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One major question in neuroscience is how to relate connectomes to neural activity, circuit function, and learning. We offer an answer in the peripheral olfactory circuit of the Drosophila larva, composed of olfactory receptor neurons (ORNs) connected through feedback loops with interconnected inhibitory local neurons (LNs). We combine structural and activity data and, using a holistic normative framework based on similarity-matching, we propose a biologically plausible mechanistic model of the circuit. Our model predicts the ORN → LN synaptic weights found in the connectome and demonstrate that they reflect correlations in ORN activity patterns. Additionally, our model explains the relation between ORN → LN and LN – LN synaptic weight and the arising of different LN types. This global synaptic organization can autonomously arise through Hebbian plasticity, and thus allows the circuit to adapt to different environments in an unsupervised manner. Functionally, we propose LNs extract redundant input correlations and dampen them in ORNs, thus partially whitening and normalizing the stimulus representations in ORNs. Our work proposes a comprehensive framework to combine structure, activity, function, and learning, and uncovers a general and potent circuit motif that can learn and extract significant input features and render stimulus representations more efficient.SignificanceThe brain represents information with patterns of neural activity. At the periphery, due to the properties of the external world and of encoding neurons, these patterns contain correlations, which are detrimental for stimulus discrimination. We study the peripheral olfactory neural circuit of the Drosophila larva, that preprocesses neural representations before relaying them to higher brain areas. A comprehensive understanding of this preprocessing is, however, lacking. Here, we propose a mechanistic and normative framework describing the function of the circuit and predict the circuit’s synaptic organization based on the circuit’s input neural activity. We show how the circuit can autonomously adapt to different environments, extracts stimulus features, and decorrelate and normalize input representations, which facilitates odor discrimination downstream.

As the study of the human brain is complicated by its sheer scale, complexity, and impracticality of invasive experiments, neuroscience research has long relied on model organisms. The brains of macaque, mouse, zebrafish, fruit fly, nematode, and others have yielded many secrets that advanced our understanding of the human brain. Here, we propose that adding miniature insects to this collection would reduce the costs and accelerate brain research. The smallest insects occupy a special place among miniature animals: despite their body sizes, comparable to unicellular organisms, they retain complex brains that include thousands of neurons. Their brains possess the advantages of those in insects, such as neuronal identifiability and the connectome stereotypy, yet are smaller and hence easier to map and understand. Finally, the brains of miniature insects offer insights into the evolution of brain design.

Animal behaviour arises from computations in neuronal circuits, but our understanding of these computations has been frustrated by the lack of detailed synaptic connection maps, or connectomes. For example, despite intensive investigations over half a century, the neuronal implementation of local motion detection in the insect visual system remains elusive. Here we develop a semi-automated pipeline using electron microscopy to reconstruct a connectome, containing 379 neurons and 8,637 chemical synaptic contacts, within the Drosophila optic medulla. By matching reconstructed neurons to examples from light microscopy, we assigned neurons to cell types and assembled a connectome of the repeating module of the medulla. Within this module, we identified cell types constituting a motion detection circuit, and showed that the connections onto individual motion-sensitive neurons in this circuit were consistent with their direction selectivity. Our results identify cellular targets for future functional investigations, and demonstrate that connectomes can provide key insights into neuronal computations. Reconstruction of a connectome within the fruitfly visual medulla, containing more than 300 neurons and over 8,000 chemical synapses, reveals a candidate motion detection circuit; such a circuit operates by combining displaced visual inputs, an operation consistent with correlation based motion detection. Three papers in this issue of Nature use the retina as a model for mapping neuronal circuits from the level of individual synaptic contacts to the long-range scale of dendritic interactions. Helmstaedter et al. used electron microscopy to map a mammalian retinal circuit of close to a thousand neurons. The work reveals a new type of retinal bipolar neuron and suggests functional mechanisms for known visual computations. The other two groups study the detection of visual motion in the Drosophila visual system — a classic neural computation model. Takemura et al. used semi-automated electron microscopy to reconstruct the basic connectome (8,637 chemical synapses among 379 neurons) of Drosophila's optic medulla. Their results reveal a candidate motion detection circuit with a wiring plan consistent with direction selectivity. Maisak et al. used calcium imaging to show that T4 and T5 neurons are divided into specific subpopulations responding to motion in four cardinal directions, and are specific to 'ON' versus 'OFF' edges, respectively.

