Mitoprotective activity of oxidized carbon nanotubes against mitochondrial swelling induced in multiple experimental conditions and predictions with new expected-value perturbation theory

Abstract

Mitochondrial Permeability Transition Pore (MPTP) is involved in neurodegeneration, hepatotoxicity, cardiac necrosis, nervous and muscular dystrophies. We used different experimental protocols to determine the mitoprotective activity (%P) of different carbon nanotubes (CNT) against mitochondrial swelling in multiple boundary conditions (b_j). The experimental boundary conditions explored included different sub-sets of combinations of the following factors b₀ = three different mitochondrial swelling assays using the MPT-inductor (Ca²⁺, Fe³⁺, H₂O₂) combined or not with a second MPT-inductor and swelling control assays using MPT-inhibitor (CsA, RR, EGTA), b₁ = exposure time (0–600 s), and b₂ = CNT concentrations (0–5 μg ml⁻¹). Other boundary conditions (b_k) changed were the CNT structural parameters b₃ = CNT type (SW, SW + DW, MW), b₄ = CNT functionalization type (H, OH, COOH). We also changed different of CNT like b₅ = molecular weight/functionalization ratio (^minW/^maxW) or b₆ = maximal and minimal diameter (D_min/D_max) as physic-chemical properties (V_k). Next, we employed chemoinformatics ideas to develop a new Perturbation Theory (PT) model able to predict the %P of CNT in multiple experimental conditions. We investigated different output functions of the absorbance ′f(ε_ij) used in PL4/PL5 methods like (ε_ij, 1/ε_ij, 1/ε_ij², or −log ε_ij) as alternative outputs of the model. The inputs are in the form an additive functions with linear/non-linear terms. The first term is a function ⁰f(〈ε_ij〉) of the average absorbance 〈ε_ij〉 (expected value) in different assays (b_j). The concentration dependent terms are linear functions of concentration, or hill-shaped curves similar to PL4/PL5 functions (used in dose–response analysis). The CNT structure perturbation terms are linear/non-linear functions of Box–Jenkins operators (ΔV_kj). The ΔV_kj are moving averages (deviations) of the V_k of the CNT with respect to their expected values 〈V_kj〉. The best model found predicted the values of absorbance (measure of mitoprotective activity vs. mitochondrial swelling) with regression coefficient R² = 0.997 for >6000 experimental data points (q² = 0.994). Last, we used the model to carry out a simulation of the changes on mitoprotective activity for CNT family after one increase of 1–10% of the ^minW_i and ^maxD_i of CNT.

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Introduction

Mitochondrial Permeability Transition (MPT) is associated with a higher permeability of the mitochondrial membranes to metabolites and xenobiotics under a threshold value of MW < 1500 Da due to the opening of MPT pore (MPTP).^1–5 The MPTP is a multi-protein complex that connects the interior and the outer mitochondrial membrane formed by the ADP/ATP carrier or adenine nucleotide translocase (ANT) and the voltage-dependent anion channel (VDAC). Since the discovery of MPTP by Haworth and Hunter in 1979, this biochemical event has been linked to hepatotoxicity, neurodegeneration (Alzheimer, Parkinson), cardiac ischemia, nervous and muscular dystrophies (amyotrophic lateral sclerosis). In these sense, MPTP has been recognized as a critical factor in the cellular responses under pathological conditions accompanied of osmotic swelling, leading to increases in volume in the mitochondrial matrix, rupture of the outer mitochondrial membrane by opening of membrane pores in mitochondria, dissipation of the membrane potential, increase of reactive oxygen species (ROS) generation and affects the normal ATP levels. This process is triggered by calcium overload, transition metals in concentrations greater than 5 μM and other pro-oxidant conditions.^2–5 Also can trigger conformational changes in inner mitochondrial membrane proteins; oxidation of thiol groups that form the MPTP and release of pro-apoptotic signals (cytochrome c, caspase 3, caspase 9), which are closely linked to mitochondria dysfunction mechanisms. Following this idea, the search of new chemical structures able to act as MPTP-inhibitors (mitoprotectors) has become a very important goal. The immunosuppressant drug cyclosporine A (CsA)⁶ is a one of the best known examples of mitoprotector agent with direct action over this target. Recently research has focused on the effects of structural changes over structure–property relationships of mitoprotectors. For instance, de Faria et al.⁶ carried out experimental studies of structure-mitoprotective activity relationships on derivatives of phenothiazine. In other recent study it was evaluated the comparative hepatoprotective effects of tocotrienol analogs by different mechanisms including mitoprotective activity.⁷

In this context, the great potential of applications of carbon nanotubes (CNT) has increased the interest with respect to other carbon biomaterials. The lipophilic character based on its high lipid/water partition coefficient and enough access to the mitochondrial membranes could induce cell death or apoptosis mediated by alteration of bioenergetic mechanisms.^7–9 Nevertheless is possible to reduce their toxicity through the chemical oxidation as in the case of SW/MWCNT-OH and/or SW/MWCNT-COOH. In this context, other authors,⁸ demonstrated in structure–property relationships studies that the acid-treated and taurine functionalized multi-walled carbon nanotubes (MWCNT) induced differential pulmonary toxicity in mice. Also, Ye et al.,¹⁰ examined the mitoprotective effects of multi-wall carbon nanotubes (MWCNT) over osteoclastogenesis in presence of cyclosporine A (CsA) (classical inhibitor of MPTP), rendering MWCNTs as a promising candidate for the treatment of osteoclast-related diseases.

