Loading [MathJax]/jax/output/SVG/jax.js
Search Advanced

AIMS Biophysics

2024, Volume 11, Issue 2: 189-233. doi: 10.3934/biophy.2024012
Previous Article Next Article
Research article Special Issues

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

  • 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.

    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

    Related Papers:

    [1] Vo Thi Nhu Uyen, Nguyen Hong Son . Improving accuracy of surface roughness model while turning 9XC steel using a Titanium Nitride-coated cutting tool with Johnson and Box-Cox transformation. AIMS Materials Science, 2021, 8(1): 1-17. doi: 10.3934/matersci.2021001
    [2] Ayumu Yasue, Keita Hayashi, Shogo Yamamoto, Toshitsugu Inukai, Shigeru Fujimori . Influence of concrete bleeding due to mix proportion on the drilling speed of hardened surface layer. AIMS Materials Science, 2021, 8(3): 486-500. doi: 10.3934/matersci.2021030
    [3] Alexandre Lavrov, Elvia Anabela Chavez Panduro, Kamila Gawel, Malin Torsæter . Electrophoresis-induced structural changes at cement-steel interface. AIMS Materials Science, 2018, 5(3): 414-421. doi: 10.3934/matersci.2018.3.414
    [4] Bauyrzhan Rakhadilov, Lyaila Bayatanova, Sherzod Kurbanbekov, Ravil Sulyubayev, Nurdaulet Shektibayev, Nurbol Berdimuratov . Investigation on the effect of technological parameters of electrolyte-plasma cementation method on phase structure and mechanical properties of structural steel 20X. AIMS Materials Science, 2023, 10(5): 934-947. doi: 10.3934/matersci.2023050
    [5] Mohamed Samy El-Feky, Passant Youssef, Ahmed El-Tair, Mohamed Serag . Indirect sonication effect on the dispersion, reactivity, and microstructure of ordinary portland cement matrix. AIMS Materials Science, 2019, 6(5): 781-797. doi: 10.3934/matersci.2019.5.781
    [6] M. P. Lavin-Lopez, L. Sanchez-Silva, J. L. Valverde, A. Romero . CVD-graphene growth on different polycrystalline transition metals. AIMS Materials Science, 2017, 4(1): 194-208. doi: 10.3934/matersci.2017.1.194
    [7] Jing Chen, Ben J. Hanson, Melissa A. Pasquinelli . Molecular Dynamics Simulations for Predicting Surface Wetting. AIMS Materials Science, 2014, 1(2): 121-131. doi: 10.3934/matersci.2014.2.121
    [8] Temitope Awolusi, Marc Azab, Oussama Accouche, Precious Ajayi, Emeka Nnochiri . Effect of binder-aggregate ratio and glass powder on the performance of concrete cured in different media. AIMS Materials Science, 2025, 12(1): 68-84. doi: 10.3934/matersci.2025006
    [9] Marta Perez, Anais Barasinski, Benoit Courtemanche, Chady Ghnatios, Francisco Chinesta . Sensitivity thermal analysis in the laser-assisted tape placement process. AIMS Materials Science, 2018, 5(6): 1053-1072. doi: 10.3934/matersci.2018.6.1053
    [10] Lu Liao, Guo Li, Junjie Zhang . Experimental investigation of cutting parameters dependence in diamond turning of monocrystalline silicon. AIMS Materials Science, 2019, 6(5): 635-645. doi: 10.3934/matersci.2019.5.635

  • 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

    1.   Introduction

    In view of the importance of C–S–H gel formation in attaining strength in concrete, the addition of pozzolanic materials will help the cause as they are rich in SiO2 [1]. The SiO2 present in pozzolanic material will play a crucial role in secondary C–S–H gel reaction, which consumes the unreacted calcium in concrete [2]. Pozzolanic materials, in a broader sense, can be seen as two types for cement replacement, i.e., natural pozzolanic materials (e.g. bentonite) [3,4,5,6] and others are waste by-products from industries (e.g. Flyash, GGBS, and Silica Fume, etc.) [7]. While fly ash is a by-product of industries and has its physical and chemical characteristics more or less defined or consistent [8], natural pozzolanic materials will have their characteristics varied from region to region or even with in the same area sometimes [9]. One of the popular pozzolanic materials being utilized at a commercial level is fly ash [10].

    The significant sources of fly ash are in general carbon-emitting sources which may not be sustainable in the long run [11]. So, the utilization of fly ash as a pozzolanic replacement of cement in concrete may not be sustainable, and we shall look at other pozzolanic materials that are from non-carbon emitting sources. Bentonite is a mineral admixture (Clay) and had plenty of applications in various fields. The major applications include the utilization of bentonite are as drilling fluids, foundry bonds, pelletizing iron ore, cat litter and absorbents [12]. In India, the significant applications of bentonite are in drilling and foundry fields. A tremendous amount of bentonite resources were located in Rajasthan (424 million tonnes) and Gujarath (134 million tonnes) states in India [13].

    The researchers examined the strength of bentonite blended concrete (Bentocrete), variances in the results are were reported [14]. Bentonite is fine clay material; it shows different physical and chemical properties concerning the source of collection. Most of the research on Bentocrete was performed in Pakistan due to its abundance. Due to its variations in physicochemical properties, the performance of Bentocrete exhibits some uncertainties to the researchers. The average particle size of bentonite is nearly 4.32 µm [15]. It contains SiO2 in high (45–65) percentages, and it shows pozzolanic properties. The specific gravity (2.6–2.85) of bentonite is lower than that of other pozzolanic materials [16]. The Bentocrete may perform less thermal resistance compared to other concretes made with pozzolanic materials like fly ash. It is attributed to the higher Loss of ignition (5–14) values of bentonite[10,14,16]. Bentocrete generally exhibited longer setting times when compared with cement paste [17,18,19].

    The better performance of Bentocrete was observed when bentonite was preheated at 150 ℃ before mixing [3]. The strength activity index (SAI) of Bentocrete was found to be significantly less during early curing days (7 d), increased gradually in later curing days (28 d) and was better than cement concrete there onwards [3,17,20]. Mirza et al., in 2009, observed that the SAI was better up to 21 percentage of bentonite blending after 28 d of curing because the pozzolans will actively participate in reaction in lateral ages [21]. The workability of bentonite blended concrete was decreased, inversely proportional to the percentage of blending [5]. Utilization of little amounts (1–2%) of sodium bentonite improves the workability of concrete upon proper mixing [12]. The water absorption of bentonite blended concrete was lesser than that of conventional concrete [3,4,22].

    100% substitution of cement in Bentocrete will have feeble strength because of scarcity in binding agents like CaO (Citation). It is generally suggested that the replacement of cement in Bentocrete shall be in the range of 5–20% and should not be beyond 30% [23,24,25,26]. Bentocrete has a very little modulus of rupture values [3] and higher in the Fleuxural strength value [27,28]. Bentonite substitution (30–40%) increased the performance of concrete against Sulphate attack (Na2SO4 and MgSO4) [3,29]. There was an increment in results was observed against acid attack (H2SO4 and HCl) [4,6]. Ventura et al. conducted tests to determine the effect of bentonite on corrosion protection of steel reinforcement, reported that bentonite addition increases the corrosion protection to steel [30]. Xie et al. held experiments by utilization of bentonite slurry, evaluated the mechanical properties of foamed concrete, almost the same strength were reported for the control mix, and 10% bentonite replaced mix [31].

