Highly nonrandom features of synaptic connectivity in local cortical circuits

Functional organization and population dynamics in the mouse primary auditory cortex

Cortical processing of auditory stimuli involves large populations of neurons with distinct individual response profiles. However, the functional organization and dynamics of local populations in the auditory cortex have remained largely unknown. Using in vivo two-photon calcium imaging, we examined the response profiles and network dynamics of layer 2/3 neurons in the primary auditory cortex (A1) of mice in response to pure tones. We found that local populations in A1 were highly heterogeneous in the large-scale tonotopic organization. Despite the spatial heterogeneity, the tendency of neurons to respond together (measured as noise correlation) was high on average. This functional organization and high levels of noise correlations are consistent with the existence of partially overlapping cortical subnetworks. Our findings may account for apparent discrepancies between ordered large-scale organization and local heterogeneity.

Can structure predict function in the human brain?

Over the past decade, scientific interest in the properties of large-scale spontaneous neural dynamics has intensified. Concurrently, novel technologies have been developed for characterizing the connective anatomy of intra-regional circuits and inter-regional fiber pathways. It will soon be possible to build computational models that incorporate these newly detailed structural network measurements to make predictions of neural dynamics at multiple scales. Here, we review the practicality and the value of these efforts, while at the same time considering in which cases and to what extent structure does determine neural function. Studies of the healthy brain, of neural development, and of pathology all yield examples of direct correspondences between structural linkage and dynamical correlation. Theoretical arguments further support the notion that brain network topology and spatial embedding should strongly influence network dynamics. Although future models will need to be tested more quantitatively and against a wider range of empirical neurodynamic features, our present large-scale models can already predict the macroscopic pattern of dynamic correlation across the brain. We conclude that as neuroscience grapples with datasets of increasing completeness and complexity, and attempts to relate the structural and functional architectures discovered at different neural scales, the value of computational modeling will continue to grow.

A few strong connections: optimizing information retention in neuronal avalanches

BACKGROUND

How living neural networks retain information is still incompletely understood. Two prominent ideas on this topic have developed in parallel, but have remained somewhat unconnected. The first of these, the "synaptic hypothesis," holds that information can be retained in synaptic connection strengths, or weights, between neurons. Recent work inspired by statistical mechanics has suggested that networks will retain the most information when their weights are distributed in a skewed manner, with many weak weights and only a few strong ones. The second of these ideas is that information can be represented by stable activity patterns. Multineuron recordings have shown that sequences of neural activity distributed over many neurons are repeated above chance levels when animals perform well-learned tasks. Although these two ideas are compelling, no one to our knowledge has yet linked the predicted optimum distribution of weights to stable activity patterns actually observed in living neural networks.

RESULTS

Here, we explore this link by comparing stable activity patterns from cortical slice networks recorded with multielectrode arrays to stable patterns produced by a model with a tunable weight distribution. This model was previously shown to capture central features of the dynamics in these slice networks, including neuronal avalanche cascades. We find that when the model weight distribution is appropriately skewed, it correctly matches the distribution of repeating patterns observed in the data. In addition, this same distribution of weights maximizes the capacity of the network model to retain stable activity patterns. Thus, the distribution that best fits the data is also the distribution that maximizes the number of stable patterns.

CONCLUSIONS

We conclude that local cortical networks are very likely to use a highly skewed weight distribution to optimize information retention, as predicted by theory. Fixed distributions impose constraints on learning, however. The network must have mechanisms for preserving the overall weight distribution while allowing individual connection strengths to change with learning.

Clustered cortical organization and the enhanced probability of intra-areal functional integration

Similarly responsive neurons organize into submillimeter-sized clusters (domains) across many neocortical areas, notably in Areas V1 and V2 of primate visual cortex. While this clustered organization may arise from wiring minimization or from self-organizing development, it could potentially support important neural computation benefits. Here, we suggest that domain organization offers an efficient computational mechanism for intra-areal functional integration in certain cortical areas and hypothesize that domain proximity could support a higher-than-expected spatial correlation of their respective terminals yielding higher probabilities of integration of differing domain preferences. To investigate this hypothesis we devised a spatial model inspired by known parameters of V2 functional organization, where neighboring domains prefer either colored or oriented stimuli. Preference-selective joint probabilities were calculated for model terminal co-occurrence with configurations encompassing diverse domain proximity, shape, and projection. Compared to random distributions, paired neighboring domains (< or =1200 microm apart) yielded significantly enhanced coincidence of terminals converging from each domain. Using this reference data, a second larger-scale model indicated that V2 domain organization may accommodate relatively complete sets of intra-areal color/orientation integrations. Together, these data indicate that domain organization could support significant and efficient intra-areal integration of different preferences and suggest further experiments investigating prevalence and mechanisms of domain-mediated intra-areal integration.

Plasticity between neuronal pairs in layer 4 of visual cortex varies with synapse state

In neocortex, the induction and expression of long-term potentiation (LTP) and long-term depression (LTD) vary depending on cortical area and laminae of presynaptic and postsynaptic neurons. Layer 4 (L4) is the initial site of sensory afference in barrel cortex and primary visual cortex (V1) in which excitatory inputs from thalamus, L6, and neighboring L4 cells are integrated. However, little is known about plasticity within L4. We studied plasticity at excitatory synaptic connections between pairs and triplets of interconnected L4 neurons in guinea pig V1 using a fixed delay pairing protocol. Plasticity outcomes were heterogeneous, with some connections undergoing LTP (n = 7 of 42), some LTD (n = 19 of 42), and some not changing (n = 16 of 42). Although quantal analysis revealed both presynaptic and postsynaptic plasticity expression components, reduction in quantal size (a postsynaptic property) contributing to LTD was ubiquitous, whereas in some cell pairs, this change was overridden by an increase in the probability of neurotransmitter release (a presynaptic property) resulting in LTP. These changes depended on the initial reliability of the connections: highly reliable connections depressed with contributions from presynaptic and postsynaptic effects, and unreliable connections potentiated as a result of the predominance of presynaptic enhancement. Interestingly, very strong, reliable pairs of connected cells showed little plasticity. Pairs of connected cells with a common presynaptic or postsynaptic L4 cell behaved independently, undergoing plasticity of different or opposite signs. Release probability of a connection with initial 100% failure rate was enhanced after pairing, potentially avoiding silencing of the presynaptic terminal and maintaining L4-L4 synapses in a broader dynamic range.