Connectivity patterns of neocortex exhibit several odd properties: for example, most neighboring excitatory neurons do not connect, which seems curiously wasteful. Brunel's elegant theoretical treatment reveals how optimal information storage can naturally impose these peculiar properties.

The shapes of dendritic arbors are fascinating and important, yet the principles underlying these complex and diverse structures remain unclear. Here, we analyzed basal dendritic arbors of 2,171 pyramidal neurons sampled from mammalian brains and discovered 3 statistical properties: the dendritic arbor size scales with the total dendritic length, the spatial correlation of dendritic branches within an arbor has a universal functional form, and small parts of an arbor are self-similar. We proposed that these properties result from maximizing the repertoire of possible connectivity patterns between dendrites and surrounding axons while keeping the cost of dendrites low. We solved this optimization problem by drawing an analogy with maximization of the entropy for a given energy in statistical physics. The solution is consistent with the above observations and predicts scaling relations that can be tested experimentally. In addition, our theory explains why dendritic branches of pyramidal cells are distributed more sparsely than those of Purkinje cells. Our results represent a step toward a unifying view of the relationship between neuronal morphology and function.

Over hundreds of millions of years, evolution has optimized brain design to maximize its functionality while minimizing costs associated with building and maintenance. This observation suggests that one can use optimization theory to rationalize various features of brain design. Here, we attempt to explain the dimensions and branching structure of dendritic arbors by minimizing dendritic cost for given potential synaptic connectivity. Assuming only that dendritic cost increases with total dendritic length and path length from synapses to soma, we find that branching, planar, and compact dendritic arbors, such as those belonging to Purkinje cells in the cerebellum, are optimal. The theory predicts that adjacent Purkinje dendritic arbors should spatially segregate. In addition, we propose two explicit cost function expressions, falsifiable by measuring dendritic caliber near bifurcations.

Several theories of early sensory processing suggest that it whitens sensory stimuli. Here, we test three key predictions of the whitening theory using recordings from 152 ganglion cells in salamander retina responding to natural movies. We confirm the previous finding that firing rates of ganglion cells are less correlated compared to natural scenes, although significant correlations remain. We show that while the power spectrum of ganglion cells decays less steeply than that of natural scenes, it is not completely flattened. Finally, we find evidence that only the top principal components of the visual stimulus are transmitted., Comment: 2016 Asilomar Conference on Signals, Systems and Computers

We reconstructed the synaptic circuits of seven columns in the second neuropil or medulla behind the fly's compound eye. These neurons embody some of the most stereotyped circuits in one of the most miniaturized of animal brains. The reconstructions allow us, for the first time to our knowledge, to study variations between circuits in the medulla's neighboring columns. This variation in the number of synapses and the types of their synaptic partners has previously been little addressed because methods that visualize multiple circuits have not resolved detailed connections, and existing connectomic studies, which can see such connections, have not so far examined multiple reconstructions of the same circuit. Here, we address the omission by comparing the circuits common to all seven columns to assess variation in their connection strengths and the resultant rates of several different and distinct types of connection error. Error rates reveal that, overall

Neurons often possess elaborate axonal and dendritic arbors. Why do these arbors exist and what determines their form and dimensions? To answer these questions, I consider the wiring up of a large highly interconnected neuronal network, such as the cortical column. Implementation of such a network in the allotted volume requires all the salient features of neuronal morphology: the existence of branching dendrites and axons and the presence of dendritic spines. Therefore, the requirement of high interconnectivity is, in itself, sufficient to account for the existence of these features. Moreover, the actual lengths of axons and dendrites are close to the smallest possible length for a given interconnectivity, arguing that high interconnectivity is essential for cortical function.

