Validation of a stereological method for estimating particle size and density from 2D projections with high accuracy.

Stereological methods for estimating the 3D particle size and density from 2D projections are essential to many research fields. These methods are, however, prone to errors arising from undetected particle profiles due to sectioning and limited resolution, known as 'lost caps'. A potential solution developed by Keiding, Jensen, and Ranek in 1972, which we refer to as the Keiding model, accounts for lost caps by quantifying the smallest detectable profile in terms of its limiting 'cap angle' (ϕ), a size-independent measure of a particle's distance from the section surface. However, this simple solution has not been widely adopted nor tested. Rather, model-independent design-based stereological methods, which do not explicitly account for lost caps, have come to the fore. Here, we provide the first experimental validation of the Keiding model by comparing the size and density of particles estimated from 2D projections with direct measurement from 3D EM reconstructions of the same tissue. We applied the Keiding model to estimate the size and density of somata, nuclei and vesicles in the cerebellum of mice and rats, where high packing density can be problematic for design-based methods. Our analysis reveals a Gaussian distribution for ϕ rather than a single value. Nevertheless, curve fits of the Keiding model to the 2D diameter distribution accurately estimate the mean ϕ and 3D diameter distribution. While systematic testing using simulations revealed an upper limit to determining ϕ, our analysis shows that estimated ϕ can be used to determine the 3D particle density from the 2D density under a wide range of conditions, and this method is potentially more accurate than minimum-size-based lost-cap corrections and disector methods. Our results show the Keiding model provides an efficient means of accurately estimating the size and density of particles from 2D projections even under conditions of a high density.

Precompensation of 3D field distortions in remote focus two-photon microscopy.

Remote focusing is widely used in 3D two-photon microscopy and 3D photostimulation because it enables fast axial scanning without moving the objective lens or specimen. However, due to the design constraints of microscope optics, remote focus units are often located in non-telecentric positions in the optical path, leading to significant depth-dependent 3D field distortions in the imaging volume. To address this limitation, we characterized 3D field distortions arising from non-telecentric remote focusing and present a method for distortion precompensation. We demonstrate its applicability for a 3D two-photon microscope that uses an acousto-optic lens (AOL) for remote focusing and scanning. We show that the distortion precompensation method improves the pointing precision of the AOL microscope to < 0.5 µm throughout the 400 × 400 × 400 µm imaging volume.

Cerebellar granule cell axons support high-dimensional representations.

In classical theories of cerebellar cortex, high-dimensional sensorimotor representations are used to separate neuronal activity patterns, improving associative learning and motor performance. Recent experimental studies suggest that cerebellar granule cell (GrC) population activity is low-dimensional. To examine sensorimotor representations from the point of view of downstream Purkinje cell 'decoders', we used three-dimensional acousto-optic lens two-photon microscopy to record from hundreds of GrC axons. Here we show that GrC axon population activity is high dimensional and distributed with little fine-scale spatial structure during spontaneous behaviors. Moreover, distinct behavioral states are represented along orthogonal dimensions in neuronal activity space. These results suggest that the cerebellar cortex supports high-dimensional representations and segregates behavioral state-dependent computations into orthogonal subspaces, as reported in the neocortex. Our findings match the predictions of cerebellar pattern separation theories and suggest that the cerebellum and neocortex use population codes with common features, despite their vastly different circuit structures.

Multidimensional population activity in an electrically coupled inhibitory circuit in the cerebellar cortex.

Inhibitory neurons orchestrate the activity of excitatory neurons and play key roles in circuit function. Although individual interneurons have been studied extensively, little is known about their properties at the population level. Using random-access 3D two-photon microscopy, we imaged local populations of cerebellar Golgi cells (GoCs), which deliver inhibition to granule cells. We show that population activity is organized into multiple modes during spontaneous behaviors. A slow, network-wide common modulation of GoC activity correlates with the level of whisking and locomotion, while faster (<1 s) differential population activity, arising from spatially mixed heterogeneous GoC responses, encodes more precise information. A biologically detailed GoC circuit model reproduced the common population mode and the dimensionality observed experimentally, but these properties disappeared when electrical coupling was removed. Our results establish that local GoC circuits exhibit multidimensional activity patterns that could be used for inhibition-mediated adaptive gain control and spatiotemporal patterning of downstream granule cells.

Real-time 3D movement correction for two-photon imaging in behaving animals.

