Highly nonrandom features of synaptic connectivity in local cortical circuits

The dendritic density field of a cortical pyramidal cell

Much is known about the computation in individual neurons in the cortical column. Also, the selective connectivity between many cortical neuron types has been studied in great detail. However, due to the complexity of this microcircuitry its functional role within the cortical column remains a mystery. Some of the wiring behavior between neurons can be interpreted directly from their particular dendritic and axonal shapes. Here, I describe the dendritic density field (DDF) as one key element that remains to be better understood. I sketch an approach to relate DDFs in general to their underlying potential connectivity schemes. As an example, I show how the characteristic shape of a cortical pyramidal cell appears as a direct consequence of connecting inputs arranged in two separate parallel layers.

Beyond statistical significance: implications of network structure on neuronal activity

It is a common and good practice in experimental sciences to assess the statistical significance of measured outcomes. For this, the probability of obtaining the actual results is estimated under the assumption of an appropriately chosen null-hypothesis. If this probability is smaller than some threshold, the results are deemed statistically significant and the researchers are content in having revealed, within their own experimental domain, a “surprising” anomaly, possibly indicative of a hitherto hidden fragment of the underlying “ground-truth”. What is often neglected, though, is the actual importance of these experimental outcomes for understanding the system under investigation. We illustrate this point by giving practical and intuitive examples from the field of systems neuroscience. Specifically, we use the notion of embeddedness to quantify the impact of a neuron's activity on its downstream neurons in the network. We show that the network response strongly depends on the embeddedness of stimulated neurons and that embeddedness is a key determinant of the importance of neuronal activity on local and downstream processing. We extrapolate these results to other fields in which networks are used as a theoretical framework.

Spatiotemporal dynamics of neocortical excitation and inhibition during human sleep

Intracranial recording is an important diagnostic method routinely used in a number of neurological monitoring scenarios. In recent years, advancements in such recordings have been extended to include unit activity of an ensemble of neurons. However, a detailed functional characterization of excitatory and inhibitory cells has not been attempted in human neocortex, particularly during the sleep state. Here, we report that such feature discrimination is possible from high-density recordings in the neocortex by using 2D multielectrode arrays. Successful separation of regular-spiking neurons (or bursting cells) from fast-spiking cells resulted in well-defined clusters that each showed unique intrinsic firing properties. The high density of the array, which allowed recording from a large number of cells (up to 90), helped us to identify apparent monosynaptic connections, confirming the excitatory and inhibitory nature of regular-spiking and fast-spiking cells, thus categorized as putative pyramidal cells and interneurons, respectively. Finally, we investigated the dynamics of correlations within each class. A marked exponential decay with distance was observed in the case of excitatory but not for inhibitory cells. Although the amplitude of that decline depended on the timescale at which the correlations were computed, the spatial constant did not. Furthermore, this spatial constant is compatible with the typical size of human columnar organization. These findings provide a detailed characterization of neuronal activity, functional connectivity at the microcircuit level, and the interplay of excitation and inhibition in the human neocortex.

Large-scale automated histology in the pursuit of connectomes

How does the brain compute? Answering this question necessitates neuronal connectomes, annotated graphs of all synaptic connections within defined brain areas. Further, understanding the energetics of the brain's computations requires vascular graphs. The assembly of a connectome requires sensitive hardware tools to measure neuronal and neurovascular features in all three dimensions, as well as software and machine learning for data analysis and visualization. We present the state of the art on the reconstruction of circuits and vasculature that link brain anatomy and function. Analysis at the scale of tens of nanometers yields connections between identified neurons, while analysis at the micrometer scale yields probabilistic rules of connection between neurons and exact vascular connectivity.

On the distribution of firing rates in networks of cortical neurons

The distribution of in vivo average firing rates within local cortical networks has been reported to be highly skewed and long tailed. The distribution of average single-cell inputs, conversely, is expected to be Gaussian by the central limit theorem. This raises the issue of how a skewed distribution of firing rates might result from a symmetric distribution of inputs. We argue that skewed rate distributions are a signature of the nonlinearity of the in vivo f-I curve. During in vivo conditions, ongoing synaptic activity produces significant fluctuations in the membrane potential of neurons, resulting in an expansive nonlinearity of the f-I curve for low and moderate inputs. Here, we investigate the effects of single-cell and network parameters on the shape of the f-I curve and, by extension, on the distribution of firing rates in randomly connected networks.

Heterogeneous reallocation of presynaptic efficacy in recurrent excitatory circuits adapting to inactivity

Recurrent excitatory circuits face extreme challenges in balancing efficacy and stability. We recorded from CA3 pyramidal neuron pairs in rat hippocampal slice cultures to characterize synaptic and circuit-level changes in recurrent synapses resulting from long-term inactivity. Chronic tetrodotoxin treatment greatly reduced the percentage of connected CA3-CA3 neurons, but enhanced the strength of the remaining connections; presynaptic release probability sharply increased, whereas quantal size was unaltered. Connectivity was decreased in activity-deprived circuits by functional silencing of synapses, whereas three-dimensional anatomical analysis revealed no change in spine or bouton density or aggregate dendrite length. The silencing arose from enhanced Cdk5 activity and could be reverted by acute Cdk5 inhibition with roscovitine. Our results suggest that recurrent circuits adapt to chronic inactivity by reallocating presynaptic weights heterogeneously, strengthening certain connections while silencing others. This restricts synaptic output and input, preserving signaling efficacy among a subset of neuronal ensembles while protecting network stability.

Dynamical changes in neurons during seizures determine tonic to clonic shift

A tonic-clonic seizure transitions from high frequency asynchronous activity to low frequency coherent oscillations, yet the mechanism of transition remains unknown. We propose a shift in network synchrony due to changes in cellular response. Here we use phase-response curves (PRC) from Morris-Lecar (M-L) model neurons with synaptic depression and gradually decrease input current to cells within a network simulation. This method effectively decreases firing rates resulting in a shift to greater network synchrony illustrating a possible mechanism of the transition phenomenon. PRCs are measured from the M-L conductance based model cell with a range of input currents within the limit cycle. A large network of 3000 excitatory neurons is simulated with a network topology generated from second-order statistics which allows a range of population synchrony. The population synchrony of the oscillating cells is measured with the Kuramoto order parameter, which reveals a transition from tonic to clonic phase exhibited by our model network. The cellular response shift mechanism for the tonic-clonic seizure transition reproduces the population behavior closely when compared to EEG data.