Brain function relies on specificity of synaptic connectivity patterns among different classes of neurons. Yet, the substrates of specificity in complex neuropil remain largely unknown. We search for imprints of specificity in the layout of axonal and dendritic arbors from the rat neocortex. An analysis of 3D reconstructions of pairs consisting of pyramidal cells (PCs) and GABAergic interneurons (GIs) revealed that the layout of GI axons is specific. This specificity is manifested in a relatively high tortuosity, small branch length of these axons, and correlations of their trajectories with the positions of postsynaptic neuron dendrites. Axons of PCs show no such specificity, usually taking a relatively straight course through neuropil. However, wiring patterns among PCs hold a large potential for circuit remodeling and specificity through growth and retraction of dendritic spines. Our results define distinct class-specific rules in establishing synaptic connectivity, which could be crucial in formulating a canonical cortical circuit.

Because direct investigation of synaptic connectivity is difficult, neurobiologists often resort to indirect methods. One method is to infer connectivity from the densities of axonal and dendritic arbors, and the arbor overlap volume. This method is valid only under the assumption that spatial positions of dendritic and axonal branches are uncorrelated on a micrometer lengthscale. We test this assumption by using 3D reconstructions of neuronal pairs from the rat neocortex. We find that the positions of GABAergic interneuron axons are correlated with their targets, while the positions of pyramidal neuron axons are independent of their targets.

How much information can be encoded in synaptic connectivity patterns through formation and elimination of dendritic spines? To answer this question, we perform geometrical analysis and derive an expression for the number of potential synapses, i.e. the number of axons that pass within a spine length of a given dendrite. We evaluate this expression by using our measurements and existing anatomical data, and find that the ratio of actual to potential synapses is 0.26 in mouse neocortex, 0.18 in rat hippocampus, and 0.12–0.23 in macaque visual cortex. Consequently, mammalian synaptic connectivity patterns may encode up to 3–5 bits per synapse.

Despite our extensive knowledge of biophysical properties of neurons, there is no commonly accepted algorithmic theory of neuronal function. Here we explore the hypothesis that single-layer neuronal networks perform online symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of the streamed data. By starting with the SNMF cost function we derive an online algorithm, which can be implemented by a biologically plausible network with local learning rules. We demonstrate that such network performs soft clustering of the data as well as sparse feature discovery. The derived algorithm replicates many known aspects of sensory anatomy and biophysical properties of neurons including unipolar nature of neuronal activity and synaptic weights, local synaptic plasticity rules and the dependence of learning rate on cumulative neuronal activity. Thus, we make a step towards an algorithmic theory of neuronal function, which should facilitate large-scale neural circuit simulations and biologically inspired artificial intelligence., 2014 Asilomar Conference on Signals, Systems and Computers

In the visual cortex of many mammals, orientation preference changes smoothly along the cortical surface, with the exception of singularities such as pinwheels and fractures. The reason for the existence of these singularities has remained elusive, suggesting that they are developmental artifacts. We show that singularities reduce the length of intracortical neuronal connections for some connection rules. Therefore, pinwheels and fractures could be evolutionary adaptations keeping cortical volume to a minimum. Wire length minimization approach suggests that interspecies differences in orientation preference maps reflect differences in intracortical neuronal circuits, thus leading to experimentally testable predictions. We discuss application of our model to direction preference maps.