Intracortical cartography in an agranular area

A well-defined granular layer 4 is a defining cytoarchitectonic feature associated with sensory areas of mammalian cerebral cortex, and one with hodological significance: the local axons ascending from cells in thalamorecipient layer 4 and connecting to layer 2/3 pyramidal neurons form a major feedforward excitatory interlaminar projection. Conversely, agranular cortical areas, lacking a distinct layer 4, pose a hodological conundrum: without a laminar basis for the canonical layer 4→2/3 pathway, what is the basic circuit organization? This review highlights current challenges and prospects for local-circuit electroanatomy and electrophysiology in agranular cortex, focusing on the mouse. Different lines of evidence, drawn primarily from studies of motor areas in frontal cortex in rodents, support the view that synaptic circuits in agranular cortex are organized around prominent descending excitatory layer 2/3→5 pathways targeting multiple classes of projection neurons.

Reverse engineering the mouse brain

Behaviour is governed by activity in highly structured neural circuits. Genetically targeted sensors and switches facilitate measurement and manipulation of activity in vivo, linking activity in defined nodes of neural circuits to behaviour. Because of access to specific cell types, these molecular tools will have the largest impact in genetic model systems such as the mouse. Emerging assays of mouse behaviour are beginning to rival those of behaving monkeys in terms of stimulus and behavioural control. We predict that the confluence of new behavioural and molecular tools in the mouse will reveal the logic of complex mammalian circuits.

Cortical circuitry implementing graphical models

In this letter, we develop and simulate a large-scale network of spiking neurons that approximates the inference computations performed by graphical models. Unlike previous related schemes, which used sum and product operations in either the log or linear domains, the current model uses an inference scheme based on the sum and maximization operations in the log domain. Simulations show that using these operations, a large-scale circuit, which combines populations of spiking neurons as basic building blocks, is capable of finding close approximations to the full mathematical computations performed by graphical models within a few hundred milliseconds. The circuit is general in the sense that it can be wired for any graph structure, it supports multistate variables, and it uses standard leaky integrate-and-fire neuronal units. Following previous work, which proposed relations between graphical models and the large-scale cortical anatomy, we focus on the cortical microcircuitry and propose how anatomical and physiological aspects of the local circuitry may map onto elements of the graphical model implementation. We discuss in particular the roles of three major types of inhibitory neurons (small fast-spiking basket cells, large layer 2/3 basket cells, and double-bouquet neurons), subpopulations of strongly interconnected neurons with their unique connectivity patterns in different cortical layers, and the possible role of minicolumns in the realization of the population-based maximum operation.

Adaptive self-organization in a realistic neural network model

Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to criticality. This is further supported by the observation of power-law distributions, which are a hallmark of phase transitions. An important open question is how neural networks could remain close to a critical point while undergoing a continual change in the course of development, adaptation, learning, and more. An influential contribution was made by Bornholdt and Rohlf, introducing a generic mechanism of robust self-organized criticality in adaptive networks. Here, we address the question whether this mechanism is relevant for real neural networks. We show in a realistic model that spike-time-dependent synaptic plasticity can self-organize neural networks robustly toward criticality. Our model reproduces several empirical observations and makes testable predictions on the distribution of synaptic strength, relating them to the critical state of the network. These results suggest that the interplay between dynamics and topology may be essential for neural information processing.

Multiquantal release underlies the distribution of synaptic efficacies in the neocortex

Inter-pyramidal synaptic connections are characterized by a wide range of EPSP amplitudes. Although repeatedly observed at different brain regions and across layers, little is known about the synaptic characteristics that contribute to this wide range. In particular, the range could potentially be accounted for by differences in all three parameters of the quantal model of synaptic transmission, i.e. the number of release sites, release probability and quantal size. Here, we present a rigorous statistical analysis of the transmission properties of excitatory synaptic connections between layer-5 pyramidal neurons of the somato-sensory cortex. Our central finding is that the EPSP amplitude is strongly correlated with the number of estimated release sites, but not with the release probability or quantal size. In addition, we found that the number of release sites can be more than an order of magnitude higher than the typical number of synaptic contacts for this type of connection. Our findings indicate that transmission at stronger synaptic connections is mediated by multiquantal release from their synaptic contacts. We propose that modulating the number of release sites could be an important mechanism in regulating neocortical synaptic transmission.

Dynamical origin of the effective storage capacity in the brain's working memory

The capacity of working memory (WM), a short-term buffer for information in the brain, is limited. We suggest a model for sequential WM that is based upon winnerless competition amongst representations of available informational items. Analytical results for the underlying mathematical model relate WM capacity and relative lateral inhibition in the corresponding neural network. This implies an upper bound for WM capacity, which is, under reasonable neurobiological assumptions, close to the "magical number seven."

Embedding multiple trajectories in simulated recurrent neural networks in a self-organizing manner

Complex neural dynamics produced by the recurrent architecture of neocortical circuits is critical to the cortex's computational power. However, the synaptic learning rules underlying the creation of stable propagation and reproducible neural trajectories within recurrent networks are not understood. Here, we examined synaptic learning rules with the goal of creating recurrent networks in which evoked activity would: (1) propagate throughout the entire network in response to a brief stimulus while avoiding runaway excitation; (2) exhibit spatially and temporally sparse dynamics; and (3) incorporate multiple neural trajectories, i.e., different input patterns should elicit distinct trajectories. We established that an unsupervised learning rule, termed presynaptic-dependent scaling (PSD), can achieve the proposed network dynamics. To quantify the structure of the trained networks, we developed a recurrence index, which revealed that presynaptic-dependent scaling generated a functionally feedforward network when training with a single stimulus. However, training the network with multiple input patterns established that: (1) multiple non-overlapping stable trajectories can be embedded in the network; and (2) the structure of the network became progressively more complex (recurrent) as the number of training patterns increased. In addition, we determined that PSD and spike-timing-dependent plasticity operating in parallel improved the ability of the network to incorporate multiple and less variable trajectories, but also shortened the duration of the neural trajectory. Together, these results establish one of the first learning rules that can embed multiple trajectories, each of which recruits all neurons, within recurrent neural networks in a self-organizing manner.

