Tunneling Proton Research Articles

A mathematical modeling of the mitochondrial proton leak via quantum tunneling

<abstract> <p>The mitochondrion is a vital intracellular organelle that is responsible for ATP production. It utilizes both the concentration gradient and the electrical potential of the inner mitochondrial membrane to drive the flow of protons from the intermembrane space to the matrix to generate ATP via ATP-synthase. However, the proton leak flow, which is mediated via the inner mitochondrial membrane and uncoupling proteins, can reduce the efficiency of ATP production. Protons can exhibit a quantum behavior within biological systems. However, the investigation of the quantum behavior of protons within the mitochondria is lacking particularly in the contribution to the proton leak. In the present study, we proposed a mathematical model of protons tunneling through the inner mitochondrial membrane and the mitochondrial carrier superfamily MCF including uncoupling proteins UCPs and the adenine nucleotide translocases ANTs. According to the model and its assumptions, the quantum tunneling of protons may contribute significantly to the proton leak if it is compared with the classical flow of protons. The quantum tunneling proton leak may depolarize the membrane potential, hence it may contribute to the physiological regulation of ATP synthesis and reactive oxygen species ROS production. In addition to that, the mathematical model of proton tunneling suggested that the proton-tunneling leak may depolarize the membrane potential to values beyond the physiological needs which in turn can harm the mitochondria and the cells. Moreover, we argued that the quantum proton leak might be more energetically favorable if it is compared with the classical proton leak. This may give the advantage for quantum tunneling of protons to occur since less energy is required to contribute significantly to the proton leak compared with the classical proton flow.</p> </abstract>

Coupling of conduction electrons to two-level systems formed by hydrogen: a scatteringapproach

An effective Hamiltonian for a two-level system (TLS) which could model the interactionbetween a tunneling proton and the conduction electrons of a metal is investigated in acomparative way. In the conventional first-order Born approximation with plane waves, andfor small-distance displacement of the tunneling particle, a simple correlation between theatomic motion and angular momentum change of the scattering electron is deduced. Forsuch a displacement, and within a distorted wave Born approximation for initial and finalstates, the change in the scattering amplitude is expressed via bounded trigonometricfunctions of the corresponding difference of scattering phase shifts. The numericalvalue of this amplitude change is analyzed in the framework of a self-consistentscreening description for an impurity embedding in a paramagnetic electron gas. Thecoupling thus obtained of the tunneling proton to a homogeneous electron gas is tooweak to be in the range required for realization of the two-channel Kondo effect.

Quantum Effects in Hydrogen-Bonded Ferroelectrics

The isotope effect and the quantum saturation effect in hydrogen-bonded ferroelectrics, such as KH 2 PO 4 (KDP), are studied by using a simple coupled dipole-proton model under two opposite adiabatic approximations. The model of interacting tunneling protons and the model of interacting dipoles, as two traditional models for KDP, are reproduced from this study and results of the latter model correspond better to experimental findings in KDP. Therefore, the modified strong dipole-proton coupling model, as a more realistic model of interacting dipoles for KDP, and the path-integral Monte Carlo method are applied to estimate the quantum saturation effect in KDP.

Adiabatic approximations of coupled dipole-proton model for hydrogen-bonded ferroelectrics

In several hydrogen-bonded ferroelectrics, such as ${\mathrm{KH}}_{2}{\mathrm{PO}}_{4}$-type ferroelectrics, the protons are strongly coupled to the dipoles produced in the heavy-ion sublattice. It is not clear whether such a coupled dipole-proton system can be described by two traditional simple models, the model of interacting tunneling protons and the model of interacting dipoles, and which one is more appropriate. We show that both models follow from the coupled dipole-proton model under the opposite adiabatic approximations, and that the model of interacting dipoles seems to correspond better with the experiments.

Bond Geometry and Phase Transition Mechanism of H-Bonded Ferroelectrics

Taking into account the bilinear coupling between the tunneling protons and the displacements of the electron shells of the surrounding ${\mathrm{PO}}_{4}$ groups, we present a new model of hydrogen-bonded ferroelectrics. The model is an extension of both the tunneling model and the nonlinear polarizability model and includes the geometrical aspects of the hydrogen bond. It leads to a structural phase transition and describes the isotope effect due to the substitution $\mathrm{H}/\mathrm{D}$ in ${\mathrm{KH}}_{2}{\mathrm{PO}}_{4}$ and the pressure dependence.

Proton tunneling in symmetric H-bond. A simple microscopic model

The dynamic of a tunneling proton in a symmetric H-bond is described in terms of a simple spin-boson model. The quantum evolution is exactly solved and this allows us to derive the expression of the rate constant in terms of the ‘microscopic’ parameters of the model and also to discuss the validity range of the transition state theory description of proton transfer phenomena.

