Independently Outgrowing Neurons and Geometry-Based Synapse Formation Produce Networks with Realistic Synaptic Connectivity

Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.     

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.     

A phenomenological theory of spatially structured local synaptic connectivity

The structure of local synaptic circuits is the key to understanding cortical function and how neuronal functional modules such as cortical columns are formed. The central problem in deciphering cortical microcircuits is the quantification of synaptic connectivity between neuron pairs. I present a theoretical model that accounts for the axon and dendrite morphologies of pre- and postsynaptic cells and provides the average number of synaptic contacts formed between them as a function of their relative locations in three-dimensional space. An important aspect of the current approach is the representation of a complex structure of an axonal/dendritic arbor as a superposition of basic structures—synaptic clouds. Each cloud has three structural parameters that can be directly estimated from two-dimensional drawings of the underlying arbor. Using empirical data available in literature, I applied this theory to three morphologically different types of cell pairs. I found that, within a wide range of cell separations, the theory is in very good agreement with empirical data on (i) axonal–dendritic contacts of pyramidal cells and (ii) somatic synapses formed by the axons of inhibitory interneurons. Since for many types of neurons plane arborization drawings are available from literature, this theory can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies. It can also have significant implications for computational models of cortical networks by making it possible to wire up simulated neural networks in a realistic fashion.     

Modeling of Neuronal Growth <Emphasis Type="Italic">In Vitro</Emphasis>: Comparison of Simulation Tools NETMORPH and CX3D

We simulate the growth of neuronal networks using the two recently published tools, NETMORPH and CX3D. The goals of the work are (1) to examine and compare the simulation tools, (2) to construct a model of growth of neocortical cultures, and (3) to characterize the changes in network connectivity during growth, using standard graph theoretic methods. Parameters for the neocortical culture are chosen after consulting both the experimental and the computational work presented in the literature. The first (three) weeks in culture are known to be a time of development of extensive dendritic and axonal arbors and establishment of synaptic connections between the neurons. We simulate the growth of networks from day 1 to day 21. It is shown that for the properly selected parameters, the simulators can reproduce the experimentally obtained connectivity. The selected graph theoretic methods can capture the structural changes during growth.     

BDNF increases synapse density in dendrites of developing tectal neurons in vivo

Neuronal connections are established through a series of developmental events that involve close communication between pre- and postsynaptic neurons. In the visual system, BDNF modulates the development of neuronal connectivity by influencing presynaptic retinal ganglion cell (RGC) axons. Increasing BDNF levels in the optic tectum of Xenopus tadpoles significantly increases both axon arborization and synapse density per axon terminal within a few hours of treatment. Here, we have further explored the mechanisms by which BDNF shapes synaptic connectivity by imaging tectal neurons, the postsynaptic partners of RGCs. Individual neurons were co-labeled with DsRed2 and a GFP-tagged postsynaptic density protein (PSD95-GFP) to visualize dendritic morphology and postsynaptic specializations simultaneously in vivo. Immunoelectron microscopy confirmed that PSD95-GFP predominantly localized to ultrastructurally identified synapses. Time-lapse confocal microscopy of individual, double-labeled neurons revealed a coincident, activity-dependent mechanism of synaptogenesis and axon and dendritic arbor growth, which is differentially modulated by BDNF. Microinjection of BDNF into the optic tectum significantly increased synapse number in tectal neuron dendritic arbors within 24 hours, without significantly influencing arbor morphology. BDNF function-blocking antibodies had opposite effects. The BDNF-elicited increase in synapse number complements the previously observed increase in presynaptic sites on RGC axons. These results, together with the timescale of the response by tectal neurons, suggest that the effects of BDNF on dendritic synaptic connectivity are secondary to its effects on presynaptic RGCs. Thus, BDNF influences synaptic connectivity in multiple ways: it enhances axon arbor complexity expanding the synaptic territory of the axon, while simultaneously coordinating synapse formation and stabilization with individual postsynaptic cells.     

