Neuronal activity in the human brain occurs in a complex physiologic environment, and noise from all aspects in this physiologic environment affects all aspects of nervous-system function. An essential issue of neural information processing is whether the environmental noise in a neural system can be estimated and quantified in a proper way. In this paper, we calculated the neural energy to estimate the range of critical values of thermal noise intensity that markedly affect the membrane potential and the energy waveform, in order to define such a noisy environment which neuronal activity relies on.

Thermal noise in neural system is critically vital for information processing, because it has a great influence on a variety of aspects of the central nervous system [

We wanted to estimate the range of critical values of noise intensity that is capable of markedly changing the energy waveform. The principal idea of our research was inspired by the fact that since it is impossible to measure the thermal noise intensity at a neuronal level which is great enough to affect neuronal activity in an experiment, and hence, according to the rule of the only corresponding relationship between the membrane potential and its energy function, the range of thermal noise intensity obtained by our neuronal energy function can be estimated to be what it should be in a real neural system. Any kind of membrane potential can be obtained by adjusting the noise intensity, but there is no intrinsic relationship between such a membrane potential and the real neuronal energy. Therefore, we studied the membrane potential starting from the point of view of neuronal energy and observing the type of order of magnitude in noise intensity that can greatly affect the energy function of the membrane potential. As a result, we obtained a range of thermal noise intensity that neurons might have in an actual thermal noisy environment.

It follows that a further discussion of thermal noise intensity range is possible for levels of networks. This part of the research is not only significant for the application of thermal noise intensity when modeling a neuron, but is also able to provide an adequate scientific basis for estimating the range of thermal noise intensity in networks and helping to establish neural network models.

Finally, it should be emphasized that we did not consider signal to noise ratio (SNR) that is beyond the scope of this paper.

Compared with the traditional simple single neuronal model, a voltage source, a current source, and an inductor are innovatively proposed in the biophysical model presented in this paper, which is shown in Figure

Physical model of the

As indicated in Figure

The current source is calculated from the formula

The solution of (

Inserting (

According to the above equations, we can obtain the solution of the action potential

To clarify our point of view, we present in a straightforward manner the action potential and its neuronal energy function represented by the corresponding power obtained by our proposed method, as shown in Figure

Action potential and its corresponding energy function.

As indicated in Figure

EPSP and its corresponding energy function.

IPSP and its corresponding energy function.

In the cerebral cortex, the excitatory neurons comprise 85% of the neurons, and the remaining neurons are inhibitory [

A single neuron acts under the condition of a neural network. In other words, the interaction among the neurons makes their functional effectiveness emerge. It is in this sense that neuronal activity is performing the process of metabolism in the thermal noisy physiologic environment. To obtain the size of thermal noise intensity of the neuronal activity in the actual environment and to further obtain the noise circumstance under the condition of networks in the brain, we need to first understand the neuronal membrane potential and its corresponding energy function under the condition of no noise interference [

Because the signal intensities of AP, EPSP, and IPSP are

After adding thermal noise, the current takes the form

The action potential together with its corresponding power plotted by the energy function calculated under the condition of different noise intensity is shown as follows.

In all of Figures

The action potential and its corresponding energy function.

The action potential and its corresponding energy function.

The action potential and its corresponding energy function.

The action potential and its corresponding energy function.

The action potential and its energy function.

The action potential and its corresponding function.

When the noise intensity

When the noise intensity

When the noise intensity

To summarize, we cannot estimate an accurate value of noise intensity for both the suprathreshold membrane potential and the corresponding neuronal energy. In estimating the range of the critical values of noise intensity, we found that when the noise intensity

As shown in Figures

According to the calculated results of Wang et al. [

The EPSP and the corresponding energy function.

The EPSP and the corresponding energy function.

The EPSP and the corresponding energy function.

The EPSP and the corresponding energy function.

The EPSP and the corresponding energy function.

The EPSP and the corresponding energy function.

The EPSP and the corresponding energy function.

The EPSP and the corresponding energy function.

The IPSP and the corresponding energy function.

The IPSP and the corresponding energy function.

The IPSP and the corresponding energy function.

The IPSP and the corresponding energy function.

The IPSP and the corresponding energy function.

The IPSP and the corresponding energy function.

The IPSP and the corresponding energy function.

When the level of noise intensity

When the level of noise intensity

When the noise intensity

When the level of noise intensity

When the noise intensity

When the level of noise

In summary, when the noise intensity

When the noise intensity

When the noise intensity

When the noise intensity

When the noise intensity

We still could not estimate the range of the noise that affects the energy function of the IPSP according to the results shown in Figures

When the noise intensity

When the level of noise intensity

When the level of noise intensity

In summary, when the level of noise intensity

In this study, we obtained the action potential, EPSP, IPSP, and their corresponding energy waveforms with thermal noise added to the current. By changing the thermal noise intensity, we found the estimated range of the critical value of thermal noise that can significantly influence the neuronal membrane potential and the corresponding energy waveform. When the thermal noise intensity

The physical model which we used in this paper was proposed by Wang et al. [

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China (11232005) and the Ministry of Education Doctoral Foundation (20120074110020).