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.     

Plasticity-Driven Self-Organization under Topological Constraints Accounts for Non-random Features of Cortical Synaptic Wiring

Understanding the structure and dynamics of cortical connectivity is vital to understanding cortical function. Experimental data strongly suggest that local recurrent connectivity in the cortex is significantly non-random, exhibiting, for example, above-chance bidirectionality and an overrepresentation of certain triangular motifs. Additional evidence suggests a significant distance dependency to connectivity over a local scale of a few hundred microns, and particular patterns of synaptic turnover dynamics, including a heavy-tailed distribution of synaptic efficacies, a power law distribution of synaptic lifetimes, and a tendency for stronger synapses to be more stable over time. Understanding how many of these non-random features simultaneously arise would provide valuable insights into the development and function of the cortex. While previous work has modeled some of the individual features of local cortical wiring, there is no model that begins to comprehensively account for all of them. We present a spiking network model of a rodent Layer 5 cortical slice which, via the interactions of a few simple biologically motivated intrinsic, synaptic, and structural plasticity mechanisms, qualitatively reproduces these non-random effects when combined with simple topological constraints. Our model suggests that mechanisms of self-organization arising from a small number of plasticity rules provide a parsimonious explanation for numerous experimentally observed non-random features of recurrent cortical wiring. Interestingly, similar mechanisms have been shown to endow recurrent networks with powerful learning abilities, suggesting that these mechanism are central to understanding both structure and function of cortical synaptic wiring.     

Dynamic Neural Network Models of the Premotoneuronal Circuitry Controlling Wrist Movements in Primates

Dynamic recurrent neural networks were derived to simulate neuronal populations generating bidirectional wrist movements in the monkey. The models incorporate anatomical connections of cortical and rubral neurons, muscle afferents, segmental interneurons and motoneurons; they also incorporate the response profiles of four populations of neurons observed in behaving monkeys. The networks were derived by gradient descent algorithms to generate the eight characteristic patterns of motor unit activations observed during alternating flexion-extension wrist movements. The resulting model generated the appropriate input-output transforms and developed connection strengths resembling those in physiological pathways. We found that this network could be further trained to simulate additional tasks, such as experimentally observed reflex responses to limb perturbations that stretched or shortened the active muscles, and scaling of response amplitudes in proportion to inputs. In the final comprehensive network, motor units are driven by the combined activity of cortical, rubral, spinal and afferent units during step tracking and perturbations.The model displayed many emergent properties corresponding to physiological characteristics. The resulting neural network provides a working model of premotoneuronal circuitry and elucidates the neural mechanisms controlling motoneuron activity. It also predicts several features to be experimentally tested, for example the consequences of eliminating inhibitory connections in cortex and red nucleus. It also reveals that co-contraction can be achieved by simultaneous activation of the flexor and extensor circuits without invoking features specific to co-contraction.     

The generation of phase differences and frequency changes in a network model of inferior olive subthreshold oscillations

It is commonly accepted that the Inferior Olive (IO) provides a timing signal to the cerebellum. Stable subthreshold oscillations in the IO can facilitate accurate timing by phase-locking spikes to the peaks of the oscillation. Several theoretical models accounting for the synchronized subthreshold oscillations have been proposed, however, two experimental observations remain an enigma. The first is the observation of frequent alterations in the frequency of the oscillations. The second is the observation of constant phase differences between simultaneously recorded neurons. In order to account for these two observations we constructed a canonical network model based on anatomical and physiological data from the IO. The constructed network is characterized by clustering of neurons with similar conductance densities, and by electrical coupling between neurons. Neurons inside a cluster are densely connected with weak strengths, while neurons belonging to different clusters are sparsely connected with stronger connections. We found that this type of network can robustly display stable subthreshold oscillations. The overall frequency of the network changes with the strength of the inter-cluster connections, and phase differences occur between neurons of different clusters. Moreover, the phase differences provide a mechanistic explanation for the experimentally observed propagating waves of activity in the IO. We conclude that the architecture of the network of electrically coupled neurons in combination with modulation of the inter-cluster coupling strengths can account for the experimentally observed frequency changes and the phase differences.     