A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex

This study provides a detailed quantitative estimate for local synaptic connectivity between neocortical pyramidal neurons. A new way of obtaining such an estimate is presented. In acute slices of the rat visual cortex, four layer 2 and four layer 3 pyramidal neurons were intracellularly injected with biocytin. Axonal and dendritic arborizations were three-dimensionally reconstructed with the aid of a computer-based camera lucida system. In a computer experiment, pairs of pre- and postsynaptic neurons were formed and potential synaptic contacts were calculated. For each pair, the calculations were carried out for a whole range of distances (0 to 500 μm) between the presynaptic and the postsynaptic neuron, in order to estimate cortical connectivity as a function of the spatial separation of neurons. It was also differentiated whether neurons were situated in the same or in different cortical layers. The data thus obtained was used to compute connection probabilities, the average number of contacts between neurons, the frequency of specific numbers of contacts and the total number of contacts a dendritic tree receives from the surrounding cortical volume. Connection probabilities ranged from 50% to 80% for directly adjacent neurons and from 0% to 15% for neurons 500 μm apart. In many cases, connections were mediated by one contact only. However, close neighbors made on average up to 3 contacts with each other. The question as to whether the method employed in this study yields a realistic estimate of synaptic connectivity is discussed. It is argued that the results can be used as a detailed blueprint for building artificial neural networks with a cortex-like architecture. Received: 30 March 1999 / Accepted in revised form: 5 August 1999     

Visualizing the Distribution of Synapses from Individual Neurons in the Mouse Brain

Background

Proper function of the mammalian brain relies on the establishment of highly specific synaptic connections among billions of neurons. To understand how complex neural circuits function, it is crucial to precisely describe neuronal connectivity and the distributions of synapses to and from individual neurons.

Methods and Findings

In this study, we present a new genetic synaptic labeling method that relies on expression of a presynaptic marker, synaptophysin-GFP (Syp-GFP) in individual neurons in vivo. We assess the reliability of this method and use it to analyze the spatial patterning of synapses in developing and mature cerebellar granule cells (GCs). In immature GCs, Syp-GFP is distributed in both axonal and dendritic regions. Upon maturation, it becomes strongly enriched in axons. In mature GCs, we analyzed synapses along their ascending segments and parallel fibers. We observe no differences in presynaptic distribution between GCs born at different developmental time points and thus having varied depths of projections in the molecular layer. We found that the mean densities of synapses along the parallel fiber and the ascending segment above the Purkinje cell (PC) layer are statistically indistinguishable, and higher than previous estimates. Interestingly, presynaptic terminals were also found in the ascending segments of GCs below and within the PC layer, with the mean densities two-fold lower than that above the PC layer. The difference in the density of synapses in these parts of the ascending segment likely reflects the regional differences in postsynaptic target cells of GCs.

Conclusions

The ability to visualize synapses of single neurons in vivo is valuable for studying synaptogenesis and synaptic plasticity within individual neurons as well as information flow in neural circuits.     

Class-specific features of neuronal wiring

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.     

The Formation of Multi-synaptic Connections by the Interaction of Synaptic and Structural Plasticity and Their Functional Consequences

Cortical connectivity emerges from the permanent interaction between neuronal activity and synaptic as well as structural plasticity. An important experimentally observed feature of this connectivity is the distribution of the number of synapses from one neuron to another, which has been measured in several cortical layers. All of these distributions are bimodal with one peak at zero and a second one at a small number (3–8) of synapses.In this study, using a probabilistic model of structural plasticity, which depends on the synaptic weights, we explore how these distributions can emerge and which functional consequences they have.We find that bimodal distributions arise generically from the interaction of structural plasticity with synaptic plasticity rules that fulfill the following biological realistic constraints: First, the synaptic weights have to grow with the postsynaptic activity. Second, this growth curve and/or the input-output relation of the postsynaptic neuron have to change sub-linearly (negative curvature). As most neurons show such input-output-relations, these constraints can be fulfilled by many biological reasonable systems.Given such a system, we show that the different activities, which can explain the layer-specific distributions, correspond to experimentally observed activities.Considering these activities as working point of the system and varying the pre- or postsynaptic stimulation reveals a hysteresis in the number of synapses. As a consequence of this, the connectivity between two neurons can be controlled by activity but is also safeguarded against overly fast changes.These results indicate that the complex dynamics between activity and plasticity will, already between a pair of neurons, induce a variety of possible stable synaptic distributions, which could support memory mechanisms.     

