Notably, clustered Pcdh gene products are known to play crucial roles in correct axonal projections, synaptic formation, and neuronal survival. Their molecular and biological features induce a hypothesis that the diverse clustered Pcdh molecules provide the molecular code by which neuronal individuality and cell assembly permit the combinatorial explosion of networks that supports enormous processing capability and plasticity of the brain.

Dynamic effective connectivity of inter-areal brain circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities.

The circuits of the brain must perform a daunting amount of functions. But how can “brain states” be flexibly controlled, given that anatomic inter-areal connections can be considered as fixed, on timescales relevant for behavior? We hypothesize that, thanks to the nonlinear interaction between brain rhythms, even a simple circuit involving few brain areas can originate a multitude of effective circuits, associated with alternative functions selectable “on demand”. A distinction is usually made between structural connectivity, which describes actual synaptic connections, and effective connectivity, quantifying, beyond correlation, directed inter-areal causal influences. In our study, we measure effective connectivity based on time-series of neural activity generated by model inter-areal circuits. We find that “causality follows dynamics”. We show indeed that different effective networks correspond to different dynamical states associated to a same structural network (in particular, different phase-locking patterns between local neuronal oscillations). We then find that “information follows causality” (and thus, again, dynamics). We demonstrate that different effective networks give rise to alternative modalities of information routing between brain areas wired together in a fixed structural network. In particular, we show that the self-organization of interacting “analog” rate oscillations control the flow of “digital-like” information encoded in complex spiking patterns.

Impact of network structure and cellular response on spike time correlations

Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative – or correlated – activity in neural populations, and in the possible impact of such correlations on the neural code. A fundamental theoretical challenge is to understand how the architecture of network connectivity along with the dynamical properties of single cells shape the magnitude and timescale of correlations. We provide a general approach to this problem by extending prior techniques based on linear response theory. We consider networks of general integrate-and-fire cells with arbitrary architecture, and provide explicit expressions for the approximate cross-correlation between constituent cells. These correlations depend strongly on the operating point (input mean and variance) of the neurons, even when connectivity is fixed. Moreover, the approximations admit an expansion in powers of the matrices that describe the network architecture. This expansion can be readily interpreted in terms of paths between different cells. We apply our results to large excitatory-inhibitory networks, and demonstrate first how precise balance – or lack thereof – between the strengths and timescales of excitatory and inhibitory synapses is reflected in the overall correlation structure of the network. We then derive explicit expressions for the average correlation structure in randomly connected networks. These expressions help to identify the important factors that shape coordinated neural activity in such networks.

Is neural activity more than the sum of its individual parts? What is the impact of cooperative, or correlated, spiking among multiple cells? We can start addressing these questions, as rapid advances in experimental techniques allow simultaneous recordings from ever-increasing populations. However, we still lack a general understanding of the origin and consequences of the joint activity that is revealed. The challenge is compounded by the fact that both the intrinsic dynamics of single cells and the correlations among then vary depending on the overall state of the network. Here, we develop a toolbox that addresses this issue. Specifically, we show how linear response theory allows for the expression of correlations explicitly in terms of the underlying network connectivity and known single-cell properties – and that the predictions of this theory accurately match simulations of a touchstone, nonlinear model in computational neuroscience, the general integrate-and-fire cell. Thus, our theory should help unlock the relationship between network architecture, single-cell dynamics, and correlated activity in diverse neural circuits.

Choice-specific sequences in parietal cortex during a virtual-navigation decision task

The posterior parietal cortex (PPC) plays an important role in many cognitive behaviors; however, the neural circuit dynamics underlying PPC function are not well understood. Here we optically imaged the spatial and temporal activity patterns of neuronal populations in mice performing a PPC-dependent task that combined a perceptual decision and memory-guided navigation in a virtual environment. Individual neurons had transient activation staggered relative to one another in time, forming a sequence of neuronal activation spanning the entire length of a task trial. Distinct sequences of neurons were triggered on trials with opposite behavioral choices and defined divergent, choice-specific trajectories through a state space of neuronal population activity. Cells participating in the different sequences and at distinct time points in the task were anatomically intermixed over microcircuit length scales (< 100 micrometers). During working memory decision tasks the PPC may therefore perform computations through sequence-based circuit dynamics, rather than long-lived stable states, implemented using anatomically intermingled microcircuits.

Sensory experience modifies spontaneous state dynamics in a large-scale barrel cortical model

Experimental evidence suggests that spontaneous neuronal activity may shape and be shaped by sensory experience. However, we lack information on how sensory experience modulates the underlying synaptic dynamics and how such modulation influences the response of the network to future events. Here we study whether spike-timing-dependent plasticity (STDP) can mediate sensory-induced modifications in the spontaneous dynamics of a new large-scale model of layers II, III and IV of the rodent barrel cortex. Our model incorporates significant physiological detail, including the types of neurons present, the probabilities and delays of connections, and the STDP profiles at each excitatory synapse. We stimulated the neuronal network with a protocol of repeated sensory inputs resembling those generated by the protraction-retraction motion of whiskers when rodents explore their environment, and studied the changes in network dynamics. By applying dimensionality reduction techniques to the synaptic weight space, we show that the initial spontaneous state is modified by each repetition of the stimulus and that this reverberation of the sensory experience induces long-term, structured modifications in the synaptic weight space. The post-stimulus spontaneous state encodes a memory of the stimulus presented, since a different dynamical response is observed when the network is presented with shuffled stimuli. These results suggest that repeated exposure to the same sensory experience could induce long-term circuitry modifications via 'Hebbian' STDP plasticity.