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

Abdallah Barjas Qaswal

doi:10.3390/quantum1020019

Abstract

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.

Highlights

The biological membrane of excitable tissue such as neurons and muscles contains voltage-gated channels such as sodium and potassium channels, which are closed at the resting state of the membrane potential by forming a hydrophobic constriction gate that prevents the permeation of ions by creating a barrier energy higher than their kinetic energy [1,2,3]
By substituting the values in Equation (8), there is no significant difference in the resting membrane potential before and after the substitution of quantum conductance of sodium and potassium ions because it is very small in comparison with the membrane conductance due to the leaky channels
The results showed that the membrane conductance of ions due to quantum tunneling does not affect the resting membrane potential

Summary

Introduction

The biological membrane of excitable tissue such as neurons and muscles contains voltage-gated channels such as sodium and potassium channels, which are closed at the resting state of the membrane potential by forming a hydrophobic constriction gate that prevents the permeation of ions by creating a barrier energy higher than their kinetic energy [1,2,3]. The quantum tunneling of lithium ions through the closed gate of voltage-gated sodium channels could explain the therapeutic effect of lithium in treating bipolar patients [7] These studies did not focus on the mathematical tunneling model itself and did not give a general picture to be applied on different ions since they focused on special cases. By applying the idea of quantum tunneling on the ions, quantum conductance can be calculated and, the role of closed voltage-gated channels at resting state would be better investigated It will serve as a general model to be applied when the issue of quantum tunneling of different ions is addressed to explain different phenomena and understand different pathologies, especially the disorders related to the central and peripheral nervous system such as epilepsy and pain disorders or even to develop new therapeutic agents to treat several diseases. The Mathematical Model of Quantum Tunneling of Ions through the Closed Voltage-Gated Channels

The Probability of Quantum Tunneling of Ions Through the Closed Channels

The Tunneling Probability of Potassium Ions

Quantum Conductance of Single Channel

The Effect of Quantum Conductance of Ions on the Resting Membrane Potential

Findings

Discussion