Two-photon microscopy is widely used to investigate brain function across multiple spatial scales. However, measurements of neural activity are compromised by brain movement in behaving animals. Brain motion-induced artifacts are typically corrected using post hoc processing of two-dimensional images, but this approach is slow and does not correct for axial movements. Moreover, the deleterious effects of brain movement on high-speed imaging of small regions of interest and photostimulation cannot be corrected post hoc. To address this problem, we combined random-access three-dimensional (3D) laser scanning using an acousto-optic lens and rapid closed-loop field programmable gate array processing to track 3D brain movement and correct motion artifacts in real time at up to 1 kHz. Our recordings from synapses, dendrites and large neuronal populations in behaving mice and zebrafish demonstrate real-time movement-corrected 3D two-photon imaging with submicrometer precision.

Open Source Brain: A Collaborative Resource for Visualizing, Analyzing, Simulating, and Developing Standardized Models of Neurons and Circuits.

Computational models are powerful tools for exploring the properties of complex biological systems. In neuroscience, data-driven models of neural circuits that span multiple scales are increasingly being used to understand brain function in health and disease. But their adoption and reuse has been limited by the specialist knowledge required to evaluate and use them. To address this, we have developed Open Source Brain, a platform for sharing, viewing, analyzing, and simulating standardized models from different brain regions and species. Model structure and parameters can be automatically visualized and their dynamical properties explored through browser-based simulations. Infrastructure and tools for collaborative interaction, development, and testing are also provided. We demonstrate how existing components can be reused by constructing new models of inhibition-stabilized cortical networks that match recent experimental results. These features of Open Source Brain improve the accessibility, transparency, and reproducibility of models and facilitate their reuse by the wider community.

Re-evaluating Circuit Mechanisms Underlying Pattern Separation.

When animals interact with complex environments, their neural circuits must separate overlapping patterns of activity that represent sensory and motor information. Pattern separation is thought to be a key function of several brain regions, including the cerebellar cortex, insect mushroom body, and dentate gyrus. However, recent findings have questioned long-held ideas on how these circuits perform this fundamental computation. Here, we re-evaluate the functional and structural mechanisms underlying pattern separation. We argue that the dimensionality of the space available for population codes representing sensory and motor information provides a common framework for understanding pattern separation. We then discuss how these three circuits use different strategies to separate activity patterns and facilitate associative learning in the presence of trial-to-trial variability.

Geppetto: a reusable modular open platform for exploring neuroscience data and models.

Geppetto is an open-source platform that provides generic middleware infrastructure for building both online and desktop tools for visualizing neuroscience models and data and managing simulations. Geppetto underpins a number of neuroscience applications, including Open Source Brain (OSB), Virtual Fly Brain (VFB), NEURON-UI and NetPyNE-UI. OSB is used by researchers to create and visualize computational neuroscience models described in NeuroML and simulate them through the browser. VFB is the reference hub for Drosophila melanogaster neural anatomy and imaging data including neuropil, segmented neurons, microscopy stacks and gene expression pattern data. Geppetto is also being used to build a new user interface for NEURON, a widely used neuronal simulation environment, and for NetPyNE, a Python package for network modelling using NEURON. Geppetto defines domain agnostic abstractions used by all these applications to represent their models and data and offers a set of modules and components to integrate, visualize and control simulations in a highly accessible way. The platform comprises a backend which can connect to external data sources, model repositories and simulators together with a highly customizable frontend.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

NeuroMatic: An Integrated Open-Source Software Toolkit for Acquisition, Analysis and Simulation of Electrophysiological Data.

Acquisition, analysis and simulation of electrophysiological properties of the nervous system require multiple software packages. This makes it difficult to conserve experimental metadata and track the analysis performed. It also complicates certain experimental approaches such as online analysis. To address this, we developed NeuroMatic, an open-source software toolkit that performs data acquisition (episodic, continuous and triggered recordings), data analysis (spike rasters, spontaneous event detection, curve fitting, stationarity) and simulations (stochastic synaptic transmission, synaptic short-term plasticity, integrate-and-fire and Hodgkin-Huxley-like single-compartment models). The merging of a wide range of tools into a single package facilitates a more integrated style of research, from the development of online analysis functions during data acquisition, to the simulation of synaptic conductance trains during dynamic-clamp experiments. Moreover, NeuroMatic has the advantage of working within Igor Pro, a platform-independent environment that includes an extensive library of built-in functions, a history window for reviewing the user's workflow and the ability to produce publication-quality graphics. Since its original release, NeuroMatic has been used in a wide range of scientific studies and its user base has grown considerably. NeuroMatic version 3.0 can be found at http://www.neuromatic.thinkrandom.com and https://github.com/SilverLabUCL/NeuroMatic.

A Commitment to Open Source in Neuroscience.