Encoding and decoding bursts by NMDA spikes in basal dendrites of layer 5 pyramidal neurons

Bursts of action potentials are important information-bearing signals in the brain, although the neuronal specializations underlying burst generation and detection are only partially understood. In apical dendrites of neocortical pyramidal neurons, calcium spikes are known to contribute to burst generation, but a comparable understanding of basal dendritic mechanisms is lacking. Here we show that NMDA spikes in basal dendrites mediate both detection and generation of bursts through a postsynaptic mechanism. High-frequency inputs to basal dendrites markedly facilitated NMDA spike initiation compared with low-frequency activation or single inputs. Unlike conventional temporal summation effects based on voltage, however, NMDA spike facilitation depended mainly on residual glutamate bound to NMDA receptors from previous activations. Once triggered by an input burst, we found that NMDA spikes in turn reliably trigger output bursts under in vivo-like stimulus conditions. Through their unique biophysical properties, NMDA spikes are thus ideally suited to promote the propagation of bursts through the cortical network.

Sensory Experience and Cortical Rewiring

Adult primary sensory cortex is not hard wired, but adapts to sensory experience. The cellular basis for cortical plasticity involves a combination of functional and structural changes in cortical neurons and the connections between them. Functional changes such as synaptic strengthening have been the focus of many investigations. However, structural modifications to the connections between neurons play an important role in cortical plasticity. In this review, the authors focus on structural remodeling that leads to rewiring of cortical circuits. Recent work has identified axonal remodeling, growth of new dendritic spines, and synapse turnover as important structural mechanisms for experience-dependent plasticity in mature cortex. These findings have begun to unravel how rewiring occurs in adult neocortex and offer new insights into the cellular mechanisms for learning and memory.

Intact long-term potentiation but reduced connectivity between neocortical layer 5 pyramidal neurons in a mouse model of Rett syndrome

Mutations in MECP2 cause Rett syndrome and some related forms of mental retardation and autism. Mecp2-null mice exhibit symptoms reminiscent of Rett syndrome including deficits in learning. Previous reports demonstrated impaired long-term potentiation (LTP) in slices of symptomatic Mecp2-null mice, and decreased excitatory neurotransmission, but the causal relationship between these phenomena is unclear. Reduced plasticity could lead to altered transmission, or reduced excitatory transmission could alter the ability to induce LTP. To help distinguish these possibilities, we compared LTP induction and baseline synaptic transmission at synapses between layer 5 cortical pyramidal neurons in slices of wild-type and Mecp2-null mice. Paired recordings reveal that LTP induction mechanisms are intact in Mecp2-null connections, even after the onset of symptoms. However, fewer connections were found in Mecp2-null mice and individual connections were weaker. These data suggest that loss of MeCP2 function reduces excitatory synaptic connectivity and that this precedes deficits in plasticity.

Frequency-dependent disynaptic inhibition in the pyramidal network: a ubiquitous pathway in the developing rat neocortex

The general structure of the mammalian neocortex is remarkably similar across different cortical areas. Despite certain cytoarchitectural specializations and deviations from the general blueprint, the principal organization of the neocortex is relatively uniform. It is not known, however, to what extent stereotypic synaptic pathways resemble each other between cortical areas, and how far they might reflect possible functional uniformity or specialization. Here, we show that frequency-dependent disynaptic inhibition (FDDI) is a generic circuit motif that is present in all neocortical areas we investigated (primary somatosensory, auditory and motor cortex, secondary visual cortex and medial prefrontal cortex of the developing rat). We did find, however, area-specific differences in occurrence and kinetics of FDDI and the short-term dynamics of monosynaptic connections between pyramidal cells (PCs). Connectivity between PCs, both monosynaptic and via FDDI, is higher in primary cortices. The long-term effectiveness of FDDI is likely to be limited by an activity-dependent attenuation of the PC-interneuron synaptic transmission. Our results suggest that the basic construction of neocortical synaptic pathways follows principles that are independent of modality or hierarchical order within the neocortex.

Spatial profile and differential recruitment of GABAB modulate oscillatory activity in auditory cortex

The interplay between inhibition and excitation is at the core of cortical network activity. In many cortices, including auditory cortex (ACx), interactions between excitatory and inhibitory neurons generate synchronous network gamma oscillations (30-70 Hz). Here, we show that differences in the connection patterns and synaptic properties of excitatory-inhibitory microcircuits permit the spatial extent of network inputs to modulate the magnitude of gamma oscillations. Simultaneous multiple whole-cell recordings from connected fast-spiking interneurons and pyramidal cells in L2/3 of mouse ACx slices revealed that for intersomatic distances <50 microm, most inhibitory connections occurred in reciprocally connected (RC) pairs; at greater distances, inhibitory connections were equally likely in RC and nonreciprocally connected (nRC) pairs. Furthermore, the GABA(B)-mediated inhibition in RC pairs was weaker than in nRC pairs. Simulations with a network model that incorporated these features showed strong, gamma band oscillations only when the network inputs were confined to a small area. These findings suggest a novel mechanism by which oscillatory activity can be modulated by adjusting the spatial distribution of afferent input.