Effective Connectivity of Depth-Structure–Selective Patches in the Lateral Bank of the Macaque Intraparietal Sulcus

Extrastriate cortical areas are frequently composed of subpopulations of neurons encoding specific features or stimuli, such as color, disparity, or faces, and patches of neurons encoding similar stimulus properties are typically embedded in interconnected networks, such as the attention or face-processing network. The goal of the current study was to examine the effective connectivity of subsectors of neurons in the same cortical area with highly similar neuronal response properties. We first recorded single- and multi-unit activity to identify two neuronal patches in the anterior part of the macaque intraparietal sulcus (IPS) showing the same depth structure selectivity and then employed electrical microstimulation during functional magnetic resonance imaging in these patches to determine the effective connectivity of these patches. The two IPS subsectors we identified—with the same neuronal response properties and in some cases separated by only 3 mm—were effectively connected to remarkably distinct cortical networks in both dorsal and ventral stream in three macaques. Conversely, the differences in effective connectivity could account for the known visual-to-motor gradient within the anterior IPS. These results clarify the role of the anterior IPS as a pivotal brain region where dorsal and ventral visual stream interact during object analysis. Thus, in addition to the anatomical connectivity of cortical areas and the properties of individual neurons in these areas, the effective connectivity provides novel key insights into the widespread functional networks that support behavior.     

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.     

Probabilistic Clustering of the Human Connectome Identifies Communities and Hubs

A fundamental assumption in neuroscience is that brain function is constrained by its structural properties. This motivates the idea that the brain can be parcellated into functionally coherent regions based on anatomical connectivity patterns that capture how different areas are interconnected. Several studies have successfully implemented this idea in humans using diffusion weighted MRI, allowing parcellation to be conducted in vivo. Two distinct approaches to connectivity-based parcellation can be identified. The first uses the connection profiles of brain regions as a feature vector, and groups brain regions with similar connection profiles together. Alternatively, one may adopt a network perspective that aims to identify clusters of brain regions that show dense within-cluster and sparse between-cluster connectivity. In this paper, we introduce a probabilistic model for connectivity-based parcellation that unifies both approaches. Using the model we are able to obtain a parcellation of the human brain whose clusters may adhere to either interpretation. We find that parts of the connectome consistently cluster as densely connected components, while other parts consistently result in clusters with similar connections. Interestingly, the densely connected components consist predominantly of major cortical areas, while the clusters with similar connection profiles consist of regions that have previously been identified as the ‘rich club’; regions known for their integrative role in connectivity. Furthermore, the probabilistic model allows quantification of the uncertainty in cluster assignments. We show that, while most clusters are clearly delineated, some regions are more difficult to assign. These results indicate that care should be taken when interpreting connectivity-based parcellations obtained using alternative deterministic procedures.     

Two’s company,three (or more) is a simplex

As a candidate mechanism of neural representation, large numbers of synfire chains can efficiently be embedded in a balanced recurrent cortical network model. Here we study a model in which multiple synfire chains of variable strength are randomly coupled together to form a recurrent system. The system can be implemented both as a large-scale network of integrate-and-fire neurons and as a reduced model. The latter has binary-state pools as basic units but is otherwise isomorphic to the large-scale model, and provides an efficient tool for studying its behavior. Both the large-scale system and its reduced counterpart are able to sustain ongoing endogenous activity in the form of synfire waves, the proliferation of which is regulated by negative feedback caused by collateral noise. Within this equilibrium, diverse repertoires of ongoing activity are observed, including meta-stability and multiple steady states. These states arise in concert with an effective connectivity structure (ECS). The ECS admits a family of effective connectivity graphs (ECGs), parametrized by the mean global activity level. Of these graphs, the strongly connected components and their associated out-components account to a large extent for the observed steady states of the system. These results imply a notion of dynamic effective connectivity as governing neural computation with synfire chains, and related forms of cortical circuitry with complex topologies.     

