On Optical Detection of Densely Labeled Synapses in Neuropil and Mapping Connectivity with Combinatorially Multiplexed Fluorescent Synaptic Markers

We propose a new method for mapping neural connectivity optically, by utilizing Cre/Lox system Brainbow to tag synapses of different neurons with random mixtures of different fluorophores, such as GFP, YFP, etc., and then detecting patterns of fluorophores at different synapses using light microscopy (LM). Such patterns will immediately report the pre- and post-synaptic cells at each synaptic connection, without tracing neural projections from individual synapses to corresponding cell bodies. We simulate fluorescence from a population of densely labeled synapses in a block of hippocampal neuropil, completely reconstructed from electron microscopy data, and show that high-end LM is able to detect such patterns with over 95% accuracy. We conclude, therefore, that with the described approach neural connectivity in macroscopically large neural circuits can be mapped with great accuracy, in scalable manner, using fast optical tools, and straightforward image processing. Relying on an electron microscopy dataset, we also derive and explicitly enumerate the conditions that should be met to allow synaptic connectivity studies with high-resolution optical tools.     

Gene expression of Caenorhabditis elegans neurons carries information on their synaptic connectivity

The claim that genetic properties of neurons significantly influence their synaptic network structure is a common notion in neuroscience. The nematode Caenorhabditis elegans provides an exciting opportunity to approach this question in a large-scale quantitative manner. Its synaptic connectivity network has been identified, and, combined with cellular studies, we currently have characteristic connectivity and gene expression signatures for most of its neurons. By using two complementary analysis assays we show that the expression signature of a neuron carries significant information about its synaptic connectivity signature, and identify a list of putative genes predicting neural connectivity. The current study rigorously quantifies the relation between gene expression and synaptic connectivity signatures in the C. elegans nervous system and identifies subsets of neurons where this relation is highly marked. The results presented and the genes identified provide a promising starting point for further, more detailed computational and experimental investigations.     

Volume electron microscopy for neuronal circuit reconstruction

The last decade has seen a rapid increase in the number of tools to acquire volume electron microscopy (EM) data. Several new scanning EM (SEM) imaging methods have emerged, and classical transmission EM (TEM) methods are being scaled up and automated. Here we summarize the new methods for acquiring large EM volumes, and discuss the tradeoffs in terms of resolution, acquisition speed, and reliability. We then assess each method's applicability to the problem of reconstructing anatomical connectivity between neurons, considering both the current capabilities and future prospects of the method. Finally, we argue that neuronal 'wiring diagrams' are likely necessary, but not sufficient, to understand the operation of most neuronal circuits: volume EM imaging will likely find its best application in combination with other methods in neuroscience, such as molecular biology, optogenetics, and physiology.     

How do high-level specifications of the brain relate to variational approaches?

High-level specification of how the brain represents and categorizes the causes of its sensory input allows to link "what is to be done" (perceptual task) with "how to do it" (neural network calculation). In this article, we describe how the variational framework, which encountered a large success in modeling computer vision tasks, has some interesting relationships, at a mesoscopic scale, with computational neuroscience. We focus on cortical map computations such that "what is to be done" can be represented as a variational approach, i.e., an optimization problem defined over a continuous functional space. In particular, generalizing some existing results, we show how a general variational approach can be solved by an analog neural network with a given architecture and conversely. Numerical experiments are provided as an illustration of this general framework, which is a promising framework for modeling macro-behaviors in computational neuroscience.     

Impact of network topology on inference of synaptic connectivity from multi-neuronal spike data simulated by a large-scale cortical network model

Many mechanisms of neural processing rely critically upon the synaptic connectivity between neurons. As our ability to simultaneously record from large populations of neurons expands, the ability to infer network connectivity from this data has become a major goal of computational neuroscience. To address this issue, we employed several different methods to infer synaptic connections from simulated spike data from a realistic local cortical network model. This approach allowed us to directly compare the accuracy of different methods in predicting synaptic connectivity. We compared the performance of model-free (coherence measure and transfer entropy) and model-based (coupled escape rate model) methods of connectivity inference, applying those methods to the simulated spike data from the model networks with different network topologies. Our results indicate that the accuracy of the inferred connectivity was higher for highly clustered, near regular, or small-world networks, while accuracy was lower for random networks, irrespective of which analysis method was employed. Among the employed methods, the model-based method performed best. This model performed with higher accuracy, was less sensitive to threshold changes, and required less data to make an accurate assessment of connectivity. Given that cortical connectivity tends to be highly clustered, our results outline a powerful analytical tool for inferring local synaptic connectivity from observations of spontaneous activity.     

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.     

Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.     

