Effect of Calcium on the Characteristics of Action Potential Under Different Electrical Stimuli
Abstract
:1. Introduction
2. Neuron Model
2.1. HH Model
2.2. HH + Ca Model
3. Action Potential Simulation Based on HH and HH + Ca Models
3.1. Characteristics of Action Potential Release Under Direct Current Stimulation
3.1.1. Characteristics of Action Potential Release Under Weak Current Stimulation
3.1.2. Characteristics of Action Potential Release Under Moderate to Strong Current Stimulation
3.1.3. Characteristics of Action Potential Release Under Strong Current Stimulation
3.2. Characteristics of Action Potential Release Under Step Current Stimulation
3.3. Characteristics of Action Potential Release Under Square Wave Current Stimulation
3.4. Characteristics of Action Potential Release Under Sine Current Stimulation
4. Discussions
5. Conclusions
- (1)
- Under a direct current stimulation, the frequency of the action potential release increases with the current intensity, and the delay time of the first action potential is shortened. However, when the current stimulation exceeds a certain threshold, , the peak amplitude of the action potential gradually diminishes. The delay time of the first action potential in the HH + Ca model is longer than that in the HH model, while the peak amplitude after a stable release is greater in the HH + Ca model. The firing frequency of the HH model is higher than that of the HH + Ca model. Under a strong current stimulation, the HH + Ca model demonstrates a greater capacity to sustain the action potential release compared to the HH model.
- (2)
- When a step current is applied, the results are approximately equivalent to those observed under the constant direct current stimulation. The step change in the current induces the depolarization of the membrane potential, thereby triggering the action potential release. As the current intensity increases, the frequency of the action potential release in both models also rises. The HH model exhibits greater sensitivity to current stimulations, as smaller currents can elicit action potentials, whereas the HH + Ca model requires higher current intensities to initiate action potentials. The HH + Ca model may exhibit subthreshold oscillations under weak current stimulations below the threshold, with the oscillation amplitude increasing alongside the current intensity.
- (3)
- When a square wave current is applied, an increase in the current intensity leads to an increase in the frequency of the action potential release in both models, accompanied by a reduction in the delay time. Increasing the frequency of the square wave current diminishes the number of peak action potentials per cluster. At a current intensity of 10 pA, high-frequency action potentials are completely suppressed in the HH + Ca model, a phenomenon not observed in the HH model. In the HH model, action potentials can still be generated when the square wave current is zero, whereas this does not occur in the HH + Ca model.
- (4)
- When a sine current is introduced, the frequency of the action potential release in both models increases with the rising current intensity at the same sine current frequency. As the frequency of the sine current escalates, the number of spikes in the action potential clusters decreases. At high current intensities, both models display lower action potential amplitudes near the peak of the sine wave. The continuous depolarizing current provided by the calcium ion current partially offsets the hyperpolarizing effect of the potassium ion current. Additionally, the slow response of the calcium-activated potassium ion channels in the HH + Ca model, along with the rapid activation and inactivation of the A-type potassium ion currents, mitigates the potassium ion outflow and prevents the excessive hyperpolarization of the membrane potential. Collectively, these factors result in a lesser degree of action potential depression in the HH + Ca model compared to the HH model.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Qiao, X.; Yao, W. Effect of Calcium on the Characteristics of Action Potential Under Different Electrical Stimuli. AppliedMath 2024, 4, 1358-1381. https://doi.org/10.3390/appliedmath4040072
Qiao X, Yao W. Effect of Calcium on the Characteristics of Action Potential Under Different Electrical Stimuli. AppliedMath. 2024; 4(4):1358-1381. https://doi.org/10.3390/appliedmath4040072
Chicago/Turabian StyleQiao, Xuan, and Wei Yao. 2024. "Effect of Calcium on the Characteristics of Action Potential Under Different Electrical Stimuli" AppliedMath 4, no. 4: 1358-1381. https://doi.org/10.3390/appliedmath4040072
APA StyleQiao, X., & Yao, W. (2024). Effect of Calcium on the Characteristics of Action Potential Under Different Electrical Stimuli. AppliedMath, 4(4), 1358-1381. https://doi.org/10.3390/appliedmath4040072