Long-period rhythmic synchronous firing in a scale-free network

Significance Understanding the mechanisms of how neural systems process temporal information is at the core to elucidate brain functions, such as for speech recognition and music appreciation. The present study investigates a simple yet effective mechanism for a neural system to extract the rhythmic information of external inputs in the order of seconds. We propose that a large-size neural network with scale-free topology is like a repertoire, which consists of a large number of loops and chains with various sizes, and these loops and chains serve as substrates to learn the rhythms of external inputs. Stimulus information is encoded in the spatial-temporal structures of external inputs to the neural system. The ability to extract the temporal information of inputs is fundamental to brain function. It has been found that the neural system can memorize temporal intervals of visual inputs in the order of seconds. Here we investigate whether the intrinsic dynamics of a large-size neural circuit alone can achieve this goal. The network models we consider have scale-free topology and the property that hub neurons are difficult to be activated. The latter is implemented by either including abundant electrical synapses between neurons or considering chemical synapses whose efficacy decreases with the connectivity of the postsynaptic neuron. We find that hub neurons trigger synchronous firing across the network, loops formed by low-degree neurons determine the rhythm of synchronous firing, and the hardness of exciting hub neurons avoids epileptic firing of the network. Our model successfully reproduces the experimentally observed rhythmic synchronous firing with long periods and supports the notion that the neural system can process temporal information through the dynamics of local circuits in a distributed way.