Oscillations and synchrony in a cortical neural network

In this paper, the oscillations and synchronization status of two different network connectivity patterns based on Izhikevich model are studied. One of the connectivity patterns is a randomly connected neuronal network, the other one is a small-world neuronal network. This Izhikevich model is a simple model which can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Detailed investigations reveal that by varying some key parameters, such as the connection weights of neurons, the external current injection, the noise of intensity and the neuron number, this neuronal network will exhibit various collective behaviors in randomly coupled neuronal network. In addition, we show that by changing the number of nearest neighbor and connection probability in small-world topology can also affect the collective dynamics of neuronal activity. These results may be instructive in understanding the collective dynamics of mammalian cortex.     

Global relationship between anatomical connectivity and activity propagation in the cerebral cortex

Anatomical connectivity is a prerequisite for cooperative interactions between cortical areas, but it has yet to be demonstrated that association fibre networks determine the macroscopical flow of activity in the cerebral cortex. To test this notion, we constructed a large-scale model of cortical areas whose interconnections were based on published anatomical data from tracing studies. Using this model we simulated the propagation of activity in response to activation of individual cortical areas and compared the resulting topographic activation patterns to electrophysiological observations on the global spread of epileptic activity following intracortical stimulation. Here we show that a neural network with connectivity derived from experimental data reproduces cortical propagation of activity significantly better than networks with different types of neighbourhood-based connectivity or random connections. Our results indicate that association fibres and their relative connection strengths are useful predictors of global topographic activation patterns in the cerebral cortex. This global structure-function relationship may open a door to explicit interpretation of cortical activation data in terms of underlying anatomical connectivity.     

Dense inhibitory connectivity in neocortex

The connectivity diagram of neocortical circuits is still unknown, and there are conflicting data as to whether cortical neurons are wired specifically or not. To investigate the basic structure of cortical microcircuits, we use a two-photon photostimulation technique that enables the systematic mapping of synaptic connections with single-cell resolution. We map the inhibitory connectivity between upper layers somatostatin-positive GABAergic interneurons and pyramidal cells in mouse frontal cortex. Most, and sometimes all, inhibitory neurons are locally connected to every sampled pyramidal cell. This dense inhibitory connectivity is found at both young and mature developmental ages. Inhibitory innervation of neighboring pyramidal cells is similar, regardless of whether they are connected among themselves or not. We conclude that local inhibitory connectivity is promiscuous, does not form subnetworks, and can approach the theoretical limit of a completely connected synaptic matrix.     

On how network architecture determines the dominant patterns of spontaneous neural activity

In the absence of sensory stimulation, neocortical circuits display complex patterns of neural activity. These patterns are thought to reflect relevant properties of the network, including anatomical features like its modularity. It is also assumed that the synaptic connections of the network constrain the repertoire of emergent, spontaneous patterns. Although the link between network architecture and network activity has been extensively investigated in the last few years from different perspectives, our understanding of the relationship between the network connectivity and the structure of its spontaneous activity is still incomplete. Using a general mathematical model of neural dynamics we have studied the link between spontaneous activity and the underlying network architecture. In particular, here we show mathematically how the synaptic connections between neurons determine the repertoire of spatial patterns displayed in the spontaneous activity. To test our theoretical result, we have also used the model to simulate spontaneous activity of a neural network, whose architecture is inspired by the patchy organization of horizontal connections between cortical columns in the neocortex of primates and other mammals. The dominant spatial patterns of the spontaneous activity, calculated as its principal components, coincide remarkably well with those patterns predicted from the network connectivity using our theory. The equivalence between the concept of dominant pattern and the concept of attractor of the network dynamics is also demonstrated. This in turn suggests new ways of investigating encoding and storage capabilities of neural networks.     

Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs.     

Use of a neural mass model for the analysis of effective connectivity among cortical regions based on high resolution EEG recordings