On the other hand,¹¹ the combination of different methods is of the major interest for the rational design of nanoscale systems like CNT, iron nanoparticles, micelle nanoparticles, etc. For this reason, Quantitative Structure–Property/Activity Relationships (QSPR/QSAR) methods may play an important role as enabling or complementary tools to experimentation. Tropsha, Leszczynski, Toropov, Puzyn, Roy, Hopfinger, and others^11–28 have published some of the pioneering works on NQSPR studies of nanoparticles (NQSPR). The main assumption of QSPR/QSAR^29–32 models in general is that similar molecules have similar properties. Consequently, small changes in the structure of the system should correlate linearly with small changes on the values of its properties. Paradoxically, not all similar molecules have similar properties. Very recently, Gonzalez-Díaz et al.,³³ formulated a general-purpose PT-QSPR method combining QSPR/QSAR approach and Perturbation Theory (PT) ideas. PT-QSPR models are very useful for the study of complex molecular systems with simultaneous variation of multiple experimental boundary conditions. In fact, González-Díaz H. et al. have applied PT-QSPR analysis for the study of chemical reactivity, drug metabolism, vaccine epitopes, metabolic networks, and also micelle nanoparticles. In addition, Luan et al.³⁶ published the first PT-QSPR model for the cytotoxicity of nanoparticles in multiple experimental conditions. Kleandrova et al.^37,38 extended the idea to the PT-QSPR studies of ecotoxicity and cytotoxicity of uncoated and coated nanoparticles under different experimental conditions. Last, Speck-Planche et al.³⁹ published the first PT-QSPR model of antibacterial profiles of nanoparticles in multiple experimental conditions.

In this context, it is clear the importance of the development of new mitoprotective drugs studying diverse types of CNT. They may become of the major importance towards both an experimental characterization of CNT in different experimental conditions using a definition of a general model for the prediction of MPT response to different kind of CNT. However, there are no reports of combined experimental and PT-QSPR theoretical studies towards the development of predictive tools for the design of new CNT with mitoprotective activity on MPTP.

In this work, we are going to report the first combined study with experimental–theoretical techniques in this direction. Firstly, we used three different experimental swelling protocols to determine the mitoprotective activity (%P) of different CNT in multiple experimental boundary conditions (b_j). The conditions explored were b₀ = specifications of the biological assay carried out (MPT-inductor: Ca²⁺, Fe²⁺, H₂O₂; MPT-inhibitor: CsA, ruthenium red (RR), EGTA, quercetin (Q) and second MPT-inductor: KCN, ascorbic acid or VitC), b₁ = exposure time to CNT, b₂ = CNT concentrations, b₃ = CNT type (SW, SW + DW, MW), b₄ = CNT functionalization type (H, OH, COOH). We also changed different of CNT like b₅ = molecular weight/functionalization ratio (^minW/^maxW) or b₆ = maximal and minimal diameter (D_min/D_max) as physic-chemical properties. Next, we developed a new PT-QSPR model of mitoprotective activity. Last, we used the model to predict the values of %P of CNTs as mitoprotective activity in many different experimental conditions or after structural changes.

Materials and methods

Experimental section

Reagents and solutions. Sucrose, ethylene glycol-bis(β-aminoethyl)-N,N,N′,N′-tetraacetic acid (EGTA), CaCl₂, KCL, Fe²⁺–citrate solutions, H₂O₂, ascorbic acid, cyclosporine A (CsA), ruthenium red (RR), potassium succinate (plus 2 μM rotenone), K₂HPO₄, piperazine-N′-2-ethanesulfonic acid (Hepes-KOH), quercetin, KCN. All other reagents were commercial products of the highest purity grade available. Pristine-carbon nanotubes, hydroxylated carbon nanotubes (CNT-OH) and carboxylated carbon nanotubes (CNT-COOH) were provided by Cheaptubes Company (http://cheaptubes.com/shortohcnts.htm).

Carbon nanotubes characterization and stock solutions. Transmission Electron Microscope (TEM, Tecnai G2-12 – SpiritBiotwin FEI – 120 kV) was used to characterize the morphology of pristine and oxidized carbon nanotubes (MWCNT: CNT1; [SWCNT + DWCNT]-OH: CNT2; MWCNT-OH: CNT3, CNT4, CNT5; MWCNT-COOH: CNT6, CNT7, and CNT9; SWCNT-COOH: CNT8) see Fig. 1. In addition, Raman spectra were measured using a Renishaw Micro-Raman Spectroscopy System (Renishaw plc, Wotton-under-Edge, UK) at room temperature at a laser excitation wavelength of 514 nm (2.33 eV). All reactions were quenched to room temperature before Raman spectra were recorded to identify the characteristic peaks in the position of 1580 cm⁻¹ (G band of graphite) and the peak in the 1350 cm⁻¹ approximately associated to the presence of disorder and/or vacancy defects in the CNT-structure produced by chemical oxidation in the graphite structure (oxidized-CNT with OH and COOH functional groups) as shown in Fig. 2. The content of metallic impurities in all the samples was less than 5%. The proportions of metal impurities were determined by mass variation as a function of temperature using thermogravimetric analysis. The impurities of MWNT and SWNT with diameter (D) < 8 nm (CNTs 1, 2, 8 and 9) including their –OH and –COOH derivatives are the same: Co, Fe, Cr, Mg. For MWNT-OH and -COOH 10–20 nm are Co, Ni, Mg and Al (CNTs 4 and 7). For larger diameter MWNT (30–50 nm), the metallic impurities and its derivatives are Fe, Ni, Cr, Co, Mg (see Table 1 for details). CNTs were dissolved in dimethyl sulfoxide (DMSO: 900 μl) and ultrapure Milli Q water (10 μl) in individual stock solutions at a concentration of 1 mg ml⁻¹. Tip-sonication regime during 5–10 min was used to prevent CNTs agglomeration for MPT-assays carried out at a range of concentrations of 0.5–5 μg ml⁻¹. In this sense, the employed sonication time is known to generate a non-agglomerated suspension in a monodisperse state at concentrations below 100 μg ml⁻¹ according to Bergin et al. (2010). The sonication power was 9.3 W, with an energy input of 16.7 kJ at 25 °C using a Ultronique/Eco-sonics Q-3.0/40A sonicator. After, samples were stirred for 10–15 min. The resulting diluted suspensions were cooled to room temperature and filtered through a 0.22 μm polycarbonate membrane (Millipore, USA), before exposure to mitochondria suspensions.

