Energy consumption of spontaneous transitions in a synaptic delay network

The delays are prevalent in a variety physical and biological systems. In this paper, we study the network firing activity, energy consumption, and energy efficiency of induced by excitatory and inhibitory synaptic delays in neuronal spontaneous transitions. Numerical results show that, synaptic delays can modulate the firing rate of neurons and regulate the synchronization of a neuronal system. Specifically, at certain synaptic delays, neurons shift from subthreshold spontaneous transitions to firing with significantly enhanced synchronization. And a greater amount of energy is expended in generating action potential, while fewer energy is spent in the subthreshold oscillations. There is a correspondent relationship between the mean firing rate and the mean synchronization rate of the neural network. The stronger the synchronization, the relatively high mean firing rate. Therefore, the more energy is consumed. Interestingly, excitatory synaptic delays have a more pronounced effect on neuronal activity than inhibitory synaptic delays. The network is significantly more active when the excitatory synaptic delays is predominant, but the mean firing rate at a lower rate as the time of synaptic delay grew. However, when the inhibitory synaptic delay is greater than the excitatory delay, neuronal firing is almost inhibited. In addition, we find that the excitatory and inhibitory synaptic delays are 4 to 1 when the mean firing rate, energy consumption, and energy efficiency are maximized, which is consistent with the ratio of excitatory to inhibitory neuron numbers. Therefore, we suggest that the excitatory–inhibitory delay balance of synaptic structures can serve as a mechanism to make neural activity processing energetically efficient.