    Model advancement included the utilization of Response Surface Methodology (RSM) employing theories of mathematical and statistical analysis techniques between variables and responses [32]. Moreover, RSM was utilized for the optimization of the wanted set of objectives, either independent variables or responses [33,34]. RSM has additionally was used to implement multi-objective optimization in different concrete materials [35,36]. Bashar et al. performed multi-objective optimization to accomplish a connection between variables and responses of the properties of roller-compacted concrete by keeping fly ash content as constant, considering the combined effect of both crumb rubber and nano-silica [37]. Mohammed et al. utilized RSM to attain a relationship between variables (fly ash, nano-silica and superplasticizer) and responses (flow value, setting time and compressive strength) [38]. Baris et al. developed a graphical interface by utilizing RSM to determine the optimal weight of agammaegates [20]. Geo et al. performed multi-response optimization by keeping alkali activator concentration and liquid-solid ratio as variables, 2 h and 3 h curing as responses [39]. Long et al. performed multi-objective optimization by restraining action of corrosion, fatigue and fiber content as independent variables and compressive strength, flexural strength and dynamic elastic modulus as responses [40].

    In general, the bentonite will attain its normal consistency at more water consumption than that of cement and fly ash due to its high-water absorption capacity. This will have an impact on water-cement ratios to be used during concrete mix design [21]. So, the current research on the effect of water cement-ratio on workability, compressive strength, split tensile strength, flexural strength and durability of concrete with different proportions of cement replacements with bentonite. The role of bentonite and water-cement ratio was assessed based on the RSM. Also, the study attempts to compare the costs involved in using bentonite as a replacement for cement.

    2.   Materials and methods

    2.1.   Materials

    In this research OPC-43 grade cement was used as per ASTM C150M, bentonite was collected from Unique bleaching clay (17°14ʹ27ʺN and 77°35ʹ14ʺE), Tandur (southern region of India). Table 1 shows the chemical analysis and physical properties of bentonite and cement. The quality of the water used for this study was within limits as per ASTM C1602M. In this study, the fine agammaegate and coarse agammaegate was used as per the standard procedure ASTM C33/C33M-18.

    Table 1.  Chemical analysis and physical properties of bentonite and cement.
    S. No. Component Chemical composition%
    Bentonite Cement
    1 SiO2 51.11 18.6
    2 Al2O3 16.38 8.17
    3 CaO 7.12 62.5
    4 MgO 7.57 1.43
    6 Fe2O3 7.65 3.26
    7 K2O 1.34 1.09
    8 Na2O 0.29 0.71
    9 P2O5 0.29 0.07
    10 MnO 0.14 -
    11 V2O5 0.07 -
    12 TiO2 1.29 -
    13 SO3 - 2.63
    Physical properties
    14 Blain fineness (cm2/gm) 1730 4750
    15 Specific gravity 3.12 2.79
    16 Initial setting time (min) - 90
    17 Final setting time (min) - 345
    18 Loss on Ignition 6.75 1.23
     | Show Table
    DownLoad: CSV
    2.1.1.   SEM and XRD analysis of bentonite

    The XRD analysis was performed by using X-Pert X-ray Diffractometer of PANalytical, model number: PW 3040/00. The investigation was conducted at a 2-theta range of 10–80 with a step size of 0.5 and a 5 degrees/min scan rate. The results (Figure 1) have shown different phases that can be further identified as five mineral crystalline structures. The calcite mineral has established a prominent presence in the XRD. Scanning electron microscopy (SEM) images were obtained by using Nova Nano SEM/FEI for further pursuit. The SEM images (Figure 2) have also shown the presence of crystalline structures in the bentonite sample.

    Figure 1.  XRD Analysis of bentonite.
    DownLoad: Full-Size Img PowerPoint
    Figure 2.  SEM Analysis of bentonite.
    DownLoad: Full-Size Img PowerPoint

    2.2.   Testing of specimens

    The standard consistency test was conducted on cement paste to determine the optimum water content for getting maximum strength with the Vicat apparatus as per standard procedure ASTM C187. Compressive strength of cement mortar tested for all mixes as per ASTM C109. The workability of all Bentocrete mixes were determined by slump cone test, and compaction factor test as per standard procedures ASTM C143 and IS 1199:1959. For determination of compressive strength, a total number of 396 concrete cubes (150 mm × 150 mm × 150 mm) were cast and tested to failure at different ages of concrete (7, 28 and 56 d) as per the standard procedure ASTM C39. Split tensile strength test was performed to determine the split tensile strength of Bentocrete mixes as per the standard procedure ASTM C496, a total number of 132 cylinders (150 mm × 300 mm) were cast and tested to failure after 28 d curing. Flexural strength test was performed to determine the flexural strength as per the standard procedure ASTM C78, a total number of 132 specimens (150 mm × 150mm × 700 mm) were cast and tested to failure (third-point loading) after 28 d curing. Rapid chloride ion penetration test was performed to determine chloride ion penetration into Bentocrete as per standard procedure ASTM C 1202-97. A total number of 528 specimens, 44 sets (a set include four samples) were tested against chloride ion permeability after 7, 28 and 56 curing; respectively, Figure 3 represents the rapid chloride penetration test setup. The mix design of each mix was prepared as per ACI committee 211; the details of each blend were shown in Table 2.

    Figure 3.  Setup for rapid chloride penetration test.
    DownLoad: Full-Size Img PowerPoint
    Table 2.  The mix design details of all mixes.
    Si No. Mix name Cement (kg) Bentonite (kg) Fine aggregate (kg) Coarse aggregate (kg) Water (L) Ratio
    1 CM60 320 0 819.299 1077.072 192 1:2.56:3.37
    2 CM61 320 0 819.265 1068.34 195.2 1:2.56:3.34
    3 CM62 320 0 819.197 1059.643 198.4 1:2.56:3.31
    4 CM63 320 0 819.096 1050.981 201.6 1:2.56:3.28
    5 CM64 320 0 818.961 1042.355 204.8 1:2.56:3.26
    6 CM65 320 0 818.793 1033.763 208 1:2.56:3.23
    7 CM66 320 0 818.592 1025.207 211.2 1:2.56:3.20
    8 CM67 320 0 818.357 1016.685 214.4 1:2.56:3.18
    9 CM68 320 0 818.088 1008.088 217.6 1:2.56:3.15
    10 CM69 320 0 817.787 999.748 220.8 1:2.56:3.12
    11 CM70 320 0 817.452 991.332 224 1:2.55:3.10
    12 10BC60 288 32 818.145 1075.548 192 1:2.56:3.36
    13 10BC61 288 32 815.54 1063.482 195.2 1:2.55:3.32
    14 10BC62 288 32 815.68 1055.8 198.4 1:2.55:3.30
    15 10BC63 288 32 816.27 1047.365 201.6 1:2.55:3.27
    16 10BC64 288 32 815.18 1037.55 204.8 1:2.55:3.24
    17 10BC65 288 32 815.23 1029.27 208 1:2.55:3.22
    18 10BC66 288 32 814.98 1019.54 211.2 1:2.55:3.19
    19 10BC67 288 32 814.77 1012.23 214.4 1:2.55:3.16
    20 10BC68 288 32 814.48 1003.74 217.6 1:2.55:3.14
    21 10BC69 288 32 814.169 995.325 220.8 1:2.54:3.11
    22 10BC70 288 32 816.29 994.29 224 1:2.55:3.11
    23 20BC60 256 64 812.346 1067.931 192 1:2.54:3.34
    24 20BC61 256 64 812.215 1058.625 195.2 1:2.54:3.31
    25 20BC62 256 64 812.18 1050.568 198.4 1:2.54:3.28
    26 20BC63 256 64 812.04 1041.939 201.6 1:2.54:3.26
    27 20BC64 256 64 811.827 1034.547 204.8 1:2.54:3.23
    28 20BC65 256 64 811.783 1024.787 208 1:2.54:3.20
    29 20BC66 256 64 811.689 1016.561 211.2 1:2.54:3.18
    30 20BC67 256 64 811.263 1008.368 214.4 1:2.54:3.15
    31 20BC68 256 64 810.885 988.38 217.6 1:2.53:3.09
    32 20BC69 256 64 810.552 990.903 220.8 1:2.53:3.10
    33 20BC70 256 64 810.185 982.52 224 1:2.53:3.07
    34 30BC60 224 96 812.513 1059.536 192 1:2.54:3.31
    35 30BC61 224 96 812.415 1050.87 195.2 1:2.54:3.28
    36 30BC62 224 96 812.285 1042.241 198.4 1:2.54:3.26
    37 30BC63 224 96 811.921 1039.418 201.6 1:2.54:3.25
    38 30BC64 224 96 811.544 1029.841 204.8 1:2.54:3.22
    39 30BC65 224 96 811.229 1020.299 208 1:2.54:3.19
    40 30BC66 224 96 811.088 1011.792 211.2 1:2.53:3.16
    41 30BC67 224 96 810.87 1003.914 214.4 1:2.53:3.14
    42 30BC68 224 96 810.53 995.77 217.6 1:2.53:3.11
    43 30BC69 224 96 810.282 987.66 220.8 1:2.53:3.09
    44 30BC70 224 96 810.007 985.457 224 1:2.53:3.08
     | Show Table
    DownLoad: CSV