Fig. 1 TEM images of carbon nanotubes used in this study. (a) Pristine-MWCMT [CNT1], (b) SW/DWCNT-OH [CNT2], (c) MWCNT-OH [CNT3], (d) MWCNT-OH [CNT4], (e) MWCNT-OH [CNT5], (f) MWCNT-COOH [CNT6], (g) MWCNT-COOH [CNT7], (h) SWCNT-COOH [CNT8], (i) MWCNT-COOH [CNT9] (TEM, Tecnai G2-12-SpiritBiotwin FEI- 120 kV).

Fig. 2 Raman spectra of carbon nanotubes used in this study. Pristine-MWCMT (CNT1), SW/DWCNT-OH (CNT2), MWCNT-OH (CNT3), MWCNT-OH (CNT4), MWCNT-OH (CNT5), MWCNT-COOH (CNT6), MWCNT-COOH (CNT7), SWCNT-COOH (CNT8), MWCNT-COOH (CNT9) (for more details see Materials and methods).

Table 1 Physico-chemical parameters (^kV_i) of CNT family

CNT properties^a			Wi (%)		Di (nm)		Li (μm)	Pi (%)	Mi (% metal)	Ci (S cm^−1)
n	Type	Function	min	max	min	max
a MWCNT = Multiple-Walled, SWCNT = Single-Walled, SW/DWCNT = DWCNT + SWCNT mixture, Wi (%) = functional groups (OH, COOH) carbon atoms ratio (%); the properties of the ith carbon nanotube (CNT) are Di = CNT outer diameter, Li = CNT length, Pi = purity, Ci = electric conductivity, Mi = metal impurities.
1	MWCNT	—	0.9^b	3.03^b	8	8	0.5–2	>95	<5	<1.5
2	SW/DWCNT	OH	0	3.96	1	4	0.5–2	>95	<5	<1.5
3	MWCNT	OH	0	3.86	1	8	0.5–2	>95	<5	<1.5
4	MWCNT	OH	3	4	10	20	0.5–2	>95	<5	<1.5
5	MWCNT	OH	1	1.06	30	50	0.5–2	>95	<5	<1.5
6	MWCNT	COOH	0	0.73	30	50	0.5–2	>95	<5	<1.5
7	MWCNT	COOH	3	4	10	20	0.5–2	>95	<5	<1.5
8	SWCNT	COOH	0	2.73	1	4	0.5–2	>95	<5	<1.5
9	MWCNT	COOH	0	3.86	1	8	0.5–2	>95	<5	<1.5

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Animal welfare. Male Wistar rats (4 month-old; approx. 200 g) received food and water ad libitum. They were kept in plastic cages with wire tops in a light-controlled room (12 h light–dark cycle) at 22 ± 2 °C before starting the study in accordance with the Guidelines on the Handling and Training of Laboratory Animals published by the Universities Federation for Animal Welfare (1992).

Isolation of rat-liver mitochondria. We used standard differential centrifugation to isolate the mitochondria.⁴⁰ Male Wistar rats weighing approximately 200 g were euthanized by decapitation; livers (10–15 g) were immediately removed, sliced in medium (50 ml) consisting of 250 mM sucrose, 1 mM ethyleneglycol-bis(β-aminoethyl)-N,N,N′,N′-tetraacetic acid (EGTA) and 10 mM HEPES-KOH, pH 7.2, and homogenized three times for 15 s at 1 min intervals using a Potter-Elvehjem homogenizer. Homogenates were centrifuged (580 g, 5 min) and the resulting supernatant further centrifuged (10 300 × g, 10 min). Pellets were then suspended in medium (10 ml) consisting of 250 mM sucrose, 0.3 mM EGTA and 10 mM HEPES-KOH, pH 7.2, and centrifuged (3400 × g, 15 min). The final mitochondrial pellet was suspended in medium (1 ml) consisting of 250 mM sucrose and 10 mM HEPES-KOH, pH 7.2, and used within 3 h. Mitochondrial protein contents were determined by the Biuret reaction.⁴¹

