Stochastic resonance in a proton pumping Complex I of mitochondria membranes

D Kaur,R H Blick,C Fendler,I Filonenko,L Mourokh

doi:10.1038/s41598-017-12746-0

Abstract

We make use of the physical mechanism of proton pumping in the so-called Complex I within mitochondria membranes. Our model is based on sequential charge transfer assisted by conformational changes which facilitate the indirect electron-proton coupling. The equations of motion for the proton operators are derived and solved numerically in combination with the phenomenological Langevin equation describing the periodic conformational changes. We show that with an appropriate set of parameters, protons can be transferred against an applied voltage. In addition, we demonstrate that only the joint action of the periodic energy modulation and thermal noise leads to efficient uphill proton transfer, being a manifestation of stochastic resonance.

Highlights

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Eqs (4, 5) are coupled, as the electrostatic force acting on the piston depends on the population of the center site, while the energy of this site involved in Eqs (8, 9) depends on the piston’s position, as shown in Eq (2)
The voltage applied across the membrane is 160 mV, so that the chemical potential of the source reservoir is assumed to be μs = −80 meV and the chemical potential of the drain reservoir is μd = 80 meV

Summary

The Hamiltonian of this system is given by

Where k is the elastic force constant, NM is the population of the M-site, A and Ω are the amplitude and frequency, respectively, of the periodic force associated with the electron transfer in the hydrophilic domain, ζ is the drag coefficient, and ξ is the fluctuation source (white noise) with zero mean value and the correlation function given by ξ(t)ξ(t′) = 2ζTδ(t − t′). Equations for the site populations can be derived using the equations of motion for the creation/annihilation operators of Eq (1). It was shown previously[12,13,14] that in the high-temperature limit the resulting rate equations can be written as. Protons are transferred from the reservoir with lower chemical potential to the reservoir with higher chemical potential

Results and Discussion

Summary

Author Contributions

Additional Information