    2.3.   Specimen designation

    Two types of nomenclatures were framed for simple identification of the mixes. Each specimen was represented by the percentage of partial replacement followed by bentonite cement (BC) followed by water/cement ratio multiplied with 100. For example, 20BC68 represents 20% of cement was replaced by bentonite with 0.68 as water/cement ratio, 10BC represents 10% of cement was replaced by calcium bentonite, control mix (CM) represents 0BC hence no blending of bentonite in that mix.

    3.   Results and discussion

    3.1.   Normal consistency of cement paste

    The determination of normal consistency for any cement is essential, the water content of paste which will produce the desired consistency. The consistency of cement was directly proportional to the percentage of bentonite blended, as shown in Figure 4. There is a strong linear correlation between percentage replacement of bentonite and normal consistency with R2 values reaching up to 0.99. According to the analysis, there is an approximately 2.5% increase in normal consistency for every 1% increase in cement replacement with bentonite; this attributes the bentonite's high water absorption capacity [12].

    Figure 4.  Normal consistency of bentonite mixtures.
    DownLoad: Full-Size Img PowerPoint

    3.2.   Compressive strength of cement mortar

    The compressive strength of hardened cement is the property of the material that is required for structural use. Figure 5 shows the compressive strengths of hardened cement mixes; maximum compressive strength was demonstrated by 10% bentonite blended mix. The strength of hardened cement mixes was examined as per standard procedure IS:650. In cement mortar mixes, 10BC and 30BC exhibits 6.41% higher and 17.00% less compressive strengths than CM.

    Figure 5.  Compressive strength (MPa) of mixes at different ages.
    DownLoad: Full-Size Img PowerPoint

    3.3.   Workability of concrete

    The workability was delineated as determination of the ease of placement and resistance to the segregation of concrete. The workability was determined by the help of a slump cone test, and compaction factor test, slump values and compaction factor were measured for each mix. 45 mm slump value was fixed by the help of trail mixes for CM61, remaining values measured while casting of each mix. The results were drawn after testing of all specimens (section testing of specimens), Figure 6 shows the slump values of all mixes.

    Figure 6.  Slump values of all bentonite mixes.
    DownLoad: Full-Size Img PowerPoint

    The degree of compaction is known as compaction factor, the ratio of achieved density of the concrete in the same at compacted state. The results were taken after performing the test for all mixes; Figure 7 shows the compaction factor values. The workability of blended mixes was reduced as the percentage of bentonite blending increased. This can be attributed to the high-water absorption capacity of bentonite. The lowest workability was observed with a 30BC60 mix. The causative is the combination of higher replacement (30%) of cement with bentonite and low water-cement ratio (0.60). Simultaneously, the highest workability was observed with CM70. The workability of blended mixes was reduced as the percentage of bentonite blending increased.

    Figure 7.  Compaction factor values of all bentonite mixes.
    DownLoad: Full-Size Img PowerPoint

    3.4.   Compressive strength of concrete

    The compressive strength of concrete is always a crucial aspect of structural design and is specified for compliance purposes. The compressive strength of all mixes is inversely proportional to the water-cement ratio as per the basic principle of concrete [21].

    Figure 8 shows the compressive strength of a set of all specimens (Table 2) after seven days of curing. CM mixes shown higher compressive strength among was all, because of 43-grade cement's property to gain early age strength [21]. The pozzolanic materials like bentonite will tend not to have early age compressive strength. Thus, the mixes with high bentonite show less compressive strength.

    Figure 8.  Compressive strength of bentonite mixes at the age of 7 d.
    DownLoad: Full-Size Img PowerPoint

    Figure 9 shows the compressive strength of a set of all specimens (Table 2) after 28 d of curing. There is an improvement in the compressive strength of bentonite mixes as the curing days were increased. The compressive strength of 10BC mixtures increases and nearly equals with CM. The occurrence of pozzolanic reactions may result in the improvement of the compressive strength for all bentonite mixes. The increase in the percentage of strength for 20BC and 30BC was observed, but those mixes showed lower compressive strength than that of CM.

    Figure 9.  Compressive strength of bentonite mixes at the age of 28 d.
    DownLoad: Full-Size Img PowerPoint

    Figure 10 shows the compressive strength of a set of all specimens (Table 2) after 56 d of curing. The compressive strength of 10BC and 20BC shown higher than CM. 10BC and 30BC shown highest and lowest compressive strength among all mixes, whereas 20BC shown greater than CM. A little amount of strength gain percentage was observed for CM. It can be assessed that bentonite fills the voids among cement particles in concrete (pore filling effect) and a pozzolanic reaction is taking place between inactive calcium in OPC and excess of SiO2 present in bentonite.

    Figure 10.  Compressive strength of bentonite mixes at the age of 56 d.
    DownLoad: Full-Size Img PowerPoint

    The compressive strength needs to increase as workability decreases, as per the fundamentals of concrete. In this study, this fundamental was applied up to 20% replacement of bentonite. It can be attributed to pore filling effect and pozzolanic reaction with bentonite. The introduction of bentonite in 30 percentage does not follow the fundamentals. Those mixes show a decrease in strength as well as workability. The causative is less CaO content presence in bentonite than cement (Table 1) and the assimilating bentonite behaviour.

    3.5.   Split tensile strength of concrete

    In the split tensile strength test, a cylinder was placed in compression testing, and it was tested up to failure. Figure 11 shows the split tensile strength of all bentonite mixes. CM has demonstrated better performance than other mixes; equal split tensile strength was observed in a few 10BC mixes compared with CM. 30BC shown lower performance among all mixes. It was observed that split tensile strength was decreasing in the case of more than 20% of bentonite blending. It can be assessed that the poor bond formation between bentonite and cement particles.