Modern neuroscience increasingly relies on custom-developed software, but much of this is not being made available to the wider community. A group of researchers are pledging to make code they produce for data analysis and modeling open source, and are actively encouraging their colleagues to follow suit.

Sparse synaptic connectivity is required for decorrelation and pattern separation in feedforward networks.

Pattern separation is a fundamental function of the brain. The divergent feedforward networks thought to underlie this computation are widespread, yet exhibit remarkably similar sparse synaptic connectivity. Marr-Albus theory postulates that such networks separate overlapping activity patterns by mapping them onto larger numbers of sparsely active neurons. But spatial correlations in synaptic input and those introduced by network connectivity are likely to compromise performance. To investigate the structural and functional determinants of pattern separation we built models of the cerebellar input layer with spatially correlated input patterns, and systematically varied their synaptic connectivity. Performance was quantified by the learning speed of a classifier trained on either the input or output patterns. Our results show that sparse synaptic connectivity is essential for separating spatially correlated input patterns over a wide range of network activity, and that expansion and correlations, rather than sparse activity, are the major determinants of pattern separation.

Assessing the Role of Inhibition in Stabilizing Neocortical Networks Requires Large-Scale Perturbation of the Inhibitory Population.

Neurons within cortical microcircuits are interconnected with recurrent excitatory synaptic connections that are thought to amplify signals (Douglas and Martin, 2007), form selective subnetworks (Ko et al., 2011), and aid feature discrimination. Strong inhibition (Haider et al., 2013) counterbalances excitation, enabling sensory features to be sharpened and represented by sparse codes (Willmore et al., 2011). This balance between excitation and inhibition makes it difficult to assess the strength, or gain, of recurrent excitatory connections within cortical networks, which is key to understanding their operational regime and the computations that they perform. Networks that combine an unstable high-gain excitatory population with stabilizing inhibitory feedback are known as inhibition-stabilized networks (ISNs) (Tsodyks et al., 1997). Theoretical studies using reduced network models predict that ISNs produce paradoxical responses to perturbation, but experimental perturbations failed to find evidence for ISNs in cortex (Atallah et al., 2012). Here, we reexamined this question by investigating how cortical network models consisting of many neurons behave after perturbations and found that results obtained from reduced network models fail to predict responses to perturbations in more realistic networks. Our models predict that a large proportion of the inhibitory network must be perturbed to reliably detect an ISN regime robustly in cortex. We propose that wide-field optogenetic suppression of inhibition under promoters targeting a large fraction of inhibitory neurons may provide a perturbation of sufficient strength to reveal the operating regime of cortex. Our results suggest that detailed computational models of optogenetic perturbations are necessary to interpret the results of experimental paradigms.SIGNIFICANCE STATEMENT Many useful computational mechanisms proposed for cortex require local excitatory recurrence to be very strong, such that local inhibitory feedback is necessary to avoid epileptiform runaway activity (an "inhibition-stabilized network" or "ISN" regime). However, recent experimental results suggest that this regime may not exist in cortex. We simulated activity perturbations in cortical networks of increasing realism and found that, to detect ISN-like properties in cortex, large proportions of the inhibitory population must be perturbed. Current experimental methods for inhibitory perturbation are unlikely to satisfy this requirement, implying that existing experimental observations are inconclusive about the computational regime of cortex. Our results suggest that new experimental designs targeting a majority of inhibitory neurons may be able to resolve this question.

Random-access scanning microscopy for 3D imaging in awake behaving animals.

Understanding how neural circuits process information requires rapid measurements of activity from identified neurons distributed in 3D space. Here we describe an acousto-optic lens two-photon microscope that performs high-speed focusing and line scanning within a volume spanning hundreds of micrometers. We demonstrate its random-access functionality by selectively imaging cerebellar interneurons sparsely distributed in 3D space and by simultaneously recording from the soma, proximal and distal dendrites of neocortical pyramidal cells in awake behaving mice.

Functional Properties of Dendritic Gap Junctions in Cerebellar Golgi Cells.

The strength and variability of electrical synaptic connections between GABAergic interneurons are key determinants of spike synchrony within neuronal networks. However, little is known about how electrical coupling strength is determined due to the inaccessibility of gap junctions on the dendritic tree. We investigated the properties of gap junctions in cerebellar interneurons by combining paired somato-somatic and somato-dendritic recordings, anatomical reconstructions, immunohistochemistry, electron microscopy, and modeling. By fitting detailed compartmental models of Golgi cells to their somato-dendritic voltage responses, we determined their passive electrical properties and the mean gap junction conductance (0.9 nS). Connexin36 immunofluorescence and freeze-fracture replica immunogold labeling revealed a large variability in gap junction size and that only 18% of the 340 channels are open in each plaque. Our results establish that the number of gap junctions per connection is the main determinant of both the strength and variability in electrical coupling between Golgi cells.