Assessment of brain connectivity among different brain areas during cognitive or motor tasks is a crucial problem in neuroscience today. Aim of this work is to use a neural mass model to assess the effect of various connectivity patterns in cortical electroencephalogram (EEG) power spectral density, and investigate the possibility to derive connectivity circuits from EEG data. To this end, a model of an individual region of interest (ROI) has been built as the parallel arrangement of three populations, each described as in Wendling et al. (Eur J Neurosci 15:1499–1508, 2002). Connectivity among ROIs includes three parameters, which specify the strength of connection in the different frequency bands. The following main steps have been followed: (1) we analyzed how the power spectral density (PSD) is significantly modified by the kind of coupling hypothesized among the ROIs; (2) with the model, and using an automatic fitting procedure, we looked for a simple connectivity circuit able to reproduce PSD of cortical EEG in three ROIs during a finger-movement task. The estimated parameters represent the strength of connections among the ROIs in the different frequency bands. Cortical EEGs were computed with an inverse propagation algorithm, starting from measurement performed with 96 electrodes on the scalp. The present study suggests that the model can be used as a simulation tool, able to mimic the effect of connectivity on EEG. Moreover, it can be used to look for simple connectivity circuits, able to explain the main features of observed cortical PSD. These results may open new prospectives in the use of neurophysiological models, instead of empirical models, to assess effective connectivity from neuroimaging information.     

State transitions through inhibitory interneurons in a cortical network model

Inhibitory interneurons shape the spiking characteristics and computational properties of cortical networks. Interneuron subtypes can precisely regulate cortical function but the roles of interneuron subtypes for promoting different regimes of cortical activity remains unclear. Therefore, we investigated the impact of fast spiking and non-fast spiking interneuron subtypes on cortical activity using a network model with connectivity and synaptic properties constrained by experimental data. We found that network properties were more sensitive to modulation of the fast spiking population, with reductions of fast spiking excitability generating strong spike correlations and network oscillations. Paradoxically, reduced fast spiking excitability produced a reduction of global excitation-inhibition balance and features of an inhibition stabilised network, in which firing rates were driven by the activity of excitatory neurons within the network. Further analysis revealed that the synaptic interactions and biophysical features associated with fast spiking interneurons, in particular their rapid intrinsic response properties and short synaptic latency, enabled this state transition by enhancing gain within the excitatory population. Therefore, fast spiking interneurons may be uniquely positioned to control the strength of recurrent excitatory connectivity and the transition to an inhibition stabilised regime. Overall, our results suggest that interneuron subtypes can exert selective control over excitatory gain allowing for differential modulation of global network state.     

Activity dependent degeneration explains hub vulnerability in Alzheimer's disease

Brain connectivity studies have revealed that highly connected 'hub' regions are particularly vulnerable to Alzheimer pathology: they show marked amyloid-β deposition at an early stage. Recently, excessive local neuronal activity has been shown to increase amyloid deposition. In this study we use a computational model to test the hypothesis that hub regions possess the highest level of activity and that hub vulnerability in Alzheimer's disease is due to this feature. Cortical brain regions were modeled as neural masses, each describing the average activity (spike density and spectral power) of a large number of interconnected excitatory and inhibitory neurons. The large-scale network consisted of 78 neural masses, connected according to a human DTI-based cortical topology. Spike density and spectral power were positively correlated with structural and functional node degrees, confirming the high activity of hub regions, also offering a possible explanation for high resting state Default Mode Network activity. 'Activity dependent degeneration' (ADD) was simulated by lowering synaptic strength as a function of the spike density of the main excitatory neurons, and compared to random degeneration. Resulting structural and functional network changes were assessed with graph theoretical analysis. Effects of ADD included oscillatory slowing, loss of spectral power and long-range synchronization, hub vulnerability, and disrupted functional network topology. Observed transient increases in spike density and functional connectivity match reports in Mild Cognitive Impairment (MCI) patients, and may not be compensatory but pathological. In conclusion, the assumption of excessive neuronal activity leading to degeneration provides a possible explanation for hub vulnerability in Alzheimer's disease, supported by the observed relation between connectivity and activity and the reproduction of several neurophysiologic hallmarks. The insight that neuronal activity might play a causal role in Alzheimer's disease can have implications for early detection and interventional strategies.     