How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains

Functional interactions between neurons in vivo are often quantified by cross-correlation functions (CCFs) between their spike trains. It is therefore essential to understand quantitatively how CCFs are shaped by different factors, such as connectivity, synaptic parameters, and background activity. Here, we study the CCF between two neurons using analytical calculations and numerical simulations. We quantify the role of synaptic parameters, such as peak conductance, decay time, and reversal potential, and analyze how various patterns of connectivity influence CCF shapes. In particular, we find that the symmetry of the CCF distinguishes in general, but not always, the case of shared inputs between two neurons from the case in which they are directly synaptically connected. We systematically examine the influence of background synaptic inputs from the surrounding network that set the baseline firing statistics of the neurons and modulate their response properties. We find that variations in the background noise modify the amplitude of the cross-correlation function as strongly as variations of synaptic strength. In particular, we show that the postsynaptic neuron spiking regularity has a pronounced influence on CCF amplitude. This suggests an efficient and flexible mechanism for modulating functional interactions.

Cortical inhibitory cell types differentially form intralaminar and interlaminar subnetworks with excitatory neurons

The neocortical circuit is composed of excitatory principal neurons and inhibitory interneurons. Recent advances have established that multiple subnetworks of synaptically coupled excitatory neurons provide distinct pathways for information flow through the cortical circuit. Here we have investigated how inhibitory interneurons are incorporated into these excitatory subnetworks in the rat frontal cortex. In layer 5 (L5), the probability of reciprocal synaptic connections between pyramidal cells and fast-spiking (FS) interneurons was significantly higher than the probability of reciprocal connections between pyramidal cells and non-FS interneurons. Further, the amplitude of synaptic currents in reciprocally connected FS/pyramidal cell pairs was larger than that in pairs connected only in one direction. To examine interlaminar connection specificity, we stimulated layer 2/3 (L2/3) pyramidal cells, using focal glutamate puff stimulation, and recorded evoked EPSCs in L5 cells. Stimulation of L2/3 cells evoked EPSCs in L5 non-FS cells more frequently than in L5 FS cells. Dual recordings from L5 interneurons and neighboring pyramidal cells revealed that connected non-FS/pyramidal cell pairs were more likely to share excitatory inputs from L2/3 cells than were unconnected cell pairs. On the other hand, the connectivity between L5 FS and pyramidal cell pairs did not affect the common input probability from L2/3. Our results suggest that L5 inhibitory interneurons form distinct intralaminar and interlaminar subnetworks with pyramidal cells, depending on inhibitory cell types.

Cell-type identity: a key to unlocking the function of neocortical circuits

A central tenet of neuroscience is that the precise patterns of connectivity among neurons in a given brain area underlie its function. However, assigning any aspect of perception or behavior to the wiring of local circuits has been challenging. Here, we review recent work in sensory neocortex that demonstrates the power of identifying specific cell types when investigating the functional organization of brain circuits. These studies indicate that knowing the identity of both the presynaptic and postsynaptic cell type is key when analyzing neocortical circuits. Furthermore, identifying the circuit organization of particular cell types in the neocortex allows the recording and manipulation of each cell type's activity and the direct testing of its functional role in perception and behavior.

Cell-type specific properties of pyramidal neurons in neocortex underlying a layout that is modifiable depending on the cortical area

To understand sensory representation in cortex, it is crucial to identify its constituent cellular components based on cell-type-specific criteria. With the identification of cell types, an important question can be addressed: to what degree does the cellular properties of neurons depend on cortical location? We tested this question using pyramidal neurons in layer 5 (L5) because of their role in providing major cortical output to subcortical targets. Recently developed transgenic mice with cell-type-specific enhanced green fluorescent protein labeling of neuronal subtypes allow reliable identification of 2 cortical cell types in L5 throughout the entire neocortex. A comprehensive investigation of anatomical and functional properties of these 2 cell types in visual and somatosensory cortex demonstrates that, with important exceptions, most properties appear to be cell-type-specific rather than dependent on cortical area. This result suggests that although cortical output neurons share a basic layout throughout the sensory cortex, fine differences in properties are tuned to the cortical area in which neurons reside.

A spike-timing pattern based neural network model for the study of memory dynamics

It is well accepted that the brain's computation relies on spatiotemporal activity of neural networks. In particular, there is growing evidence of the importance of continuously and precisely timed spiking activity. Therefore, it is important to characterize memory states in terms of spike-timing patterns that give both reliable memory of firing activities and precise memory of firing timings. The relationship between memory states and spike-timing patterns has been studied empirically with large-scale recording of neuron population in recent years. Here, by using a recurrent neural network model with dynamics at two time scales, we construct a dynamical memory network model which embeds both fast neural and synaptic variation and slow learning dynamics. A state vector is proposed to describe memory states in terms of spike-timing patterns of neural population, and a distance measure of state vector is defined to study several important phenomena of memory dynamics: partial memory recall, learning efficiency, learning with correlated stimuli. We show that the distance measure can capture the timing difference of memory states. In addition, we examine the influence of network topology on learning ability, and show that local connections can increase the network's ability to embed more memory states. Together theses results suggest that the proposed system based on spike-timing patterns gives a productive model for the study of detailed learning and memory dynamics.

Correlations in spiking neuronal networks with distance dependent connections

Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types.

Spontaneous events outline the realm of possible sensory responses in neocortical populations

Neocortical assemblies produce complex activity patterns both in response to sensory stimuli and spontaneously without sensory input. To investigate the structure of these patterns, we recorded from populations of 40-100 neurons in auditory and somatosensory cortices of anesthetized and awake rats using silicon microelectrodes. Population spike time patterns were broadly conserved across multiple sensory stimuli and spontaneous events. Although individual neurons showed timing variations between stimuli, these were not sufficient to disturb a generally conserved sequential organization observed at the population level, lasting for approximately 100 ms with spiking reliability decaying progressively after event onset. Preserved constraints were also seen in population firing rate vectors, with vectors evoked by individual stimuli occupying subspaces of a larger but still constrained space outlined by the set of spontaneous events. These results suggest that population spike patterns are drawn from a limited "vocabulary," sampled widely by spontaneous events but more narrowly by sensory responses.

