Abstract
The resting membrane voltage of excitable cells such as neurons and muscle cells is determined by the electrochemical equilibrium of potassium and sodium ions. This voltage is calculated by using the Goldman–Hodgkin–Katz equation. However, from the quantum perspective, ions with significant quantum tunneling through closed channels can interfere with the electrochemical equilibrium and affect the value of the membrane voltage. Hence, in this case the equilibrium becomes quantum electrochemical. Therefore, the model of quantum tunneling of ions is used in this study to modify the Goldman–Hodgkin–Katz equation in such a way to calculate the resting membrane voltage at the point of equilibrium. According to the present calculations, it is found that lithium—with its lower mass—shows a significant depolarizing shift in membrane voltage. In addition to this, when the free gating energy of the closed channels decreases, even sodium and potassium ions depolarize the resting membrane voltage via quantum tunneling. This study proposes the concept of quantum electrochemical equilibrium, at which the electrical potential gradient, the concentration gradient and the quantum gradient (due to quantum tunneling) are balanced. Additionally, this concept may be used to solve many issues and problems in which the quantum behavior becomes more influential.
Highlights
Resting membrane voltage is determined by the electrochemical equilibrium of the ions such as potassium and sodium ions [1]
The aim of the present study is to modify the Goldman–Hodgkin–Katz equation in a way to integrate the effect of quantum tunneling so that the resting membrane potential can be calculated at the equilibrium point
The resting membrane potential is set when the electrochemical equilibrium has been established and it is calculated by the Goldman–Hodgkin–Katz equation
Summary
Resting membrane voltage is determined by the electrochemical equilibrium of the ions such as potassium and sodium ions [1]. It has been proposed that ions can use the phenomenon of quantum tunneling to pass through the closed voltage-gated channels of the biologic membrane [8]. On the other hand, when ions with significant tunneling probability such as lithium ions are introduced to the biologic system, they will affect the resting membrane voltage [8,11]. This study proposes new concept that may serve to solve future paradoxes, problems and medical issues such as epilepsy and cardiac arrhythmias caused by channelopathies. This insight will be discussed in this article
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