    Figure 11.  Split tensile strength of bentonite mixes.
    DownLoad: Full-Size Img PowerPoint

    3.6.   Flexural strength of concrete

    In the flexural strength test, a plain concrete beam is subjected to flexure using third-point loading test. Figure 12 shows the flexural strength of all bentonite mixes. CM exhibits better flexural strength than other mixes comparatively. Few 10BC mixes shown equal flexural strength. The flexural strength of concrete is inversely proportional to bentonite blending (after 20%) and W/C ratio. It can be attributed to the week bond formation between bentonite and cement particles.

    Figure 12.  Flexural strength of bentonite mixes.
    DownLoad: Full-Size Img PowerPoint

    3.7.   Rapid chloride penetration test (RCPT) of concrete

    Figure 13 shows the average charge (Columbus) passed through 4 cells after seven days of curing. CM exhibits less Charge Passed (CP) (1200–1250) through it compared to others. All bentonite substituted mixes shown poor performance against chloride ion penetration at the age of seven days. This result may be because the pozzolanic reaction will not happen within seven days. The chloride ion penetration was decreased by increasing the water-cement ratio.

    Figure 13.  Charge passed in concrete after 7 d curing.
    DownLoad: Full-Size Img PowerPoint

    Figure 14 shows the average charge passed through 4 cells after 28 d curing. 10 BC exhibits less CP (360–410) through it comparatively with other mixes. 30 BC has shown abysmal performance against chloride ion penetration. This may attribute the occurrence of pozzolanic reaction at lateral (28 d) ages.

    Figure 14.  Charge passed in concrete after 28 d curing.
    DownLoad: Full-Size Img PowerPoint

    Figure 15 shows the average charge passed through 4 cells after 56 d curing. 10 BC exhibits less CP (290–320) through it comparatively with other mixes. CM and 20BC performed 30 BC shown abysmal performance against chloride ion penetration. This may attribute the occurrence of pozzolanic reaction at lateral (56 d) ages.

    Figure 15.  Charge passed in concrete after 56 d curing.
    DownLoad: Full-Size Img PowerPoint

    3.8.   Cost analysis

    Lesser cost is one of the reasons to blend bentonite with cement. The bentonite was brought from the company named "Unique Bleaching Clay" located at Tandur in Telangana state in India. The cost comparison was made according to "Standard Schedules of Rates" (SSR), Andhra Pradesh-2018-19, India, the points of interest of the cost of all blends have appeared in Table 3.

    Table 3.  Cost comparison of all mixes per cubic meter.
    Description of item CM 10BC 20BC 30BC
    Quantity Price Quantity Price Quantity Price Quantity Price
    OPC (kg) 320 2240 288 2016 256 1026 224 896
    Calcium bentonite (kg) 0 0 32 32 64 64 96 96
    Fine aggregate (m3) 819.2 148.7 818.1 148.7 812.3 148.7 812.5 148.7
    Coarse aggregate (m3) 1077.0 487.6 1075.5 487.6 1067.9 487.6 1059.5 487.6
    Total price in Indian rupees 2876.3 2684.3 2492.4 2312.9
     | Show Table
    DownLoad: CSV

    4.   RSM modeling

    4.1.   Development of the model

    In RSM, various types of models are available like Central Composite, Box Behnken and optimal (custom) in a randomized design. Choosing a model type depends on the nature of accessible information and levels for each factor. For the most part, for an experiment matrix that has been as of now built up, the historical data or user-defined model or is applied for the development and investigation of a model [41]. The linear model is signified by the first order as shown in Eq 1. Similarly, polynomial models were signified by the second order as shown in Eq 2.

    y=β0+β1X1+β2X2+β3X3+⋯⋯+βnXn+ε (1)

    where y represents the response modeled, β0 is the y-intercept at X1 = X2 = 0, whereas β1 and β2 are the coefficients of first and second independent variables, respectively, while X1 and X2 are the first and second independent variables, and ε is the error.

    y=β0+∑ki=1βiXi+∑ki=1βiiX2j+∑kj=2∑j=1i=1βijXiXj+ε (2)

    where y represents the response's model, the coded values of independent variables are represented by Xi and Xj, i and j are the coefficients for the linear and quadratic equations, respectively, βo stands for the y-intercept at X1 = X2 = 0, whereas k represents the number of independent variables used in the analyses, and ε is the error [41].

    4.2.   Mix matrix design

    Design Expert 11.0 version was used for modelling in this investigation. The design of experiments was generated using central composite design method based on two variables (bentonite replacement and W/C ratio). Four levels of % of bentonite replacement (0%, 10%, 20% and 30%) and ten levels of W/C ratio (0.60, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69 and 0.70) were used. A total number of 44 combinations of mixtures was developed in RSM. Table 4 represents the details of all mixtures and their combination of variables. The responses of bentonite blended concrete (slump value, compaction factor, CS 28 d, split tensile strength, flexural strength and 28 d CP) were determined for all mixtures, considered for RSM analysis and optimization.

    Table 4.  Design matrix of experiments and responses.
    Run F:1 F:2 R1 R2 R3 R4 R5 R6
    Bentonite substitution (%) W/C Slump value (mm) Compactor factor CS 28 d (MPa) Split tensile strength (MPa) Flexural strength (MPa) CP 28 d (Columbus)
    1 0 0.6 30 0.82 34.65 3.54 4.63 488.3
    2 0 0.61 45 0.85 32.04 3.40 4.43 494.3
    3 0 0.62 65 0.88 30.09 3.26 4.25 495.0
    4 0 0.63 75 0.91 28.54 3.26 4.06 503.8
    5 0 0.64 90 0.92 26.22 3.11 3.89 505.5
    6 0 0.65 115 0.93 24.44 2.97 3.69 506.5
    7 0 0.66 125 0.94 23.07 2.83 3.54 507.0
    8 0 0.67 140 0.95 22.22 2.83 3.47 508.0
    9 0 0.68 165 0.97 21.33 2.69 3.38 511.5
    10 0 0.69 210 0.98 20.00 2.69 3.24 519.5
    11 0 0.7 235 0.99 19.03 2.55 3.13 532.0
    12 10 0.6 5 0.74 32.23 3.40 4.45 367.5
    13 10 0.61 10 0.76 31.62 3.40 4.38 369.5
    14 10 0.62 30 0.81 30.12 3.26 4.23 379.0
    15 10 0.63 50 0.84 28.63 3.26 4.12 384.0
    16 10 0.64 75 0.88 26.02 3.11 3.83 388.3
    17 10 0.65 95 0.9 24.09 2.83 3.66 390.8
    18 10 0.66 110 0.92 22.96 2.83 3.54 391.0
    19 10 0.67 120 0.93 21.85 2.83 3.43 396.0
    20 10 0.68 135 0.94 20.34 2.69 3.28 403.3
    21 10 0.69 160 0.95 19.32 2.55 3.17 407.0
    22 10 0.7 195 0.97 17.99 2.41 3.03 411.8
    23 20 0.6 0 0.72 28.33 3.26 4.08 521.5
    24 20 0.61 0 0.74 27.44 3.11 3.96 529.5
    25 20 0.62 10 0.76 26.11 3.11 3.84 532.5
    26 20 0.63 15 0.78 25.22 2.97 3.74 533.0
    27 20 0.64 45 0.82 24.56 2.97 3.68 535.5
    28 20 0.65 60 0.85 22.05 2.83 3.46 540.8
    29 20 0.66 70 0.88 21.12 2.69 3.33 541.8
    30 20 0.67 85 0.9 19.96 2.55 3.21 543.8
    31 20 0.68 95 0.92 18.34 2.41 3.07 545.8
    32 20 0.69 110 0.93 17 2.41 2.91 555.8
    33 20 0.7 135 0.94 15.37 2.26 2.72 563.5
    34 30 0.6 0 0.71 25.03 2.97 3.78 655.8
    35 30 0.61 0 0.72 23.96 2.83 3.63 657.0
    36 30 0.62 5 0.74 22.45 2.83 3.5 659.3
    37 30 0.63 10 0.76 21.23 2.69 3.35 673.3
    38 30 0.64 20 0.79 19.43 2.60 3.17 676.3
    39 30 0.65 30 0.82 18.96 2.55 3.1 677.5
    40 30 0.66 45 0.84 17.2 2.41 2.91 683.0
    41 30 0.67 50 0.86 16.99 2.41 2.87 683.5
    42 30 0.68 70 0.89 15.62 2.26 2.74 684.3
    43 30 0.69 85 0.91 14.6 2.12 2.58 689.5
    44 30 0.7 95 0.93 13.33 2.12 2.47 691.8
     | Show Table
    DownLoad: CSV