The primary visual area (V1) of the mammalian brain is a thin sheet of neurons. Because each neuron is dominated by either right or left eye one can treat V1 as a binary mixture of neurons. The spatial arrangement of neurons dominated by dierent eyes is known as the ocular dominance (OD) pattern. We propose a theory for OD patterns based on the premise that they are evolutionary adaptations to minimize the length of intra-cortical connections. Thus, the existing OD patterns are obtained by solving a wire length minimization problem. We divide all the neurons into two classes: right- and left-eye dominated. We nd that if the number of connections of each neuron with the neurons of the same class diers from that with the other class, the segregation of neurons into monocular regions indeed reduces the wire length. The shape of the regions depends on the relative number of neurons in the two classes. If both classes are equally represented we nd that the optimal OD pattern consists of alternating stripes. If one class is less numerous than the other, the optimal OD pattern consists of patches of the underrepresented (ipsilateral) eye dominated neurons surrounded by the neurons of the other class. We predict the transition from stripes to patches when the fraction of neurons dominated by the ipsilateral eye is about 40%. This prediction agrees with the data in macaque and Cebus monkeys. Our theory can be applied to other binary cortical systems. c 2000 Elsevier Science B.V. All rights reserved.

In the primate primary visual area (V1), the ocular dominance pattern consists of alternating monocular stripes. Stripe orientation follows systematic trends preserved across several species. I propose that these trends result from minimizing the length of intra-cortical wiring needed to recombine information from the two eyes in order to achieve the perception of depth. I argue that the stripe orientation at any point of V1 should follow the direction of binocular disparity in the corresponding point of the visual field. The optimal pattern of stripes determined from this argument agrees with the ocular dominance pattern of macaque and Cebus monkeys. This theory predicts that for any point in the visual field the limits of depth perception are greatest in the direction along the ocular dominance stripes at that point.

I consider a topographic projection between two neuronal layers with different densities of neurons. Given the number of output neurons connected to each input neuron (divergence) and the number of input neurons synapsing on each output neuron (convergence) I determine the widths of axonal and dendritic arbors which minimize the total volume of axons and dendrites. Analytical results for one-dimensional and two-dimensional projections can be summarized qualitatively in the following rule: neurons of the sparser layer should have arbors wider than those of the denser layer. This agrees with the anatomical data from retinal and cerebellar neurons whose morphology and connectivity are known. The rule may be used to infer connectivity of neurons from their morphology., Comment: 8 pages, 7 figures, submitted to Nature Neuroscience

The subcellular locations of synapses on pyramidal neurons strongly influences dendritic integration and synaptic plasticity. Despite this, there is little quantitative data on spatial distributions of specific types of synaptic input. Here we use array tomography (AT), a high-resolution optical microscopy method, to examine thalamocortical (TC) input onto layer 5 pyramidal neurons. We first verified the ability of AT to identify synapses using parallel electron microscopic analysis of TC synapses in layer 4. We then use large-scale array tomography (LSAT) to measure TC synapse distribution on L5 pyramidal neurons in a 1.00 × 0.83 × 0.21 mm(3) volume of mouse somatosensory cortex. We found that TC synapses primarily target basal dendrites in layer 5, but also make a considerable input to proximal apical dendrites in L4, consistent with previous work. Our analysis further suggests that TC inputs are biased toward certain branches and, within branches, synapses show significant clustering with an excess of TC synapse nearest neighbors within 5-15 μm compared to a random distribution. Thus, we show that AT is a sensitive and quantitative method to map specific types of synaptic input on the dendrites of entire neurons. We anticipate that this technique will be of wide utility for mapping functionally-relevant anatomical connectivity in neural circuits.

A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing device that represents the incoming streaming data matrix as a sparse vector of synaptic weights scaled by an outgoing sparse activity vector. Formally, a neuron minimizes a cost function comprising a cumulative squared representation error and regularization terms. We derive an online algorithm that minimizes such cost function by alternating between the minimization with respect to activity and with respect to synaptic weights. The steps of this algorithm reproduce well-known physiological properties of a neuron, such as weighted summation and leaky integration of synaptic inputs, as well as an Oja-like, but parameter-free, synaptic learning rule. Our theoretical framework makes several predictions, some of which can be verified by the existing data, others require further experiments. Such framework should allow modeling the function of neuronal circuits without necessarily measuring all the microscopic biophysical parameters, as well as facilitate the design of neuromorphic electronics., Comment: 2013 Asilomar Conference on Signals, Systems and Computers, see http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6810296

We are interested in establishing the correspondence between neuron activity and body curvature during various movements of C. Elegans worms. Given long sequences of images, specifically recorded to glow when the neuron is active, it is required to track all identifiable neurons in each frame. The characteristics of the neuron data, e.g., the uninformative nature of neuron appearance and the sequential ordering of neurons, renders standard single and multi-object tracking methods either ineffective or unnecessary for our task. In this paper, we propose a multi-target tracking algorithm that correctly assigns each neuron to one of several candidate locations in the next frame preserving shape constraint. The results demonstrate how the proposed method can robustly track more neurons than several existing methods in long sequences of images.