Patterning and organization of motor neuron dendrites in the Drosophila larva

Precise patterns of motor neuron connectivity depend on the proper establishment and positioning of the dendritic arbor. However, how different motor neurons orient their dendrites to selectively establish synaptic connectivity is not well understood. The Drosophila neuromuscular system provides a simple model to investigate the underlying organizational principles by which distinct subclasses of motor neurons orient their dendrites within the central neuropil. Here we used genetic mosaic techniques to characterize the diverse dendritic morphologies of individual motor neurons from five main nerve branches (ISN, ISNb, ISNd, SNa, and SNc) in the Drosophila larva. We found that motor neurons from different nerve branches project their dendrites to largely stereotyped mediolateral domains in the dorsal region of the neuropil providing full coverage of the receptive territory. Furthermore, dendrites from different motor neurons overlap extensively, regardless of subclass, suggesting that repulsive dendrite-dendrite interactions between motor neurons do not influence the mediolateral positioning of dendritic fields. The anatomical data in this study provide important information regarding how different subclasses of motor neurons organize their dendrites and establishes a foundation for the investigation of the mechanisms that control synaptic connectivity in the Drosophila motor circuit.     

Synaptic activation of metabotropic glutamate receptors regulates dendritic outputs of thalamic interneurons

Information gating through the thalamus is dependent on the output of thalamic relay neurons. These relay neurons receive convergent innervation from a number of sources, including GABA-containing interneurons that provide feed-forward inhibition. These interneurons are unique in that they have two distinct outputs: axonal and dendritic. In addition to conventional axonal outputs, these interneurons have presynaptic dendrites that may provide localized inhibitory influences. Our study indicates that synaptic activation of metabotropic glutamate receptors (mGluRs) increases inhibitory activity in relay neurons by increasing output of presynaptic dendrites of interneurons. Optic tract stimulation increases inhibitory activity in thalamic relay neurons in a frequency- and intensity-dependent manner and is attenuated by mGluR antagonists. Our data suggest that synaptic activation of mGluRs selectively alters dendritic output but not axonal output of thalamic interneurons. This mechanism could serve an important role in focal, feed-forward information processing in addition to dynamic information processing in thalamocortical circuits.     

Deriving physical connectivity from neuronal morphology

 A model is presented that allows prediction of the probability for the formation of appositions between the axons and dendrites of any two neurons based only on their morphological statistics and relative separation. Statistics of axonal and dendritic morphologies of single neurons are obtained from 3D reconstructions of biocytin-filled cells, and a statistical representation of the same cell type is obtained by averaging across neurons according to the model. A simple mathematical formulation is applied to the axonal and dendritic statistical representations to yield the probability for close appositions. The model is validated by a mathematical proof and by comparison of predicted appositions made by layer 5 pyramidal neurons in the rat somatosensory cortex with real anatomical data. The model could be useful for studying microcircuit connectivity and for designing artificial neural networks. Received: 11 February 2002 / Accepted: 5 November 2002 / Published online: 20 February 2003 Correspondence to: H. Markram (e-mail: Henry.Markram@epfl.ch Tel.: +41-21-6939537, Fax: +41-21-6935350) Acknowledgements. This study was supported by the National Alliance for Autism Research, the Minerva Foundation, the US Navy, the Ebner Center for Biomedical Research, and the Edith Blum Foundation.     