Standard incubation procedure. Mitochondria isolated were energized with 5 mM potassium succinate (plus 2.5 μM rotenone) in a standard incubation medium consisting of 125 mM sucrose, 65 mM KCl, 2 mM inorganic phosphate (K₂HPO₄) and 10 mM HEPES-KOH pH 7.4 at 30 °C.⁴¹

Determinations of MPT induction in different conditions. MPT was measured through monitoring the decrease in apparent absorbance of the mitochondrial suspension measured at 540 nm in a Hitachi U-3000 spectrophotometer equipped with magnetic stirring and temperature control (28 °C).⁴² Mitochondria were incubated in the standard incubation medium at 1 mg of mitochondrial protein per ml. Before the spectrophotometric MPT-measurements the blanks with CNTs were run to compare with mitochondria exposed to CNT and interferences of carbon nanotubes were not observed at 400–550 nm. MPT was induced by three different experimental conditions: (1) swelling assay induced by Ca²⁺ 20 μM, for this instance, we designed three protocols using different MPT-inhibitors controls as CsA 1 μM a known classic MPT-inhibitor of mitochondrial swelling induced by calcium overload; ruthenium red (RR), 1 μM an specific blocker of mitochondrial calcium uniporter that interferes with Ca²⁺ influx from cytoplasm to mitochondrial matrix and EGTA 100 μM as chelating agent. The combinations tested were: [Ca²⁺ 20 μM]; [Ca²⁺ 20 μM + CsA 1 μM]; [Ca²⁺ 20 μM + RR 1 μM]; [Ca²⁺ 20 μM + EGTA 100 μM] to represent MPT-inhibition (100%) and [Ca²⁺ 20 μM + CNTs]; (2) for swelling assay induced by Fe²⁺ 20 μM were used as MPT-inhibitors control (EGTA 100 μM) and additional control as second MPT-inductors to recreate synergistic action on MPT. Followed this idea it was used (KCN 1 μM: indirect MPT-inductor by inhibition of cytochrome c oxidase associated to ROS-formation; ascorbic acid or VitC 100 μM: a strong reducing agent that induce similarly MPT based in ROS-generation). For this instance, the combinations evaluated were: [Fe²⁺ 20 μM], [Fe²⁺ 20 μM + EGTA 100 μM] (100% of MPT-inhibition), [Fe²⁺ 20 μM + CNTs]. For evaluate the maximum value of MPT-induction induced by iron we performed the following combinations in order to mitotoxic potential: [Fe²⁺ 20 μM + VitC 1 μM + CNTs, 5 μg ml⁻¹] > [Fe²⁺ 20 μM + KCN 1 μM + CNTs, 5 μg ml⁻¹] > [Fe²⁺ 20 μM + CNTs]. Please note that this conditions proposed are propitious to induce mitochondrial permeability transition based in Fenton–Haber–Weiss reaction. (3) Swelling assay induced by H₂O₂ 300 μM in this test was used Fe²⁺ 20 μM as second MPT-inductors to recreate synergistic action on MPT based in pro-oxidant conditions (Fenton–Haber–Weiss reaction) and quercetin 50 μM (Q: MPT-inhibitor, known antioxidant, employed as control based in ROS-inhibition that prevent the MPTP-thiols group oxidation associated to MPT-induction in pro-oxidant conditions). The combinations tested were [H₂O₂ 300 μM], [H₂O₂ 300 μM + quercetin 50 μM] (100% of MPT-inhibition in pro-oxidant conditions), [H₂O₂ 300 μM + CsA 1 μM], [H₂O₂ 300 μM + CNTs], [H₂O₂ 300 μM + Fe²⁺ 20 μM + CNTs, 5 μg ml⁻¹] (100% of MPT-induction in pro-oxidant conditions). These three mitochondrial swelling protocols: (1) Ca²⁺ 20 μM, (2) Fe²⁺ 20 μM, and (3) H₂O₂ 300 μM; were performed in the presence of CNT in different concentrations (0–5 μg ml⁻¹) to investigate in parallel the mechanisms and factors directly or indirectly involved in MPTP-inhibition. All the swelling experiments where the second MPT-inductor is present were performed with the highest concentration (5 μg ml⁻¹) to challenge the mitoprotective potential of CNT.^41,43–48 In addition, we considered other factors as metal impurities. In this context, the maximum expected concentration of metal impurities should be 0.25 μg ml⁻¹ (5% of the highest concentration in the CNTs samples) which possess no risk of MPT induction in this low levels.^1–5 In Fig. 3, we illustrate the workflow of this Experimental section.

Fig. 3 Workflow of the Experimental section.

Microscopy analysis of mitochondrial swelling induction associated to membrane potential. The suspension of isolated rat-liver mitochondria were pre-incubated with a specific mitochondrial dye (JC-1) in 0.2 mg ml⁻¹ for 15 min according Reers et al.⁴⁹ Images were analyzed using a fluorescent microscope (Olympus IX81, Markham, Ontario, Canada) equipped with a DP72 digital camera to study the effects of different mitochondrial swelling assays associated with the loss mitochondrial membrane potential (red to green fluorescent) after incubation with a MPT-inductor (Ca²⁺, Fe²⁺, or H₂O₂) and in the presence or the absence of a MPT-inhibitor (CsA, RR, EGTA or one kind of CNT).