Self-organizing circuit assembly through spatiotemporally coordinated neuronal migration within geometric constraints

BACKGROUND

Neurons are dynamically coupled with each other through neurite-mediated adhesion during development. Understanding the collective behavior of neurons in circuits is important for understanding neural development. While a number of genetic and activity-dependent factors regulating neuronal migration have been discovered on single cell level, systematic study of collective neuronal migration has been lacking. Various biological systems are shown to be self-organized, and it is not known if neural circuit assembly is self-organized. Besides, many of the molecular factors take effect through spatial patterns, and coupled biological systems exhibit emergent property in response to geometric constraints. How geometric constraints of the patterns regulate neuronal migration and circuit assembly of neurons within the patterns remains unexplored.

METHODOLOGY/PRINCIPAL FINDINGS

We established a two-dimensional model for studying collective neuronal migration of a circuit, with hippocampal neurons from embryonic rats on Matrigel-coated self-assembled monolayers (SAMs). When the neural circuit is subject to geometric constraints of a critical scale, we found that the collective behavior of neuronal migration is spatiotemporally coordinated. Neuronal somata that are evenly distributed upon adhesion tend to aggregate at the geometric center of the circuit, forming mono-clusters. Clustering formation is geometry-dependent, within a critical scale from 200 µm to approximately 500 µm. Finally, somata clustering is neuron-type specific, and glutamatergic and GABAergic neurons tend to aggregate homo-philically.

CONCLUSIONS/SIGNIFICANCE

We demonstrate self-organization of neural circuits in response to geometric constraints through spatiotemporally coordinated neuronal migration, possibly via mechanical coupling. We found that such collective neuronal migration leads to somata clustering, and mono-cluster appears when the geometric constraints fall within a critical scale. The discovery of geometry-dependent collective neuronal migration and the formation of somata clustering in vitro shed light on neural development in vivo.

Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model

Transfer entropy (TE) is an information-theoretic measure which has received recent attention in neuroscience for its potential to identify effective connectivity between neurons. Calculating TE for large ensembles of spiking neurons is computationally intensive, and has caused most investigators to probe neural interactions at only a single time delay and at a message length of only a single time bin. This is problematic, as synaptic delays between cortical neurons, for example, range from one to tens of milliseconds. In addition, neurons produce bursts of spikes spanning multiple time bins. To address these issues, here we introduce a free software package that allows TE to be measured at multiple delays and message lengths. To assess performance, we applied these extensions of TE to a spiking cortical network model (Izhikevich, 2006) with known connectivity and a range of synaptic delays. For comparison, we also investigated single-delay TE, at a message length of one bin (D1TE), and cross-correlation (CC) methods. We found that D1TE could identify 36% of true connections when evaluated at a false positive rate of 1%. For extended versions of TE, this dramatically improved to 73% of true connections. In addition, the connections correctly identified by extended versions of TE accounted for 85% of the total synaptic weight in the network. Cross correlation methods generally performed more poorly than extended TE, but were useful when data length was short. A computational performance analysis demonstrated that the algorithm for extended TE, when used on currently available desktop computers, could extract effective connectivity from 1 hr recordings containing 200 neurons in ∼5 min. We conclude that extending TE to multiple delays and message lengths improves its ability to assess effective connectivity between spiking neurons. These extensions to TE soon could become practical tools for experimentalists who record hundreds of spiking neurons.

Intrinsic morphological diversity of thick-tufted layer 5 pyramidal neurons ensures robust and invariant properties of in silico synaptic connections

The morphology of neocortical pyramidal neurons is not only highly characteristic but also displays an intrinsic diversity that renders each neuron morphologically unique. We investigated the significance of this intrinsic morphological diversity in in silico networks composed of thick-tufted layer 5 (TTL5) pyramidal neurons, by comparing the in silico and in vitro properties of TTL5 synaptic connections. The synaptic locations of in silico connections were determined by placing 3D reconstructed TTL5 neurons randomly in a volume equivalent to that of layer 5 in the juvenile rat somatosensory cortex and using a 'collision-detection' algorithm to identify the incidental loci of axo-dendritic overlap. The activation time of the modelled synapses and their biophysical properties were characterized based on experimental measurements. We found that the anatomical loci of synapses and the physiological properties of the somatically recorded EPSPs closely matched those recorded experimentally without the need for any fine-tuning. Furthermore, perturbations to both the physiological or anatomical parameters of the model did not alter the average physiological properties of the population of modelled synaptic connections. This microcircuit-level robust behaviour was due to the intrinsic diversity of the morphology of pyramidal neurons in the microcircuit. We conclude that synaptic transmission in a network of TTL5 neurons is highly invariant across microcircuits suggesting that intrinsic diversity is a mechanism to ensure the same average synaptic properties in different animals of the same species. Finally, we show that the average physiological properties of the TTL5 microcircuit are surprisingly robust to anatomical and physiological perturbations also partly due to the intrinsic diversity of pyramidal neuron morphology.

Impact of cortical plasticity on patterns of suprathreshold activity in the cerebral cortex

There are many cellular and synaptic mechanisms of plasticity in the vertebrate cortex. How the patterns of suprathreshold spiking activity in a population of neurons change because of this plasticity, however, has hardly been subjected to experimental studies. Here, we measured how evoked patterns of suprathreshold spiking activity in a cortical network were modified by cortical plasticity with single-cell and single-spike resolution. To record patterns of activity in the rodent barrel cortex, we used optical methods to detect suprathreshold activity from up to 40 neurons simultaneously. Pairing of two inputs resulted in a long-lasting modification of the cortical responses evoked by one of the inputs. The results indicate that plasticity rules on the network level inherit properties from synaptic plasticity rules but are also determined by the functional synaptic architecture, as well as the computations carried out in cortical networks. The largest determinants of the modified cortical responses were those observed when inducing changes by pairing the two inputs. On the single-neuron level, the modified responses only weakly reflected those observed when pairing the two inputs for induction of plasticity. Despite the weak reflection on the cellular level, however, the modified patterns reflected the pairing patterns to the degree that a simple decoding mechanism-a linear separator-correctly discriminated the modified responses from other patterns of activity.

