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Biointerface Research in Applied Chemistry

Quantum Tunneling of Protons through Respiratory Complex I of Mitochondria

Published Aug 15, 2025• 0 citations
Publisher

Abstract

Mitochondria are the major cellular organelles responsible for ATP production. They produce ATP through the process of oxidative phosphorylation, in which the proton motive force (pmf) is the driving force by which protons pass through ATPase. The pmf is generated by the pumping activity of the electron transport chain ETC, particularly complexes I, III, and IV. As the proton can be physically described as a quantum wave, it is important to explore the role of the quantum behavior in its transport through the ETC proteins, particularly the respiratory complex I. In the present study, the potential functions of three subunits of complex I were identified, and the Schrödinger equation was solved numerically by the finite difference method using MATLAB to obtain the eigenstates and their corresponding eigenvalues. In addition, quantum tunneling probability and quantum conductance values were calculated using WKB approximation for the eigenenergies of the proton in each potential barrier. Moreover, entropic tunneling delay time and tunneling currents were calculated. Our results indicate that quantum tunneling transport yields significant values of quantum conductance that can contribute significantly to the pmf while utilizing less than 45 % of the required energy to overcome the barriers of the subunits in respiratory complex I.

DOI
10.33263/briac154.059

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Mitochondria are the major cellular organelles responsible for ATP production. They produce ATP through the process of oxidative phosphorylation, in which the proton motive force (pmf) is the driving force by which protons pass through ATPase. The pmf is generated by the pumping activity of the electron transport chain ETC, particularly complexes I, III, and IV. As the proton can be physically described as a quantum wave, it is important to explore the role of the quantum behavior in its transport through the ETC proteins, particularly the respiratory complex I. In the present study, the potential functions of three subunits of complex I were identified, and the Schrödinger equation was solved numerically by the finite difference method using MATLAB to obtain the eigenstates and their corresponding eigenvalues. In addition, quantum tunneling probability and quantum conductance values were calculated using WKB approximation for the eigenenergies of the proton in each potential barrier. Moreover, entropic tunneling delay time and tunneling currents were calculated. Our results indicate that quantum tunneling transport yields significant values of quantum conductance that can contribute significantly to the pmf while utilizing less than 45 % of the required energy to overcome the barriers of the subunits in respiratory complex I.
The standard explanation for proton–electron separation at the entry point of the mitochondrial electron transport chain (ETC) invokes reduction potential: iron–sulfur clusters at Complex I possess a higher electrochemical affinity for electrons than NADH, and this differential drives the split. While operationally correct, this account is descriptive rather than mechanistic. It names the energetic gradient but does not explain why the electron moves through a protein structure while the proton cannot follow, nor does it specify the physical process by which the transition occurs. This paper proposes a three-mechanism framework — state transition, directed energy flow, and quantum tunnelling — that provides a more complete mechanistic account. The framework also offers a more precise formulation of the relationship between ETC congestion and reactive oxygen species (ROS) overproduction, replacing the imprecise notion of extended electron “dwell time” with the more accurate concept of increased tunnelling-event frequency per unit time.
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Quantum tunneling is conventionally described using the stationary Schrödinger equation with an externally imposed potential barrier. In this work, we present a dynamical formulation of quantum tunneling in which the barrier is modeled as a structured medium possessing quantized internal modes that interact coherently with an incident electron. Using the Heisenberg operator formalism and a second-quantized representation of the barrier medium, we derive coupled dynamical equations governing the electron–barrier interaction. Under a continuum-mode and mean-field approximation, the collective response of the barrier modes generates an effective potential that reproduces the conventional rectangular barrier model and the standard tunneling transmission probability obtained from the Schrödinger equation. Within this framework, a tunneling traversal time is naturally defined from the dynamical evolution of the electron and is shown to depend on the barrier width, barrier height, and incident electron energy. Numerical simulations illustrating the transmission probability and tunneling-time behavior are presented. The results provide a complementary microscopic interpretation of tunneling processes in structured quantum media and may be relevant to nanoscale transport, photonic barriers, and coherent quantum devices.
Quantum tunneling, a quintessential quantum phenomenon, challenges classical intuitions by allowing particles to pass through seemingly insurmountable barriers. This study delves into the intricate dynamics of electron tunneling, focusing on the critical role of sub-barrier interactions and complex time processes. Through a combination of experimental measurements and simulations based on Feynman’s path integral of complex time trajectories, we reveal that the sub-barrier potential interaction introduces an asymmetric electron wave packet probability distribution along the real time axis and a marked delay at the tunneling exit. The energy-dependent behavior of this delay in electronic tunneling agrees with that observed in the previous atomic tunneling studies, suggesting a universal mechanism underlying quantum tunneling across different scales. Our findings underscore the necessity of incorporating both the wave and particle aspects of quantum entities to fully comprehend tunneling dynamics, which holds promise for an intuitive interpretation of complex-number quantum processes.