Identifying the pulsed neuron networks' structures by a nonlinear Granger causality method.

BACKGROUND: It is a crucial task of brain science researches to explore functional connective maps of Biological Neural Networks (BNN). The maps help to deeply study the dominant relationship between the structures of the BNNs and their network functions. RESULTS: In this study, the ideas of linear Granger causality modeling and causality identification are extended to those of nonlinear Granger causality modeling and network structure identification. We employed Radial Basis Functions to fit the nonlinear multivariate dynamical responses of BNNs with neuronal pulse firing. By introducing the contributions from presynaptic neurons and detecting whether the predictions for postsynaptic neurons' pulse firing signals are improved or not, we can reveal the information flows distribution of BNNs. Thus, the functional connections from presynaptic neurons can be identified from the obtained network information flows. To verify the effectiveness of the proposed method, the Nonlinear Granger Causality Identification Method (NGCIM) is applied to the network structure discovery processes of Spiking Neural Networks (SNN). SNN is a simulation model based on an Integrate-and-Fire mechanism. By network simulations, the multi-channel neuronal pulse sequence data of the SNNs can be used to reversely identify the synaptic connections and strengths of the SNNs. CONCLUSIONS: The identification results show: for 2-6 nodes small-scale neural networks, 20 nodes medium-scale neural networks, and 100 nodes large-scale neural networks, the identification accuracy of NGCIM with the Gaussian kernel function was 100%, 99.64%, 98.64%, 98.37%, 98.31%, 84.87% and 80.56%, respectively. The identification accuracies were significantly higher than those of a traditional Linear Granger Causality Identification Method with the same network sizes. Thus, with an accumulation of the data obtained by the existing measurement methods, such as Electroencephalography, functional Magnetic Resonance Imaging, and Multi-Electrode Array, the NGCIM can be a promising network modeling method to infer the functional connective maps of BNNs.

Discerning Functional Connections in the Pulsed Neural Networks with the Dynamic Bayesian Network Structure Search Method Based on a Genetic Algorithm.

It is important to explore potential structural characteristics of biological networks and regulatory mechanisms of network behaviors at the system level. In this study, a dynamic Bayesian network structure search method (DBNSSM) based on a genetic algorithm is employed to infer and locate functional connections in pulsed neural networks (PNNs) as typical artificial neural networks. In the process of network structure searching, a minimum description length score is calculated for each candidate network structure. The score indicates two characteristics of the network structure: (1) the likelihood based on network dynamic response data and (2) the complexity. Both should be considered together on selecting network structures. The DBNSSM is applied to analyze time-series data from PNNs, thereby discerns functional connections showing network structures collectively. It is feasible to analyze multichannel electrophysiological data of biological neural networks using the DBNSSM.

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.

Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components.

Feedback circuits are crucial dynamic motifs which occur in many biomolecular regulatory networks. They play a pivotal role in the regulation and control of many important cellular processes such as gene transcription, signal transduction, and metabolism. In this study, we develop a novel computationally efficient method to identify feedback loops embedded in intracellular networks, which uses only time-series experimental data and requires no knowledge of the network structure. In the proposed approach, a non-parametric system identification technique, as well as a spectral factor analysis, is applied to derive a graphical criterion based on non-causal components of the system's impulse response. The appearance of non-causal components in the impulse response sequences arising from stochastic output perturbations is shown to imply the presence of underlying feedback connections within a linear network. In order to extend the approach to nonlinear networks, we linearize the intracellular networks about an equilibrium point, and then choose the magnitude of the output perturbations sufficiently small so that the resulting time-series responses remain close to the chosen equilibrium point. In this way, the impulse response sequences of the linearized system can be used to determine the presence or absence of feedback loops in the corresponding nonlinear network. The proposed method utilizes the time profile data from intracellular perturbation experiments and only requires the perturbability of output nodes. Most importantly, the method does not require any a priori knowledge of the system structure. For these reasons, the proposed approach is very well suited to identifying feedback loops in large-scale biomolecular networks. The effectiveness of the proposed method is illustrated via two examples: a synthetic network model with a negative feedback loop and a nonlinear caspase function model of apoptosis with a positive feedback loop.

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

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.