RESUMO
The results of many experimental and theoretical works indicate that after transport of protons across the mitochondrial inner membrane (MIM) in the oxidative phosphorylation (OXPHOS) system, they are retained on the membrane-water interface in nonequilibrium state with free energy excess due to low proton surface-to-bulk release. This well-established phenomenon suggests that proton trapping on the membrane interface ensures vectorial lateral transport of protons from proton pumps to ATP synthases (proton acceptors). Despite the key role of the proton transport in bioenergetics, the molecular mechanism of proton transfer in the OXPHOS system is not yet completely established. Here, we developed a dynamics model of long-range transport of energized protons along the MIM accompanied by collective excitation of localized waves propagating on the membrane surface. Our model is based on the new data on the macromolecular organization of the OXPHOS system showing the well-ordered structure of respirasomes and ATP synthases on the cristae membrane folds. We developed a two-component dynamics model of the proton transport considering two coupled subsystems: the ordered hydrogen bond (HB) chain of water molecules and lipid headgroups of MIM. We analytically obtained a two-component soliton solution in this model, which describes the motion of the proton kink, corresponding to successive proton hops in the HB chain, and coherent motion of a compression soliton in the chain of lipid headgroups. The local deformation in a soliton range facilitates proton jumps due to water molecules approaching each other in the HB chain. We suggested that the proton-conducting structures formed along the cristae membrane surface promote direct lateral proton transfer in the OXPHOS system. Collective excitations at the water-membrane interface in a form of two-component soliton ensure the coupled non-dissipative transport of charge carriers and elastic energy of MIM deformation to ATP synthases that may be utilized in ATP synthesis providing maximal efficiency in mitochondrial bioenergetics.
RESUMO
Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic catalysis, intra-protein energy/charge transport, recognition, and allostery. To explain high effectiveness of these processes, two possible mechanisms of the long-lived excitation were proposed by H. Fröhlich and A.S. Davydov, which relate to either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with the aqueous environment. In the model, we distinguished three coupled subsystems, i.e., (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of the side-chain residuals which in turn interact with (iii) the environment, surrounding water responsible for dissipation and fluctuation in the system. It was shown that the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation which admits bifurcation into the solution corresponding to the weak-damped vibrational modes (Fröhlich-type regime) and Davydov solitons. A bifurcation parameter is derived through the strength of phonon-phonon interaction between the side-chains and hydration-shell water molecules. As shown, the energy of these excited states is pumped through the interaction of the side-chains with fluctuating water environment of the proteins. The suggested mechanism of the collective vibrational mode excitation is discussed in connection with the recent experiments on the long-lived collective protein excitations in the terahertz frequency region and vibrational energy transport pathways in proteins.
