Dmitri B. Chklovskii

Structural Properties of the Caenorhabditis elegans Neuronal Network

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.

Semi-automated reconstruction of neural circuits using electron microscopy.

Reconstructing neuronal circuits at the level of synapses is a central problem in neuroscience, and the focus of the nascent field of connectomics. Previously used to reconstruct the C. elegans wiring diagram, serial-section transmission electron microscopy (ssTEM) is a proven technique for the task. However, to reconstruct more complex circuits, ssTEM will require the automation of image processing. We review progress in the processing of electron microscopy images and, in particular, a semi-automated reconstruction pipeline deployed at Janelia Farm. Drosophila circuits underlying identified behaviors are being reconstructed in the pipeline with the goal of generating a complete Drosophila connectome.

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 brains 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.

Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors

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.

Machine Learning of Hierarchical Clustering to Segment 2D and 3D Images

We aim to improve segmentation through the use of machine learning tools during region agglomeration. We propose an active learning approach for performing hierarchical agglomerative segmentation from superpixels. Our method combines multiple features at all scales of the agglomerative process, works for data with an arbitrary number of dimensions, and scales to very large datasets. We advocate the use of variation of information to measure segmentation accuracy, particularly in 3D electron microscopy (EM) images of neural tissue, and using this metric demonstrate an improvement over competing algorithms in EM and natural images.

Synaptic circuits and their variations within different columns in the visual system of Drosophila

Significance Circuit diagrams of brains are generally reported only as absolute or consensus networks; these diagrams fail to identify the accuracy of connections, however, for which multiple circuits of the same neurons must be documented. For this reason, the modular composition of the Drosophila visual system, with many identified neuron classes, is ideal. Using EM, we identified synaptic connections in the fly’s second visual relay neuropil, or medulla, in the 20 neuron classes in a so-called “core connectome,” those neurons present in seven neighboring columns. These connections identify circuits for motion. Their error rates for wiring reveal that <1% of contacts overall are not part of a consensus circuit but incorporate errors of either omission or commission. Autapses are occasionally seen. 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, <1% of contacts are not part of a consensus circuit, and we classify those contacts that supplement (E+) or are missing from it (E−). Autapses, in which the same cell is both presynaptic and postsynaptic at the same synapse, are occasionally seen; two cells in particular, Dm9 and Mi1, form ≥20-fold more autapses than do other neurons. These results delimit the accuracy of developmental events that establish and normally maintain synaptic circuits with such precision, and thereby address the operation of such circuits. They also establish a precedent for error rates that will be required in the new science of connectomics.

Neuronal Circuits Underlying Persistent Representations Despite Time Varying Activity

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

Toward large-scale connectome reconstructions

Recent results have shown the possibility of both reconstructing connectomes of small but biologically interesting circuits and extracting from these connectomes insights into their function. However, these reconstructions were heroic proof-of-concept experiments, requiring person-months of effort per neuron reconstructed, and will not scale to larger circuits, much less the brains of entire animals. In this paper we examine what will be required to generate and use substantially larger connectomes, finding five areas that need increased attention: firstly, imaging better suited to automatic reconstruction, with excellent z-resolution; secondly, automatic detection, validation, and measurement of synapses; thirdly, reconstruction methods that keep and use uncertainty metrics for every object, from initial images, through segmentation, reconstruction, and connectome queries; fourthly, processes that are fully incremental, so that the connectome may be used before it is fully complete; and finally, better tools for analysis of connectomes, once they are obtained.

Thalamocortical input onto layer 5 pyramidal neurons measured using quantitative large-scale array tomography

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 mm3 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.

The comprehensive connectome of a neural substrate for 'ON' motion detection in Drosophila

Analysing computations in neural circuits often uses simplified models because the actual neuronal implementation is not known. For example, a problem in vision, how the eye detects image motion, has long been analysed using Hassenstein-Reichardt (HR) detector or Barlow-Levick (BL) models. These both simulate motion detection well, but the exact neuronal circuits undertaking these tasks remain elusive. We reconstructed a comprehensive connectome of the circuits of Drosophila‘s motion-sensing T4 cells using a novel EM technique. We uncover complex T4 inputs and reveal that putative excitatory inputs cluster at T4’s dendrite shafts, while inhibitory inputs localize to the bases. Consistent with our previous study, we reveal that Mi1 and Tm3 cells provide most synaptic contacts onto T4. We are, however, unable to reproduce the spatial offset between these cells reported previously. Our comprehensive connectome reveals complex circuits that include candidate anatomical substrates for both HR and BL types of motion detectors. DOI: http://dx.doi.org/10.7554/eLife.24394.001