Systematic analysis of synchronized oscillatory neuronal networks reveals an enrichment for coupled direct and indirect feedback motifs

Small modifications to network topology can induce stochastic bistable spiking dynamics in a balanced cortical model

Directed random graph models frequently are used successfully in modeling the population dynamics of networks of cortical neurons connected by chemical synapses. Experimental results consistently reveal that neuronal network topology is complex, however, in the sense that it differs statistically from a random network, and differs for classes of neurons that are physiologically different. This suggests that complex network models whose subnetworks have distinct topological structure may be a useful, and more biologically realistic, alternative to random networks. Here we demonstrate that the balanced excitation and inhibition frequently observed in small cortical regions can transiently disappear in otherwise standard neuronal-scale models of fluctuation-driven dynamics, solely because the random network topology was replaced by a complex clustered one, whilst not changing the in-degree of any neurons. In this network, a small subset of cells whose inhibition comes only from outside their local cluster are the cause of bistable population dynamics, where different clusters of these cells irregularly switch back and forth from a sparsely firing state to a highly active state. Transitions to the highly active state occur when a cluster of these cells spikes sufficiently often to cause strong unbalanced positive feedback to each other. Transitions back to the sparsely firing state rely on occasional large fluctuations in the amount of non-local inhibition received. Neurons in the model are homogeneous in their intrinsic dynamics and in-degrees, but differ in the abundance of various directed feedback motifs in which they participate. Our findings suggest that (i) models and simulations should take into account complex structure that varies for neuron and synapse classes; (ii) differences in the dynamics of neurons with similar intrinsic properties may be caused by their membership in distinctive local networks; (iii) it is important to identify neurons that share physiological properties and location, but differ in their connectivity.

Impaired coupling of local and global functional feedbacks underlies abnormal synchronization and negative symptoms of schizophrenia

Background

Abnormal synchronization of brain oscillations is found to be associated with various core symptoms of schizophrenia. However, the underlying mechanism of this association remains yet to be elucidated.

Results

In this study, we found that coupled local and global feedback (CLGF) circuits in the cortical functional network are related to the abnormal synchronization and also correlated to the negative symptom of schizophrenia. Analysis of the magnetoencephalography data obtained from patients with chronic schizophrenia during rest revealed an increase in beta band synchronization and a reduction in gamma band power compared to healthy controls. Using a feedback identification method based on non-causal impulse responses, we constructed functional feedback networks and found that CLGF circuits were significantly reduced in schizophrenia. From computational analysis on the basis of the Wilson-Cowan model, we unraveled that the CLGF circuits are critically involved in the abnormal synchronization and the dynamical switching between beta and gamma bands power in schizophrenia. Moreover, we found that the abundance of CLGF circuits was negatively correlated with the development of negative symptoms of schizophrenia, suggesting that the negative symptom is closely related to the impairment of this circuit.

Conclusions

Our study implicates that patients with schizophrenia might have the impaired coupling of inter- and intra-regional functional feedbacks and that the CLGF circuit might serve as a critical bridge between abnormal synchronization and the negative symptoms of schizophrenia.

Identification of feedback loops in neural networks based on multi-step Granger causality

MOTIVATION

Feedback circuits are crucial network motifs, ubiquitously found in many intra- and inter-cellular regulatory networks, and also act as basic building blocks for inducing synchronized bursting behaviors in neural network dynamics. Therefore, the system-level identification of feedback circuits using time-series measurements is critical to understand the underlying regulatory mechanism of synchronized bursting behaviors.

RESULTS

Multi-Step Granger Causality Method (MSGCM) was developed to identify feedback loops embedded in biological networks using time-series experimental measurements. Based on multivariate time-series analysis, MSGCM used a modified Wald test to infer the existence of multi-step Granger causality between a pair of network nodes. A significant bi-directional multi-step Granger causality between two nodes indicated the existence of a feedback loop. This new identification method resolved the drawback of the previous non-causal impulse response component method which was only applicable to networks containing no co-regulatory forward path. MSGCM also significantly improved the ratio of correct identification of feedback loops. In this study, the MSGCM was testified using synthetic pulsed neural network models and also in vitro cultured rat neural networks using multi-electrode array. As a result, we found a large number of feedback loops in the in vitro cultured neural networks with apparent synchronized oscillation, indicating a close relationship between synchronized oscillatory bursting behavior and underlying feedback loops. The MSGCM is an efficient method to investigate feedback loops embedded in in vitro cultured neural networks. The identified feedback loop motifs are considered as an important design principle responsible for the synchronized bursting behavior in neural networks.

An optimally evolved connective ratio of neural networks that maximizes the occurrence of synchronized bursting behavior

Background

Synchronized bursting activity (SBA) is a remarkable dynamical behavior in both ex vivo and in vivo neural networks. Investigations of the underlying structural characteristics associated with SBA are crucial to understanding the system-level regulatory mechanism of neural network behaviors.

Results

In this study, artificial pulsed neural networks were established using spike response models to capture fundamental dynamics of large scale ex vivo cortical networks. Network simulations with synaptic parameter perturbations showed the following two findings. (i) In a network with an excitatory ratio (ER) of 80-90%, its connective ratio (CR) was within a range of 10-30% when the occurrence of SBA reached the highest expectation. This result was consistent with the experimental observation in ex vivo neuronal networks, which were reported to possess a matured inhibitory synaptic ratio of 10-20% and a CR of 10-30%. (ii) No SBA occurred when a network does not contain any all-positive-interaction feedback loop (APFL) motif. In a neural network containing APFLs, the number of APFLs presented an optimal range corresponding to the maximal occurrence of SBA, which was very similar to the optimal CR.

Conclusions

In a neural network, the evolutionarily selected CR (10-30%) optimizes the occurrence of SBA, and APFL serves a pivotal network motif required to maximize the occurrence of SBA.

Spiking signatures of spontaneous activity bursts in hippocampal cultures

Dense dissociated hippocampal cultures are known to generate spontaneous bursting electrical activity which can be recorded by multielectrode arrays. We have analyzed spatio-temporal profiles of the distribution of spikes in the bursts recorded after 2 weeks in vitro. We have found a statistically significant similarity between the spiking patterns in sequential bursting events, we refer to these spiking patterns as spiking signatures. Such spiking signatures may appear in different parts of the bursts, including the activation patterns - the first spike times in the bursts, and deactivation patterns - the last spike times in the bursts. Moreover, these patterns may display apparent time scaling, e.g., they may be replayed in the subsequent bursts at different speeds, while preserving the spiking order. We discuss how such properties of the bursts may be associated with the formation of repeatable signaling pathways in cultured networks in vitro.