Theoretical section

Theoretical details of the PT-NQSPR models. Very recently, Gonzalez-Díaz et al.³³ formulated a general-purpose Perturbation Theory (PT) model for Chemoinformatics problems with multiple-boundary experimental conditions. In this work, we are going to re-formulate this theory in order to develop a new type of PT-QSPR models for Nanomaterials (PT-NQSPR models). In Fig. 4, we illustrate the workflow for this theoretical part. Specifically, the new PT-NQSPR models developed here are expected values to predict the effect of different CNT structures in three different MPT induction assays under multiple experimental boundary conditions. The PT-NQSPR model proposed here is an additive equation with linear/non-linear terms expressed in the following form:

Fig. 4 Workflow used here to seek the PT-QSPR models.

We used Multivariate Linear Regression (MLR) and Non-Linear Regression (NLR) algorithms implemented in the software STATISTICA⁵⁰ to determine the values of the coefficients (a_k) and other parameters of the model. In our PT-NQSPR model, the output ′f(ε_ij)_new is a function of the expected absorbance. In the simplest case we use the identity function and ′f(ε_ij)_new = ^newε_ij is equal to the predicted absorbance value under the new sub-set of experimental boundary conditions of reference. Other transformation functions applied to ε_ij were: ′f(ε_ij) = 1/ε_ij, (1/ε_ij)², or −log(ε_ij), see Table 2.

Table 2 Description of input variables and functions

Coefficient	Input variable	MA	Function ^kf	Function examples	Information
—	—	—	′f	(εij)new, 1/(εij)new^2, −log(εij)new	Predicted absorbance
e0	—	—	—	—	Error term
a0	—	—	^0f	〈εij〉	Average of value of absorbance for all CNTs samples for multiple experimental conditions (assay, CNT-type, chemical function, MPT-inductors, MPT-inhibitors)
a1	tij	Δtij	^1f	Δtij (s), exp(−Δtij (s))	Exposure time
a2	cij	Δcij	^2f	Δcij (μg ml^−1), 1/(1 + Δcij (μg ml^−1))	CNT concentration
a3	^maxWi	ΔWij	^3f	ΔWij (%)max	CNT maximum function/carbon ratio
a4	^minDi	ΔDij	^4f	ΔDij (nm)min	CNT minimum outer diameter

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In addition, we are going to consider different sub-sets of input experimental boundary conditions of reference ^refb_j ≡ (b₀, b₁, b₂, b₃… b₆). In the equation we introduced one specific input term to quantify each one of these conditions. The elements of the vectors v_i = [⁰f(ε_ij)_ref, ¹f(ΔV_1,j),… ²f(ΔV_2,j),… ^kmaxf(ΔV_kmax,j)] are the inputs of this model.

This first term of this PT-NQSPR model is the function ⁰f(ε_ij)_ref = 〈ε_ij〉_new. This function is the average of absorbance value for all CNTs measured under the experimental conditions of the output. It means that we could interpret ⁰f(ε_ij)_new as the new expected value of absorbance for CNTs measured under the same sub-set of experimental conditions (for a normal distribution).

Following this idea were incorporated the ΔV_kj parameters as the second class of terms, which are functions of the Box–Jenkins operators (moving average) used here as perturbation terms ^kf(ΔV_k,j). The functions ^kf represent transformations ^kf(ΔV_kj) of the moving averages ΔV_kj of the original input variables ^kV_i for i-th type of CNT in j-th MPT-assay of one specify boundary condition b_kj.

The value 〈V_kj〉 is interpreted as the average of the k-th physicochemical properties (^kV_ij), see the eqn (3):

This (^kV_ij) of CNT was used to quantify the effect over the output ⁰f(ε_ij)_new of perturbations on different experimental boundary conditions (b_j). The following set of conditions are related to the CNT-structure, b₃ = CNT type (SW, SW + DW, MW), b₄ = CNT functionalization type (H, OH, COOH), b₅ = CNT chemical function (OH, COOH, or none) in term of molecular weight/functionalization ratio and b₆ = maximal and minimal diameter (D_min/D_max) and for b₀ = multiple experimental boundary conditions. That include the average of the values with the same conditions as mitochondrial swelling assays using the MPT-inductor (Ca²⁺, Fe³⁺, H₂O₂, or none) or toxic control TC₁(+), second MPT-inductor (KCN, VitC, or none) or second toxic control TC₂(+), MPT-inhibitors or inhibitor control IC₁(−) (CsA or none) and non-classical MPT-inhibitor control (RR, EGTA, quercetin, or none). Last, included other conditions related to the assay like, solvent (DMSO, or none), replicate sample (Yes, No).

For instance, for exposure time the condition b₁ = exposure time (t_ij) of samples corresponding to the i-th CNT used in bj-th MPT-assay. Some of the functions used to transform these variables where: ¹f(Δt_ij) = 1/(Δt_ij), exp(−Δt_ij), and the other b₂ = concentration (c_ij) of i-th CNT in the j-th assay is ²f(Δc_ij) = 1/Δc_ij or 1/(1 + Δc_ij) for CNT concentration. In addition other functions as ³f(ΔW_ij) to molecular weight/functionalization ratio (b₅), ⁴f(ΔD_ij) for maximal and minimal diameter (b₆) (see Table 2).