SummaryLocomotion requires coordinated motor activity throughout an animal’s body. In both vertebrates and invertebrates, chains of coupled central pattern generators (CPGs) are commonly evoked to explain local rhythmic behaviors. In C. elegans, we report that proprioception within the motor circuit is responsible for propagating and coordinating rhythmic undulatory waves from head to tail during forward movement. Proprioceptive coupling between adjacent body regions transduces rhythmic movement initiated near the head into bending waves driven along the body by a chain of reflexes. Using optogenetics and calcium imaging to manipulate and monitor motor circuit activity of moving C. elegans held in microfluidic devices, we found that the B-type cholinergic motor neurons transduce the proprioceptive signal. In C. elegans, a sensorimotor feedback loop operating within a specific type of motor neuron both drives and organizes body movement.

Summary Background Our brains are capable of remarkably stable stimulus representations despite time-varying neural activity. For instance, during delay periods in working memory tasks, while stimuli are represented in working memory, neurons in the prefrontal cortex, thought to support the memory representation, exhibit time-varying neuronal activity. Since neuronal activity encodes the stimulus, its time-varying dynamics appears to be paradoxical and incompatible with stable network stimulus representations. Indeed, this finding raises a fundamental question: can stable representations only be encoded with stable neural activity, or, its corollary, is every change in activity a sign of change in stimulus representation? Results Here we explain how different time-varying representations offered by individual neurons can be woven together to form a coherent, time-invariant, representation. Motivated by two ubiquitous features of the neocortex—redundancy of neural representation and sparse intracortical connections—we derive a network architecture that resolves the apparent contradiction between representation stability and changing neural activity. Unexpectedly, this network architecture exhibits many structural properties that have been measured in cortical sensory areas. In particular, we can account for few-neuron motifs, synapse weight distribution, and the relations between neuronal functional properties and connection probability. Conclusions We show that the intuition regarding network stimulus representation, typically derived from considering single neurons, may be misleading and that time-varying activity of distributed representation in cortical circuits does not necessarily imply that the network explicitly encodes time-varying properties.

Despite recent interest in reconstructing neuronal networks, complete wiring diagrams on the level of individual synapses remain scarce and the insights into function they can provide remain unclear. Even for Caenorhabditis elegans, whose neuronal network is relatively small and stereotypical from animal to animal, published wiring diagrams are neither accurate nor complete and self-consistent. Using materials from White et al. and new electron micrographs we assemble whole, self-consistent gap junction and chemical synapse networks of hermaphrodite C. elegans. We propose a method to visualize the wiring diagram, which reflects network signal flow. We calculate statistical and topological properties of the network, such as degree distributions, synaptic multiplicities, and small-world properties, that help in understanding network signal propagation. We identify neurons that may play central roles in information processing, and network motifs that could serve as functional modules of the network. We explore propagation of neuronal activity in response to sensory or artificial stimulation using linear systems theory and find several activity patterns that could serve as substrates of previously described behaviors. Finally, we analyze the interaction between the gap junction and the chemical synapse networks. Since several statistical properties of the C. elegans network, such as multiplicity and motif distributions are similar to those found in mammalian neocortex, they likely point to general principles of neuronal networks. The wiring diagram reported here can help in understanding the mechanistic basis of behavior by generating predictions about future experiments involving genetic perturbations, laser ablations, or monitoring propagation of neuronal activity in response to stimulation., National Science Foundation (U.S.) (Grant No. 0325774), National Science Foundation (U.S.) (Grant No. 0836720), National Science Foundation (U.S.) (Grant No. 0729069), National Institute of Mental Health (U.S.) (Grant 69838), Swartz Foundation, Klingenstein Foundation