Synaptic scaling in combination with many generic plasticity mechanisms stabilizes circuit connectivity

Synaptic scaling is a slow process that modifies synapses, keeping the firing rate of neural circuits in specific regimes. Together with other processes, such as conventional synaptic plasticity in the form of long term depression and potentiation, synaptic scaling changes the synaptic patterns in a network, ensuring diverse, functionally relevant, stable, and input-dependent connectivity. How synaptic patterns are generated and stabilized, however, is largely unknown. Here we formally describe and analyze synaptic scaling based on results from experimental studies and demonstrate that the combination of different conventional plasticity mechanisms and synaptic scaling provides a powerful general framework for regulating network connectivity. In addition, we design several simple models that reproduce experimentally observed synaptic distributions as well as the observed synaptic modifications during sustained activity changes. These models predict that the combination of plasticity with scaling generates globally stable, input-controlled synaptic patterns, also in recurrent networks. Thus, in combination with other forms of plasticity, synaptic scaling can robustly yield neuronal circuits with high synaptic diversity, which potentially enables robust dynamic storage of complex activation patterns. This mechanism is even more pronounced when considering networks with a realistic degree of inhibition. Synaptic scaling combined with plasticity could thus be the basis for learning structured behavior even in initially random networks.

A sparse coding model with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptive fields

Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have developed a biophysically motivated spiking network, relying solely on synaptically local information, that can predict the full diversity of V1 simple cell receptive field shapes when trained on natural images. This represents the first demonstration that sparse coding principles, operating within the constraints imposed by cortical architecture, can successfully reproduce these receptive fields. We further prove, mathematically, that sparseness and decorrelation are the key ingredients that allow for synaptically local plasticity rules to optimize a cooperative, linear generative image model formed by the neural representation. Finally, we discuss several interesting emergent properties of our network, with the intent of bridging the gap between theoretical and experimental studies of visual cortex.

In a sparse coding model, individual input stimuli are represented by the activities of model neurons, the majority of which are inactive in response to any particular stimulus. For a given class of stimuli, the neurons are optimized so that the stimuli can be faithfully represented with the minimum number of co-active units. This has been proposed as a model for visual cortex. While it has previously been demonstrated that sparse coding model neurons, when trained on natural images, learn to represent the same features as do neurons in primate visual cortex, it remains to be demonstrated that this can be achieved with physiologically realistic plasticity rules. In particular, learning in cortex appears to occur by the modification of synaptic connections between neurons, which must depend only on information available locally, at the synapse, and not, for example, on the properties of large numbers of distant cells. We provide the first demonstration that synaptically local plasticity rules are sufficient to learn a sparse image code, and to account for the observed response properties of visual cortical neurons: visual cortex actually could learn a sparse image code.

Stability versus neuronal specialization for STDP: long-tail weight distributions solve the dilemma

Spike-timing-dependent plasticity (STDP) modifies the weight (or strength) of synaptic connections between neurons and is considered to be crucial for generating network structure. It has been observed in physiology that, in addition to spike timing, the weight update also depends on the current value of the weight. The functional implications of this feature are still largely unclear. Additive STDP gives rise to strong competition among synapses, but due to the absence of weight dependence, it requires hard boundaries to secure the stability of weight dynamics. Multiplicative STDP with linear weight dependence for depression ensures stability, but it lacks sufficiently strong competition required to obtain a clear synaptic specialization. A solution to this stability-versus-function dilemma can be found with an intermediate parametrization between additive and multiplicative STDP. Here we propose a novel solution to the dilemma, named log-STDP, whose key feature is a sublinear weight dependence for depression. Due to its specific weight dependence, this new model can produce significantly broad weight distributions with no hard upper bound, similar to those recently observed in experiments. Log-STDP induces graded competition between synapses, such that synapses receiving stronger input correlations are pushed further in the tail of (very) large weights. Strong weights are functionally important to enhance the neuronal response to synchronous spike volleys. Depending on the input configuration, multiple groups of correlated synaptic inputs exhibit either winner-share-all or winner-take-all behavior. When the configuration of input correlations changes, individual synapses quickly and robustly readapt to represent the new configuration. We also demonstrate the advantages of log-STDP for generating a stable structure of strong weights in a recurrently connected network. These properties of log-STDP are compared with those of previous models. Through long-tail weight distributions, log-STDP achieves both stable dynamics for and robust competition of synapses, which are crucial for spike-based information processing.

From understanding cellular function to novel drug discovery: the role of planar patch-clamp array chip technology

All excitable cell functions rely upon ion channels that are embedded in their plasma membrane. Perturbations of ion channel structure or function result in pathologies ranging from cardiac dysfunction to neurodegenerative disorders. Consequently, to understand the functions of excitable cells and to remedy their pathophysiology, it is important to understand the ion channel functions under various experimental conditions - including exposure to novel drug targets. Glass pipette patch-clamp is the state of the art technique to monitor the intrinsic and synaptic properties of neurons. However, this technique is labor intensive and has low data throughput. Planar patch-clamp chips, integrated into automated systems, offer high throughputs but are limited to isolated cells from suspensions, thus limiting their use in modeling physiological function. These chips are therefore not most suitable for studies involving neuronal communication. Multielectrode arrays (MEAs), in contrast, have the ability to monitor network activity by measuring local field potentials from multiple extracellular sites, but specific ion channel activity is challenging to extract from these multiplexed signals. Here we describe a novel planar patch-clamp chip technology that enables the simultaneous high-resolution electrophysiological interrogation of individual neurons at multiple sites in synaptically connected neuronal networks, thereby combining the advantages of MEA and patch-clamp techniques. Each neuron can be probed through an aperture that connects to a dedicated subterranean microfluidic channel. Neurons growing in networks are aligned to the apertures by physisorbed or chemisorbed chemical cues. In this review, we describe the design and fabrication process of these chips, approaches to chemical patterning for cell placement, and present physiological data from cultured neuronal cells.