Dendritic spines and distributed circuits

Dendritic spines receive most excitatory connections in pyramidal cells and many other principal neurons. But why do neurons use spines, when they could accommodate excitatory contacts directly on their dendritic shafts? One suggestion is that spines serve to connect with passing axons, thus increasing the connectivity of the dendrites. Another hypothesis is that spines are biochemical compartments that enable input-specific synaptic plasticity. A third possibility is that spines have an electrical role, filtering synaptic potentials and electrically isolating inputs from each other. In this review, I argue that, when viewed from the perspective of the circuit function, these three functions dovetail with one another to achieve a single overarching goal: to implement a distributed circuit with widespread connectivity. Spines would endow these circuits with nonsaturating, linear integration and input-specific learning rules, which would enable them to function as neural networks, with emergent encoding and processing of information.     

Synapses on axon collaterals of pyramidal cells are spaced at random intervals: a Golgi study in the mouse cerebral cortex

In this study we investigated the arrangement of synapses on local axon collaterals of Golgi-stained pyramidal neurons in the mouse cerebral cortex. As synaptic markers we considered axonal swellings visible at high magnification under the light microscope. Such axonal swellings coincide with synaptic boutons, as has been demonstrated in a number of combined light and electron microscopic studies. These studies also indicated that, in most cases, one bouton corresponds precisely to one synapse. Golgi-impregnated axonal trees of 20 neocortical pyramidal neurons were drawn with a camera lucida. Axonal swellings were marked on the drawings. Most swellings were ‘en passant’; occasionally, they were situated at the tip of short, spine-like processes. On axon collaterals, the average interval between swellings was 4.5 μm. On the axonal main stem, the swellings were always less densely packed than on the collaterals. Statistical analysis of the spatial distribution of the swellings did not reveal any special patterns. Instead, the arrangement of swellings on individual collaterals follows a Poisson distribution. Moreover, the same holds to a large extent for the entire collection of pyramidal cell collaterals. This suggests that a single Poisson process, characterized by only one rate parameter (number of synapses per unit length), describes most of the spatial distribution of synapses along pyramidal cell collaterals. These findings do not speak in favour of a pronounced target specificity of pyramidal neurons at the synaptic level. Instead, our results support a probabilistic model of cortical connectivity. Received: 6 June 1993/Accepted in revised form: 22 December 1993     

Spike propagation synchronized by temporally asymmetric Hebbian learning

 Synchronously spiking neurons have been observed in the cerebral cortex and the hippocampus. In computer models, synchronous spike volleys may be propagated across appropriately connected neuron populations. However, it is unclear how the appropriate synaptic connectivity is set up during development and maintained during adult learning. We performed computer simulations to investigate the influence of temporally asymmetric Hebbian synaptic plasticity on the propagation of spike volleys. In addition to feedforward connections, recurrent connections were included between and within neuron populations and spike transmission delays varied due to axonal, synaptic and dendritic transmission. We found that repeated presentations of input volleys decreased the synaptic conductances of intragroup and feedback connections while synaptic conductances of feedforward connections with short delays became stronger than those of connections with longer delays. These adaptations led to the synchronization of spike volleys as they propagated across neuron populations. The findings suggests that temporally asymmetric Hebbian learning may enhance synchronized spiking within small populations of neurons in cortical and hippocampal areas and familiar stimuli may produce synchronized spike volleys that are rapidly propagated across neural tissue. Received: 28 May 2002 / Accepted: 3 June 2002 RID="*" ID="*" Correspondence to: R. E. Suri Intelligent Optical Systems (IOS), 2520 W 237th St, Torrance, CA 90505-5217, USA (e-mail: rsuri@intopsys.com, Tel.: +1-310-5307130 ext. 108, Fax: +1-210-5307417)     

Dendritic normalisation improves learning in sparsely connected artificial neural networks

Artificial neural networks, taking inspiration from biological neurons, have become an invaluable tool for machine learning applications. Recent studies have developed techniques to effectively tune the connectivity of sparsely-connected artificial neural networks, which have the potential to be more computationally efficient than their fully-connected counterparts and more closely resemble the architectures of biological systems. We here present a normalisation, based on the biophysical behaviour of neuronal dendrites receiving distributed synaptic inputs, that divides the weight of an artificial neuron’s afferent contacts by their number. We apply this dendritic normalisation to various sparsely-connected feedforward network architectures, as well as simple recurrent and self-organised networks with spatially extended units. The learning performance is significantly increased, providing an improvement over other widely-used normalisations in sparse networks. The results are two-fold, being both a practical advance in machine learning and an insight into how the structure of neuronal dendritic arbours may contribute to computation.     

