Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-Term Plastic Synapses

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.     

Highly nonrandom features of synaptic connectivity in local cortical circuits

How different is local cortical circuitry from a random network? To answer this question, we probed synaptic connections with several hundred simultaneous quadruple whole-cell recordings from layer 5 pyramidal neurons in the rat visual cortex. Analysis of this dataset revealed several nonrandom features in synaptic connectivity. We confirmed previous reports that bidirectional connections are more common than expected in a random network. We found that several highly clustered three-neuron connectivity patterns are overrepresented, suggesting that connections tend to cluster together. We also analyzed synaptic connection strength as defined by the peak excitatory postsynaptic potential amplitude. We found that the distribution of synaptic connection strength differs significantly from the Poisson distribution and can be fitted by a lognormal distribution. Such a distribution has a heavier tail and implies that synaptic weight is concentrated among few synaptic connections. In addition, the strengths of synaptic connections sharing pre- or postsynaptic neurons are correlated, implying that strong connections are even more clustered than the weak ones. Therefore, the local cortical network structure can be viewed as a skeleton of stronger connections in a sea of weaker ones. Such a skeleton is likely to play an important role in network dynamics and should be investigated further.     

Dynamic effective connectivity of inter-areal brain circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities.     

Directional Transport Is Mediated by a Dynein-Dependent Step in an RNA Localization Pathway

Cytoplasmic RNA localization is a key biological strategy for establishing polarity in a variety of organisms and cell types. However, the mechanisms that control directionality during asymmetric RNA transport are not yet clear. To gain insight into this crucial process, we have analyzed the molecular machinery directing polarized transport of RNA to the vegetal cortex in Xenopus oocytes. Using a novel approach to measure directionality of mRNA transport in live oocytes, we observe discrete domains of unidirectional and bidirectional transport that are required for vegetal RNA transport. While kinesin-1 appears to promote bidirectional transport along a microtubule array with mixed polarity, dynein acts first to direct unidirectional transport of RNA towards the vegetal cortex. Thus, vegetal RNA transport occurs through a multistep pathway with a dynein-dependent directional cue. This provides a new framework for understanding the mechanistic basis of cell and developmental polarity.     

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.     

Convergence among Non-Sister Dendritic Branches: An Activity-Controlled Mean to Strengthen Network Connectivity

The manner by which axons distribute synaptic connections along dendrites remains a fundamental unresolved issue in neuronal development and physiology. We found in vitro and in vivo indications that dendrites determine the density, location and strength of their synaptic inputs by controlling the distance of their branches from those of their neighbors. Such control occurs through collective branch convergence, a behavior promoted by AMPA and NMDA glutamate receptor activity. At hubs of convergence sites, the incidence of axo-dendritic contacts as well as clustering levels, pre- and post-synaptic protein content and secretion capacity of synaptic connections are higher than found elsewhere. This coupling between synaptic distribution and the pattern of dendritic overlapping results in ‘Economical Small World Network’, a network configuration that enables single axons to innervate multiple and remote dendrites using short wiring lengths. Thus, activity-mediated regulation of the proximity among dendritic branches serves to pattern and strengthen neuronal connectivity.     

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)     

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.     

Influence of connection type on phase synchrony: analysis of a neural mass model

Empirical studies have demonstrated synchronized frontal and parietal electrophysiological signals at 22-34?Hz during a conjunctive visual search task and at 36-56?Hz during a pop-out visual search task. Bidirectional (conjunctive) versus unidirectional (pop-out) information transfer between neuronal populations is hypothesized to underly this difference in synchronization frequency. This study modeled the influence of connection type (i.e., unidirectional vs. bidirectional) on phase synchrony between two neural populations using a neural mass model. Phase-locking values (PLVs) were used as the measure of synchrony between populations. Consistent with the connectivity hypothesis, the model revealed greater PLVs at 22-34?Hz when the two populations were connected bidirectionally than unidirectionally, but greater PLVs at 34-52?Hz when connected unidirectionally than bidirectionally. The model suggests that inter-population connectivity also changes with bottom-up versus top-down control of attention.     

Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity.     

Identifying and Tracking Simulated Synaptic Inputs from Neuronal Firing: Insights from In Vitro Experiments

Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.     