Extracting quantal properties of transmission at central synapses.

Chemical synapses enable neurons to communicate rapidly, process and filter signals and to store information. However, studying their functional properties is difficult because synaptic connections typically consist of multiple synaptic contacts that release vesicles stochastically and exhibit time-dependent behavior. Moreover, most central synapses are small and inaccessible to direct measurements. Estimation of synaptic properties from responses recorded at the soma is complicated by the presence of nonuniform release probability and nonuniform quantal properties. The presence of multivesicular release and postsynaptic receptor saturation at some synapses can also complicate the interpretation of quantal parameters. Multiple-probability fluctuation analysis (MPFA; also known as variance-mean analysis) is a method that has been developed for estimating synaptic parameters from the variance and mean amplitude of synaptic responses recorded at different release probabilities. This statistical approach, which incorporates nonuniform synaptic properties, has become widely used for studying synaptic transmission. In this chapter, we describe the statistical models used to extract quantal parameters and discuss their interpretation when applying MPFA.

Nanoscale distribution of presynaptic Ca(2+) channels and its impact on vesicular release during development.

Synaptic efficacy and precision are influenced by the coupling of voltage-gated Ca(2+) channels (VGCCs) to vesicles. But because the topography of VGCCs and their proximity to vesicles is unknown, a quantitative understanding of the determinants of vesicular release at nanometer scale is lacking. To investigate this, we combined freeze-fracture replica immunogold labeling of Cav2.1 channels, local [Ca(2+)] imaging, and patch pipette perfusion of EGTA at the calyx of Held. Between postnatal day 7 and 21, VGCCs formed variable sized clusters and vesicular release became less sensitive to EGTA, whereas fixed Ca(2+) buffer properties remained constant. Experimentally constrained reaction-diffusion simulations suggest that Ca(2+) sensors for vesicular release are located at the perimeter of VGCC clusters (<30 nm) and predict that VGCC number per cluster determines vesicular release probability without altering release time course. This "perimeter release model" provides a unifying framework accounting for developmental changes in both synaptic efficacy and time course.

LEMS: a language for expressing complex biological models in concise and hierarchical form and its use in underpinning NeuroML 2.

Computational models are increasingly important for studying complex neurophysiological systems. As scientific tools, it is essential that such models can be reproduced and critically evaluated by a range of scientists. However, published models are currently implemented using a diverse set of modeling approaches, simulation tools, and computer languages making them inaccessible and difficult to reproduce. Models also typically contain concepts that are tightly linked to domain-specific simulators, or depend on knowledge that is described exclusively in text-based documentation. To address these issues we have developed a compact, hierarchical, XML-based language called LEMS (Low Entropy Model Specification), that can define the structure and dynamics of a wide range of biological models in a fully machine readable format. We describe how LEMS underpins the latest version of NeuroML and show that this framework can define models of ion channels, synapses, neurons and networks. Unit handling, often a source of error when reusing models, is built into the core of the language by specifying physical quantities in models in terms of the base dimensions. We show how LEMS, together with the open source Java and Python based libraries we have developed, facilitates the generation of scripts for multiple neuronal simulators and provides a route for simulator free code generation. We establish that LEMS can be used to define models from systems biology and map them to neuroscience-domain specific simulators, enabling models to be shared between these traditionally separate disciplines. LEMS and NeuroML 2 provide a new, comprehensive framework for defining computational models of neuronal and other biological systems in a machine readable format, making them more reproducible and increasing the transparency and accessibility of their underlying structure and properties.

Network structure within the cerebellar input layer enables lossless sparse encoding.

The synaptic connectivity within neuronal networks is thought to determine the information processing they perform, yet network structure-function relationships remain poorly understood. By combining quantitative anatomy of the cerebellar input layer and information theoretic analysis of network models, we investigated how synaptic connectivity affects information transmission and processing. Simplified binary models revealed that the synaptic connectivity within feedforward networks determines the trade-off between information transmission and sparse encoding. Networks with few synaptic connections per neuron and network-activity-dependent threshold were optimal for lossless sparse encoding over the widest range of input activities. Biologically detailed spiking network models with experimentally constrained synaptic conductances and inhibition confirmed our analytical predictions. Our results establish that the synaptic connectivity within the cerebellar input layer enables efficient lossless sparse encoding. Moreover, they provide a functional explanation for why granule cells have approximately four dendrites, a feature that has been evolutionarily conserved since the appearance of fish.