Development of cell type-specific connectivity patterns of converging excitatory axons in the retina

To integrate information from different presynaptic cell types, dendrites receive distinct patterns of synapses from converging axons. How different afferents in vivo establish specific connectivity patterns with the same dendrite is poorly understood. Here, we examine the synaptic development of three glutamatergic bipolar cell types converging onto a common postsynaptic retinal ganglion cell. We find that after axons and dendrites target appropriate synaptic layers, patterns of connections among these neurons diverge through selective changes in the conversion of axo-dendritic appositions to synapses. This process is differentially regulated by neurotransmission, which is required for the shift from single to multisynaptic appositions of one bipolar cell type but not for maintenance and elimination, respectively, of connections from the other two types. Thus, synaptic specificity among converging excitatory inputs in the retina emerges via differential synaptic maturation of axo-dendritic appositions and is shaped by neurotransmission in a cell type-dependent manner.

Multiplicative dynamics underlie the emergence of the log-normal distribution of spine sizes in the neocortex in vivo

What fundamental properties of synaptic connectivity in the neocortex stem from the ongoing dynamics of synaptic changes? In this study, we seek to find the rules shaping the stationary distribution of synaptic efficacies in the cortex. To address this question, we combined chronic imaging of hundreds of spines in the auditory cortex of mice in vivo over weeks with modeling techniques to quantitatively study the dynamics of spines, the morphological correlates of excitatory synapses in the neocortex. We found that the stationary distribution of spine sizes of individual neurons can be exceptionally well described by a log-normal function. We furthermore show that spines exhibit substantial volatility in their sizes at timescales that range from days to months. Interestingly, the magnitude of changes in spine sizes is proportional to the size of the spine. Such multiplicative dynamics are in contrast with conventional models of synaptic plasticity, learning, and memory, which typically assume additive dynamics. Moreover, we show that the ongoing dynamics of spine sizes can be captured by a simple phenomenological model that operates at two timescales of days and months. This model converges to a log-normal distribution, bridging the gap between synaptic dynamics and the stationary distribution of synaptic efficacies.

Excitatory, inhibitory, and structural plasticity produce correlated connectivity in random networks trained to solve paired-stimulus tasks

The pattern of connections among cortical excitatory cells with overlapping arbors is non-random. In particular, correlations among connections produce clustering – cells in cliques connect to each other with high probability, but with lower probability to cells in other spatially intertwined cliques. In this study, we model initially randomly connected sparse recurrent networks of spiking neurons with random, overlapping inputs, to investigate what functional and structural synaptic plasticity mechanisms sculpt network connections into the patterns measured in vitro. Our Hebbian implementation of structural plasticity causes a removal of connections between uncorrelated excitatory cells, followed by their random replacement. To model a biconditional discrimination task, we stimulate the network via pairs (A + B, C + D, A + D, and C + B) of four inputs (A, B, C, and D). We find networks that produce neurons most responsive to specific paired inputs – a building block of computation and essential role for cortex – contain the excessive clustering of excitatory synaptic connections observed in cortical slices. The same networks produce the best performance in a behavioral readout of the networks’ ability to complete the task. A plasticity mechanism operating on inhibitory connections, long-term potentiation of inhibition, when combined with structural plasticity, indirectly enhances clustering of excitatory cells via excitatory connections. A rate-dependent (triplet) form of spike-timing-dependent plasticity (STDP) between excitatory cells is less effective and basic STDP is detrimental. Clustering also arises in networks stimulated with single stimuli and in networks undergoing raised levels of spontaneous activity when structural plasticity is combined with functional plasticity. In conclusion, spatially intertwined clusters or cliques of connected excitatory cells can arise via a Hebbian form of structural plasticity operating in initially randomly connected networks.

Highly differentiated projection-specific cortical subnetworks

Pyramidal cells in the neocortex are differentiated into several subgroups based on their extracortical projection targets. However, little is known regarding the relative intracortical connectivity of pyramidal neurons specialized for these specific output channels. We used paired recordings and quantitative morphological analysis to reveal distinct synaptic transmission properties, connection patterns, and morphological differentiation correlated with heterogeneous thalamic input to two different groups of pyramidal cells residing in layer 5 (L5) of rat frontal cortex. Retrograde tracers were used to label two projection subtypes in L5: crossed-corticostriatal (CCS) cells projecting to both sides of the striatum, and corticopontine (CPn) cells projecting to the ipsilateral pons. Although CPn/CPn and CCS/CCS pairs had similar connection probabilities, CPn/CPn pairs exhibited greater reciprocal connectivity, stronger unitary synaptic transmission, and more facilitation of paired-pulse responses. These synaptic characteristics were strongly correlated to the projection subtype of the presynaptic neuron. CPn and CCS cells were further differentiated according to their somatic position (L5a and L5b, the latter denser thalamic afferent fibers) and their dendritic/axonal arborizations. Together, our data demonstrate that the pyramidal projection system is segregated into different output channels according to subcortical target and thalamic input, and that information flow within and between these channels is selectively organized.

Dendritic slow dynamics enables localized cortical activity to switch between mobile and immobile modes with noisy background input

Mounting lines of evidence suggest the significant computational ability of a single neuron empowered by active dendritic dynamics. This motivates us to study what functionality can be acquired by a network of such neurons. The present paper studies how such rich single-neuron dendritic dynamics affects the network dynamics, a question which has scarcely been specifically studied to date. We simulate neurons with active dendrites networked locally like cortical pyramidal neurons, and find that naturally arising localized activity--called a bump--can be in two distinct modes, mobile or immobile. The mode can be switched back and forth by transient input to the cortical network. Interestingly, this functionality arises only if each neuron is equipped with the observed slow dendritic dynamics and with in vivo-like noisy background input. If the bump activity is considered to indicate a point of attention in the sensory areas or to indicate a representation of memory in the storage areas of the cortex, this would imply that the flexible mode switching would be of great potential use for the brain as an information processing device. We derive these conclusions using a natural extension of the conventional field model, which is defined by combining two distinct fields, one representing the somatic population and the other representing the dendritic population. With this tool, we analyze the spatial distribution of the degree of after-spike adaptation and explain how we can understand the presence of the two distinct modes and switching between the modes. We also discuss the possible functional impact of this mode-switching ability.