Proton Tunneling Model for the Ferroelectric Phase Transition in CsH2PO4

To understand the isotope effect in the ferroelectric phase transition of CsH 2 PO 4 and CsD 2 PO 4 , a quasi-one-dimensional model is proposed. In contrast to the existing models which consider only either the proton's degree of freedom or the polarization dipoles, both of them are regarded as essential elements of the system, while the tunneling protons are assumed to have nothing to do with dielectric polarization. The static dielectric constant, calculated on the assumption of no tunneling for CsD 2 PO 4 and a finite tunneling frequency for CsH 2 PO 4 , reproduces well the experimental data by using model parameters consistent with the saturated polarization data. The model predicts absence of soft modes despite proton tunneling, in agreement with the order-disorder behavior of the phase transition as has been confirmed by experiments.

Paraelectric-ferroelectric phase transitions of KH2PO

The infrared-reflectivity spectra of ${\mathrm{KH}}_{2}$${\mathrm{PO}}_{4}$ (KDP) and its isomorphs ${\mathrm{RbH}}_{2}$${\mathrm{PO}}_{4}$ (RDP) and ${\mathrm{KH}}_{2}$${\mathrm{AsO}}_{4}$ (KDA) are reported in a wide spectral range (from 20 to 4000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), in the paraelectric and ferroelectric phases. The phonon responses are obtained by fitting the factorized form of the dielectric function to the experimental spectra. The comparison of the data obtained in the three compounds allows the assignment of all vibrational modes. In RDP, the internal ${\ensuremath{\nu}}_{4c}$ polar mode polarized along the ferroelectric axis is found to soften upon approaching ${T}_{C}$ from below or above, although to a lesser extent. The eigenvector pattern of this mode shows that it interacts strongly via electrostatic coupling with the intersite tunneling proton motions perpendicular to the ferroelectric axis. This phenomenon is thought to be the origin of the ${\ensuremath{\nu}}_{4c}$ mode softening. This mode also couples with other polar modes of the same symmetry via a mechanism intermediate between Fano-type interference and classical mode-mode coupling. The coupled excitation evolves to yield the overdamped ferroelectric mode that triggers the paraelectric-ferroelectric phase transition. The temperature dependence of its oscillator strength agrees with that of the dielectric constant measured above piezoelectric resonances or in single domain samples. The temperature dependence of the effective charges carried by the ions, deduced from TO-LO splittings, is also consistent with a displacive mechanism.

Tunnel effect on the kinetics of a sigmatropic shift

Non-linear Arrhenius plots and large kinetic isotope effects observed in sigmatropic hydrogen shifts of photochemically generated transient di- and hexa-hydrocarbazoles are interpreted as tunnel contributions. An Eckart barrier was used to calculate the quantum-mechanical transmission probabilities of the tunneling protons.

Infrared investigation of poly-L-histidine structure dependent on protonation.

AbstractPoly‐L‐histidine (PLH) films at different degrees of protonation were produced mid subjected to infrared spectroscopic investigation (range 4000‐650 cm−1). In addition, the N‐deuterated film spectra were plotted. The amide II and III bands show that the peptide group is present in the trans form. The amide I and II bands show that at 0% and 50% protonation the PLH occurs as an α‐helix and at 100% protonation as a random coil with some ranges in β structure. At 0% and 50% protonation, no hydration water is bound to the backbone. At 0% protonation all NH groups are linked to each other or to water molecules via hydrogen bonds. At 50% protonation NH+ċN bonds form between the imidazole rings. These protons are present in continuous energy level distribution. Such bonds with tunneling protons are extremely polarizable and between these bonds may act proton dispersion forces. The Cl− ions are bonded to the NH groups of the imidazole groups. The hydration water is bonded to the Cl−− ions and to the NH groups. At 100% protonation, hydration water is bonded also to the CO groups of the backbone. The NH groups of the backbone, like those of the rings, endeavor especially in the dry state to bond to the Cl− ions. This leads to a strong steric constraint of the random coil.

Models of the phase transition in kdp type ferroelectrics

Recent typical models proposed for KDP type ferroelectrics, the Ising spin models, the tunneling proton model, and the 'mixed' proton and phonon model (the modified tunneling model), are briefly reviewed and compared with experimental facts. The relations between these models are correctly shown paying attention to the expressions for the electric polarization in them. Experimental and theoretical work necessary for deciding upon a definite final model are suggested.

Protonen-Dispersionskr�fte und IR-Kontinuumsabsorption bei S�ure- und Lauge-L�sungen

In the investigation of acid and alkali solutions a continuum absorption is observed in the IR spectrum, which is caused by protons or defect protons tunneling in hydrogen bridges. By means of a perturbation calculation it is shown that the variations of the electromagnetic fields caused by the tunneling of the protons give rise to coupling forces, which we term proton or defect-proton dispersion forces. These are dependent of the distance between the hydrogen bridges, of their orientation, and of the tunneling frequency. Since these quantities are statistically distributed and the forces are very considerable, the energy terms of the tunneling protons are spread out to broad energy bands.