Transcriptional regulation and alternative splicing make for better brains

In this issue of Neuron, Johnson et al. employ a unique whole-genome exon-level analysis of the developing human brain showing that 76% of genes are expressed along with unexpectedly high levels of differential expression. These results have important consequences for understanding normal and pathological function and provide implications about the uniqueness of being human.

Motif distribution, dynamical properties, and computational performance of two data-based cortical microcircuit templates

The neocortex is a continuous sheet composed of rather stereotypical local microcircuits that consist of neurons on several laminae with characteristic synaptic connectivity patterns. An understanding of the structure and computational function of these cortical microcircuits may hold the key for understanding the enormous computational power of the neocortex. Two templates for the structure of laminar cortical microcircuits have recently been published by Thomson et al. and Binzegger et al., both resulting from long-lasting experimental studies (but based on different methods). We analyze and compare in this article the structure of these two microcircuit templates. In particular, we examine the distribution of network motifs, i.e. of subcircuits consisting of a small number of neurons. The distribution of these building blocks has recently emerged as a method for characterizing similarities and differences among complex networks. We show that the two microcircuit templates have quite different distributions of network motifs, although they both have a characteristic small-world property. In order to understand the dynamical and computational properties of these two microcircuit templates, we have generated computer models of them, consisting of Hodgkin-Huxley point neurons with conductance based synapses that have a biologically realistic short-term plasticity. The performance of these two cortical microcircuit models was studied for seven generic computational tasks that require accumulation and merging of information contained in two afferent spike inputs. Although the two models exhibit a different performance for some of these tasks, their average computational performance is very similar. When we changed the connectivity structure of these two microcircuit models in order to see which aspects of it are essential for computational performance, we found that the distribution of degrees of nodes is a common key factor for their computational performance. We also show that their computational performance is correlated with specific statistical properties of the circuit dynamics that is induced by a particular distribution of degrees of nodes.

Nonrandom local circuits in the dentate gyrus

The dentate hilus has been extensively studied in relation to its potential role in memory and in temporal lobe epilepsy. Little is known, however, about the synapses formed between the two major cell types in this region, glutamatergic mossy cells and hilar interneurons, or the organization of local circuits involving these cells. Using triple and quadruple simultaneous intracellular recordings in rat hippocampal slices, we find that mossy cells evoke EPSPs with high failure rates onto hilar neurons. Mossy cells show profound synapse specificity; 87.5% of their intralamellar connections are onto hilar interneurons. Hilar interneurons also show synapse specificity and preferentially inhibit mossy cells; 81% of inhibitory hilar synapses are onto mossy cells. Hilar IPSPs have low failure rates, are blocked by the GABA(A) receptor antagonist gabazine, and exhibit short-term depression when tested at 17 Hz. Surprisingly, more than half (57%) of the mossy cell synapses we found onto interneurons were part of reciprocal excitatory/inhibitory local circuit motifs. Neither the high degree of target cell specificity, nor the significant enrichment of structured polysynaptic local circuit motifs, could be explained by nonrandom sampling or somatic proximity. Intralamellar hilar synapses appear to function primarily by integrating synchronous inputs and presynaptic burst discharges, allowing hilar cells to respond over a large dynamic range of input strengths. The reciprocal mossy cell/interneuron local circuit motifs we find enriched in the hilus may generate sparse neural representations involved in hippocampal memory operations.

Burst spiking of a single cortical neuron modifies global brain state

Different global patterns of brain activity are associated with distinct arousal and behavioral states of an animal, but how the brain rapidly switches between different states remains unclear. We here report that repetitive high-frequency burst spiking of a single rat cortical neuron could trigger a switch between the cortical states resembling slow-wave and rapid-eye-movement sleep. This is reflected in the switching of the membrane potential of the stimulated neuron from slow UP/DOWN oscillations to a persistent-UP state or vice versa, with concurrent changes in the temporal pattern of cortical local field potential (LFP) recorded several millimeters away. These results point to the power of single cortical neurons in modulating the behavioral state of an animal.

Synaptic output of individual layer 4 neurons in guinea pig visual cortex

More than 90% of geniculocortical axons from the dorsal lateral geniculate nucleus of the thalamus innervate layer 4 (L4) of V1 (primary visual cortex). Excitatory neurons, which comprise >80% of the neuronal population in L4, synapse mainly onto adjacent L4 neurons and layer 2/3 (L2/3) neurons. It has been suggested that intralaminar L4-L4 connections contribute to amplifying and refining thalamocortical signals before routing to L2/3. To unambiguously probe the properties of the synaptic outputs from these L4 excitatory neurons, we used multiple simultaneous whole-cell patch-clamp recording and stimulation from two to four neighboring L4 neurons. We recorded uEPSCs (evoked unitary synaptic currents) in response to pairs of action potentials elicited in single presynaptic L4 neurons for 102 L4 cell pairs and found that their properties are more diverse than previously described. Averaged unitary synaptic response peak amplitudes spanned almost three orders of magnitude, from 0.42 to 192.92 pA. Although connections were, on average, reliable (average failure rate, 25%), we recorded a previously unknown subset of unreliable (failure rates from 30 to 100%) and weak (averaged response amplitudes, <5 pA) connections. Reliable connections with high probability of neurotransmitter release responded to paired presynaptic pulses with depression, whereas unreliable connections underwent paired-pulse facilitation. Recordings from interconnected sets of L4 triplets revealed that synaptic response amplitudes and reliability were equally variable between independent cell pairs and those that shared a common presynaptic or postsynaptic cell, suggesting local perisynaptic influences on the development and/or state of synaptic function.

Reading the book of memory: sparse sampling versus dense mapping of connectomes

Many theories of neural networks assume rules of connection between pairs of neurons that are based on their cell types or functional properties. It is finally becoming feasible to test such pairwise models of connectivity, due to emerging advances in neuroanatomical techniques. One method will be to measure the functional properties of connected pairs of neurons, sparsely sampling pairs from many specimens. Another method will be to find a "connectome," a dense map of all connections in a single specimen, and infer functional properties of neurons through computational analysis. For the latter method, the most exciting prospect would be to decode the memories that are hypothesized to be stored in connectomes.

Stochastic and coherence resonance in feed-forward-loop neuronal network motifs

The relationships between noise and complex dynamic behaviors of neuronal ensembles are key questions in computational neuroscience, particularly in understanding some basic signal transmission mechanisms of the brain. Here we systemically investigate both the stochastic resonance (SR) and coherence resonance (CR) in the triple-neuron feed-forward-loop (FFL) network motifs by computational modeling. We use the Izhikevich neuron model as well as the chemical coupling to build the FFL motifs, and consider all possible motif types. The simulation results demonstrate that these motifs can exploit noise to enrich its dynamic performance. With a proper choice of noise intensities, both the SR and CR can be exhibited in many types of the FFLs. On the other hand, our results also indicate that the coupling strength serves as a control parameter, which has great impacts on the stochastic dynamics of the FFL motifs. Additionally, biological implications of presented results in the field of neuroscience are outlined.

Rapid neocortical dynamics: cellular and network mechanisms

The highly interconnected local and large-scale networks of the neocortical sheet rapidly and dynamically modulate their functional connectivity according to behavioral demands. This basic operating principle of the neocortex is mediated by the continuously changing flow of excitatory and inhibitory synaptic barrages that not only control participation of neurons in networks but also define the networks themselves. The rapid control of neuronal responsiveness via synaptic bombardment is a fundamental property of cortical dynamics that may provide the basis of diverse behaviors, including sensory perception, motor integration, working memory, and attention.

Reverse optical trawling for synaptic connections in situ

We introduce a new method to unveil the network connectivity among dozens of neurons in brain slice preparations. While synaptic inputs were whole cell recorded from given postsynaptic neurons, the spatiotemporal firing patterns of presynaptic neuron candidates were monitored en masse with functional multineuron calcium imaging, an optical technique that records action potential-evoked somatic calcium transients with single-cell resolution. By statistically screening the neurons that exhibited calcium transients immediately before the postsynaptic inputs, we identified the presynaptic cells that made synaptic connections onto the patch-clamped neurons. To enhance the detection power, we devised the following points: 1) [K+]e was lowered and [Ca2+]e and [Mg2+]e were elevated, to reduce background synaptic activity and minimize the failure rate of synaptic transmission; and 2) a small fraction of presynaptic neurons was specifically activated by glutamate applied iontophoretically through a glass pipette that was moved to survey the presynaptic network of interest ("trawling"). Then we could theoretically detect 96% of presynaptic neurons activated in the imaged regions with a 1% false-positive error rate. This on-line probing technique would be a promising tool in the study of the wiring topography of neuronal circuits.

Correlated connectivity and the distribution of firing rates in the neocortex

Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of nonzero synaptic strengths between nearby cortical neurons can also be described by a lognormal distribution. Here we use a simple model of cortical activity to reconcile these observations. The model makes the experimentally testable prediction that synaptic efficacies onto a given cortical neuron are statistically correlated, i.e., it predicts that some neurons receive stronger synapses than other neurons. We propose a simple Hebb-like learning rule that gives rise to such correlations and yields both lognormal firing rates and synaptic efficacies. Our results represent a first step toward reconciling sparse activity and sparse connectivity in cortical networks.

Traveling waves in developing cerebellar cortex mediated by asymmetrical Purkinje cell connectivity

Correlated network activity is important in the development of many neural circuits. Purkinje cells are among the first neurons to populate the cerebellar cortex, where they sprout exuberant axon collaterals. We used multiple patch-clamp recordings targeted with two-photon microscopy to characterize monosynaptic connections between the Purkinje cells of juvenile mice. We found that Purkinje cell axon collaterals projected asymmetrically in the sagittal plane, directed away from the lobule apex. On the basis of our anatomical and physiological characterization of this connection, we constructed a network model that robustly generated waves of activity that traveled along chains of connected Purkinje cells. Consistent with the model, we observed traveling waves of activity in Purkinje cells in sagittal slices from young mice that require GABA(A) receptor-mediated transmission and intact Purkinje cell axon collaterals. These traveling waves are absent in adult mice, suggesting they have a developmental role in wiring the cerebellar cortical microcircuit.

Memory retention and spike-timing-dependent plasticity

Memory systems should be plastic to allow for learning; however, they should also retain earlier memories. Here we explore how synaptic weights and memories are retained in models of single neurons and networks equipped with spike-timing-dependent plasticity. We show that for single neuron models, the precise learning rule has a strong effect on the memory retention time. In particular, a soft-bound, weight-dependent learning rule has a very short retention time as compared with a learning rule that is independent of the synaptic weights. Next, we explore how the retention time is reflected in receptive field stability in networks. As in the single neuron case, the weight-dependent learning rule yields less stable receptive fields than a weight-independent rule. However, receptive fields stabilize in the presence of sufficient lateral inhibition, demonstrating that plasticity in networks can be regulated by inhibition and suggesting a novel role for inhibition in neural circuits.

The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex

Local microcircuits within neocortical columns form key determinants of sensory processing. Here, we investigate the excitatory synaptic neuronal network of an anatomically defined cortical column, the C2 barrel column of mouse primary somatosensory cortex. This cortical column is known to process tactile information related to the C2 whisker. Through multiple simultaneous whole-cell recordings, we quantify connectivity maps between individual excitatory neurons located across all cortical layers of the C2 barrel column. Synaptic connectivity depended strongly upon somatic laminar location of both presynaptic and postsynaptic neurons, providing definitive evidence for layer-specific signaling pathways. The strongest excitatory influence upon the cortical column was provided by presynaptic layer 4 neurons. In all layers we found rare large-amplitude synaptic connections, which are likely to contribute strongly to reliable information processing. Our data set provides the first functional description of the excitatory synaptic wiring diagram of a physiologically relevant and anatomically well-defined cortical column at single-cell resolution.

Precisely timed signal transmission in neocortical networks with reliable intermediate-range projections

The mammalian neocortex has a remarkable ability to precisely reproduce behavioral sequences or to reliably retrieve stored information. In contrast, spiking activity in behaving animals shows a considerable trial-to-trial variability and temporal irregularity. The signal propagation and processing underlying these conflicting observations is based on fundamental neurophysiological processes like synaptic transmission, signal integration within single cells, and spike formation. Each of these steps in the neuronal signaling chain has been studied separately to a great extend, but it has been difficult to judge how they interact and sum up in active sub-networks of neocortical cells. In the present study, we experimentally assessed the precision and reliability of small neocortical networks consisting of trans-columnar, intermediate-range projections (200-1000 mum) on a millisecond time-scale. Employing photo-uncaging of glutamate in acute slices, we activated a number of distant presynaptic cells in a spatio-temporally precisely controlled manner, while monitoring the resulting membrane potential fluctuations of a postsynaptic cell. We found that signal integration in this part of the network is highly reliable and temporally precise. As numerical simulations showed, the residual membrane potential variability can be attributed to amplitude variability in synaptic transmission and may significantly contribute to trial-to-trial output variability of a rate signal. However, it does not impair the temporal accuracy of signal integration. We conclude that signals from intermediate-range projections onto neocortical neurons are propagated and integrated in a highly reliable and precise manner, and may serve as a substrate for temporally precise signal transmission in neocortical networks.

Specific synapses develop preferentially among sister excitatory neurons in the neocortex

Neurons in the mammalian neocortex are organized into functional columns 1, 2. Within a column, highly specific synaptic connections are formed to ensure that similar physiological properties are shared by neuron ensembles spanning from the pia to the white matter. Recent studies suggest that synaptic connectivity in the neocortex is sparse and highly specific 3–8 to allow even adjacent neurons to convey information independently 9–12. How this fine-scale microcircuit is constructed to create a functional columnar architecture at the level of individual neurons largely remains a mystery. Here we investigate whether radial clones of excitatory neurons arising from the same mother cell in the developing neocortex serve as a substrate for the formation of this highly specific microcircuit. We labelled ontogenetic radial clones of excitatory neurons in the mouse neocortex by in utero intraventricular injection of EGFP-expressing retroviruses around the onset of the peak phase of neocortical neurogenesis. Multiple-electrode whole-cell recordings were performed to probe synapse formation among these EGFP-labelled sister excitatory neurons in radial clones and the adjacent non-siblings during postnatal stages. We found that radially aligned sister excitatory neurons have a propensity for developing unidirectional chemical synapses with each other rather than with neighbouring non-siblings. Moreover, these synaptic connections display the same interlaminar directional preference as those observed in the mature neocortex. These results suggest that specific microcircuits develop preferentially within ontogenetic radial clones of excitatory neurons in the developing neocortex and contribute to the emergence of functional columnar microarchitectures in the mature neocortex.

Complex brain networks: graph theoretical analysis of structural and functional systems

Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Intracortical circuits of pyramidal neurons reflect their long-range axonal targets

Cortical columns generate separate streams of information that are distributed to numerous cortical and subcortical brain regions1. We asked whether local intracortical circuits reflect these different processing streams by testing if the intracortical connectivity among pyramids reflects their long-range axonal targets. We recorded simultaneously from up to four retrogradely labelled pyramids that projected to the superior colliculus, the contralateral striatum or the contralateral cortex to assess their synaptic connectivity. Here we show that the probability of synaptic connection depends on the functional identity of both the presynaptic and postsynaptic neurons. We first found that the frequency of monosynaptic connections among corticostriatal pyramids is significantly higher than among corticocortical or corticotectal pyramids. We then show that the probability of feedforward connections from corticocortical neurons to corticotectal pyramids is approximately three- to fourfold higher than the probability of monosynaptic connections among corticocortical or corticotectal cells. Moreover, we found that the average axodendritic overlap of the presynaptic and postsynaptic pyramids could not fully explain the differences in connection probability that we observed. The selective synaptic interactions we describe demonstrate that the organization of local networks of pyramidal cells reflects the long-range targets of both the presynaptic and postsynaptic neurons.

Paired-recordings from synaptically coupled cortical and hippocampal neurons in acute and cultured brain slices

Analysis of synaptic transmission, synaptic plasticity, axonal processing, synaptic timing or electrical coupling requires the simultaneous recording of both the pre- and postsynaptic compartments. Paired-recording technique of monosynaptically connected neurons is also an appropriate technique to probe the function of small molecules (calcium buffers, peptides or small proteins) at presynaptic terminals that are too small to allow direct whole-cell patch-clamp recording. We describe here a protocol for obtaining, in acute and cultured slices, synaptically connected pairs of cortical and hippocampal neurons, with a reasonably high probability. The protocol includes four main stages (acute/cultured slice preparation, visualization, recording and analysis) and can be completed in approximately 4 h.

Stimulus contrast modulates functional connectivity in visual cortex

Neurons in visual cortex are linked by an extensive network of lateral connections. To study the effect of these connections on neural responses, we recorded spikes and local field potentials (LFPs) from multi-electrode arrays that were implanted in monkey and cat primary visual cortex. Spikes at each location generated outward traveling LFP waves. When the visual stimulus was absent or had low contrast, these LFP waves had large amplitudes and traveled over long distances. Their effect was strong: LFP traces at any site could be predicted by the superposition of waves that were evoked by spiking in a approximately 1.5-mm radius. As stimulus contrast increased, both the magnitude and the distance traveled by the waves progressively decreased. We conclude that the relative weight of feedforward and lateral inputs in visual cortex is not fixed, but rather depends on stimulus contrast. Lateral connections dominate at low contrast, when spatial integration of signals is perhaps most beneficial.

Firing-pattern-dependent specificity of cortical excitatory feed-forward subnetworks

The cortical circuit includes networks of highly interconnected pyramidal neurons. Here, we investigated whether pyramidal cells form subnetworks depending on pyramidal subtypes. We classified layer V (L5) pyramidal cells in rat frontal cortex into three physiological subtypes based on the presence (SA-d type) or absence (SA type) of an initial burst in neurons displaying slowly adapting spike trains, or fast spike frequency adaptation (FA type) against current pulse injections. Pyramidal cells projecting to the particular subcortical areas were correlated with the physiological subtypes. Focal glutamate stimulation of a L2/3 pyramidal cell induced EPSCs in SA and SA-d cells more frequently than in FA cells. FA cells in upper L5 received more inputs from the upper L2/3, and those in lower L5 received inputs from cells in lower L2/3, suggesting topographic interlaminar projections to FA cells. Dual recordings from L5 pyramidal cells revealed that common input probability that two L5 cells share inputs from a L2/3 cell was high in cell pairs of the same subtypes, compared with those in different subtype pairs. Furthermore, the common input probability was highly selective when cell pairs of the same subtypes, but not different subtypes, had connections between them. Our results suggest that L2/3 pyramidal cells selectively innervate L5 cells, depending on their firing subtypes.

The statistics of repeating patterns of cortical activity can be reproduced by a model network of stochastic binary neurons

Calcium imaging of the spontaneous activity in cortical slices has revealed repeating spatiotemporal patterns of transitions between so-called down states and up states (Ikegaya et al., 2004). Here we fit a model network of stochastic binary neurons to data from these experiments, and in doing so reproduce the distributions of such patterns. We use two versions of this model: (1) an unconnected network in which neurons are activated as independent Poisson processes; and (2) a network with an interaction matrix, estimated from the data, representing effective interactions between the neurons. The unconnected model (model 1) is sufficient to account for the statistics of repeating patterns in 11 of the 15 datasets studied. Model 2, with interactions between neurons, is required to account for pattern statistics of the remaining four. Three of these four datasets are the ones that contain the largest number of transitions, suggesting that long datasets are in general necessary to render interactions statistically visible. We then study the topology of the matrix of interactions estimated for these four datasets. For three of the four datasets, we find sparse matrices with long-tailed degree distributions and an overrepresentation of certain network motifs. The remaining dataset exhibits a strongly interconnected, spatially localized subgroup of neurons. In all cases, we find that interactions between neurons facilitate the generation of long patterns that do not repeat exactly.

Detecting synfire chain activity using massively parallel spike train recording

The synfire chain model has been proposed as the substrate that underlies computational processes in the brain and has received extensive theoretical study. In this model cortical tissue is composed of a superposition of feedforward subnetworks (chains) each capable of transmitting packets of synchronized spikes with high reliability. Computations are then carried out by interactions of these chains. Experimental evidence for synfire chains has so far been limited to inference from detection of a few repeating spatiotemporal neuronal firing patterns in multiple single-unit recordings. Demonstration that such patterns actually come from synfire activity would require finding a meta organization among many detected patterns, as yet an untried approach. In contrast we present here a new method that directly visualizes the repetitive occurrence of synfire activity even in very large data sets of multiple single-unit recordings. We achieve reliability and sensitivity by appropriately averaging over neuron space (identities) and time. We test the method with data from a large-scale balanced recurrent network simulation containing 50 randomly activated synfire chains. The sensitivity is high enough to detect synfire chain activity in simultaneous single-unit recordings of 100 to 200 neurons from such data, enabling application to experimental data in the near future.

A self-regulating feed-forward circuit controlling C. elegans egg-laying behavior

BACKGROUND

Egg laying in Caenorhabditis elegans has been well studied at the genetic and behavioral levels. However, the neural basis of egg-laying behavior is still not well understood; in particular, the roles of specific neurons and the functional nature of the synaptic connections in the egg-laying circuit remain uncharacterized.

RESULTS

We have used in vivo neuroimaging and laser surgery to address these questions in intact, behaving animals. We have found that the HSN neurons play a central role in driving egg-laying behavior through direct excitation of the vulval muscles and VC motor neurons. The VC neurons play a dual role in the egg-laying circuit, exciting the vulval muscles while feedback-inhibiting the HSNs. Interestingly, the HSNs are active in the absence of synaptic input, suggesting that egg laying may be controlled through modulation of autonomous HSN activity. Indeed, body touch appears to inhibit egg laying, in part by interfering with HSN calcium oscillations.

CONCLUSIONS

The egg-laying motor circuit comprises a simple three-component system combining feed-forward excitation and feedback inhibition. This microcircuit motif is common in the C. elegans nervous system, as well as in the mammalian cortex; thus, understanding its functional properties in C. elegans may provide insight into its computational role in more complex brains.

Rhythm generation through period concatenation in rat somatosensory cortex

Rhythmic voltage oscillations resulting from the summed activity of neuronal populations occur in many nervous systems. Contemporary observations suggest that coexistent oscillations interact and, in time, may switch in dominance. We recently reported an example of these interactions recorded from in vitro preparations of rat somatosensory cortex. We found that following an initial interval of coexistent gamma ( approximately 25 ms period) and beta2 ( approximately 40 ms period) rhythms in the superficial and deep cortical layers, respectively, a transition to a synchronous beta1 ( approximately 65 ms period) rhythm in all cortical layers occurred. We proposed that the switch to beta1 activity resulted from the novel mechanism of period concatenation of the faster rhythms: gamma period (25 ms)+beta2 period (40 ms) = beta1 period (65 ms). In this article, we investigate in greater detail the fundamental mechanisms of the beta1 rhythm. To do so we describe additional in vitro experiments that constrain a biologically realistic, yet simplified, computational model of the activity. We use the model to suggest that the dynamic building blocks (or motifs) of the gamma and beta2 rhythms combine to produce a beta1 oscillation that exhibits cross-frequency interactions. Through the combined approach of in vitro experiments and mathematical modeling we isolate the specific components that promote or destroy each rhythm. We propose that mechanisms vital to establishing the beta1 oscillation include strengthened connections between a population of deep layer intrinsically bursting cells and a transition from antidromic to orthodromic spike generation in these cells. We conclude that neural activity in the superficial and deep cortical layers may temporally combine to generate a slower oscillation.