Quantum Tunneling of Ions through the Closed Voltage-Gated Channels of the Biological Membrane: A Mathematical Model and Implications

Voltage-gated channels play an essential role in action potential propagation when their closed gates open, but their role when they are closed needs to be investigated. So, in this study, a quantum mechanical approach using the idea of quantum tunneling was used to calculate the conductance of closed channels for different ions. It was found that the conductance due to quantum tunneling of ions through the closed channels does not affect the resting membrane potential. However, under different circumstances, including change in the mass or the charge of the ion and the residues of the hydrophobic gate, the model of quantum tunneling would be useful to understand and explain several actions, processes, and phenomena in the biological systems.

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Mathematical Modeling of Ion Quantum Tunneling Reveals Novel Properties of Voltage-Gated Channels and Quantum Aspects of Their Pathophysiology in Excitability-Related Disorders

Pathophysiology ◽

10.3390/pathophysiology28010010 ◽

2021 ◽

Vol 28 (1) ◽

pp. 116-154

Author(s):

Abdallah Barjas Qaswal ◽

Omar Ababneh ◽

Lubna Khreesha ◽

Abdallah Al-Ani ◽

Ahmad Suleihat ◽

...

Keyword(s):

Quantum Mechanics ◽

Membrane Potential ◽

Quantum Tunneling ◽

Experimental Studies ◽

Classical Mechanics ◽

Membrane Conductance ◽

Resting Membrane Potential ◽

Voltage Gated ◽

Voltage Gated Channels ◽

Quantum Aspects

Voltage-gated channels are crucial in action potential initiation and propagation and there are many diseases and disorders related to them. Additionally, the classical mechanics are the main mechanics used to describe the function of the voltage-gated channels and their related abnormalities. However, the quantum mechanics should be considered to unravel new aspects in the voltage-gated channels and resolve the problems and challenges that classical mechanics cannot solve. In the present study, the aim is to mathematically show that quantum mechanics can exhibit a powerful tendency to unveil novel electrical features in voltage-gated channels and be used as a promising tool to solve the problems and challenges in the pathophysiology of excitability-related diseases. The model of quantum tunneling of ions through the intracellular hydrophobic gate is used to evaluate the influence of membrane potential and gating free energy on the tunneling probability, single channel conductance, and quantum membrane conductance. This evaluation is mainly based on graphing the mathematical relationships between these variables. The obtained mathematical graphs showed that ions can achieve significant quantum membrane conductance, which can affect the resting membrane potential and the excitability of cells. In the present work, quantum mechanics reveals original electrical properties associated with voltage-gated channels and introduces new insights and implications into the pathophysiology of excitability- related disorders. In addition, the present work sets a mathematical and theoretical framework that can be utilized to conduct experimental studies in order to explore the quantum aspects of voltage-gated channels and the quantum bioelectrical property of biological membranes.

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