# The Quantum Tunneling of Ions Model Can Explain the Pathophysiology of Tinnitus

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## Abstract

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## 1. Introduction

## 2. Mathematical Model of the Quantum Tunneling of Ions

#### 2.1. Mathematical Equations That Describe the Quantum Tunneling-Induced Membrane Depolarization of Inner Hair Cells

_{m}is the membrane potential.

^{2}). The unit for quantum membrane conductance used in the present study is mS/cm

^{2}.

^{2}[44,45,46] is the leak membrane conductance of potassium ions at the resting state, and $M{C}_{Na}=0.01$ mS/cm

^{2}[44,45,46] is the leak membrane conductance of sodium ions at the resting state. The ratio between $M{C}_{K}$ and $M{C}_{Na}$ is 100 to 2, which is the same as the ratio reported in [46], ${V}_{m}$ is the resting membrane potential of the inner hair cell, F is Faraday’s constant ($\mathrm{96,485.33}$ C/mol), R is the gas constant ($8.31$ J/Kmol), and T is absolute body temperature (310 K). The minus sign is added to the term ${e}^{\frac{-F{V}_{m}}{RT}}$ to obtain an absolute value of the membrane potential, which is negative inside with regard to the outside. Throughout the paper, the value of the membrane potential is referred to as an absolute value (positive). When the above parameters are substituted in Equation (11), ${V}_{m}=0.073$ V, which is near the normal membrane potential of inner hair cells at the basolateral sides (50 to 70 mV) [46].

#### 2.2. Mathematical Equations That Describe the Probability of Inducing an Action Potential in Demyelinated Neurons of the Auditory Pathway (the Formation of a Quantum Synapse)

^{−1}into Equation (14) to get ${\left[K\right]}_{AP}=4.3\times {10}^{-2}$ mmol/L. We give this example to make it easier to follow the subsequent ideas to facilitate an understanding the concept of a quantum synapse between neurons.

^{2}), ${N}_{K}=44$ ions, which is the number of potassium ions that hit a single closed channel. Thus, the number of potassium ions ${N}_{K}$ corresponds to the change in the extracellular potassium concentration of $4.3\times {10}^{-2}$ mmol/L. As the change in the extracellular potassium concentration increases, the average number of potassium ions hitting the channel increases.

^{2}(which corresponds to 1 channel/$\mathsf{\mu}{\mathrm{m}}^{2}$) will be substituted in Equation (16). Accordingly, by substituting the values of concentrations and conductance in Equation (16), the relationship between ${T}_{Q(Thr)}$ and ${[K]}_{AP}$ can be obtained:

^{2}= 100 $\mathsf{\mu}{\mathrm{m}}^{2}$, then ${N}_{\mu {m}^{2}}=100$. This means that there are 100 areas available for the quantum tunneling of potassium ions to induce an action potential. Inducing an action potential in at least one area will be enough to transmit the action potential to the next areas on the same neuron until it reaches the brain hearing centers.

## 3. Results

#### 3.1. Quantum Tunneling-Induced Membrane Depolarization

^{2}[44,45], which corresponds to $D={10}^{2}$ channels/$\mathsf{\mu}{\mathrm{m}}^{2}$, will be substituted.

#### 3.1.1. The Influence of the Length of the Gate on Quantum Tunneling-Induced Membrane Depolarization

#### 3.1.2. The Influence of Gate Location on Quantum Tunneling-Induced Membrane Depolarization

#### 3.2. The Probability of Action Potential Induction via Quantum Tunneling of Potassium Ions (the Formation of a Quantum Synapse)

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The symmetric Eckart potential. (

**a**) Schematic diagram of the symmetric Eckart potential in which G is the barrier height and L is the gate length at which U(L) = 0.42 G, according to Equation (1). (

**b**) Actual plots of the symmetric Eckart potential at different gate lengths L.

**Figure 2.**Schematic diagram for the possible locations of the closed activation and inactivation gates.

**Figure 3.**The three major compartments in the cochlea: the perilymph, the endolymph, and the cytoplasm of the inner hair cell. The endolymphatic potential is around + 100 mV and the potential inside the inner hair cell is around −50 to −70 mV.