    4.3.   Analysis of variance

    The summaries of ANOVA for the responses of the Bentocrete properties (slump value, compaction factor, CS 28 d, split tensile strength, flexural strength and 28 d CP) were shown in Tables 5–11. The models' F-values are 553.10,363.29,550.10,381.30,609.69 and 5635.79 for slump value, compaction factor, CS 28 d, split tensile strength, flexural strength and 28 d CP respectively, pointing all models to be significant, with 0.01% chances for all models. The Confidence Interval (CI) of the data presented in the model is 95%. This could be used to find out the significance of all the models and their terms. For slump value and split tensile strength, a quadratic model was used, and A, B, AB, A2, B2 were the terms, as per the p-value of 0.05. The significant models of compaction factor, CS 28 d, flexural strength, and CP 28 d, and its terms were cubic and, A, B, AB, A2, B2, A2B, AB2, A3 and, B3, respectively, based on the p-values were less than 0.05.

    Table 5.  ANOVA for Quadratic model, R1: slump value.
    Source Sum of squares df Mean square F-value p-value
    Model 1.550E + 05 5 31007.90 553.10 < 0.0001 significant
    A-bentonite replacement 41319.20 1 41319.20 737.02 < 0.0001
    B-water/cement ratio 1.063E + 05 1 1.063E + 05 1896.65 < 0.0001
    AB 5923.68 1 5923.68 105.66 < 0.0001
    A2 205.11 1 205.11 3.66 0.0633
    B2 1260.61 1 1260.61 22.49 < 0.0001
    Residual 2130.37 38 56.06
    Cor total 1.572E + 05 43
     | Show Table
    DownLoad: CSV
    Table 6.  ANOVA for Cubic model, R2: compaction factor.
    Source Sum of squares df Mean square F-value p-value
    Model 0.2826 9 0.0314 363.29 < 0.0001 significant
    A-bentonite replacement 0.0068 1 0.0068 78.30 < 0.0001
    B-water/cement ratio 0.0332 1 0.0332 384.19 < 0.0001
    AB 0.0030 1 0.0030 35.00 < 0.0001
    A2 0.0012 1 0.0012 13.91 0.0007
    B2 0.0027 1 0.0027 31.56 < 0.0001
    A2B 0.0017 1 0.0017 19.44 < 0.0001
    AB2 0.0011 1 0.0011 12.23 0.0013
    A3 4.091E-06 1 4.091E-06 0.0473 0.8291
    B3 0.0001 1 0.0001 0.8009 0.3771
    Residual 0.0029 34 0.0001
    Cor total 0.2856 43
     | Show Table
    DownLoad: CSV
    Table 7.  ANOVA for Cubic model, R3: CS 28 d.
    Source Sum of squares df Mean square F-value p-value
    Model 1150.93 9 127.88 550.10 < 0.0001 significant
    A-bentonite replacement 24.93 1 24.93 107.24 < 0.0001
    B-water/cement ratio 113.81 1 113.81 489.57 < 0.0001
    AB 9.70 1 9.70 41.74 < 0.0001
    A2 20.78 1 20.78 89.40 < 0.0001
    B2 2.49 1 2.49 10.71 0.0025
    A2B 0.4925 1 0.4925 2.12 0.1547
    AB2 2.54 1 2.54 10.94 0.0022
    A3 1.19 1 1.19 5.12 0.0302
    B3 0.1151 1 0.1151 0.4951 0.4865
    Residual 7.90 34 0.2325
    Cor total 1158.84 43
     | Show Table
    DownLoad: CSV
    Table 8.  ANOVA for Quadratic model, R4: split tensile strength.
    Source Sum of squares df Mean square F-value p-value
    Model 5.66 5 1.13 381.30 < 0.0001 significant
    A-bentonite replacement 1.46 1 1.46 492.99 < 0.0001
    B-water/cement ratio 4.08 1 4.08 1374.26 < 0.0001
    AB 0.0052 1 0.0052 1.74 0.1954
    A2 0.1108 1 0.1108 37.31 < 0.0001
    B2 0.0007 1 0.0007 0.2208 0.6411
    Residual 0.1129 38 0.0030
    Cor total 5.78 43
     | Show Table
    DownLoad: CSV
    Table 9.  ANOVA for Cubic model, R5: flexural strength.
    Source Sum of squares df Mean square F-value p-value
    Model 12.07 9 1.34 609.69 < 0.0001 significant
    A-bentonite replacement 0.2878 1 0.2878 130.83 < 0.0001
    B-water/cement ratio 1.12 1 1.12 510.87 < 0.0001
    AB 0.0305 1 0.0305 13.86 0.0007
    A2 0.2490 1 0.2490 113.18 < 0.0001
    B2 0.0114 1 0.0114 5.17 0.0294
    A2B 0.0006 1 0.0006 0.2902 0.5936
    AB2 0.0172 1 0.0172 7.81 0.0085
    A3 0.0139 1 0.0139 6.33 0.0168
    B3 0.0006 1 0.0006 0.2662 0.6093
    Residual 0.0748 34 0.0022
    Cor total 12.15 43
     | Show Table
    DownLoad: CSV
    Table 10.  ANOVA for Cubic model, R6: CP 28 d.
    Source Sum of squares df Mean square F-value p-value
    Model 4.626E + 05 9 51397.11 5635.79 < 0.0001 significant
    A-bentonite replacement 1.050E + 05 1 1.050E+05 11509.10 < 0.0001
    B-water/cement ratio 388.24 1 388.24 42.57 < 0.0001
    AB 0.0525 1 0.0525 0.0058 0.9399
    A2 1.745E+05 1 1.745E + 05 19135.34 < 0.0001
    B2 0.4838 1 0.4838 0.0531 0.8192
    A2B 8.67 1 8.67 0.9502 0.3365
    AB2 38.92 1 38.92 4.27 0.0465
    A3 43851.07 1 43851.07 4808.35 < 0.0001
    B3 116.64 1 116.64 12.79 0.0011
    Residual 310.07 34 9.12
    Cor total 4.629E + 05 43
     | Show Table
    DownLoad: CSV
    Table 11.  Validation of models.
    Response R2 Adj. R2 Pred. R2 Adj.R2-Pred.R2 SD Adeq. Prec. Mean
    Slump value 0.9864 0.9847 0.9821 0.0026 7.49 85.9629 75.34
    Compaction factor 0.9897 0.9870 0.9802 0.0068 0.0093 62.4137 0.8634
    28 d CS 0.9932 0.9914 0.9873 0.0041 0.4821 91.3261 22.98
    Split tensile strength 0.9805 0.9779 0.9743 0.0036 0.0545 72.18 2.82
    Flexural strength 0.9938 0.9922 0.9889 0.0033 0.0469 96.7725 3.52
    CP 28 d 0.9993 0.9992 0.9988 0.0004 3.02 225.9156 528.03
     | Show Table
    DownLoad: CSV