Experience-Dependent Rewiring of Specific Inhibitory Connections in Adult Neocortex

Although neocortical connectivity is remarkably stereotyped, the abundance of some wiring motifs varies greatly between cortical areas. To examine if regional wiring differences represent functional adaptations, we have used optogenetic raster stimulation to map the laminar distribution of GABAergic interneurons providing inhibition to pyramidal cells in layer 2/3 (L2/3) of adult mouse barrel cortex during sensory deprivation and recovery. Whisker trimming caused large, motif-specific changes in inhibitory synaptic connectivity: ascending inhibition from deep layers 4 and 5 was attenuated to 20%–45% of baseline, whereas inhibition from superficial layers remained stable (L2/3) or increased moderately (L1). The principal mechanism of deprivation-induced plasticity was motif-specific changes in inhibitory-to-excitatory connection probabilities; the strengths of extant connections were left unaltered. Whisker regrowth restored the original balance of inhibition from deep and superficial layers. Targeted, reversible modifications of specific inhibitory wiring motifs thus contribute to the adaptive remodeling of cortical circuits.     

Ultrastructure and morphometric parameters of glutamatergic synapses on nigrothalamic and unidentified neurons of the reticular zone of theSubstantia nigra in cats

Nigrothalamic neurons were identified into thesubstantia nigra by their retrograde labelling with horseradish peroxidase. Axon terminals that contain glutamate (the excitatory transmitter) were revealed immunocytochemically with an immunogold electron microscopic technique. Ultrastructural parameters (the large and small diameters of axon terminals, area of their profiles, coefficient of form of profiles, large and small diameters of synaptic vesicles) were analyzed in all 240 synapses under study. Synaptic contacts localized on both nigrothalamic and unidentified neurons belonged to three morphologically specific groups. Synapses of the groups I and III, according to classification by Rinvik and Grofova, were characterized by a symmetric type of synaptic contact and contained polymorphic synaptic vesicles. Contacts in group-II synapses were asymmetric, and respective terminals contained round vesicles. Among the studied synapses, 65.8% were classified as group-I contacts, 25.0% belonged to group II, and 9.2% belonged to group III. Glutamate-positive axon terminals formed predominantly group-II synapses; such connections constituted 70% of this group's synapses. Sixty percent of glutamate-positive synapses were localized on the distal dendrites and 23% on the proximal dendrites, while 17% of such synapses were distributed on the somata of nigral neurons. Such a pattern of distribution of glutamate-positive synapses was observed on both nigrothalamic and unidentified nigral neurons. About 7% of glutamate-positive synapses were formed by very large axon terminals containing round synaptic vesicles; yet, the contacts of these terminals were of a symmetric type. Twenty percent of group-I synapses, i.e., synapses considered inhibitory connections, were found to manifest a weak immune reaction to glutamate.Neirofiziologiya/Neurophysiology, Vol. 28, No. 6, pp. 285–295, November–December, 1996.     

Synaptic Symmetry Increases Coherence in a Pair of Excitable Electronic Neurons

We study how the synaptic connections in a pair of excitable electronic neurons affect the coherence of their spike trains when the neurons are submitted to noise from independent sources. The coupling is provided by electronic circuits which mimic the dynamics of chemical AMPA synapses. In particular, we show that increasing the strength of an unidirectional synapse leads to a decrease of coherence in the post-synaptic neuron. More interestingly, we show that the decrease of coherence can be reverted if we add a synapse of sufficient strength in the reverse direction. Synaptic symmetry plays an important role in this process and, under the right choice of parameters, increases the network coherence beyond the value achieved at the resonance due to noise alone in uncoupled neurons. We also show that synapses with a longer time scale sharpen the dependency of the coherence on the synaptic symmetry. The results were reproduced by numerical simulations of a pair of synaptically coupled FitzHugh-Nagumo models.     

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.     