**Figure 4.**Schematic diagram of the quantum synapse between two neurons. (

**a**) Neuron 1 carries an action potential (AP). During action potential propagation, potassium ions exit to the outside when potassium channels (represented in red ) open. The classical passage of ions through open channels is indicated by the straight arrows. These potassium ions also have the chance to tunnel through the closed exposed potassium channels in the membrane of an adjacent unstimulated neuron (Neuron 2) that has been demyelinated. The quantum tunneling of potassium ions through the closed channels is indicated by the wavy arrows. (

**b**) An action potential is induced in Neuron 2 due to the depolarization mediated by the quantum tunneling of potassium ions.

**Figure 5.**Relationship between the barrier height of the gate G and the membrane potential according to the values specified above the figure and varying values of gate length: (

**a**) $L=0.5\times {10}^{-10}$ m, (

**b**) $L=1\times {10}^{-10}$ m, (

**c**) $L=1.5\times {10}^{-10}$ m, and (

**d**) $L=2\times {10}^{-10}$ m. The figure clearly delineates the ability of all the three cations to depolarize the membrane potential.

**Figure 6.**Relationship between the barrier height of the gate G and the membrane potential according to the values specified above the figure and varying values of gate location: (

**a**) n = 1, (

**b**) n = 2, (

**c**) n = 3, and (

**d**) n = 4. The figure clearly delineates the ability of all the three cations to depolarize the membrane potential.

**Figure 7.**Relationship between the barrier height of the gate G and the probability of action potential (AP) induction according to the values specified above the figure and varying values of gate length L.

**Figure 8.**Relationship between the barrier height of the gate G and the probability of action potential (AP) induction according to the values specified above the figure and varying values of membrane potential.

**Figure 9.**Relationship between the barrier height of the gate G and the probability of action potential (AP) induction according to the values specified above the figure and varying values of the number of potassium ions ${N}_{K}$.

**Figure 10.**Relationship between the barrier height of the gate G and the probability of action potential (AP) induction according to the values specified above the figure and varying values of channel density D.

**Figure 11.**Relationship between the barrier height of the gate G and the probability of action potential (AP) induction according to the values specified above the figure and varying values of ${N}_{\mu {m}^{2}}$.

**Figure 12.**Schematic diagram of the quantum tunneling action of calcium ions, potassium ions, and sodium ions at the basolateral membrane of inner hair cells and through the membrane of auditory pathway neurons. This quantum tunneling of ions can depolarize the membrane potential when the quantum version of the GHK equation is applied.

**Figure 13.**Schematic diagram of the pathophysiology of tinnitus according to the quantum tunneling model of ions.

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**MDPI and ACS Style**

Al-Rawashdeh, B.M.; Qaswal, A.B.; Suleiman, A.; Zayed, F.M.; Al-Rawashdeh, S.M.; Tawalbeh, M.; Khreesha, L.; Alzubaidi, A.; Al-Zubidi, E.; Ghala, Z.;
et al. The Quantum Tunneling of Ions Model Can Explain the Pathophysiology of Tinnitus. *Brain Sci.* **2022**, *12*, 426.
https://doi.org/10.3390/brainsci12040426

**AMA Style**

Al-Rawashdeh BM, Qaswal AB, Suleiman A, Zayed FM, Al-Rawashdeh SM, Tawalbeh M, Khreesha L, Alzubaidi A, Al-Zubidi E, Ghala Z,
et al. The Quantum Tunneling of Ions Model Can Explain the Pathophysiology of Tinnitus. *Brain Sciences*. 2022; 12(4):426.
https://doi.org/10.3390/brainsci12040426

**Chicago/Turabian Style**

Al-Rawashdeh, Baeth M, Abdallah Barjas Qaswal, Aiman Suleiman, Fuad Mohammed Zayed, S. M. Al-Rawashdeh, Mohamed Tawalbeh, Lubna Khreesha, Ayham Alzubaidi, Enas Al-Zubidi, Zuhir Ghala,
and et al. 2022. "The Quantum Tunneling of Ions Model Can Explain the Pathophysiology of Tinnitus" *Brain Sciences* 12, no. 4: 426.
https://doi.org/10.3390/brainsci12040426