Results and discussion

Experimental measure of CNT-MPT modulation in different conditions

The important role of mitochondria to regulate intracellular calcium levels has been associated with several chronic diseases as neurodegenerative diseases, cardiovascular and cancer, which currently have high levels of morbidity and mortality.⁵¹ In this study, we performed three experimental protocols to evaluate the effect of CNT in mitochondrial permeability transition (swelling) induced by different mechanisms, basing each experimental protocol on the causes and factors that trigger this process, as Ca²⁺ overload in the mitochondrial matrix and loss of redox balance under conditions of iron overload and high peroxide production. Under these conditions, the physic-chemicals properties of CNT family were evaluated and linked to their capacity for the inhibition of MPT.^52,53 For this instances the CNT-interferences in spectrophotometric MPT-measurements it were not detected based on the non-existence of the classic UV-visible absorption peaks of mitochondrial redox hemoprotein (408 to 550 nm) as oxidized cytochrome c (Fe³⁺) at 408 nm and 530 nm and three peaks of reduced cytochrome c (Fe²⁺) at 415 nm, 520 nm, and 550 nm when we monitored the decrease in absorbance of the mitochondrial suspension measured at 540 nm used to evaluate the mitochondria swelling in the presence of carbon nanotubes as mentioned in Materials and methods section.⁵²

At first, we evaluated the effect of CNT family on MPT induced by Ca²⁺ 20 μM, which has been described in many pathological conditions as cancer, neurodegenerative diseases and ischemia-reperfusion processes.^1–3

In this sense, the selective MPT-modulation with CNT could lead to alternatives for the treatment of cancer and its inhibition may prevent cell and tissue damage associated with a number of diseases. The isolated mitochondria exposed to high calcium concentrations are susceptible to the opening of mitochondrial permeability transition pore, the larger implications of this phenomenon are the diffusion of solutes of up to 1500 Dalton, through the inner mitochondrial membrane, depletion of ATP levels and dissipation of mitochondrial membrane potential as illustrated in Fig. 5. These effects are accompanied by mitochondrial swelling caused by the osmotic difference between the mitochondrial matrix and the extra-mitochondrial medium, followed by outer membrane rupture and release of pro-apoptotic signals (caspases 3 and 9) from the inter-membrane space.^3,4

Fig. 5 Isolated rat-liver mitochondria were incubated with a specific mitochondrial dye (JC-1) in 0.2 mg ml⁻¹ for 15 min. Show representative fluorescent images of effects on mitochondrial membrane potential for different swelling conditions after exposure with MPT-inductor (Ca²⁺, Fe²⁺ or H₂O₂) (A) and MPT-inhibitor (CsA, RR, EGTA or CNT-COOH > CNT-OH > pristine-CNT) (B) were examined under a fluorescence microscope (×600 magnification). Scale bars 50 μm.

Firstly the calcium dependence on MPT was verified by different mechanism, performing teste in the presence of Ca²⁺ (20 μM) with CsA that inhibits the binding of Ca²⁺ to cyclophilin D, in this condition calcium overload produce conformational changes that induce MPT⁵⁴ (assay P₁). Also, other non-specific MPT-inhibitors controls were evaluated as EGTA, a calcium chelating agent (assay P₂) and ruthenium red (RR), which interfere in the Ca²⁺ uptake by the mitochondrial uniporter⁵⁵ (assay P₃). All these tests were conducted as experimental controls to express the maximum of mitoprotective activity (%P) by different mechanisms.

Swelling assays was performed to study the MPT-effects of CNT family induced by Ca²⁺ 20 μM to find similarities or differences in the pattern of inhibition between CNT family and classic and non-classical MPT-inhibitor controls as showed in Table 3. The results showed low capacity of CNT family to inhibit the MPT induced by Ca²⁺ 20 μM in most cases, when compared with CsA, the main specific inhibitor of MPT pore induced by calcium overload and also using non-specific MPT-inhibitors controls (EGTA 100 μM, RR 1 μM) used as negative control or MPT-inhibitors.⁵⁵

Table 3 Experimental values of mitochondrial swelling induced by Ca²⁺ for CNT family