Myelinated and non-myelinated axons co-exist in the brain. What determines whether an axon should be myelinated or not? Rushton proposed that among myelinated and non-myelinated alternatives with the same conduction velocity (CV), a thinner fiber is chosen due to its smaller volume cost. If the required CV is below a critical value, a non-myelinated axon is thinner and used. Otherwise, a myelinated axon should be used. This argument leads to the prediction of a critical axon diameter, which segregates myelinated and non-myelinated axons. We show that minimizing axonal cost does not necessarily lead to a critical diameter. By considering two optimization scenarios, we show that the appearance of an axon diameter spectrum depends on the relative unit volume cost between a myelinated and a non-myelinated axon. Both scenarios suggest that if unit volume cost of a myelinated axon were significantly less than that of a non-myelinated axon, there would be a gap between the distributions of non-myelinated and myelinated axon diameters. Otherwise, there would be an overlap between the distributions of non-myelinated and myelinated axon diameters. In addition, the second optimization scenario predicts a gap in the CV spectrum. By comparing our predictions with data from the corpus callosum, which shows overlap of the diameter distributions, we conclude that myelinated axons are costlier than non-myelinated ones. Prediction of a gap in the CV spectrum needs to be tested experimentally.

A ubiquitous feature of the vertebrate anatomy is the segregation of the brain into white and gray matter. Assuming that evolution maximized brain functionality, what is the reason for such segregation? To answer this question, we posit that brain functionality requires high interconnectivity and short conduction delays. Based on this assumption we searched for the optimal brain architecture by comparing different candidate designs. We found that the optimal design depends on the number of neurons, interneuronal connectivity, and axon diameter. In particular, the requirement to connect neurons with many fast axons drives the segregation of the brain into white and gray matter. These results provide a possible explanation for the structure of various regions of the vertebrate brain, such as the mammalian neocortex and neostriatum, the avian telencephalon, and the spinal cord., Synopsis Vertebrate brains generally contain two kinds of tissue: gray matter and white matter. Gray matter contains local networks of neurons that are wired by dendrites and mostly nonmyelinated local axons. White matter contains long-range axons that implement global communication via often myelinated axons. What is the evolutionary advantage of segregating the brain into white and gray matter rather than intermixing them? In this study, the authors postulate that brain functionality benefits from high synaptic connectivity and short conduction delays—the time required for a signal from one neuron soma to reach another. Using this postulate, they show quantitatively that the existence of many fast, long-range axons drives the segregation of the brain into gray and white matter. The theory not only provides a possible explanation for the structure of various brain regions such as cerebral cortex, neostriatum, and spinal cord, but also makes several testable predictions such as the scaling estimate of the cortical thickness.

Can neuronal morphology predict functional synaptic circuits? In the rat barrel cortex, 'barrels' and 'septa' delineate an orderly matrix of cortical columns. Using quantitative laser scanning photostimulation we measured the strength of excitatory projections from layer 4 (L4) and L5A to L2/3 pyramidal cells in barrel- and septum-related columns. From morphological reconstructions of excitatory neurons we computed the geometric circuit predicted by axodendritic overlap. Within most individual projections, functional inputs were predicted by geometry and a single scale factor, the synaptic strength per potential synapse. This factor, however, varied between projections and, in one case, even within a projection, up to 20-fold. Relationships between geometric overlap and synaptic strength thus depend on the laminar and columnar locations of both the pre- and postsynaptic neurons, even for neurons of the same type. A large plasticity potential appears to be incorporated into these circuits, allowing for functional 'tuning' with fixed axonal and dendritic arbor geometry.

The advent of high-quality 3D reconstructions of neuronal arbors has revived the hope of inferring synaptic connectivity from the geometric shapes of axons and dendrites, or 'neurogeometry'. A quantitative description of connectivity must be built on a sound theoretical framework. Here, we review recent developments in neurogeometry that can provide such a framework. We base the geometric description of connectivity on the concept of a 'potential synapse' - the close apposition between axons and dendrites necessary to form an actual synapse. In addition to describing potential synaptic connectivity in neuronal circuits, neurogeometry provides insight into basic features of functional connectivity, such as specificity and plasticity.

Current thinking about long-term memory in the cortex is focused on changes in the strengths of connections between neurons. But ongoing structural plasticity in the adult brain, including synapse formation/elimination and remodelling of axons and dendrites, suggests that memory could also depend on learning-induced changes in the cortical 'wiring diagram'. Given that the cortex is sparsely connected, wiring plasticity could provide a substantial boost in storage capacity, although at a cost of more elaborate biological machinery and slower learning.

▪ Abstract In mammalian visual cortex, neurons are organized according to their functional properties into multiple maps such as retinotopic, ocular dominance, orientation preference, direction of motion, and others. What determines the organization of cortical maps? We argue that cortical maps reflect neuronal connectivity in intracortical circuits. Because connecting distant neurons requires costly wiring (i.e., axons and dendrites), there is an evolutionary pressure to place connected neurons as close to each other as possible. Then, cortical maps may be viewed as solutions that minimize wiring cost for given intracortical connectivity. These solutions can help us in inferring intracortical connectivity and, ultimately, in understanding the function of the visual system.

Wiring economy has successfully explained the individual placement of neurons in simple nervous systems like that of Caenorhabditis elegans [ [1] , [2] and [3] ] and the locations of coarser structures like cortical areas in complex vertebrate brains [4]. However, it remains unclear whether wiring economy can explain the placement of individual neurons in brains larger than that of C. elegans. Indeed, given the greater number of neuronal interconnections in larger brains, simply minimizing the length of connections results in unrealistic configurations, with multiple neurons occupying the same position in space. Avoiding such configurations, or volume exclusion, repels neurons from each other, thus counteracting wiring economy. Here we test whether wiring economy together with volume exclusion can explain the placement of neurons in a module of the Drosophila melanogaster brain known as lamina cartridge [ [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] and [13] ]. We used newly developed techniques for semiautomated reconstruction from serial electron microscopy (EM) [14] to obtain the shapes of neurons, the location of synapses, and the resultant synaptic connectivity. We show that wiring length minimization and volume exclusion together can explain the structure of the lamina microcircuit. Therefore, even in brains larger than that of C. elegans, at least for some circuits, optimization can play an important role in individual neuron placement., We are grateful to Richard Fetter for assistance in EM imaging and Janelia FlyEM Project Team and Aljoshcha Nern for helpful comparisons with images from Gal4-driven expression of green fluorescent protein in lamina cells. M.R.-A. acknowledges a Formación del Personal de Investigación (FPI) fellowship from Ministerio de Ciencia e Innovación (MICINN) and support from the Janelia Farm Research Campus (JFRC) (Howard Hughes Medical Institute [HHMI]) visitor program; G.G.d.P. acknowledges funding by MICINN (Spain) as Plan Nacional, including a FPI fellowship, and as partners of the ERASysBio+ initiative supported under the EU ERA-NET Plus scheme in FP7, and support from the JFRC (HHMI) visitor program. I.A.M. also acknowledges support from the JFRC (HHMI) visitor program.

Does the C. elegans nervous system contain multi-neuron computational modules that perform stereotypical functions? We attempt to answer this question by searching for recurring multi-neuron inter-connectivity patterns in the C. elegans nervous system's wiring diagram. Our statistical analysis reveals that some inter-connectivity patterns containing two, three and four (but not five) neurons are significantly over-represented relative to the expectations based on the statistics of smaller inter-connectivity patterns. Over-represented patterns (or motifs) are candidates for computational modules that may perform stereotypical functions in the C. elegans nervous system. These modules may appear in other species and need to be investigated further.