    For slump value, A2 was the insignificant term and interaction in the quadratic model. The insignificant terms in compaction factor model were A3 and B3, while A2B and B3 were insignificant terms in CS 28 d cubic model, whereas the insignificant terms in split tensile strength quadratic model were AB and B2. The insignificant terms in flexural strength cubic model were A2B and B3, whereas AB, B2 and A2B were insignificant terms in CP 28 d. A few interactions were not significant in all bentonite mixes influencing factors because of their higher (>0.05) p-values. The positive and negative signs were assigned in the models and their interactions to show the effects of the variables on all bentonite mixes factors.

    The final models for slump value, compaction factor, CS 28 d, split tensile strength, flexural strength and 28 d CP of all mixes comprising all the terms are presented in Eqs 3–8, respectively.

     Slump value =+1342.72727+17.94318 A−5831.96970 B−32.81818AB+0.021591 A2+6060.60606 B2 (3)
     Compaction factor =+7.45830+0.151008 A−44.12313 B−0.563364AB+0.001302 A2+86.85606 B2−0.001955 A2 B+0.496503AB2+4.54545E−07 A3−52.93318 B3 (4)
    CS28 d=−196.85548−10.37951 A+1752.40855 B+31.98212 A B−0.039650 A2−3573.76457 B2+0.033455 A2 B+0.000245 A3+2158.11966 B3 (5)
     Spilt tensile strength =+7.73014−0.021167 A−4.40756 B+0.030625AB−0.000502 A2−4.37166 B2 (6)
     Flexural strength =−8.19684−0.856959 A+117.10348 B+2.63983AB−0.002728 A2−251.96096 B2+0.001205 A2 B−2.00117AB2+0.000027 A3+153.94328 B3 (7)
    CP28 d=−17862.46208−77.38314 A+85306.42113 B+128.13371AB+2.83872 A2−1.32425E+05 B2−0.140341 A2 B−95.25058AB2−0.047061 A3+68703.86558 B3 (8)

    The properties of formulated models of for slump value, compaction factor, CS 28 d, split tensile strength, flexural strength and 28 d CP of all mixes were presented in Table 11. The adequacy of the formulated models was validated by their degree of correlation (R2). A high degree of correlation (R2) was observed for all models based on their values were close to unity (R2 > 0.97). This shows that the experimental values slump value, compaction factor, CS 28 d, split tensile strength, flexural strength and 28 d CP cannot be represented by the models only about 1.36%, 1.03%, 0.68%, 1.95%, 0.62%, and 0.07%, respectively.

    3-dimensional (3D) response surface plot was used to illustrate the relationship between responses and independent variables. Figures 16–21 show the 3D response surface plots illustrating the relationship between responses (slump value, compaction factor, CS 28 d, split tensile strength, flexural strength and 28 d CP) and independent variables (W/C ratio and bentonite) for all mixes. The high-water absorption capacity of bentonite may have caused a rise in slump values with increasing w/c ratio, which decreases upon the addition of bentonite [12]. Bentocrete mixes exhibit Lower CS at early ages (7 d) curing, higher compressive strength at later curing period (28 d and 56 d). The reason behind this was the formation of secondary C–S–H gel since the bentonite obeys pozzolanic properties [42]. The split tensile strength and flexural strength of CM exhibits equal for 10BC for a few mixes, less strength was observed for 20BC and 30BC mixes. Bentocrete mixes display better durability upon addition of bentonite up to some extent (20%). This attributes the pore filling effect and happening of pozzolanic reaction caused by the addition of bentonite.

    Figure 16.  Response surface model for slump value.
    DownLoad: Full-Size Img PowerPoint
    Figure 17.  Response surface model for compaction factor.
    DownLoad: Full-Size Img PowerPoint
    Figure 18.  Response surface model for CS 28 d.
    DownLoad: Full-Size Img PowerPoint
    Figure 19.  Response surface model for split tensile strength.
    DownLoad: Full-Size Img PowerPoint
    Figure 20.  Response surface model for flexuleral strength.
    DownLoad: Full-Size Img PowerPoint
    Figure 21.  Response surface model for CP 28 d.
    DownLoad: Full-Size Img PowerPoint

    4.4.   Optimization

    Optimization was used with the aim of finding an optimized value among all mixes, performed by using Design Expert Software. The upper limit, lower limit and goal were set to perform the optimization, displayed in Table 12. The optimized solution was found with a desirability of 0.881, Table 13 shows the optimized Bentocrete mixes. The optimized mix was achieved at 3.92% of bentonite substitution and 0.62 W/C ratio. The optimum values of responses were 49.65 mm slump value, 0.85 compaction factor, 30.04 MPa CS 28 d, 3.28 MPa split tensile strength, 4.23 MPa flexural strength and 401.87 28 d CP.

    Table 12.  Criteria setting for optimization.
    Variables/responses Goal Lower limit Upper limit
    Bentonite replacement In range 0 30
    W/C ratio In range 0.60 0.70
    Slump value Target-50 0 235
    Compaction factor Target-0.85 0.71 173
    CS 28 d Maximize 13.33 34.65
    Split tensile strength Maximize 2.12 3.53
    Flexural strength Maximize 2.47 4.63
    28 d CP Minimize 367.5 691.75
     | Show Table
    DownLoad: CSV
    Table 13.  Optimized Bentocrete mixes.
    Bentonite replacement W-C ratio Slump value Compaction factor CS 28 d Split tensile strength Flexural strength 28 d CP
    3.92 0.62 49.65 0.85 30.04 3.28 4.23 401.87
     | Show Table
    DownLoad: CSV

    5.   Conclusions

    The following conclusions were drawn based on the experiments and analyses performed: The standard consistency of cement paste is directly proportional to the bentonite substitution. 10 BC showed maximum compressive strength among all cement mortar mixes due to pozzolanic nature of bentonite. Workability is directly proportional to W/C ratio, because of the high-water absorption capacity of bentonite. The compression strength of Bentocrete shown lesser at 7 d equals at 28 d, and higher at 56 d than cement concrete. However, Bentocrete with more than 20 percentage of bentonite exhibits lesser compressive strength than concrete at all curing periods. In split tensile strength and flexural strength, the lower performance was observed for more than 10% of bentonite substitution. The durability against chloride ion was improved for Bentocrete than cement concrete up to 20% upon curing for enough time; this attribute the pore filling effect since bentonite's particle size is lesser than cement. Cost analysis was performed, 9.91% of the cost can be cut down for Bentocrete with 20 percentage bentonite. The RSM model has fitted the experimental data with the full agreement with R2 values not less than 0.985 in all the cases. 3.92 % of bentonite substitution and 0.62 W/C ratio provided optimum solution for the intended goals with desirability of 0.881.