A history of spike-timing-dependent plasticity

How learning and memory is achieved in the brain is a central question in neuroscience. Key to today's research into information storage in the brain is the concept of synaptic plasticity, a notion that has been heavily influenced by Hebb's (1949) postulate. Hebb conjectured that repeatedly and persistently co-active cells should increase connective strength among populations of interconnected neurons as a means of storing a memory trace, also known as an engram. Hebb certainly was not the first to make such a conjecture, as we show in this history. Nevertheless, literally thousands of studies into the classical frequency-dependent paradigm of cellular learning rules were directly inspired by the Hebbian postulate. But in more recent years, a novel concept in cellular learning has emerged, where temporal order instead of frequency is emphasized. This new learning paradigm - known as spike-timing-dependent plasticity (STDP) - has rapidly gained tremendous interest, perhaps because of its combination of elegant simplicity, biological plausibility, and computational power. But what are the roots of today's STDP concept? Here, we discuss several centuries of diverse thinking, beginning with philosophers such as Aristotle, Locke, and Ribot, traversing, e.g., Lugaro's plasticità and Rosenblatt's perceptron, and culminating with the discovery of STDP. We highlight interactions between theoretical and experimental fields, showing how discoveries sometimes occurred in parallel, seemingly without much knowledge of the other field, and sometimes via concrete back-and-forth communication. We point out where the future directions may lie, which includes interneuron STDP, the functional impact of STDP, its mechanisms and its neuromodulatory regulation, and the linking of STDP to the developmental formation and continuous plasticity of neuronal networks.

Neural feedback for instantaneous spatiotemporal modulation of afferent pathways in bi-directional brain-machine interfaces

In bi-directional brain-machine interfaces (BMIs), precisely controlling the delivery of microstimulation, both in space and in time, is critical to continuously modulate the neural activity patterns that carry information about the state of the brain-actuated device to sensory areas in the brain. In this paper, we investigate the use of neural feedback to control the spatiotemporal firing patterns of neural ensembles in a model of the thalamocortical pathway. Control of pyramidal (PY) cells in the primary somatosensory cortex (S1) is achieved based on microstimulation of thalamic relay cells through multiple-input multiple-output (MIMO) feedback controllers. This closed loop feedback control mechanism is achieved by simultaneously varying the stimulation parameters across multiple stimulation electrodes in the thalamic circuit based on continuous monitoring of the difference between reference patterns and the evoked responses of the cortical PY cells. We demonstrate that it is feasible to achieve a desired level of performance by controlling the firing activity pattern of a few "key" neural elements in the network. Our results suggest that neural feedback could be an effective method to facilitate the delivery of information to the cortex to substitute lost sensory inputs in cortically controlled BMIs.

Specificity and randomness: structure-function relationships in neural circuits

A fundamental but unsolved problem in neuroscience is how connections between neurons might underlie information processing in central circuits. Building wiring diagrams of neural networks may accelerate our understanding of how they compute. But even if we had wiring diagrams, it is critical to know what neurons in a circuit are doing: their physiology. In both the retina and cerebral cortex, a great deal is known about topographic specificity, such as lamination and cell-type specificity of connections. Little, however, is known about connections as they relate to function. Here, we review how advances in functional imaging and electron microscopy have recently allowed the examination of relationships between sensory physiology and synaptic connections in cortical and retinal circuits.

Hippocampal CA1 pyramidal cells form functionally distinct sublayers

Hippocampal CA1 pyramidal neurons have frequently been regarded as a homogeneous cell population in biophysical, pharmacological and modeling studies. Here we report robust differences between pyramidal neurons residing in the deep and superficial CA1 sublayers in the rat. Compared to their superficial peers, deep pyramidal cells fired at higher rates, burst more frequently, were more likely to have place fields and were more strongly modulated by slow oscillations of sleep. Both deep and superficial pyramidal cells fired preferentially at the trough of theta oscillations during maze exploration, yet during Rapid eye movement (REM) sleep, deep pyramidal cells shifted their preferred phase of firing to the peak of theta. Furthermore, whereas in waking, the majority of REM theta phase-shifting cells fired at the ascending phase of gamma oscillations, non-shifting cells preferred the trough. Thus, CA1 pyramidal cells in adjacent sublayers can address their targets jointly or differentially, depending on brain states.

Model-based analysis and control of a network of basal ganglia spiking neurons in the normal and parkinsonian states

Controlling the spatiotemporal firing pattern of an intricately connected network of neurons through microstimulation is highly desirable in many applications. We investigated in this paper the feasibility of using a model-based approach to the analysis and control of a basal ganglia (BG) network model of Hodgkin-Huxley (HH) spiking neurons through microstimulation. Detailed analysis of this network model suggests that it can reproduce the experimentally observed characteristics of BG neurons under a normal and a pathological Parkinsonian state. A simplified neuronal firing rate model, identified from the detailed HH network model, is shown to capture the essential network dynamics. Mathematical analysis of the simplified model reveals the presence of a systematic relationship between the network's structure and its dynamic response to spatiotemporally patterned microstimulation. We show that both the network synaptic organization and the local mechanism of microstimulation can impose tight constraints on the possible spatiotemporal firing patterns that can be generated by the microstimulated network, which may hinder the effectiveness of microstimulation to achieve a desired objective under certain conditions. Finally, we demonstrate that the feedback control design aided by the mathematical analysis of the simplified model is indeed effective in driving the BG network in the normal and Parskinsonian states to follow a prescribed spatiotemporal firing pattern. We further show that the rhythmic/oscillatory patterns that characterize a dopamine-depleted BG network can be suppressed as a direct consequence of controlling the spatiotemporal pattern of a subpopulation of the output Globus Pallidus internalis (GPi) neurons in the network. This work may provide plausible explanations for the mechanisms underlying the therapeutic effects of deep brain stimulation (DBS) in Parkinson's disease and pave the way towards a model-based, network level analysis and closed-loop control and optimization of DBS parameters, among many other applications.

