scholarly journals Mechanism of Proton Pumping in Complex I of the Mitochondrial Respiratory Chain

2021 ◽  
Vol 3 (3) ◽  
pp. 425-434
Author(s):  
Jonathan Friedman ◽  
Lev Mourokh ◽  
Michele Vittadello
Keyword(s):  
Complex I ◽  
Equations Of Motion ◽  
Mitochondrial Respiratory Chain ◽  
Proton Pumping ◽  
Rate Equations ◽  
Coupled Equations ◽  
Proton Current ◽  
Elastic Forces ◽  
Heisenberg Equations ◽  
Heisenberg Equations Of Motion

We propose a physical mechanism of conformation-induced proton pumping in mitochondrial Complex I. The structural conformations of this protein are modeled as the motion of a piston having positive charges on both sides. A negatively charged electron attracts the piston, moving the other end away from the proton site, thereby reducing its energy and allowing a proton to populate the site. When the electron escapes, elastic forces assist the return of the piston, increasing proton site energy and facilitating proton transfer. We derive the Heisenberg equations of motion for electron and proton operators and rewrite them in the form of rate equations coupled to the phenomenological Langevin equation describing piston dynamics. This set of coupled equations is solved numerically. We show that proton pumping can be achieved within this model for a reasonable set of parameters. The dependencies of proton current on geometry, temperature, and other parameters are examined.

scholarly journals Five decades of research on mitochondrial NADH-quinone oxidoreductase (complex I)

2018 ◽  
Vol 399 (11) ◽  
pp. 1249-1264 ◽  
Author(s):  
Tomoko Ohnishi ◽  
S. Tsuyoshi Ohnishi ◽  
John C. Salerno
Keyword(s):  
Electron Transfer ◽  
Respiratory Chain ◽  
Complex I ◽  
Proton Translocation ◽  
Atp Synthesis ◽  
Mitochondrial Respiratory Chain ◽  
Proton Pumping ◽  
Entry Site ◽  
Quinone Oxidoreductase ◽  
Terminal Electron Acceptor

AbstractNADH-quinone oxidoreductase (complex I) is the largest and most complicated enzyme complex of the mitochondrial respiratory chain. It is the entry site into the respiratory chain for most of the reducing equivalents generated during metabolism, coupling electron transfer from NADH to quinone to proton translocation, which in turn drives ATP synthesis. Dysfunction of complex I is associated with neurodegenerative diseases such as Parkinson’s and Alzheimer’s, and it is proposed to be involved in aging. Complex I has one non-covalently bound FMN, eight to 10 iron-sulfur clusters, and protein-associated quinone molecules as electron transport components. Electron paramagnetic resonance (EPR) has previously been the most informative technique, especially in membranein situanalysis. The structure of complex 1 has now been resolved from a number of species, but the mechanisms by which electron transfer is coupled to transmembrane proton pumping remains unresolved. Ubiquinone-10, the terminal electron acceptor of complex I, is detectable by EPR in its one electron reduced, semiquinone (SQ) state. In the aerobic steady state of respiration the semi-ubiquinone anion has been observed and studied in detail. Two distinct protein-associated fast and slow relaxing, SQ signals have been resolved which were designated SQNfand SQNs. This review covers a five decade personal journey through the field leading to a focus on the unresolved questions of the role of the SQ radicals and their possible part in proton pumping.

scholarly journals Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sh. Saedi ◽  
F. Kheirandish
Keyword(s):  
Density Matrix ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Characteristic Functions ◽  
Matrix Elements ◽  
Exact Density ◽  
Quadratic Hamiltonian ◽  
Heisenberg Equations ◽  
Reduced Density ◽  
Heisenberg Equations Of Motion

AbstractFor a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations of motion and operator calculus. The special and limiting cases are discussed.

scholarly journals Mechanistic insight from the crystal structure of mitochondrial complex I