    Acknowledgments

    The authors are thankful to the authorities of the Koneru Lakshmaiah Education Foundation for funding this research as a part of the internal funding project scheme.

    Conflict of interest

    All authors declare no conflicts of interest in this paper.



    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.

    [1] Picard M, Taivassalo T, Gouspillou G, et al. (2011) Mitochondria: isolation, structure and function. J Physiol 589: 4413-4421. https://doi.org/10.1113/jphysiol.2011.212712
    [2] Duchen MR (2004) Roles of mitochondria in health and disease. Diabetes 1: S96-102. https://doi.org/10.2337/diabetes.53.2007.S96
    [3] Ardalan A, Smith MD, Jelokhani-Niaraki M (2022) Uncoupling proteins and regulated proton leak in mitochondria. Int J Mol Sci 23: 1528. https://doi.org/10.3390/ijms23031528
    [4] Nesci S (2023) Proton leak through the UCPs and ANT carriers and beyond: a breath for the electron transport chain. Biochimie 214: 77-85. https://doi.org/10.1016/j.biochi.2023.06.008
    [5] Jastroch M, Divakaruni AS, Mookerjee S, et al. (2010) Mitochondrial proton and electron leaks. Essays Biochem 47: 53-67. https://doi.org/10.1042/bse0470053
    [6] Bertholet AM, Kirichok Y (2022) Mitochondrial H+ leak and thermogenesis. Annu Rev Physiol 84: 381-407. https://doi.org/10.1146/annurev-physiol-021119-034405
    [7] Nicholls DG (1997) The non-Ohmic proton leak—25 years on. Biosci Rep 17: 251-257. https://doi.org/10.1023/A:1027376426860
    [8] Rupprecht A, Sokolenko EA, Beck V, et al. (2010) Role of the transmembrane potential in the membrane proton leak. Biophys J 98: 1503-1511. https://doi.org/10.1016/j.bpj.2009.12.4301
    [9] Kenwood BM, Weaver JL, Bajwa A, et al. (2014) Identification of a novel mitochondrial uncoupler that does not depolarize the plasma membrane. Mol Metab 3: 114-123. https://doi.org/10.1016/j.molmet.2013.11.005
    [10] Sack MN (2006) Mitochondrial depolarization and the role of uncoupling proteins in ischemia tolerance. Cardiovasc Res 72: 210-219. https://doi.org/10.1016/j.cardiores.2006.07.010
    [11] Padmaraj D, Pande R, Miller JH, et al. (2014) Mitochondrial membrane studies using impedance spectroscopy with parallel pH monitoring. PLoS One 9: e101793. https://doi.org/10.1371/journal.pone.0101793
    [12] Serway RA, Kirkpatrick LD Physics for Scientists and Engineers with Modern Physics James Madison University (2005). https://doi.org/10.1119/1.2342517
    [13] Calvillo L, Redaelli V, Ludwig N, et al. (2022) Quantum biology research meets pathophysiology and therapeutic mechanisms: a biomedical perspective. Quantum Rep 4: 148-712. https://doi.org/10.3390/quantum4020011
    [14] Kim Y, Bertagna F, D'souza EM, et al. (2021) Quantum biology: an update and perspective. Quantum Rep 3: 80-126. https://doi.org/10.3390/quantum3010006
    [15] Bennett JP, Onyango IG (2021) Energy, entropy and quantum tunneling of protons and electrons in brain mitochondria: relation to mitochondrial impairment in aging-related human brain diseases and therapeutic measures. Biomedicines 9: 225. https://doi.org/10.3390/biomedicines9020225
    [16] Nunn AV, Guy GW, Bell JD (2022) Thermodynamics and inflammation: insights into quantum biology and ageing. Quantum Rep 4: 47-74. https://doi.org/10.3390/quantum4010005
    [17] Slocombe L, Sacchi M, Al-Khalili J (2022) An open quantum systems approach to proton tunnelling in DNA. Commun Phys 5: 109. https://doi.org/10.1038/s42005-022-00881-8
    [18] Çelebi G, Özçelik E, Vardar E, et al. (2021) Time delay during the proton tunneling in the base pairs of the DNA double helix. Prog Biophys Mol Biol 167: 96-103. https://doi.org/10.1016/j.pbiomolbio.2021.06.001
    [19] Layfield JP, Hammes-Schiffer S (2014) Hydrogen tunneling in enzymes and biomimetic models. Chem Rev 114: 3466-3494. https://doi.org/10.1021/cr400400p
    [20] Xin H, Sim WJ, Namgung B, et al. (2019) Quantum biological tunnel junction for electron transfer imaging in live cells. Nat Commun 10: 3245. https://doi.org/10.1038/s41467-019-11212-x
    [21] Hayashi T, Stuchebrukhov AA (2010) Electron tunneling in respiratory complex I. Proc Natl Acad Sci USA 107: 19157-19162. https://doi.org/10.1073/pnas.1009181107
    [22] Hagras MA, Hayashi T, Stuchebrukhov AA (2015) Quantum calculations of electron tunneling in respiratory complex III. J Phys Chem B 119: 14637-14651. https://doi.org/10.1021/acs.jpcb.5b09424
    [23] Gray HB, Winkler JR (2003) Electron tunneling through proteins. Q Rev Biophys 36: 341-372. https://doi.org/10.1017/S0033583503003913
    [24] Qaswal AB (2019) Quantum tunneling of ions through the closed voltage-gated channels of the biological membrane: A mathematical model and implications. Quantum Rep 1: 219-225. https://doi.org/10.3390/quantum1020019
    [25] Qaswal AB, Ababneh O, Khreesha L, et al. (2021) Mathematical modeling of ion quantum tunneling reveals novel properties of voltage-gated channels and quantum aspects of their pathophysiology in excitability-related disorders. Pathophysiology 28: 116-154. https://doi.org/10.3390/pathophysiology28010010
    [26] Vorobyov I, Olson TE, Kim JH, et al. (2014) Ion-induced defect permeation of lipid membranes. Biophys. J 106: 586-597. https://doi.org/10.1016/j.bpj.2013.12.027
    [27] Aryal P, Sansom MS, Tucker SJ (2015) Hydrophobic gating in ion channels. J Mol Biol 427: 121-130. https://doi.org/10.1016/j.jmb.2014.07.030
    [28] Khavrutskii IV, Gorfe AA, Lu B (2009) Free energy for the permeation of Na+ and Cl− ions and their ion-pair through a zwitterionicdimyristoyl phosphatidylcholine lipid bilayer by umbrella integration with harmonic fourier beads. J Am Chem Soc 131: 1706-1716. https://doi.org/10.1021/ja8081704
    [29] Klesse G, Tucker SJ, Sansom MS (2020) Electric field induced wetting of a hydrophobic gate in a model nanopore based on the 5-HT3 receptor channel. ACS Nano 14: 10480-10491. https://doi.org/10.1021/acsnano.0c04387
    [30] Miyazaki T (2004) Atom Tunneling Phenomena in Physics, Chemistry and Biology. Berlin: Springer Science & Business Media. https://doi.org/10.1007/978-3-662-05900-5
    [31] Bertil H, Bertil H (2001) Ion Channels of Excitable Membranes. Sunderland: Sinauer Associates. https://doi.org/10.1016/0014-5793(92)81020-m
    [32] Lee JW (2019) Electrostatically localized proton bioenergetics: better understanding membrane potential. Heliyon 5: e01961. https://doi.org/10.1016/j.heliyon.2019.e01961
    [33] Silverstein TP (2022) A critique of the capacitor-based “transmembrane electrostatically localized proton” hypothesis. J Bioenerg Biomembr 54: 59-65. https://doi.org/10.1007/s10863-022-09931-w
    [34] Qaswal AB (2020) Quantum electrochemical equilibrium: quantum version of the Goldman–Hodgkin–Katz equation. Quantum Rep 2: 266-277. https://doi.org/10.3390/quantum2020017
    [35] Lee JW (2020) Protonic capacitor: elucidating the biological significance of mitochondrial cristae formation. Sci Rep 10: 10304. https://doi.org/10.1038/s41598-020-66203-6
    [36] Lee C, Wallace DC, Burke PJ (2023) Super-resolution imaging of voltages in the interior of individual, vital mitochondria. Acs Nano 18: 1345-1356. https://doi.org/10.1021/acsnano.3c02768
    [37] Nicholls D (2002) Mitochondrial bioenergetics, aging, and aging-related disease. Sci Aging Knowl Environ 2002: pe12. https://doi.org/10.1126/sageke.2002.31.pe12
    [38] Norat P, Soldozy S, Sokolowski JD, et al. (2020) Mitochondrial dysfunction in neurological disorders: Exploring mitochondrial transplantation. NPJ Regen Med 5: 22. https://doi.org/10.1038/s41536-020-00107-x
    [39] Brookes PS, Land JM, Clark JB, et al. (1998) Peroxynitrite and brain mitochondria: evidence for increased proton leak. J Neurochem 70: 2195-2202. https://doi.org/10.1046/j.1471-4159.1998.70052195.x
    [40] Xie P, Zhang H, Qin Y, et al. (2023) Membrane proteins and membrane curvature: mutual interactions and a perspective on disease treatments. Biomolecules 13: 1772. https://doi.org/10.3390/biom13121772
    [41] Morris CE (2011) Voltage-gated channel mechanosensitivity: fact or friction?. Front Physiol 2: 25. https://doi.org/10.3389/fphys.2011.00025
    [42] Cortassa S, O'Rourke B, Aon MA (2014) Redox-optimized ROS balance and the relationship between mitochondrial respiration and ROS. Biochim Biophys Acta 1837: 287-295. https://doi.org/10.1016/j.bbabio.2013.11.007
    [43] vanHameren G, Campbell G, Deck M, et al. (2019) In vivo real-time dynamics of ATP and ROS production in axonal mitochondria show decoupling in mouse models of peripheral neuropathies. Acta Neuropathol Commun 7: 86. https://doi.org/10.1186/s40478-019-0740-4
    [44] Berry BJ, Kaeberlein M (2021) An energetics perspective on geroscience: mitochondrial protonmotive force and aging. Geroscience 43: 1591-1604. https://doi.org/10.1007/s11357-021-00365-7
    [45] Berry BJ, Mjelde E, Carreno F, et al. (2023) Preservation of mitochondrial membrane potential is necessary for lifespan extension from dietary restriction. GeroScience 45: 1573-1581. https://doi.org/10.1007/s11357-023-00766-w
    [46] Sutherland TC, Sefiani A, Horvat D, et al. (2021) Age-dependent decline in neuron growth potential and mitochondria functions in cortical neurons. Cells 10: 1625. https://doi.org/10.3390/cells10071625
    [47] Zhang H, Alder NN, Wang W, et al. (2020) Reduction of elevated proton leak rejuvenates mitochondria in the aged cardiomyocyte. Elife 9: e60827. https://doi.org/10.7554/eLife.60827
    [48] Barnstable CJ, Zhang M, Tombran-Tink J (2022) Uncoupling proteins as therapeutic targets for neurodegenerative diseases. Int J Mol Sci 23: 5672. https://doi.org/10.3390/ijms23105672