Background: Axon calibers vary widely among different animals, neuron classes, and even within the same neuron. What determines the diameter of axon branches? Results: We pursue the hypothesis that the axon caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. For a general cost function, we show that the optimal diameters of mother and daughter branches at a bifurcation satisfy a power law. The derivation relies on the fact that the axon conduction speed scales as a power of axon diameter. Although available data are consistent with the law, there is a large spread in the data. Future experimental tests will determine whether th is spread is due to biological variability or measurement error. Conclusions: Minimization of arbor volume and signal propagation delay may have been an important factor in the evolution of the brain.

SummaryComplete reconstructions of vertebrate neuronal circuits on the synaptic level require new approaches. Here, serial section transmission electron microscopy was automated to densely reconstruct four volumes, totaling 670 μm3, from the rat hippocampus as proving grounds to determine when axo-dendritic proximities predict synapses. First, in contrast with Peters' rule, the density of axons within reach of dendritic spines did not predict synaptic density along dendrites because the fraction of axons making synapses was variable. Second, an axo-dendritic touch did not predict a synapse; nevertheless, the density of synapses along a hippocampal dendrite appeared to be a universal fraction, 0.2, of the density of touches. Finally, the largest touch between an axonal bouton and spine indicated the site of actual synapses with about 80% precision but would miss about half of all synapses. Thus, it will be difficult to predict synaptic connectivity using data sets missing ultrastructural details that distinguish between axo-dendritic touches and bona fide synapses.

Changes in synaptic connectivity patterns through the formation and elimination of dendritic spines may contribute to structural plasticity in the brain. We characterize this contribution quantitatively by estimating the number of different synaptic connectivity patterns attainable without major arbor remodeling. This number depends on the ratio of the synapses on a dendrite to the axons that pass within a spine length of that dendrite. We call this ratio the filling fraction and calculate it from geometrical analysis and anatomical data. The filling fraction is 0.26 in mouse neocortex, 0.22–0.34 in rat hippocampus. In the macaque visual cortex, the filling fraction increases by a factor of 1.6–1.8 from area V1 to areas V2, V4, and 7a. Since the filling fraction is much smaller than 1, spine remodeling can make a large contribution to structural plasticity.

How different is local cortical circuitry from a random network? To answer this question, we probed synaptic connections with several hundred simultaneous quadruple whole-cell recordings from layer 5 pyramidal neurons in the rat visual cortex. Analysis of this dataset revealed several nonrandom features in synaptic connectivity. We confirmed previous reports that bidirectional connections are more common than expected in a random network. We found that several highly clustered three-neuron connectivity patterns are overrepresented, suggesting that connections tend to cluster together. We also analyzed synaptic connection strength as defined by the peak excitatory postsynaptic potential amplitude. We found that the distribution of synaptic connection strength differs significantly from the Poisson distribution and can be fitted by a lognormal distribution. Such a distribution has a heavier tail and implies that synaptic weight is concentrated among few synaptic connections. In addition, the strengths of synaptic connections sharing pre- or postsynaptic neurons are correlated, implying that strong connections are even more clustered than the weak ones. Therefore, the local cortical network structure can be viewed as a skeleton of stronger connections in a sea of weaker ones. Such a skeleton is likely to play an important role in network dynamics and should be investigated further., A dataset of hundreds of recordings in which four neurons were simultaneously monitored reveals clustered connectivity patterns among cortical neurons

SummaryThe placement of neuronal cell bodies relative to the neuropile differs among species and brain areas. Cell bodies can be either embedded as in mammalian cortex or segregated as in invertebrates and some other vertebrate brain areas. Why are there such different arrangements? Here we suggest that the observed arrangements may simply be a reflection of wiring economy, a general principle that tends to reduce the total volume of the neuropile and hence the volume of the inclusions in it. Specifically, we suggest that the choice of embedded versus segregated arrangement is determined by which neuronal component — the cell body or the neurite connecting the cell body to the arbor — has a smaller volume. Our quantitative predictions are in agreement with existing and new measurements.