Quantum tunnelling and the activated complex theory

Joachim Ankerhold

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.

Joachim Ankerhold, Hermann Grabert

The time evolution of the density matrix of a system with potential barrier is determined using path integrals. Describing the quantum dynamics in terms of the semiclassical motion in the complex coordinate plane, a detailed picture of barrier penetration in the time domain and the change-over from thermal activation to quantum tunneling is gained. Deep tunneling is shown to arise from specific fluctuations about the semiclassical real time trajectories.

Mohsen Razavy

Ying-Hua Huang, Hang Wong, Zhide Chen

Temperature effect on quantum tunneling in a Cooper-pair-box coupled to a quantum oscillator is studied by both numerical and analytical calculations. It is found that, in strong coupling regions, coherent tunneling of a Cooper-pair-box can be destroyed by its coupling to a quantum oscillator and the tunneling becomes thermally activated as the temperature rises, leading to failure of the Cooper-pair-box. The transition temperature between the coherent tunneling and thermo-activated hopping is determined and physics analysis based on small polaron theory is also provided.

Max Meynig, Hal M. Haggard