CNT^a						Experimental mitoprotective activity vs. Ca^2+^b
ni	Type	Function	Wi	Di	cij	P1	Nj	P2	Nj	P3	Nj
a MWCNT = Multiple-Walled, SWCNT = Single-Walled, SW/WTCNT = MWCNT + SWCNT mixture.b Mitoprotective activity, P(%) = 100[εij(CNT + TC + S)obs − εij(TC + S)obs]/[εij(IC + TC + S)obs − εij(TC + S)obs] and Nj is the number of replicates of the assay. CNT = carbon nanotube, TC = toxic control (MPT-inductor), IC = inhibitor control (MPT-inhibitor), S = solvent. The details of the assays are the following: for toxicity assay P1 (a = 1), TC = Ca^2+, IC = CsA, and solvent = DMSO, for assay P2 (a = 2) TC = Ca^2+, IC = EGTA and solvent = DMSO; and for assay P3 (a = 3), TC = Ca^2+, IC = RR, and solvent = DMSO.
1	MWCNT	—	3.03^b	8	0.5	0	42	0	42	0	42
					1	3.5	42	3.4	42	4.1	42
					3	0	42	0	42	0	42
					5	32.3	42	31.2	42	37.8	42
2	SW/DWCNT	OH	3.96	1	0.5	0	21	0	21	0	21
					1	0	21	0	21	0	21
					3	31.9	21	30.7	21	37.3	21
					5	60.7	21	58.5	21	71.0	21
3	MWCNT	OH	3.86	1	0.5	8.3	42	8.0	42	9.8	42
					1	17.3	42	16.7	42	20.3	42
					3	7.3	42	7.1	42	8.6	42
					5	20.2	42	19.5	42	23.7	42
4	MWCNT	OH	4	10	0.5	0	21	0	21	0	21
					1	0	21	0	21	0	21
					3	0	21	0	21	0	21
					5	0	21	0	21	0	21
5	MWCNT	OH	1.06	30	0.5	0	42	0	42	0	42
					1	0	42	0	42	0	42
					3	0	42	0	42	0	42
					5	6.4	42	6.2	42	7.5	42
6	MWCNT	COOH	0.73	30	0.5	10.6	21	10.2	21	12.4	21
					1	0	21	0	21	0	21
					3	0	21	0	21	0	21
					5	0	21	0	21	0	21
7	MWCNT	COOH	4	10	0.5	0	21	0	21	0	21
					1	0	21	0	21	0	21
					3	66.9	21	64.5	21	78.2	21
					5	71.2	21	68.7	21	83.3	21
8	SWCNT	COOH	2.73	1	0.5	0	21	0	21	0	21
					1	0	21	0	21	0	21
					3	22.9	21	22.1	21	26.8	21
					5	67.3	21	64.9	21	78.7	21
9	MWCNT	COOH	3.86	1	0.5	0	21	0	21	0	21
					1	0	21	0	21	0	21
					3	75.9	21	73.2	21	88.8	21
					5	81.4	21	78.5	21	95.2	21
	Groups		Wi	Di	cij	eij	Nj	eij	Nj	eij	Nj
	IC + S	Average	2.435	10.25	2.5	0.353	1071	0.353	1071	0.353	1071
		± SD				0.000		0.000		0.000
	TC + IC + S	Average				0.395	63	0.397	63	0.389	63
		± SD				0.0075		0.001		0.0079

---

Several aspects must be considered to explain the low and variable MPT inhibition induced by CNT family against mitochondrial Ca²⁺ overload. First, CNT should cross the outer mitochondrial membrane, mitochondrial inter-membrane space, and matrix, process that should be facilitated in virtue of its high lipid partition coefficient/water.⁵⁶ However the modest mitoprotective effects (%P) found may be related with certain structural characteristics of CNT family. In this sense, higher %P consistent with a decreased of mitochondrial swelling induced by Ca²⁺ was observed for functionalized CNT, following the order CNT-COOH (MWCNT-9, MWCNT-7, SWCNT8, MWCNT-6) > CNT-OH (SWCNT-2, MWCNT-3, MWCNT-5, MWCNT-4) > pristine MWCNT (MWCNT-1). According to the mitoprotective values (%P), CNT-9 is the more mitoprotector and CNT-1 is mitotoxic. We suggest a mechanism based in Ca²⁺ adsorption by carboxyl groups (COO⁻) of CNT-COOH, which should reduce the free concentration of this divalent ion in the mitochondrial matrix. Chemical adsorption capacity of oxidized CNT has been demonstrated in other nanoQSAR studies using aromatic organic and inorganic MPT inductors.⁵⁷ Also for carboxylated-CNT, specifically CNT-7, CNT-8, and CNT-9 it was observed a significant increase of %P at higher concentrations (3.0 and 5.0 μg ml⁻¹). The lower %P of hydroxylated-CNT compared with their similar carboxylated-CNT could be related with a lower Ca²⁺ adsorption capacity, although higher when compared with similar pristine-CNT, that presented mitotoxic effect.⁵⁷

In this case, the absence of COOH functionalization (MWCNT) could generate mitotoxic effects based in this mechanism and, under this context, the toxicity of carbon nanomaterials should be reduced through the chemical oxidation as in the case of CNT-OH and CNT-COOH according to Zhenbao et al.⁵⁸ Other possible inhibitory mechanisms could be the interaction of carboxyl groups of carboxylated-CNT with positive NH₂ groups of VDAC and ANT to prevent conformational changes necessary for MPTP components assembly and apoptosis.^59–61 A significant number of studies have demonstrated that MPT-modulation is mediated by conformational changes of VDAC and ANT located on the outer and inner mitochondrial membrane respectively.^61–63

Next, experiments were performed to study the MPT-effects induced by iron overload for CNT family. Iron overloading has been proposed to cause dissipation of membrane potential and increase of calcium efflux in mitochondria dynamics that are often associated with loss of redox balance, involving oxidation of MPT pore-sulfhydryl groups.^64–66 For this instance were conducted swelling assays in the presence of Fe²⁺ 20 μM. Also it were considered other more aggressive mitotoxic or condition of synergism to enhance the MPT-effects of iron overload combining separately with KCN 1 μM, an inhibitor of mitochondrial complex IV (cytochrome c oxidase) and consequently of the electrons transport chain (assay P₂). Also with ascorbic acid 300 μM, a strong reducing agent that favors the reduction of Fe³⁺ to Fe²⁺ and thus inducing pro-oxidant states (assay P₃).^53,67 Both non-classical MPT inductors and second inductor were used as positive controls to challenge the mitoprotective potential of CNT family to reverse mitochondrial swelling induced by Fe²⁺ 20 μM.⁶⁸ Under this protocol, EGTA 100 μM was used as negative control or MPT-inhibitors as show in Table 4.