When are populations not connected like a circuit? Identifying biases in gene flow from coalescent times

Connectivity and movement patterns of populations are influenced by past and present environmental and biotic factors, which are reflected in genetic relatedness among populations. Methods that estimate the “commute time” between populations based on electrical resistance (i.e., isolation‐by‐resistance [IBR]) have been widely applied to either infer movement patterns directly from environmental factors or detect possible barriers to gene flow given empirical genetic relatedness. Yet, the commute time is only equivalent to the coalescence time between populations under symmetric migration with isotropic landscapes. Asymmetric gene flow is relatively common when populations are expanding, retreating, or with source‐sink dynamics. In a From the Cover paper in this issue of Molecular Ecology Resources, Lundgren and Ralph (Molecular Ecology Resources, 19, 2019) describe a Bayesian method to infer bidirectional gene flow rates and population sizes without the assumption of symmetry. The method shows great accuracy in connectivity estimations under symmetric, as well as asymmetric gene flow scenarios where resistance methods fail. However, computational complexity limits the method to a few populations, preventing its application to finescale environmental maps. Also, as a discrete‐deme static model, the inferred differences in gene flow rates are sensitive to population discretization and cannot be directly used to differentiate among processes (e.g., past expansion vs. current barrier). Here, we discuss scenarios where the new method can best be utilized and provide potential directions to identify the underlying processes causing deviations in gene flow patterns.     

From Caenorhabditis elegans to the human connectome: a specific modular organization increases metabolic,functional and developmental efficiency

The connectome, or the entire connectivity of a neural system represented by a network, ranges across various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether the connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of Caenorhabditis elegans and the fibre tract network of human brains obtained through diffusion spectrum imaging. We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of both C. elegans and human connectomes are higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution, and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in the C. elegans connectome or each region of interest in the human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared with the alternative arrangements. This implies that fewer genes are needed to encode for the organization of neural systems. While the first two findings show that the neural topologies are efficient in information processing, this suggests that they are also efficient from a developmental point of view. Together, these results show that neural systems are organized in such a way as to yield efficient features beyond those given by their modularity alone.     

Mechanism of inhibition of site-specific recombination by the Holliday junction-trapping peptide WKHYNY: insights into phage lambda integrase-mediated strand exchange

Holliday junctions are central intermediates in site-specific recombination reactions mediated by tyrosine recombinases. Because these intermediates are extremely transient, only artificially assembled Holliday junctions have been available for study. We have recently identified hexapeptides that cause the accumulation of natural Holliday junctions of bacteriophage lambda Integrase (Int)-mediated reactions. We now show that one of these peptides acts after the first DNA cleavage event to stabilize protein-bound junctions and to prevent their resolution. The peptide acts before the step affected by site affinity (saf) mutations in the core region, in agreement with a model that the peptide stabilizes the products of strand exchange (i.e. Holliday junctions) while saf mutations reduce ligation of exchanged strands.Strand exchange events leading to Holliday junctions in phage lambda integration and excision are asymmetric, presumably because interactions between Int and some of its core-binding sites determine the order of strand cleavage. We have compared the structure of Holliday junctions in one unidirectional and in two bidirectional Int-mediated pathways and show that the strand cleavage steps are much more symmetric in the bidirectional pathways. Thus Int-DNA interactions which determine the order of top and bottom strand cleavage and exchange are unique in each recombination pathway.     

Energy Efficient Sparse Connectivity from Imbalanced Synaptic Plasticity Rules

It is believed that energy efficiency is an important constraint in brain evolution. As synaptic transmission dominates energy consumption, energy can be saved by ensuring that only a few synapses are active. It is therefore likely that the formation of sparse codes and sparse connectivity are fundamental objectives of synaptic plasticity. In this work we study how sparse connectivity can result from a synaptic learning rule of excitatory synapses. Information is maximised when potentiation and depression are balanced according to the mean presynaptic activity level and the resulting fraction of zero-weight synapses is around 50%. However, an imbalance towards depression increases the fraction of zero-weight synapses without significantly affecting performance. We show that imbalanced plasticity corresponds to imposing a regularising constraint on the L ₁-norm of the synaptic weight vector, a procedure that is well-known to induce sparseness. Imbalanced plasticity is biophysically plausible and leads to more efficient synaptic configurations than a previously suggested approach that prunes synapses after learning. Our framework gives a novel interpretation to the high fraction of silent synapses found in brain regions like the cerebellum.