Energy features in spontaneous up and down oscillations

Abstract

Spontaneous brain activities consume most of the brain's energy. So if we want to understand how the brain operates, we must take into account these spontaneous activities. Up and down transitions of membrane potentials are considered to be one of significant spontaneous activities. This kind of oscillation always shows bistable and bimodal distribution of membrane potentials. Our previous theoretical studies on up and down oscillations mainly looked at the ion channel dynamics. In this paper, we focus on energy feature of spontaneous up and down transitions based on a network model and its simulation. The simulated results indicate that the energy is a robust index and distinguishable of excitatory and inhibitory neurons. Meanwhile, one the whole, energy consumption of neurons shows bistable feature and bimodal distribution as well as the membrane potential, which turns out that the indicator of energy consumption encodes up and down states in this spontaneous activity. In detail, energy consumption mainly occurs during up states temporally, and mostly concentrates inside neurons rather than synapses spatially. The stimulation related energy is small, indicating that energy consumption is not driven by external stimulus, but internal spontaneous activity. This point of view is also consistent with brain imaging results. Through the observation and analysis of the findings, we prove the validity of the model again, and we can further explore the energy mechanism of more spontaneous activities.

Keywords: Energy consumption; Energy feature; Spontaneous activity; Up and down states.

Fig. 1

The network size-dependent change of three indicators. a Mean synchronization rate for excitatory and inhibitory neurons. b Mean firing rate for excitatory and inhibitory neurons. c Mean energy consumption for excitatory and inhibitory neurons. d Mean energy consumption for all neurons (the green dotted line) in the network. (Color figure online)

Fig. 2

Energy gradient of one single neuron shows up and down oscillations similar to membrane potential oscillations. a Membrane potential of neuron#1. b Power consumption of neuron#1. c Energy consumption of neuron#1. d Correlation between membrane potential and power consumption of neurons in the network

Fig. 3

Power and membrane potential are always stable at two states and both show bimodal distribution, whenever in spontaneous activities or during continuous external stimulus (10–12 s). a Membrane potential distribution of one neuron in the network. b Membrane potential distribution of all the neurons in the network. c Power distribution of one neuron in the network. d Power distribution of all the neurons in the network

Fig. 4

Spike raster plots of neurons in the network. a In the case of spontaneous oscillations. b In the case of 2 s external stimulus from 10–12 s

Fig. 5

Membrane potential versus energy consumption planes of a single neuron and network, respectively. a Membrane potential versus energy consumption rate plane of a single neuron. b Mean membrane potential versus mean energy consumption rate plane of the network. c Membrane potential versus energy consumption plane of a single neuron. d Mean membrane potential versus mean energy consumption plane of the network

Fig. 6

Intrinsic and synaptic energy consumption of a single neuron and network. a Intrinsic and total energy consumption of one neuron in the network. b Ratio of synaptic to total energy consumption of one neuron in the network. c Mean ratio of synaptic to total energy consumption of all the neurons in the network

Fig. 7

Spontaneous and stimulation related energy consumption of neurons in the network. a Mean energy consumption of neurons in the network during spontaneous and stimulated periods. b Stimulation related increases in energy consumption of neurons in the network