The vast computational power of the brain has traditionally been viewed as arising from the complex connectivity of neural networks, in which an individual neuron acts as a simple linear summation ...and thresholding device. However, recent studies show that individual neurons utilize a wealth of nonlinear mechanisms to transform synaptic input into output firing. These mechanisms can arise from synaptic plasticity, synaptic noise, and somatic and dendritic conductances. This tool kit of nonlinear mechanisms confers considerable computational power on both morphologically simple and more complex neurons, enabling them to perform a range of arithmetic operations on signals encoded ina variety of different ways.
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.
•Network connectivity sets trade-off between informative and sparse encoding•Feedforward networks with few connections are optimal for lossless, sparse encoding•Best-performing networks match synaptic connectivity in the cerebellar input layer•Explanation for why cerebellar granule cells have approximately 4 dendrites
Synaptic connectivity is thought to determine information processing in neuronal networks, yet network structure-function relationships are poorly understood. Billings et al. show that synaptic connectivity within feedforward networks determines the trade-off between information transmission and sparse encoding.
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.
Pattern separation is a fundamental neural computation thought to facilitate associative learning. Cayco-Gajic and Silver review recent theoretical and experimental advances on the key determinants of pattern separation in the cerebellar cortex, insect mushroom body, and dentate gyrus.
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.
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.
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.
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.
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.
•The mean conductance of dendritic gap junctions between Golgi cells is 0.9 nS•Dendritic gap junctions have 340 connexin36 channels of which 18% are open•Dendritic location contributes little to coupling strength variability•Gap junction number is the main determinant of coupling strength variability
Variation in the strength of electrical synapses influences spike synchrony in interneuron networks. Szoboszlay et al. investigated the properties of electrical synapses between cerebellar Golgi cells and showed that the number of gap junctions is the main determinant of coupling strength variability.
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.
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•Inhibitory circuit population activity is organized on multiple spatiotemporal scales•Slow circuit-wide Golgi cell activation reflects general level of behavioral activity•Multidimensional differential population activity encodes behavioral information•Electrically coupled Golgi cell circuit model reproduces population-level properties
Inhibitory interneurons orchestrate the activity of neural circuits, but little is known about their population dynamics. By using 3D random-access calcium imaging, Gurnani and Silver show that cerebellar Golgi cell circuits exhibit multidimensional activity with common and distributed modes. A biologically detailed circuit model implicates electrical coupling in shaping the population dynamics.
Electrically coupled inhibitory interneurons dynamically control network excitability, yet little is known about how chemical and electrical synapses regulate their activity. Using two-photon ...glutamate uncaging and dendritic patch-clamp recordings, we found that the dendrites of cerebellar Golgi interneurons acted as passive cables. They conferred distance-dependent sublinear synaptic integration and weakened distal excitatory inputs. Gap junctions were present at a higher density on distal dendrites and contributed substantially to membrane conductance. Depolarization of one Golgi cell increased firing in its neighbors, and inclusion of dendritic gap junctions in interneuron network models enabled distal excitatory synapses to drive network activity more effectively. Our results suggest that dendritic gap junctions counteract sublinear dendritic integration by enabling excitatory synaptic charge to spread into the dendrites of neighboring inhibitory interneurons.