Maturation of dendritic architecture: lessons from insect identified neurons

The highly complex geometry of dendritic trees is crucial for neural signal integration and the proper wiring of neuronal circuits. The morphogenesis of dendritic trees is regulated by innate genetic factors, neuronal activity, and external molecular cues. How each of these factors contributes to dendritic maturation has been addressed in studies of the developing nervous systems of animals ranging from insects to mammals. This article reviews our current knowledge and understanding of the role of afferent input in the establishment of the architecture of mature dendritic trees, using insect neurons as models. With these model systems and using quantitative morphometry, it is possible to define the contributions of intrinsic and extrinsic factors in dendritic morphogenesis of identified neurons and to evaluate the impact of dendritic maturation on the integration of identified neurons into functional circuits subserving identified behaviors. The commonly held view of dendritic morphogenesis is that general structural features result from genetic instructions, whereas fine connectivity details rely mostly on substrate interactions and functional activity. During early dendritic maturation, dendritic growth cone formation produces new branches at all dendritic roots. The second phase is growth cone independent and afferent input dependent, during which branching is limited to high order distal dendrites. During the third phase, activity-dependent synaptic maturation occurs with limited or subtle remodeling of branching.     

Kinesin-3 mediated axonal delivery of presynaptic neurexin stabilizes dendritic spines and postsynaptic components

The functional properties of neural circuits are defined by the patterns of synaptic connections between their partnering neurons, but the mechanisms that stabilize circuit connectivity are poorly understood. We systemically examined this question at synapses onto newly characterized dendritic spines of C. elegans GABAergic motor neurons. We show that the presynaptic adhesion protein neurexin/NRX-1 is required for stabilization of postsynaptic structure. We find that early postsynaptic developmental events proceed without a strict requirement for synaptic activity and are not disrupted by deletion of neurexin/nrx-1. However, in the absence of presynaptic NRX-1, dendritic spines and receptor clusters become destabilized and collapse prior to adulthood. We demonstrate that NRX-1 delivery to presynaptic terminals is dependent on kinesin-3/UNC-104 and show that ongoing UNC-104 function is required for postsynaptic maintenance in mature animals. By defining the dynamics and temporal order of synapse formation and maintenance events in vivo, we describe a mechanism for stabilizing mature circuit connectivity through neurexin-based adhesion.     

Morphological characteristics of various segments of local connections in the rat somatosensory cortex

Pyramidal, aspinous, sparsely-spinous bipolar and multipolar neurons of the rat sensomotor cerebral cortex, impregnated after Golgi method, have been studied at an electron microscopical level. The ultrastructural characteristics of the pyramidal neurons differs from that of the nonpyramidal cells. Distribution of various synaptic contacts on the cellular surface and cortical postsynaptic targets of the axonal arborizations of the neurons are revealed. On the body of the pyramidal cells only symmetrical synapses exist, on large dendritic trunks symmetrical synapses prevail, on the spines and the terminal dendritic branches assymetrical synapses mainly predominate. Axonal collateralies of the pyramidal cells form asymmetrical synapses on the spines, small and middle dendrites. There are more axo-somatic synapses on the bodies of the nonpyramidal neurons than on the pyramidal cells, among them both symmetrical and asymmetrical types of the synapses occur. On the trunks and small dendrites of the nonpyramidal cells both types of synaptic contacts are revealed. In the distal direction of the dendrites the number of the asymmetrical synapses becomes predominating. Axons of the bipolar cells form asymmetrical synapses on the spines, small and middle dendrites. Axons of the multipolar cells form symmetrical synapses on the dendrites and the dendritic trunks of the nondifferentiated cells. Differences in the distribution character of the synaptic inlets and various postsynaptic targets of the axonal systems in the cells assume various functional role of the identified neurons.