Interplay between Short- and Long-Term Plasticity in Cell-Assembly Formation

Various hippocampal and neocortical synapses of mammalian brain show both short-term plasticity and long-term plasticity, which are considered to underlie learning and memory by the brain. According to Hebb’s postulate, synaptic plasticity encodes memory traces of past experiences into cell assemblies in cortical circuits. However, it remains unclear how the various forms of long-term and short-term synaptic plasticity cooperatively create and reorganize such cell assemblies. Here, we investigate the mechanism in which the three forms of synaptic plasticity known in cortical circuits, i.e., spike-timing-dependent plasticity (STDP), short-term depression (STD) and homeostatic plasticity, cooperatively generate, retain and reorganize cell assemblies in a recurrent neuronal network model. We show that multiple cell assemblies generated by external stimuli can survive noisy spontaneous network activity for an adequate range of the strength of STD. Furthermore, our model predicts that a symmetric temporal window of STDP, such as observed in dopaminergic modulations on hippocampal neurons, is crucial for the retention and integration of multiple cell assemblies. These results may have implications for the understanding of cortical memory processes.     

Driving reservoir models with oscillations: a solution to the extreme structural sensitivity of chaotic networks

A large body of experimental and theoretical work on neural coding suggests that the information stored in brain circuits is represented by time-varying patterns of neural activity. Reservoir computing, where the activity of a recurrently connected pool of neurons is read by one or more units that provide an output response, successfully exploits this type of neural activity. However, the question of system robustness to small structural perturbations, such as failing neurons and synapses, has been largely overlooked. This contrasts with well-studied dynamical perturbations that lead to divergent network activity in the presence of chaos, as is the case for many reservoir networks. Here, we distinguish between two types of structural network perturbations, namely local (e.g., individual synaptic or neuronal failure) and global (e.g., network-wide fluctuations). Surprisingly, we show that while global perturbations have a limited impact on the ability of reservoir models to perform various tasks, local perturbations can produce drastic effects. To address this limitation, we introduce a new architecture where the reservoir is driven by a layer of oscillators that generate stable and repeatable trajectories. This model outperforms previous implementations while being resistant to relatively large local and global perturbations. This finding has implications for the design of reservoir models that capture the capacity of brain circuits to perform cognitively and behaviorally relevant tasks while remaining robust to various forms of perturbations. Further, our work proposes a novel role for neuronal oscillations found in cortical circuits, where they may serve as a collection of inputs from which a network can robustly generate complex dynamics and implement rich computations.     

Neural development features: spatio-temporal development of the Caenorhabditis elegans neuronal network

The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage, provides a unique system for understanding the development of neural networks. Although C. elegans has been widely studied in the past, we present the first statistical study from a developmental perspective, with findings that raise interesting suggestions on the establishment of long-distance connections and network hubs. Here, we analyze the neuro-development for temporal and spatial features, using birth times of neurons and their three-dimensional positions. Comparisons of growth in C. elegans with random spatial network growth highlight two findings relevant to neural network development. First, most neurons which are linked by long-distance connections are born around the same time and early on, suggesting the possibility of early contact or interaction between connected neurons during development. Second, early-born neurons are more highly connected (tendency to form hubs) than later-born neurons. This indicates that the longer time frame available to them might underlie high connectivity. Both outcomes are not observed for random connection formation. The study finds that around one-third of electrically coupled long-range connections are late forming, raising the question of what mechanisms are involved in ensuring their accuracy, particularly in light of the extremely invariant connectivity observed in C. elegans. In conclusion, the sequence of neural network development highlights the possibility of early contact or interaction in securing long-distance and high-degree connectivity.     

Structure of spontaneous UP and DOWN transitions self-organizing in a cortical network model

Synaptic plasticity is considered to play a crucial role in the experience-dependent self-organization of local cortical networks. In the absence of sensory stimuli, cerebral cortex exhibits spontaneous membrane potential transitions between an UP and a DOWN state. To reveal how cortical networks develop spontaneous activity, or conversely, how spontaneous activity structures cortical networks, we analyze the self-organization of a recurrent network model of excitatory and inhibitory neurons, which is realistic enough to replicate UP–DOWN states, with spike-timing-dependent plasticity (STDP). The individual neurons in the self-organized network exhibit a variety of temporal patterns in the two-state transitions. In addition, the model develops a feed-forward network-like structure that produces a diverse repertoire of precise sequences of the UP state. Our model shows that the self-organized activity well resembles the spontaneous activity of cortical networks if STDP is accompanied by the pruning of weak synapses. These results suggest that the two-state membrane potential transitions play an active role in structuring local cortical circuits.