  • This article has been cited by:

    1. S. Sahith Reddy, M. Achyutha Kumar Reddy, LIME CALCINED CLAY CEMENT (LC3): A Review, 2021, 796, 1755-1307, 012037, 10.1088/1755-1315/796/1/012037
    2. Ch. Vijay, M. Achyutha Kumar Reddy, Optimization of bentonite modified cement mortar parameters at elevated temperatures using RSM, 2021, 1197, 1757-8981, 012040, 10.1088/1757-899X/1197/1/012040
    3. Mingxue Ma, Vivian WY. Tam, Khoa N. Le, Robert Osei-Kyei, Factors affecting the price of recycled concrete: A critical review, 2022, 46, 23527102, 103743, 10.1016/j.jobe.2021.103743
    4. M. Achyutha Kumar Reddy, V. Ranga Rao, Veerendrakumar C. Khed, Kavuri Naga Chaitanya, Optimization of reinforced bentocrete column parameters under eccentric compression, 2022, 41, 23520124, 1027, 10.1016/j.istruc.2022.05.050
    5. Jawad Ahmad, Karolos J. Kontoleon, Mohammed Zuhear Al-Mulali, Saboor Shaik, Mohamed Hechmi El Ouni, Mohammed A. El-Shorbagy, Partial Substitution of Binding Material by Bentonite Clay (BC) in Concrete: A Review, 2022, 12, 2075-5309, 634, 10.3390/buildings12050634
    6. Hany A. Dahish, Ahmed D. Almutairi, Effect of Elevated Temperatures on the Compressive Strength of Nano-silica and Nano-clay Modified Concretes Using Response Surface Methodology, 2023, 22145095, e02032, 10.1016/j.cscm.2023.e02032
    7. Raman Saini, Gyanendra Kumar Chaturvedy, Umesh Kumar Pandey, Examining the effects of nano iron oxide on physical and mechanical characteristics of rubberized concrete, 2024, 9, 2364-4176, 10.1007/s41062-024-01494-6
    8. Dhrub Kumar Das, Aditya Kumar Tiwary, Influence of nano bentonite clay and nano fly ash on the mechanical and durability properties of concrete, 2024, 26, 1618-954X, 3881, 10.1007/s10098-023-02610-3
    9. Mohammed Salman Khizar, M. Achyutha Kumar Reddy, Naga Chaitanya Kavuri, Veerendrakumar C. Khed, 2023, 2759, 0094-243X, 060005, 10.1063/5.0144106
    10. Kamrul Hasan, Ramadhansyah Putra Jaya, Fadzil Mat Yahaya, Application of bentonite in cement-based composites: A review of current status, challenges and future prospects, 2024, 98, 23527102, 111171, 10.1016/j.jobe.2024.111171
    11. Muhammad Saeed Zafar, Adnan Shahid, Reza Sedghi, Maryam Hojati, Optimization of biopolymer additives for 3D printable cementitious systems: A design of experiment approach, 2025, 22, 22145095, e04515, 10.1016/j.cscm.2025.e04515
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Biophysics
1.1 2.4

Metrics

Article views(1850) PDF downloads(80) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline
Abstract
   Introduction
   Materials and methods
   Results and discussion
   RSM modeling
   Conclusions
Acknowledgments
Conflict of interest
References

Figures and Tables

Figures(32)  /  Tables(1)

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog