New Mechanistic Insights on Carbon Nanotubes Nanotoxicity Using Isolated Submitochondrial Particles, Molecular Docking, and Nano-QSTR Approaches

Herein, we present a combination of experimental and computational study on the mitochondrial F0F1-ATPase nanotoxicity inhibition induced by single-walled carbon nanotubes (SWCNT-pristine, SWCNT-COOH). To this end, the in vitro inhibition responses in submitochondrial particles (SMP) as F0F1-ATPase enzyme were strongly dependent on the concentration assay (from 3 to 5 μg/ml) for both types of carbon nanotubes. Besides, both SWCNTs show an interaction inhibition pattern like the oligomycin A (the specific mitochondria F0F1-ATPase inhibitor). Furthermore, the best crystallography binding pose obtained for the docking complexes based on the free energy of binding (FEB), fit well with the previous in vitro evidences from the thermodynamics point of view. Following an affinity order as: FEB (oligomycin A/F0-ATPase complex) = -9.8 kcal/mol > FEB (SWCNT-COOH/F0-ATPase complex) = 6.8 kcal/mol ~ FEB (SWCNT-pristine complex) = -5.9 kcal/mol. With predominance of van der Waals hydrophobic nanointeractions with key F0-ATPase binding site residues (Phe 55 and Phe 64). By the other hand, results on elastic network models, and fractal-surface analysis suggest that SWCNTs induce significant perturbations by triggering abnormal allosteric responses and signals propagation in the inter-residue network which could affect the substrate recognition ligand geometrical specificity of the F0F1-ATPase enzyme in order (SWCNT-pristine > SWCNT-COOH). Besides, the performed Nano-QSTR models for both SWCNTs show that this method may be used for the prediction of the nanotoxicity induced by SWCNT. Overall, the obtained results may open new avenues toward to the better understanding and prediction of new nanotoxicity mechanisms, rational drug-design based nanotechnology, and potential biomedical application in precision nanomedicine.


Introduction
The coupled mechanical co-rotating between the γ and ε subunits that form the mitochondrial F1-ATP synthase (complex V) favors the H + protons flux necessary for ATP synthesis in all eukaryotic cells 1,2 . This bioenergetic process involves several synchronized conformational changes which are critical for the survival or death of the cells [1][2][3] . In this regard, a few years ago has been shown that under pathological conditions like chronic diseases as cancer, Alzheimer, Parkinson, MELAS syndrome, several toxic events, including nanotoxicity-induced by SWCNT may trigger F0F1ATPase dysfunction [3][4][5] . The ATP cellular reserves are abruptly consumed by a reverse biochemical reaction which paradoxically hydrolyses significant amounts of ATP compromising the cellular homeostasis and viability 3,5 .
To the best of our knowledge, the toxicological modulation of mitochondrial ATP bioenergetic mechanisms released by the exposure with SWCNT has been insufficiently characterized in order to explain the mitochondrial nanotoxicity-induced by SWCNT. By the other hand, this mechanistic knowledge could be very useful to implement strategies on the named "precision mitochondrial nanomedicine" to improve selectivity for the treatment of brain, cardiac diseases, and cancer using the mitotropic behavior of SWCNT to address active pharmacological principles as new targeting of the mitochondrial F0F1-ATPase [8][9][10][11][12][13][14] . In this context, we hypothesize that SWCNT could acts mimicking the pharmacodynamic behavior of the Oligomycin A, which is the specific inhibitor of the mitochondrial ATP-hydrolysis that modulate the activity of the c-ring-F0-ATP hydrolase subunit. The c-ring-F0-ATP hydrolase subunit represent an uncoupling channel which is part of the mitochondrial permeability transition pore-induced associated to mitochondrial dysfunction and apoptosis 15,16 . Following this idea, we suggest that SWCNT could promote the selective inhibition of the F0-ATPase under pathological conditions [16][17][18][19][20] .
In this regard, computational approaches like molecular docking simulation, elastic network models, fractal-surface approaches linked to nano-quantitative-structure-toxicity relationships (Nano-QSAR/QSTR models) and others 8,[21][22][23][24] , could be efficiently applied to the exhaustive exploration of the underlying mechanisms of mitochondrial bioenergetic dysfunction (pathological ATP-hydrolysis) from the structural point of view for therapeutic purposes.
Particularly, computational Nano-QSAR/QSTR approaches are essential tools to support the discovery process of toxicological effects of nanomaterials (SWCNT). Several approaches have been developed and applied recently able to predict potential harmfulness of nanoparticles and nanomaterials [8][9][10][11][12][13][14] . One of the most used is the so called nanoquantitative-structure-toxicity-relationships (Nano-QSTR models) due to the fact that was successfully applied in very different fields [25][26][27] . This in silico tools have the quality of being versatile and reconfigurable to many problems. For example, the nano-quantitativestructure-binding-relationship (Nano-QSBR) models is a type of Nano-QSTR which is able to associate the physico-chemical properties of nanomaterials (nanodescriptors) with the theoretical free energy of binding (FEB values, kcal/mol) obtained from the molecular docking studies and also to experimental nanotoxicological outputs 13, 14, 28 . Due to this, QSAR (Nano-QSTR) paradigm has been applied since the beginning of the "nano revolution" as a useful methodology able to support toxicity profiling of nanomaterials and CNT [29][30][31][32][33] . Several approaches by many authors have been reported combining different molecular descriptors, methodologies and algorithms, including machine learning and deep learning [32][33][34][35][36][37][38][39][40] . In this sense, in strongly advisable use Nano-QSTR approaches while performing toxicity profiling of CNT and nanomaterials also considering in silico approaches are strongly encouraged by authorities in order to improve the EU 3R principles (replacement, reduction, refinement) in Alternative Toxicology.
Currently, the main limitation of these computational methods is to address a feasible mechanistic interpretation of the nanotoxicity phenomena at the atomic level, in many cases 41 .
Then, in this work we propose for the first time, a combination of computational modeling approaches, based on molecular docking simulations, elastic network models, fractal-surface approaches and Nano-QSTR calculations, along with experimental validation to tackle the study of binding interactions between single-walled carbon nanotubes with the mitochondrial F0F1-ATPase toward to contribute to the rational drug-design based nanotechnology, mitotarget-drug discovery and the new area of precision mitochondrial nanomedicine.

Isolation of rat-liver sub-mitochondrial particles (SMP).
The frozen RLM pellet was thawed and diluted with homogenization medium to contain 20 mg of protein/ml. The mitochondrial suspension was subjected to sonic oscillation four times for 15 s with 30 s intervals, using 80 watts at 4°C [42][43][44][45] . The suspension was then centrifuged at 9750 x g for 10 min at 4°C and the submitochondrial particles in the supernatant were isolated by additional centrifugation in a Sorval SV-80 vertical rotor for one hour at 15 000 rev/min at 4°C, using discontinuous gradient containing 1ml of 0.5 M sucrose and 1 ml of 2.0 M sucrose in 5 mM Tris-HCl, pH 7.4. Finally, the SMP were suspended in the isolation medium, and the final volume adjusted to give a stock suspension containing 1 mg of protein/ml.
Statistical procedures for the mitochondrial assays using SMP.
Analysis of variance (ANOVA) followed by a post hoc Newman-Keuls multiple comparison test to determine statistical differences between F0-ATPase inhibition assay experimental groups was performed. All the biochemical tests by using isolated rat-liver mitochondria (RLM) and submitochondrial particles (SMP) were performed at least three times in triplicate. Normality and variance homogeneity were verified using Shapiro-Wilks and Levene tests, respectively, before using ANOVA analysis. In all cases, significance level was set in 5%.

Molecular docking study
Docking simulations were performed using Autodock tools mixed Autodock Vina to understand the strength of biochemical interactions across CNT-family member (pristine-CNT, CNT-OH, CNT-COOH), and oligomycin A on F0-ATPase. These binding in silico interactions were performed only to explain hidden biophysical and pharmacodynamic mechanisms observed in the mitochondrial in vitro assays. For this instance, it was modeled only three types of single walled zig-zag SWCNTs (Hamada index n = 8, m = 0) like SWCNT(8.0), SWCNT-COOH(8.0) and SWCNT-OH(8.0) as F0F1-ATPase ligands in order to reproduce and modeling some critical experimental conditions from CNT-properties like CNT-functionalization linked to observed F0-ATPase inhibition (ATP-hydrolysis inhibition) in isolated-RLM and isolated-SMP. Following this idea, the F0F1-ATPase C10 ring with oligomycin A from yeast (Saccharomyces cerevisiae) as the receptor (PDB ID: 5BPS, Resolution 2.1Å ) was obtained from the RCSB Protein Data Bank (PDB) 46 . It is important to note that, c-ring-F0-ATPase subunit.pdb x-ray structure from Saccharomyces cerevisiae (5BPS) can be used in the context of the present docking approaches taking into account that mitochondrial cring-F0-ATPase subunit.pdb x-ray structure from Rattus norvegicus with oligomycin A has not been crystallized and included in the RCSB Protein Data Bank 46 . However, the oligomycin Apharmacodynamics mechanism is highly conserved in Rattus norvegicus according to previous experimental evidences 17 .
Before the molecular docking, ATPase C10 ring molecular structure was optimized using the AutoDock Tools 4 software for AutoDock Vina. The algorithm includes the removal of crystallographic water molecules and all the co-crystallized ATPase C10 ring ligand molecules, such as Oligomycin A (Oligo A: C45H74O11 like ID: EFO) from ATPase C10 ring chains (B, E, K, L, M, O). Oligomycin A a recognized classical inhibitor of F0F1-ATPase inhibition it was used as a control to compare the affinity and/or relevant interactions by re-docking procedure.
This theoretical algorithm was performed to the c-ring F0-ATPase subunit using a grid box size with dimensions of X= 22 Å , Y= 22 Å , Z= 22 Å and the c-ring F0-ATPase subunit grid box center X=19.917 Å , Y= 19.654 Å , Z= 29.844 Å to evaluate the SWCNT-c-ring F0-ATPase interaction 47 , considering the oligomycin A environment to evaluate the SWCNT-surface affinity in the c-ring F0-ATPase subunit active binding site.
The docking free energy of binding output results (or FEB values) is defined by affinity (like ΔGbind values) for all docked poses of the formed complexes (SWCNT-F0ATPase) and include the internal steric forces of a given ligands (SWCNT) which can be expressed as the sum of individual molecular mechanics terms of standard-chemical potentials as: van der Waals interactions (ΔGvdW), hydrogen bond (ΔGH-bond), electrostatic interactions (ΔGelectrost), and intramolecular interactions (ΔGinternal) ligands (SWCNTs) from empirically validated Autodock Vina scoring function based on default Amber force-field parameters 21-23 .
Then the (SWCNTs-F0-ATPase) complexes free energy of binding (FEBdock) was calculated based on the following scoring function: ΔG= -RT(ln Ki), R (gas constant) is 1.98 cal*(mol*K) -1 , and Ki represents the predicted inhibition constants at T = 298.15 K. The first term describes the van der Waals interaction as Aij/dij 12 (attractive Guassian function) and Bij/dij 6 (repulsive hyparabolic function) to represent a typical Lennard-Jones potential (SWCNT-F0ATPase). The Gaussian term is negative and the parabolic positive, dij is the surface distance calculated as dij = rij -Ri -Rj, where rij is the interatomic distance and Ri and Rj are the radii of the atoms in the pair of interaction of SWCNTi-F0ATPasej atoms. The second term is the pair consisting of an H-bond donor and an H-bond acceptor as a directional 12-10 hydrogen-bonding potential term such as Cij/dij 12 and Dij/dij 10 (H-bonding potential with Goodford directionality), where E(t) is an angular weight factor to represents the hydrogen bonds directionality and dij follows the criteria mentioned above. Atoms with dij below of cutoff value of 7 Å were considered as interacting atoms 21-23 .
The third term represents the Coulomb electrostatic potential stored for the formed complex (SWCNT/F0ATPase)ij of N charges (qi, qj) of pairs of charged atoms of SWCNT(i) and F0ATPase(j). For this instance, appropriated Gasteiger partial atomic charges of the F0ATPase enzyme were assigned. Herein, dij is the interatomic distance between the point charges as the reference positions of interaction based on distance-dependent dielectric constant. Herein, Autodock Vina based on Amber force field was parameterized with default options for the pristine-SWCNT, SWCNT-OH and SWCNT-COOH by summing up individual molecular mechanic contributions like: SWCNTintra-molecular contributions, SWCNT-aromaticity criterion and the set number of active torsions moving of each SWCNT-ligand following to general preparation procedures of ligand. For this instance, the fourth term of the equation (2) as (ΔGinternal) was used to validate the internal steric energy of each SWCNT-ligand including dispersion-repulsion energy and a torsional energy through the sum of the default Amber force field parameters (ligand conformation-independent parameters of the Autodock Vina scoring function) 21-23 .

Local-perturbation response induced by SWCNT on the F0-ATPase subunit.
In parallel with docking simulation a new model based elastic network model was performed to propose potential mechanism-based on the SWCNT-propensity to perturb the intrinsic motion of F0-ATPase subunit binding residues involved in the docking interactions. To this purpose, the F0-ATPase is represented as a network, or graph of the interresidue contacts from Cα-F0-ATPase atoms of a residue and the overall potential is simply the sum of harmonic potentials between interacting nodes (F0-ATPase residues). The network includes all interactions within a cutoff distance < 4 Å . Information about the orientation of each interaction with respect to the global coordinates system is considered within the force constant matrix and allows prediction of perturbed anisotropic motions 48 . The force constant of the F0-ATPase protein system can be described by a Kirchhoff or Hessian matrix (Hi,j) to evaluate potential perturbations induced by SWCNT-ligand in the transduction properties of the F0-ATPase enzyme according to the following equation: Where each Hi,j is a 3×3 matrix which holds the anisotropic informations regarding the orientation of residues (i, j-nodes). Each such sub matrix (or the "super element" of the Hi,j -Hessian matrix) is defined by the equation 4 as: The second partial derivatives are the harmonic potentials V between interacting F0-ATPase residues. These partial derivatives are formed by a simple matrix of cosines and the off-diagonal super elements of the Hi,j -Hessian matrix are calculated according to equation 5 as: , where γ is an interaction constant. The si,j is the instantaneous distance between nodes or residues i and j. The diagonal super elements are calculated by: Herein, the force constant matrix Hi,j holds information regarding the F0-ATPase-residues position/orientation. The inverse of the Hessian matrix is the covariance matrix of 3N multi-variant Gaussian distribution where p is an empirical parameter according to the equation (7) for the new off-diagonal elements of the Hessian matrix which hold the desired information on the residuefluctuations including the F0-ATPase binding-site residues (i, j) involved in the SWCNT-F0-ATPase docking interactions.

Performing Nano-QSTR approaches
The Nano-QSTR models have been developed using a linear regression approach to predict the mitochondrial F0F1-ATPase inhibition values of the SWCNT herein studied. The values used for the development of the continuous model were obtained from molecular docking experiments considering the free energy of binding (FEB values) obtained from the complexes SWCNTpristine/F0-ATPase, and SWCNT-COOH/F0-ATPase. For this purpose, two different sets for both ligands (SWCNT-pristine, SWCNT-COOH) were efficiently built. Considering the three recognized categories of geometric topologies as: zig-zag-SWCNT (Hamada index m = 0, n > 0), amchair-SWCNT (Hamada index m = n) and chiral-SWCNT, characterized by Hamada index (n, m), with m > 0 and m ≠ n; and with its enantiomers (or mirror images) present Hamada index (m,n), which is different from (n, m) no reflection symmetry 13,14 . Then, regression Nano-QSTR models were developed using the linear regression tool implemented in the Statistica® suite.
The validation of the Nano-QSTR model was performed using the cross-validation module implemented in the software. This procedure is aimed at assessing the predictive accuracy of a model. The test randomly split the dataset into a training set and a validation set, ensuring that if an entry was included in the test set it could not be used in the validation test. In so doing, the model was developed using the cases in the training or learning sample, which, in our study, was 70% of the dataset. The predictive accuracy was then assessed using the remaining 30% of the dataset.
Finally, the performance of the model was evaluated using the residuals, R and R 2 and other relevant statistics. Regarding the molecular descriptors (MD), we used the DRAGON 7.0® software to calculate the variables that have been used for the development of the models. This software suite is able to calculate up to 7,500 different descriptors, belonging to very different classes, such as topological, 2D, 3D, connectivity, and so on 49 . In order to select the best subset of MD, we have performed a feature selection process using a forward stepwise methodology 33 for both models. At the end of this procedure, we were able to develop the pristine and the carboxylate model using respectively two and three MD belonging to the Topological class. The two MD used in the SWCNT-pristine model are the Narumi geometric topological index (GNar) and the electrotopological positive variation (MAXDP). The Narumi index of a graph G is defined as the product of degrees of all its vertices: The MAXDP is calculated as follow: which is calculated as the maximum positive value of ΔIi.
Regarding the SWCNT-COOH model, the continuous model was developed using three MD, one is the same GNAR used for the pristine model. The other two are defined as follow. The first one is the path/walk Randic shape indices that is calculated by summing, over the non-H atoms, the ratios of the atomic path count over the atomic walk count of the same order k and, then, dividing by the total number of non-H atoms (nSK). Since path/walk count ratio is independent of molecular size, these descriptors can be considered as measures of molecular shape. Dragon calculates path/walk shape indices from order 2 up to 5; the index of first order is not provided as the counts of the paths and walks of length one is equal and, therefore, the corresponding molecular index equals one for all molecules. The formula in this case is not reported in the Dragon manual.
Finally, the last molecular descriptor used is the so called lopping centric index (LOC), which is calculated as the mean information content derived from the pruning partition of a graph: where nk is the number of terminal vertices removed at the kth step and nSK the number of non-H atoms.

CNT effects on sub-mitochondrial particles (SMP).
Herein, we present the in vitro assay on the inhibitory effect of the SWCNT-ligands (SWCNTpristine, SWCNT-COOH) at the range of concentration of 0.5-5 µ g/ml over F0-ATPase using isolated rat-liver sub-mitochondrial particles (isolated F0F1-ATPase) from mitochondrial inner membrane. In general, we can see that the SWCNT-tested exhibit high ability to act as F0-ATPase inhibitors (ATP-hydrolysis) at a range of concentration of 3-5 µ g/ml. Besides, a concentration dependence with significant statistical difference (p < 0.05) when compared with SMP (untreated-SMP group) and the DMSO-treated SMP was observed. We note an oligomycin A-like pattern (positive control group used) for both SWCNT-ligand in a range of concentration of 3-5 µ g/ml without significant statistical difference (p > 0.05) when compared with oligomycin A (Figure 1). According to this, the treated-SMP from mixed CNT-ligand (5µ g/ml) plus oligomycin A (1µ M) showed strongest F0-ATPase inhibition (p < 0.05) when compared with untreated-SMP and the DMSO-treated SMP, and the remaining CNT-treated-SMP (3-5 µ g/ml). Suggesting a strong synergistic effect on F0-ATPase inhibition (mitochondrial nanotoxicity). Details of these experimental results can see in Figure 1.

Modeling F0ATPase inhibition induced by SWCNTs
Herein, molecular docking was carried out in order to evaluate the influence of the carbon nanotubes (SWCNT-pristine and SWCNT-COOH) in the F0-ATPase inhibition response. Herein, the best docking binding pose from each modeled-CNT (SWCNT-pristine, SWCNT-COOH), theoretically suggest that these CNT could act in the same biophysical environment that the oligomycin A based on hydrophobic non-covalently interaction (π-π interactions) involving phenylalanine hydrophobic residues (Phe 55 and Phe 64 of the chains C, D and M), which are critically involved in the F0-ATPase inhibition (ATP-hydrolysis) in the F0-ATPase subunit active binding-site. See Figure 2. The free energy of binding (FEB)-values of the formed docking complexes following the order: FEB (oligomycin A/F0-ATPase complex) = -9.8 kcal/mol > FEB (SWCNT-COOH/F0-ATPase complex) = -6.8 kcal/mol ~ FEB (SWCNT-pristine complex) = -5.9 kcal/mol with interatomic distance of interaction lower than 5 Å , in all the cases. Besides, we note that the presence of π-π interactions like Y-shaped and pseudo parallel-displaced motif-orientation preferences for both single-walled carbon nanotubes. Besides, a more electrostatically favored interactions in the CNT-sidewall than the CNT-tips were observed in both simulations (SWCNT-pristine and SWCNT-COOH). Probably, due to better orientation and stability between the planar-benzene-quadrupoles formed between van der Waals surface from the modeled-SWCNT and the phenylalanine hydrophobic residues (Phe 55 and Phe 64) of the F0-ATPase binding site and interacting in the same biophysical environment that the F0-ATPase specific inhibitor (oligomycin A) 17 .
Next, we carried out the theoretical modeling based on the local perturbation response scanning maps (LPRS-maps). The LPRS maps are based in elastic network models (ENM models) and have been widely recognized to study relevant conformational changes of target proteins (as F0-ATPase under unbound and bound states) at the atomistic and molecular level 48 , It is wellknown that the ENM models could explain a large number the conformational differences based on the perturbation pattens of the network formed by the target residues evaluated (Phe 55 and Phe 64) For this instance, LPRS maps generates a comprehensive visualizations of the F0-ATPase inhibition response which allows evaluate allosteric signal propagations in response to external perturbations under the presence of a given ligand (i.e., the oligomycin A as F0-ATPase-specific inhibitor, SWCNT-pristine, and SWCNT-COOH. The results can see in the  The results on LPRS-maps show that both single-walled carbon nanotubes promote a significant change in the perturbation patterns of the network of target residues compared with the physiological condition represented by the unbound state of F0-ATPase. In this regard, we note abrupt perturbations in several blocks of residues more pronounced for the SWCNT-pristine (strong F0-ATPase inhibition) than the SWCNT-COOH (moderate F0-ATPase inhibition) during the interaction with the F0-ATPase. Interestingly, the LPRS map of the SWCNT-pristine/F0-ATPase complex mimicking the toxicodynamic behavior of the oligomycin A/F0-ATPase complex inducing strong F0-ATPase inhibition (See Figure Figure 3, B and C) suggesting a similar pattern of allosteric network perturbation. However, the LPRS map obtained from the SWCNT-COOH/F0-ATPase complex exhibits a pattern of perturbation closer to the physiological condition maintaining a certain coupling between the residues composing the F0-ATPase network suggesting the presence of a moderate nanotoxicity-based F0-ATPase inhibition. The relevance of these results is that strong local perturbations promote triggering strong allosteric responses in the j-effector residues from F0-ATPase receptor affecting its mitochondrial catalytic function involving the signal transduction of the perturbations from the block of i-sensor residues which trigger abnormal signals propagation across inter-residue network for j-effector F0-ATPase residues. We could suggest that considering the SWCNT-docking position, both ligands (SWCNT-pristine >> SWCNT-COOH) can theoretically disrupt the H + -proton flux dynamic in the mitochondrial H + -F0-ATPase subunit, compromising the coupling between oxidative phosphorylation and electron transport in the respiratory chain inducing potential bioenergetic dysfunction and the mitochondria nanotoxicity 8 .
In order to quantify potential fractal geometrical perturbations, a fractal surface analysis was carried out to model changes-based perturbations in the geometric surface of the binding effector residues of the F0-ATPase under unbound and bound state (i.e., under SWCNT-pristine and SWCNT-COOH interactions) 8 . To this end, several fractal dimensions (FDs namely: DBW, DBBW and DWBW) were calculated using the box-counting methods from the LPRS maps previously obtained 50 . The Fractal Theory allows the mathematical modeling of the geometric complexity (across multiple scales) and self-similarity (scale-invariant structure) from non-Euclidean real or virtual objects (as SWCNT-tested). One of the most important properties in the fractal modeling is the degree of selfsimilarity. Then, a topological fractal dimension near to 2 is categorized-like high complexity (high variety of geometrical information) and low self-similarity, in opposite a topological fractal dimension closer to 1 informs about little complexity and high self-similarity. Herein, the non-Euclidean geometrical patterns were included according to the fractal dimension like FDBW, that describes the surface geometric perturbations in the border of LPRS map fractal pattern 50 . The FDB+BW, characterizes the surface geometric perturbations on the white background, and the FDW+BW the fractal perturbations pattern on the black background from the LPRS images calculated for each simulation conditions. See  Herein, the obtained FDs are related to the F0-ATPase surface and backbone non-Euclidean geometry 8,50 FDs, inform about how the F0-ATPase folding, packing density, solvent-accessibility, and binding-interaction properties could be perturbed under the presence of different ligands forming docking complexes (oligomycin A/F0-ATPase complex, SWCNT-pristine/F0-ATPase complex, and SWCNT-COOH/F0-ATPase complex). In this context, we suggest that, SWCNTpristine with FDBW = 1.29 lead to a higher change in F0-ATPase roughness-based FD (FDBW) than the SWCNT-COOH (FDBW = 1.45) which exhibits very similar features-based fractal dimension compared physiological condition of unbound F0-ATPase used as control (FDBW = 1.45. These, results fit with the previous on LPRS maps strongly suggesting that the SWCNT-pristine mimicking the nanotoxicological behavior of the specific inhibitor oligomycin A with calculated equal to FDBW = 1.32 also low than the physiological condition of unbound F0-ATPase cited above. As previously cited, a FD ≈ 2 reveals high variety of geometrical information and low self-similarity, while FD ≈ 1 represents little complexity and high self-similarity. By the other hand, the FD-values obtained for FDB+BW and FDW+BW remain as unperturbed around 1.85 in all the cases revealing high complexity of geometrical information 8,50 . The results of fractal surface perturbation suggest that the SWCNT-pristine can induce significant changes in the geometrical selectivity of the F0-ATPase like oligomycin A. It is wellknown that perturbation (global and local perturbations) in the three-dimensional spatial arrangement of atoms composing effector residues (j-effector allosteric residues) of proteins can be studied using their FDs. Fractal surface-perturbations could negatively impact on catalytic function of F0-ATPase, affecting irreversibly the structural properties of the binding cavities, which are the paramount importance in the complementary processes like substrate recognition and ligand geometrical specificity.
[64] Probably, topologically perturbed van der Waals fractal-surface of F0-ATPase after the docking interaction with SWCNT-COOH could theoretically explain the moderate mitochondrial nanotoxicity observed from the SWCNT-COOH/F0-ATPase docking complex (refer to Figure 3, A and D).
Lastly, we carried out a nano-quantitative-structure-toxicity-relationship approaches (Nano-QSRT models) in order to evaluate the influence of additional geometric properties of the ligands SWCNT-pristine and SWCNT-COOH based on the well-known relationship between the topology geometry-based on n,m-Hamada index with their nanotoxicological properties (i.e., SWCNTmitotoxicity).

Performed Nano-QSTR models
As reported in the Material and methods section, the Nano-QSTR model for SWCNT-pristine was developed using only two variables belonging to the topological index category. The observed vs predicted values and the other relevant statistics, are reported in the Table 1, Table 2, and Figure 5, respectively.   As can be seen in the Table 1 and 2, the Nano-QSTR model shows an overall accuracy and a goodness of fit high, thus indicating this model can be used for a continuous prediction of the likelihood induced mitochondria nanotoxicity inhibition on F0F1-ATPase by interaction with SWCNT-pristine (f(FEB_1)). In this regard, the best Nano-QSTR regression model is based on the Afterward, we performed Nano-QSTR model for SWCNT-COOH. For this instance, was carried out a QSTR regression model by using three variables and as in the case of the previous model (i.e., using SWCNT-pristine). Herein, the results obtained on observed vs predicted values, and the other relevant statistics parameters are summarized in the Table 3, Table 4, and Figure 6, respectively.

Conclusions
In the present study we present a combination of experimental and computational approaches to tackle the SWCNT nanotoxicity based on the mitochondrial F0F1-ATPase inhibition. Experimental evidences supported that the in vitro F0F1-ATPase inhibition responses in submitochondrial particles (SMP) are strongly dependent on the higher level of concentration (from 3 to 5 µ g/ml) in both types of carbon nanotubes (SWCNT-pristine and SWCNT-COOH) evaluated. In addition, both types of carbon nanotubes show an interaction inhibition pattern for the F0F1-ATPase enzyme, similar to the oligomycin A (specific F0F1-ATPase inhibitor). By the other hand, the best binding pose for the obtained complexes fit well with the previous experimental results. The free energy of binding (FEB-values) for the formed docking complexes following the affinity order as: FEB (oligomycin A/F0-ATPase complex) = -9.8 kcal/mol > FEB (SWCNT-COOH/F0-ATPase complex) = -6.8 kcal/mol ~ FEB (SWCNT-pristine complex) = -5.9 kcal/mol with relevant interatomic distance of interaction lower than 5 Å , in all the cases and with predominance of van der Waals hydrophobic interactions with critical F0-ATPase binding site residues (Phe 55 and Phe 64) belonging to the same biophysical environment that the oligomycin A inhibitor. In addition, results on elastic network models (LPRS-maps) show that both SWCNT-pristine and SWCNT-COOH promote an abrupt perturbations in several blocks of residues more pronounced for the SWCNT-pristine (strong F0-ATPase nanotoxicity inhibition) than the SWCNT-COOH (moderate F0-ATPase nanotoxicity inhibition) triggering pertubation on the allosteric responses, abnormal signals propagation across inter-residue network of the F0F1-ATPase. In accordance to this, results on fractal-surface of interactions suggest that, the SWCNT-interactions topologically affect the van der Waals fractal-surface of F0-ATPase (SWCNT-pristine > SWCNT-COOH) inducing from strong to moderate mitochondrial nanotoxicity. Lastly, the predictive Nano-QSTR models show that a linear correlation between SWCNT topology and the nanotoxicity induced is present and can be predicted using a Nano-QSTR approach. Finally, this results open new opportunities toward to the better better understanding of the molecular nanotoxicity mechanisms, relevance of mitotarget-drug discovery and rational drugdesign based nanotechnology with potential biomedical application in precision nanomedicine.

Author Contributions:
The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript.

Declaration of interest statement:
The authors declare no competing financial interests.