After-hyperpolarization currents and acetylcholine control sigmoid transfer functions in a spiking cortical model

Recurrent networks are ubiquitous in the brain, where they enable a diverse set of transformations during perception, cognition, emotion, and action. It has been known since the 1970's how, in rate-based recurrent on-center off-surround networks, the choice of feedback signal function can control the transformation of input patterns into activity patterns that are stored in short term memory. A sigmoid signal function may, in particular, control a quenching threshold below which inputs are suppressed as noise and above which they may be contrast enhanced before the resulting activity pattern is stored. The threshold and slope of the sigmoid signal function determine the degree of noise suppression and of contrast enhancement. This article analyses how sigmoid signal functions and their shape may be determined in biophysically realistic spiking neurons. Combinations of fast, medium, and slow after-hyperpolarization (AHP) currents, and their modulation by acetylcholine (ACh), can control sigmoid signal threshold and slope. Instead of a simple gain in excitability that was previously attributed to ACh, cholinergic modulation may cause translation of the sigmoid threshold. This property clarifies how activation of ACh by basal forebrain circuits, notably the nucleus basalis of Meynert, may alter the vigilance of category learning circuits, and thus their sensitivity to predictive mismatches, thereby controlling whether learned categories code concrete or abstract information, as predicted by Adaptive Resonance Theory.

Information content of colored motifs in complex networks

We study complex networks in which the nodes are tagged with different colors depending on their function (colored graphs), using information theory applied to the distribution of motifs in such networks. We find that colored motifs can be viewed as the building blocks of the networks (much more than the uncolored structural motifs can be) and that the relative frequency with which these motifs appear in the network can be used to define its information content. This information is defined in such a way that a network with random coloration (but keeping the relative number of nodes with different colors the same) has zero color information content. Thus, colored motif information captures the exceptionality of coloring in the motifs that is maintained via selection. We study the motif information content of the C. elegans brain as well as the evolution of colored motif information in networks that reflect the interaction between instructions in genomes of digital life organisms. While we find that colored motif information appears to capture essential functionality in the C. elegans brain (where the color assignment of nodes is straightforward), it is not obvious whether the colored motif information content always increases during evolution, as would be expected from a measure that captures network complexity. For a single choice of color assignment of instructions in the digital life form Avida, we find rather that colored motif information content increases or decreases during evolution, depending on how the genomes are organized, and therefore could be an interesting tool to dissect genomic rearrangements.

Maturation of a recurrent excitatory neocortical circuit by experience-dependent unsilencing of newly formed dendritic spines

Local recurrent excitatory circuits are ubiquitous in neocortex, yet little is known about their development or architecture. Here we introduce a quantitative technique for efficient single-cell resolution circuit mapping using 2-photon (2P) glutamate uncaging and analyze experience-dependent neonatal development of the layer 4 barrel cortex local excitatory circuit. We show that sensory experience specifically drives a 3-fold increase in connectivity at postnatal day (P) 9, producing a highly recurrent network. A profound dendritic spinogenesis occurs concurrent with the connectivity increase, but this is not experience dependent. However, in experience-deprived cortex, a much greater proportion of spines lack postsynaptic AMPA receptors (AMPARs) and synaptic connectivity via NMDA receptors (NMDARs) is the same as in normally developing cortex. Thus we describe a approach for quantitative circuit mapping and show that sensory experience sculpts an intrinsically developing template network, which is based on NMDAR-only synapses, by driving AMPARs into newly formed silent spines.

Synchronization from second order network connectivity statistics

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates.

Network algorithmics and the emergence of information integration in cortical models

An information-theoretic framework known as integrated information theory (IIT) has been introduced recently for the study of the emergence of consciousness in the brain [D. Balduzzi and G. Tononi, PLoS Comput. Biol. 4, e1000091 (2008)]. IIT purports that this phenomenon is to be equated with the generation of information by the brain surpassing the information that the brain's constituents already generate independently of one another. IIT is not fully plausible in its modeling assumptions nor is it testable due to severe combinatorial growth embedded in its key definitions. Here we introduce an alternative to IIT which, while inspired in similar information-theoretic principles, seeks to address some of IIT's shortcomings to some extent. Our alternative framework uses the same network-algorithmic cortical model we introduced earlier [A. Nathan and V. C. Barbosa, Phys. Rev. E 81, 021916 (2010)] and, to allow for somewhat improved testability relative to IIT, adopts the well-known notions of information gain and total correlation applied to a set of variables representing the reachability of neurons by messages in the model's dynamics. We argue that these two quantities relate to each other in such a way that can be used to quantify the system's efficiency in generating information beyond that which does not depend on integration. We give computational results on our cortical model and on variants thereof that are either structurally random in the sense of an Erdős-Rényi random directed graph or structurally deterministic. We have found that our cortical model stands out with respect to the others in the sense that many of its instances are capable of integrating information more efficiently than most of those others' instances.

The architecture of functional interaction networks in the retina

Sensory information is represented in the brain by the joint activity of large groups of neurons. Recent studies have shown that, although the number of possible activity patterns and underlying interactions is exponentially large, pairwise-based models give a surprisingly accurate description of neural population activity patterns. We explored the architecture of maximum entropy models of the functional interaction networks underlying the response of large populations of retinal ganglion cells, in adult tiger salamander retina, responding to natural and artificial stimuli. We found that we can further simplify these pairwise models by neglecting weak interaction terms or by relying on a small set of interaction strengths. Comparing network interactions under different visual stimuli, we show the existence of local network motifs in the interaction map of the retina. Our results demonstrate that the underlying interaction map of the retina is sparse and dominated by local overlapping interaction modules.

Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons

Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in the brain is theoretically appealing and is supported by recent neurophysiological studies. Despite this, the neurobiological determinants of these dynamics have not been previously sought. Here, we systematically examined the influence of such determinants in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterized emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assessed these distributions for power-law scaling. We found that spike-timing-dependent synaptic plasticity enabled a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broadened this transition, and enabled a regime indicative of self-organized criticality. The regime only occurred when modular connectivity, low wiring cost and synaptic plasticity were simultaneously present, and the regime was most evident when between-module connection density scaled as a power-law. The regime was robust to variations in other neurobiologically relevant parameters and favored systems with low external drive and strong internal interactions. Increases in system size and connectivity facilitated internal interactions, permitting reductions in external drive and facilitating convergence of postsynaptic-response magnitude and synaptic-plasticity learning rate parameter values towards neurobiologically realistic levels. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity. The central role of these features in our model may reflect their importance for neuronal information processing.

Cell diversity and connection specificity between callosal projection neurons in the frontal cortex

Recent advances have established that intralaminar and interlaminar excitatory networks between neocortical pyramidal cells are specialized into subnetworks. Here, we have investigated how the commissural system organizes the intracortical excitatory subnetworks to communicate between cortical hemispheres. Whole-cell recordings were obtained from callosal projection neurons [commissural (COM) cells], identified by in vivo injection of retrograde fluorescent tracer into one hemisphere, in rat frontal cortical slices. We found that layer V (L5) COM cells were heterogeneous in physiological and morphological properties that correlated with projection patterns to contralateral and ipsilateral cortical areas. The probability of synaptically connected pairs of L5 COM cells was higher in cell pairs of the same firing subtypes than that in different cell subtype pairs. In interlaminar connections, layer II/III (L2/3) COM cells preferentially innervated L5 COM cells. Moreover, pairs of the same L5 COM subtypes were more likely to share inputs from L2/3 COM cells than were different COM subtype cell pairs. In addition, common inputs from L2/3 COM cells were frequently observed in L5 pairs of corticopontine cells and given firing subtypes of COM cells. Our results suggest that callosal communications are achieved via several distinct COM cell subnetworks differentiated according to the ipsilateral corticocortical and subcortical projection patterns.

Functional specificity of local synaptic connections in neocortical networks

Neuronal connectivity is fundamental to information processing in the brain. Therefore, understanding the mechanisms of sensory processing requires uncovering how connection patterns between neurons relate to their function. On a coarse scale, long-range projections can preferentially link cortical regions with similar responses to sensory stimuli. But on the local scale, where dendrites and axons overlap substantially, the functional specificity of connections remains unknown. Here we determine synaptic connectivity between nearby layer 2/3 pyramidal neurons in vitro, the response properties of which were first characterized in mouse visual cortex in vivo. We found that connection probability was related to the similarity of visually driven neuronal activity. Neurons with the same preference for oriented stimuli connected at twice the rate of neurons with orthogonal orientation preferences. Neurons responding similarly to naturalistic stimuli formed connections at much higher rates than those with uncorrelated responses. Bidirectional synaptic connections were found more frequently between neuronal pairs with strongly correlated visual responses. Our results reveal the degree of functional specificity of local synaptic connections in the visual cortex, and point to the existence of fine-scale subnetworks dedicated to processing related sensory information.

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.

Emergence of physiological oscillation frequencies in a computer model of neocortex

Coordination of neocortical oscillations has been hypothesized to underlie the "binding" essential to cognitive function. However, the mechanisms that generate neocortical oscillations in physiological frequency bands remain unknown. We hypothesized that interlaminar relations in neocortex would provide multiple intermediate loops that would play particular roles in generating oscillations, adding different dynamics to the network. We simulated networks from sensory neocortex using nine columns of event-driven rule-based neurons wired according to anatomical data and driven with random white-noise synaptic inputs. We tuned the network to achieve realistic cell firing rates and to avoid population spikes. A physiological frequency spectrum appeared as an emergent property, displaying dominant frequencies that were not present in the inputs or in the intrinsic or activated frequencies of any of the cell groups. We monitored spectral changes while using minimal dynamical perturbation as a methodology through gradual introduction of hubs into individual layers. We found that hubs in layer 2/3 excitatory cells had the greatest influence on overall network activity, suggesting that this subpopulation was a primary generator of theta/beta strength in the network. Similarly, layer 2/3 interneurons appeared largely responsible for gamma activation through preferential attenuation of the rest of the spectrum. The network showed evidence of frequency homeostasis: increased activation of supragranular layers increased firing rates in the network without altering the spectral profile, and alteration in synaptic delays did not significantly shift spectral peaks. Direct comparison of the power spectra with experimentally recorded local field potentials from prefrontal cortex of awake rat showed substantial similarities, including comparable patterns of cross-frequency coupling.

Beyond the cortical column: abundance and physiology of horizontal connections imply a strong role for inputs from the surround

Current concepts of cortical information processing and most cortical network models largely rest on the assumption that well-studied properties of local synaptic connectivity are sufficient to understand the generic properties of cortical networks. This view seems to be justified by the observation that the vertical connectivity within local volumes is strong, whereas horizontally, the connection probability between pairs of neurons drops sharply with distance. Recent neuroanatomical studies, however, have emphasized that a substantial fraction of synapses onto neocortical pyramidal neurons stems from cells outside the local volume. Here, we discuss recent findings on the signal integration from horizontal inputs, showing that they could serve as a substrate for reliable and temporally precise signal propagation. Quantification of connection probabilities and parameters of synaptic physiology as a function of lateral distance indicates that horizontal projections constitute a considerable fraction, if not the majority, of inputs from within the cortical network. Taking these non-local horizontal inputs into account may dramatically change our current view on cortical information processing.

Clustering predicts memory performance in networks of spiking and non-spiking neurons

The problem we address in this paper is that of finding effective and parsimonious patterns of connectivity in sparse associative memories. This problem must be addressed in real neuronal systems, so that results in artificial systems could throw light on real systems. We show that there are efficient patterns of connectivity and that these patterns are effective in models with either spiking or non-spiking neurons. This suggests that there may be some underlying general principles governing good connectivity in such networks. We also show that the clustering of the network, measured by Clustering Coefficient, has a strong negative linear correlation to the performance of associative memory. This result is important since a purely static measure of network connectivity appears to determine an important dynamic property of the network.