Science ◽  
2015 ◽  
Vol 347 (6217) ◽  
pp. 44-49 ◽  
Author(s):  
Volker Zickermann ◽  
Christophe Wirth ◽  
Hamid Nasiri ◽  
Karin Siegmund ◽  
Harald Schwalbe ◽  
...  
Keyword(s):  
Complex I ◽  
Protein Complexes ◽  
Active Form ◽  
Mitochondrial Respiratory Chain ◽  
Structural Rearrangement ◽  
Proton Pumping ◽  
Mitochondrial Complex I ◽  
Mitochondrial Complex ◽  
Degenerative Disorders ◽  
Pumping Units

Proton-pumping complex I of the mitochondrial respiratory chain is among the largest and most complicated membrane protein complexes. The enzyme contributes substantially to oxidative energy conversion in eukaryotic cells. Its malfunctions are implicated in many hereditary and degenerative disorders. We report the x-ray structure of mitochondrial complex I at a resolution of 3.6 to 3.9 angstroms, describing in detail the central subunits that execute the bioenergetic function. A continuous axis of basic and acidic residues running centrally through the membrane arm connects the ubiquinone reduction site in the hydrophilic arm to four putative proton-pumping units. The binding position for a substrate analogous inhibitor and blockage of the predicted ubiquinone binding site provide a model for the “deactive” form of the enzyme. The proposed transition into the active form is based on a concerted structural rearrangement at the ubiquinone reduction site, providing support for a two-state stabilization-change mechanism of proton pumping.

Heisenberg equations of motion in the Caldirola-Montaldi procedure

1982 ◽  
Vol 67 (2) ◽  
pp. 161-172 ◽  
Author(s):  
A. Jannussis ◽  
A. Leodaris ◽  
P. Filippakis ◽  
Th. Filippakis ◽  
V. Zisis
Keyword(s):  
Equations Of Motion ◽  
Heisenberg Equations ◽  
Heisenberg Equations Of Motion

QUANTUM TREATMENT OF A TIME DEPENDENT SINGLE-TRAPPED ION INTERACTING WITH A BIMODAL CAVITY FIELD

2003 ◽  
Vol 17 (31n32) ◽  
pp. 5925-5941 ◽  
Author(s):  
MAHMOUD ABDEL-ATY ◽  
A.-S. F. OBADA ◽  
M. SEBAWE ABDALLA
Keyword(s):  
Cross Correlation ◽  
Analytic Solution ◽  
Coupling Parameter ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Field Interaction ◽  
Trapped Ion ◽  
Heisenberg Equations ◽  
Quantum Treatment ◽  
Heisenberg Equations Of Motion

In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.

The quantum mechanics of non-holonomic systems

1951 ◽  
Vol 205 (1083) ◽  
pp. 583-595 ◽  
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Equations Of Motion ◽  
Classical Dynamics ◽  
Holonomic System ◽  
Holonomic Systems ◽  
Classical Analogue ◽  
Heisenberg Equations ◽  
Subsequent Motion ◽  
Heisenberg Equations Of Motion

Interactions of a non-holonomic type are fundamentally different from interactions which can be treated as part of the Hamiltonian of a system. They usually lead to constraints which do not commute with the Hamiltonian, and cause important alterations in the development of a state vector. This paper deals with the Heisenberg equations of motion by analogy with classical dynamics using the Poisson bracket formalism of a previous paper (Eden 1951). The Schrödinger equation is investigated in co-ordinate representation, and it is shown that the wave function will have a non-integrabie phase factor or quasi phase. The quasi phase leads to an indefiniteness in the wave function, but does not violate the fundamental laws of quantum mechanics nor lead to any ambiguity in the physical interpretation of the theory. The relation between the Schrödinger and the Heisenberg equations shows that the Schrödinger treatment is also consistent with the classical analogue. If there is a given initial probability that the non-holonomic system has co-ordinates q (0) r , then there will be the same probability that the wave function in the subsequent motion will be zero except in a certain region of co-ordinate space. This region is the part of co-ordinate space which is accessible in the classical theory from the point q (0) r .

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