Learning neural connectivity from firing activity: efficient algorithms with provable guarantees on topology

The connectivity of a neuronal network has a major effect on its functionality and role. It is generally believed that the complex network structure of the brain provides a physiological basis for information processing. Therefore, identifying the network’s topology has received a lot of attentions in neuroscience and has been the center of many research initiatives such as Human Connectome Project. Nevertheless, direct and invasive approaches that slice and observe the neural tissue have proven to be time consuming, complex and costly. As a result, the inverse methods that utilize firing activity of neurons in order to identify the (functional) connections have gained momentum recently, especially in light of rapid advances in recording technologies; It will soon be possible to simultaneously monitor the activities of tens of thousands of neurons in real time. While there are a number of excellent approaches that aim to identify the functional connections from firing activities, the scalability of the proposed techniques plays a major challenge in applying them on large-scale datasets of recorded firing activities. In exceptional cases where scalability has not been an issue, the theoretical performance guarantees are usually limited to a specific family of neurons or the type of firing activities. In this paper, we formulate the neural network reconstruction as an instance of a graph learning problem, where we observe the behavior of nodes/neurons (i.e., firing activities) and aim to find the links/connections. We develop a scalable learning mechanism and derive the conditions under which the estimated graph for a network of Leaky Integrate and Fire (LIf) neurons matches the true underlying synaptic connections. We then validate the performance of the algorithm using artificially generated data (for benchmarking) and real data recorded from multiple hippocampal areas in rats.     

A Graph Algorithmic Approach to Separate Direct from Indirect Neural Interactions

Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between multiple neural sources. Interactions are often reconstructed using pairwise bivariate analyses, overlooking the multivariate nature of interactions: it is neglected that investigating the effect of one source on a target necessitates to take all other sources as potential nuisance variables into account; also combinations of sources may act jointly on a given target. Bivariate analyses produce networks that may contain spurious interactions, which reduce the interpretability of the network and its graph metrics. A truly multivariate reconstruction, however, is computationally intractable because of the combinatorial explosion in the number of potential interactions. Thus, we have to resort to approximative methods to handle the intractability of multivariate interaction reconstruction, and thereby enable the use of networks in neuroscience. Here, we suggest such an approximative approach in the form of an algorithm that extends fast bivariate interaction reconstruction by identifying potentially spurious interactions post-hoc: the algorithm uses interaction delays reconstructed for directed bivariate interactions to tag potentially spurious edges on the basis of their timing signatures in the context of the surrounding network. Such tagged interactions may then be pruned, which produces a statistically conservative network approximation that is guaranteed to contain non-spurious interactions only. We describe the algorithm and present a reference implementation in MATLAB to test the algorithm’s performance on simulated networks as well as networks derived from magnetoencephalographic data. We discuss the algorithm in relation to other approximative multivariate methods and highlight suitable application scenarios. Our approach is a tractable and data-efficient way of reconstructing approximative networks of multivariate interactions. It is preferable if available data are limited or if fully multivariate approaches are computationally infeasible.     

Computer Assisted Assembly of Connectomes from Electron Micrographs: Application to Caenorhabditis elegans

A rate-limiting step in determining a connectome, the set of all synaptic connections in a nervous system, is extraction of the relevant information from serial electron micrographs. Here we introduce a software application, Elegance, that speeds acquisition of the minimal dataset necessary, allowing the discovery of new connectomes. We have used Elegance to obtain new connectivity data in the nematode worm Caenorhabditis elegans. We analyze the accuracy that can be obtained, which is limited by unresolvable ambiguities at some locations in electron microscopic images. Elegance is useful for reconstructing connectivity in any region of neuropil of sufficiently small size.     

A Morpho-Density Approach to Estimating Neural Connectivity

Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity.     

Causal measures of structure and plasticity in simulated and living neural networks

A major goal of neuroscience is to understand the relationship between neural structures and their function. Recording of neural activity with arrays of electrodes is a primary tool employed toward this goal. However, the relationships among the neural activity recorded by these arrays are often highly complex making it problematic to accurately quantify a network's structural information and then relate that structure to its function. Current statistical methods including cross correlation and coherence have achieved only modest success in characterizing the structural connectivity. Over the last decade an alternative technique known as Granger causality is emerging within neuroscience. This technique, borrowed from the field of economics, provides a strong mathematical foundation based on linear auto-regression to detect and quantify "causal" relationships among different time series. This paper presents a combination of three Granger based analytical methods that can quickly provide a relatively complete representation of the causal structure within a neural network. These are a simple pairwise Granger causality metric, a conditional metric, and a little known computationally inexpensive subtractive conditional method. Each causal metric is first described and evaluated in a series of biologically plausible neural simulations. We then demonstrate how Granger causality can detect and quantify changes in the strength of those relationships during plasticity using 60 channel spike train data from an in vitro cortical network measured on a microelectrode array. We show that these metrics can not only detect the presence of causal relationships, they also provide crucial information about the strength and direction of that relationship, particularly when that relationship maybe changing during plasticity. Although we focus on the analysis of multichannel spike train data the metrics we describe are applicable to any stationary time series in which causal relationships among multiple measures is desired. These techniques can be especially useful when the interactions among those measures are highly complex, difficult to untangle, and maybe changing over time.     