Network anatomy and in vivo physiology of visual cortical neurons

In the cerebral cortex, local circuits consist of tens of thousands of neurons, each of which makes thousands of synaptic connections. Perhaps the biggest impediment to understanding these networks is that we have no wiring diagrams of their interconnections. Even if we had a partial or complete wiring diagram, however, understanding the network would also require information about each neuron's function. Here we show that the relationship between structure and function can be studied in the cortex with a combination of in vivo physiology and network anatomy. We used two-photon calcium imaging to characterize a functional property—the preferred stimulus orientation—of a group of neurons in the mouse primary visual cortex. We then used large-scale electron microscopy (EM) of serial thin sections to trace a portion of these neurons’ local network. Consistent with a prediction from recent physiological experiments, inhibitory interneurons received convergent anatomical input from nearby excitatory neurons with a broad range of preferred orientations, although weak biases could not be rejected.

Regular mosaic of synaptic contacts among three retinal neurons

Retinal bipolar, amacrine, and ganglion cells contact each other within precisely defined synaptic laminae, but the spatial distribution of contacts between the cells is generally treated as random. Here we show that not to be the case. Excitatory inputs to inner retinal neurons were visualized by introduction of a plasmid coding for the postsynaptic protein PSD95-GFP. Our initial finding was that synapses on the dendrites of retinal ganglion cells are regularly spaced, at 2-3-μm intervals, along the dendrites. Thus, the presence of a PSD95 punctum creates a nearby zone from which other inputs appear to be excluded. Despite their great variation in size and different morphologies, the spacing is similar for the arbors of different retinal ganglion cell types. Regular spacing was also observed for the starburst amacrine cells. This regularity is mirrored in the spacing of axonal varicosities of the stratified bipolar cells, which have a regular, nonrandom interval consistent with that of the PSD95 puncta on ganglion cells. Thus, for each level of the inner plexiform layer all three cell types participate in a single 2D mosaic of synaptic contacts. These findings raise a new set of questions: How does the self-avoidance of synaptic sites along an individual dendrite arise and how is it physically maintained? Why is a regular spacing of inputs important for the computational function of the cells? Finally, which of the three players, if any, is developmentally responsible for the initial establishment of the pattern?

Methods for generating complex networks with selected structural properties for simulations: a review and tutorial for neuroscientists

Many simulations of networks in computational neuroscience assume completely homogenous random networks of the Erdös–Rényi type, or regular networks, despite it being recognized for some time that anatomical brain networks are more complex in their connectivity and can, for example, exhibit the “scale-free” and “small-world” properties. We review the most well known algorithms for constructing networks with given non-homogeneous statistical properties and provide simple pseudo-code for reproducing such networks in software simulations. We also review some useful mathematical results and approximations associated with the statistics that describe these network models, including degree distribution, average path length, and clustering coefficient. We demonstrate how such results can be used as partial verification and validation of implementations. Finally, we discuss a sometimes overlooked modeling choice that can be crucially important for the properties of simulated networks: that of network directedness. The most well known network algorithms produce undirected networks, and we emphasize this point by highlighting how simple adaptations can instead produce directed networks.

The role of degree distribution in shaping the dynamics in networks of sparsely connected spiking neurons

Neuronal network models often assume a fixed probability of connection between neurons. This assumption leads to random networks with binomial in-degree and out-degree distributions which are relatively narrow. Here I study the effect of broad degree distributions on network dynamics by interpolating between a binomial and a truncated power-law distribution for the in-degree and out-degree independently. This is done both for an inhibitory network (I network) as well as for the recurrent excitatory connections in a network of excitatory and inhibitory neurons (EI network). In both cases increasing the width of the in-degree distribution affects the global state of the network by driving transitions between asynchronous behavior and oscillations. This effect is reproduced in a simplified rate model which includes the heterogeneity in neuronal input due to the in-degree of cells. On the other hand, broadening the out-degree distribution is shown to increase the fraction of common inputs to pairs of neurons. This leads to increases in the amplitude of the cross-correlation (CC) of synaptic currents. In the case of the I network, despite strong oscillatory CCs in the currents, CCs of the membrane potential are low due to filtering and reset effects, leading to very weak CCs of the spike-count. In the asynchronous regime of the EI network, broadening the out-degree increases the amplitude of CCs in the recurrent excitatory currents, while CC of the total current is essentially unaffected as are pairwise spiking correlations. This is due to a dynamic balance between excitatory and inhibitory synaptic currents. In the oscillatory regime, changes in the out-degree can have a large effect on spiking correlations and even on the qualitative dynamical state of the network.

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm's locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.

A synaptic organizing principle for cortical neuronal groups

Neuronal circuitry is often considered a clean slate that can be dynamically and arbitrarily molded by experience. However, when we investigated synaptic connectivity in groups of pyramidal neurons in the neocortex, we found that both connectivity and synaptic weights were surprisingly predictable. Synaptic weights follow very closely the number of connections in a group of neurons, saturating after only 20% of possible connections are formed between neurons in a group. When we examined the network topology of connectivity between neurons, we found that the neurons cluster into small world networks that are not scale-free, with less than 2 degrees of separation. We found a simple clustering rule where connectivity is directly proportional to the number of common neighbors, which accounts for these small world networks and accurately predicts the connection probability between any two neurons. This pyramidal neuron network clusters into multiple groups of a few dozen neurons each. The neurons composing each group are surprisingly distributed, typically more than 100 μm apart, allowing for multiple groups to be interlaced in the same space. In summary, we discovered a synaptic organizing principle that groups neurons in a manner that is common across animals and hence, independent of individual experiences. We speculate that these elementary neuronal groups are prescribed Lego-like building blocks of perception and that acquired memory relies more on combining these elementary assemblies into higher-order constructs.