A mathematical modeling of the mitochondrial proton leak via quantum tunneling

Mahmoud Abdallat; Abdallah Barjas Qaswal; Majed Eftaiha; Abdel Rahman Qamar; Qusai Alnajjar; Rawand Sallam; Lara Kollab; Mohammad Masa'deh; Anas Amayreh; Hiba Mihyar; Hesham Aboushakra; Bayan Alkelani; Rawan Owaimer; Mohannad Abd-Alhadi; Salwa Ireiqat; Fahed Turk; Ahmad Daoud; Bashar Darawsheh; Ahmad Hiasat; Majd Alhalaki; Shahem Abdallat; Salsabiela Bani Hamad; Rand Murshidi; Mahmoud Abdallat; Abdallah Barjas Qaswal; Majed Eftaiha; Abdel Rahman Qamar; Qusai Alnajjar; Rawand Sallam; Lara Kollab; Mohammad Masa'deh; Anas Amayreh; Hiba Mihyar; Hesham Aboushakra; Bayan Alkelani; Rawan Owaimer; Mohannad Abd-Alhadi; Salwa Ireiqat; Fahed Turk; Ahmad Daoud; Bashar Darawsheh; Ahmad Hiasat; Majd Alhalaki; Shahem Abdallat; Salsabiela Bani Hamad; Rand Murshidi

doi:10.3934/biophy.2024012

AIMS Biophysics

2024, Volume 11, Issue 2: 189-233. doi: 10.3934/biophy.2024012

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Research article

A mathematical modeling of the mitochondrial proton leak via quantum tunneling

1.
Department of Neurosurgery, Jordan University Hospital, School of Medicine, University of Jordan, Amman 11942, Jordan
2.
Department of Psychiatry, Jordan University Hospital, Amman 11942, Jordan (A.B.Q)
3.
Department of Neurosurgery, Jordan University Hospital, Amman 11942, Jordan
4.
School of Medicine, The Hashemite University, Zarqa 13133, Jordan. (A.R.Q)
5.
Department of Internal Medicine, Jordan University Hospital, Amman 11942, Jordan
6.
Department of General Surgery, Jordan University Hospital, Amman 11942, Jordan
7.
Department of Emergency, Jordan University Hospital, Amman 11942, Jordan
8.
Department of Family Medicine, Jordan University Hospital, Amman 11942, Jordan
9.
School of Medicine, Near East University, Nicosia, Cyprus
10.
School of Medicine, Jordan University of Science and Technology, Irbid 22110, Jordan
11.
Tver State Medical University, Ulitsa Sovetskaya, 4, Tver, Tver Oblast, Russia, 170100
12.
Cardiovascular Research Department, King's College London, London WC2R 2LS, United Kingdom
13.
School of Medicine, Yarmouk University, Irbid 21163, Jordan
14.
Hamad Medical Corporation, PO Box 3050 Doha, Qatar
15.
School of Medicine, University of Jordan, Amman 11942, Jordan
16.
School of Medicine, Xavier University, Santa Helenastraat 23, Oranjestad, Aruba
17.
Department of Dermatology, Jordan University Hospital, Amman 11942, Jordan

Received: 06 March 2024 Revised: 26 April 2024 Accepted: 27 May 2024 Published: 04 June 2024

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.
- quantum tunneling,
- quantum biology,
- mitochondria,
- proton leak,
- UCPs,
- ANTs
Citation: Mahmoud Abdallat, Abdallah Barjas Qaswal, Majed Eftaiha, Abdel Rahman Qamar, Qusai Alnajjar, Rawand Sallam, Lara Kollab, Mohammad Masa'deh, Anas Amayreh, Hiba Mihyar, Hesham Aboushakra, Bayan Alkelani, Rawan Owaimer, Mohannad Abd-Alhadi, Salwa Ireiqat, Fahed Turk, Ahmad Daoud, Bashar Darawsheh, Ahmad Hiasat, Majd Alhalaki, Shahem Abdallat, Salsabiela Bani Hamad, Rand Murshidi. A mathematical modeling of the mitochondrial proton leak via quantum tunneling[J]. AIMS Biophysics, 2024, 11(2): 189-233. doi: 10.3934/biophy.2024012

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Abstract

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.

Abbreviations

Adenosine triphosphate

ATP

Proton motive force

pmf

Adenine nucleotide translocase

ANT

Uncoupling protein

UCP

Reactive oxygen species

ROS

Adenosine diphosphate

ADT

Guanosine triphosphate

GTP

Guanosine diphosphate

GDP

Mitochondrial carrier superfamily

MCF

Inner mitochondrial membrane

IMM

Potential mean force

PMF

Intermembrane space

IMS

Electron transport chain

ETC

Data Availability Statement

The data are available upon a reasonable request from the corresponding author.

Conflict of Interest

The authors declare no conflict of interest.

Author contributions

Conceptualization, A.B.Q and M.A; methodology, A.B.Q; software, A.B.Q.; validation, A.B.Q, M.A., M.E.,A.R.Q., Q.A., R.S., L.K., M.M., A.A., H.M., H.A., B.A., R.O., M.A., S.I., F.T., A.D., B.D.,A.H., M.A., S.A., S.B.H., and R.M.; formal analysis, A.B.Q.; investigation, A.B.Q..; resources, A.B.Q, M.A., M.E.,A.R.Q., Q.A., R.S., L.K., M.M., A.A., H.M., H.A., B.A., R.O., M.A., S.I., F.T., A.D., B.D.,A.H., M.A.,S.A., S.B.H., and R.M.; data curation, A.B.Q, M.A., M.E.,A.R.Q., Q.A., R.S., L.K., M.M., A.A., H.M., H.A., B.A., R.O., M.A., S.I., F.T., A.D., B.D.,A.H., M.A., S.A., S.B.H., and R.M.; writing—original draft preparation, A.B.Q.; writing—review and editing, A.B.Q, M.A., M.E.,A.R.Q., Q.A., R.S., L.K., M.M., A.A., H.M., H.A., B.A., R.O., M.A., S.I., F.T., A.D., B.D., A.H., M.A., S.A., S.B.H., and R.M.; visualization, A.B.Q.; supervision, M.A. and R.M..; project administration, M.A. and R.M. All authors have read and agreed to the published version of the manuscript.

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