Inferring network activity from synaptic noise

During intense network activity in vivo, cortical neurons are in a high-conductance state, in which the membrane potential (V(m)) is subject to a tremendous fluctuating activity. Clearly, this "synaptic noise" contains information about the activity of the network, but there are presently no methods available to extract this information. We focus here on this problem from a computational neuroscience perspective, with the aim of drawing methods to analyze experimental data. We start from models of cortical neurons, in which high-conductance states stem from the random release of thousands of excitatory and inhibitory synapses. This highly complex system can be simplified by using global synaptic conductances described by effective stochastic processes. The advantage of this approach is that one can derive analytically a number of properties from the statistics of resulting V(m) fluctuations. For example, the global excitatory and inhibitory conductances can be extracted from synaptic noise, and can be related to the mean activity of presynaptic neurons. We show here that extracting the variances of excitatory and inhibitory synaptic conductances can provide estimates of the mean temporal correlation-or level of synchrony-among thousands of neurons in the network. Thus, "probing the network" through intracellular V(m) activity is possible and constitutes a promising approach, but it will require a continuous effort combining theory, computational models and intracellular physiology.     

Finding Needles in a Haystack with Light: Resolving the Microcircuitry of the Brain with Fluorescence Microscopy

To understand the microcircuitry of the brain, the anatomical and functional connectivity among neurons must be resolved. One of the technical hurdles to achieving this goal is that the anatomical connections, or synapses, are often smaller than the diffraction limit of light and thus are difficult to resolve by conventional microscopy, while the microcircuitry of the brain is on the scale of 1 mm or larger. To date, the gold standard method for microcircuit reconstruction has been electron microscopy (EM). However, despite its rapid development, EM has clear shortcomings as a method for microcircuit reconstruction. The greatest weakness of this method is arguably its incompatibility with functional and molecular analysis. Fluorescence microscopy, on the other hand, is readily compatible with numerous physiological and molecular analyses. We believe that recent advances in various fluorescence microscopy techniques offer a new possibility for reliable synapse detection in large volumes of neural circuits. In this minireview, we summarize recent advances in fluorescence-based microcircuit reconstruction. In the same vein as these studies, we introduce our recent efforts to analyze the long-range connectivity among brain areas and the subcellular distribution of synapses of interest in relatively large volumes of cortical tissue with array tomography and superresolution microscopy.     

Cortical dynamic tuning: the role of intrinsic connections, as revealed by modeling

A current challenge in computational neuroscience is to elucidate the role of cortical circuitry in information processing and in generating motor output. Our understanding of the functional significance of specifically organized feedback connections is progressing rapidly as researchers establish the equivalence of theoretical models to biological neural circuits. Modeling studies of different neural structures, along with quantitative comparisons of model performance to biological data, have recently helped to identify the basic features of synaptic connectivity that may play important roles in cortical operations.     

Exact reconstruction of gene regulatory networks using compressive sensing

Background

We consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network’s sparseness.

Results

For the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented.

Conclusions

The method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0400-4) contains supplementary material, which is available to authorized users.     

Mental illness from the perspective of theoretical neuroscience

Theoretical neuroscience, which characterizes neural mechanisms using mathematical and computational models, is highly relevant to central problems in the philosophy of psychiatry. These models can help to solve the explanation problem of causally connecting neural processes with the behaviors and experiences found in mental illnesses. Such explanations will also be useful for generating better classifications and treatments of psychiatric disorders. The result should help to eliminate concerns that mental illnesses such as depression and schizophrenia are not objectively real. A philosophical approach to mental illness based on neuroscience need not neglect the inherently social and historical nature of mental phenomena.     

Quantifying Synapses: an Immunocytochemistry-based Assay to Quantify Synapse Number

One of the most important goals in neuroscience is to understand the molecular cues that instruct early stages of synapse formation. As such it has become imperative to develop objective approaches to quantify changes in synaptic connectivity. Starting from sample fixation, this protocol details how to quantify synapse number both in dissociated neuronal culture and in brain sections using immunocytochemistry. Using compartment-specific antibodies, we label presynaptic terminals as well as sites of postsynaptic specialization. We define synapses as points of colocalization between the signals generated by these markers. The number of these colocalizations is quantified using a plug in Puncta Analyzer (written by Bary Wark, available upon request, c.eroglu@cellbio.duke.edu) under the ImageJ analysis software platform. The synapse assay described in this protocol can be applied to any neural tissue or culture preparation for which you have selective pre- and postsynaptic markers. This synapse assay is a valuable tool that can be widely utilized in the study of synaptic development.Download video file.^{(114M, mov)}     

TrakEM2 software for neural circuit reconstruction

A key challenge in neuroscience is the expeditious reconstruction of neuronal circuits. For model systems such as Drosophila and C. elegans, the limiting step is no longer the acquisition of imagery but the extraction of the circuit from images. For this purpose, we designed a software application, TrakEM2, that addresses the systematic reconstruction of neuronal circuits from large electron microscopical and optical image volumes. We address the challenges of image volume composition from individual, deformed images; of the reconstruction of neuronal arbors and annotation of synapses with fast manual and semi-automatic methods; and the management of large collections of both images and annotations. The output is a neural circuit of 3d arbors and synapses, encoded in NeuroML and other formats, ready for analysis.