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.

MOTIVATION: Synchronized bursting behavior is a remarkable phenomenon in neural dynamics. So, identification of the underlying functional structure is crucial to understand its regulatory mechanism at a system level. On the other hand, we noted that feedback loops (FBLs) are commonly used basic building blocks in engineering circuit design, especially for synchronization, and they have also been considered as important regulatory network motifs in systems biology. From these motivations, we have investigated the relationship between synchronized bursting behavior and feedback motifs in neural networks. RESULTS: Through extensive simulations of synthetic spike oscillation models, we found that a particular structure of FBLs, coupled direct and indirect positive feedback loops (PFLs), can induce robust synchronized bursting behaviors. To further investigate this, we have developed a novel FBL identification method based on sampled time-series data and applied it to synchronized spiking records measured from cultured neural networks of rat by using multi-electrode array. As a result, we have identified coupled direct and indirect PFLs. CONCLUSION: We therefore conclude that coupled direct and indirect PFLs might be an important design principle that causes the synchronized bursting behavior in neuronal networks although an extrapolation of this result to in vivo brain dynamics still remains an unanswered question.