Table 4 Experimental values of mitochondrial swelling induced by Fe²⁺ for CNT family

CNTi^a						Experimental mitoprotective activity vs. Fe^2+^b
ni	Type	Function	Wi	Di	cij	P1	Nj	P2	Nj	P3	Nj
a MWCNT = Multiple-Walled, SWCNT = Single-Walled, SW/WTCNT = MWCNT + SWCNT mixture.b Mitoprotective activity, P(%) = 100[εij(CNT + TC + S)obs − εij(TC + S)obs]/[εij(IC + TC + S)obs − εij(TC + S)obs] and Nj is the number of replicates of the jth assay. CNT = carbon nanotube, TC = toxic control (MPT-inductor), IC = inhibitor control (MPT-inhibitor), S = solvent. The details of the assays are the following: assay P1 (a = 1) TC1 = Fe^2+, IC = EGTA and S = DMSO; assay P2 (a = 3), TC1 = Fe^2+, TC2 = KCN, IC = EGTA and solvent = DMSO and assay P3 (a = 3), TC1 = Fe^2+, TC2 = VitC, IC = EGTA and solvent = DMSO.
1	MWCNT	—	3.03^b	8	0.5	0	14	0	14	0	14
					1	0	14	0	14	0	14
					3	0	16	0	16	0	16
					5	20.3	14	90.8	14	0	14
2	SW/DWCNT	OH	3.96	1	0.5	0	14	0	14	0	14
					1	35.3	14	100	14	0	14
					3	84.8	16	100	16	0	16
					5	100	14	100	14	67.2	14
3	MWCNT	OH	3.86	1	0.5	0	14	42.5	14	0	14
					1	0	14	79.4	14	0	14
					3	93.3	16	100	16	0	16
					5	92.5	14	100	14	0	14
4	MWCNT	OH	4	10	0.5	0	14	0	14	0	14
					1	44.4	14	100	14	0	14
					3	100	16	100	16	0	16
					5	100	14	100	14	10.7	14
5	MWCNT	OH	1.06	30	0.5	0	14	0	14	0	14
					1	0	14	0	14	0	14
					3	0	16	0	16	0	16
					5	6.8	14	30.2	14	0	14
6	MWCNT	COOH	0.73	30	0.5	0	14	68.4	14	0	14
					1	0	14	14.7	14	0	14
					3	0	16	16.9	16	0	16
					5	80.4	14	100	14	0	14
7	MW	COOH	4	10	0.5	12.0	14	53.8	14	0	14
					1	91.0	14	100	14	0	14
					3	100	16	100	16	0	16
					5	100	14	100	14	0	14
8	SWCNT	COOH	2.73	1	0.5	0	14	0	14	0	14
					1	37.6	14	100	14	0	14
					3	90.7	16	100	16	0	16
					5	100	14	100	14	2.3	14
9	MW	COOH	3.86	1	0.5	0	14	0	14	0	14
					1	30.8	14	100	14	0	14
					3	100	16	100	16	0	16
					5	100	14	100	14	24.8	14
	Groups		〈Wi〉	〈Di〉	〈cij〉	〈eij〉	Nj	〈eij〉	Nj	〈eij〉	Nj
	IC + S	Average	2.435	10.25	2.5	0.393	189	0.378	189	0.337	126
		± SD				0.000		0.000		0.000
	TC + IC + S	Average				0.374	781	0.374	781	0.374	781
		± SD				0.003		0.001		0.030

---

Mitoprotective activity (%P) was higher for carboxylated-CNT and hydroxylated-CNT in comparison with the lowest %P of pristine-CNT, more mitotoxic, results that fits with a previous study that reported increased cytotoxicity to pristine CNT in relation to the functionalized-CNT.⁶⁹ It is important to note that the %P of CNT family was considerably higher to Fe²⁺ swelling than to Ca²⁺ swelling tests. But in both cases the response pattern was similar, according to the functionalization type: CNT-COOH (MWCNT-9, MWCNT-7, SWCNT-8, MWCNT-6) > CNT-OH (SWCNT-2, MWCNT-3, MWCNT-5, MWCNT-4) > pristine-CNT (MWCNT-1). A direct chelation of mitochondrial iron has been suggested as an attractive therapeutic strategy for several clinical disorders involving iron imbalance.⁵³ In present study, the inhibition of MPT could involve the interaction of the COOH and OH groups of oxidized-CNT with the reduced state (Fe²⁺) of heme group in the mitochondrial complexes I and III, known to be mitochondrial ROS producers. This interaction should form a coordination complex between the oxidized-CNT and the metallic center, helping to reduce the levels of ferrous ions (Fe²⁺), preventing Fenton–Haber–Weiss reaction that leads to the generation of hydroxyl radical.⁵³ Following this idea, we suggest a possible mechanism based on iron coordination by COOH and OH groups of the CNT combined with chemical adsorption mechanisms onto oxidized-MWCNT to reduce the excess in the Fe²⁺ free concentrations, thus preventing mitochondrial swelling in pro-oxidant conditions.^53,58 The P% for the MPT-assay using the [Fe²⁺ 20 μM + KCN 1 μM + CNTs, 5 μg ml⁻¹] (P₂) showed a similar behavior to MPT-assay using [Fe²⁺ 20 μM + CNTs, 5 μg ml⁻¹] (P₁) in the order carboxylated-CNT > hydroxylated-CNT > pristine-CNT for mitoprotective activity (%P). The evidences suggest therapeutic potential of oxidized nanotubes to reverse the swelling induced by Fe²⁺ overload despite the participation of uncoupling mitochondrial mechanisms as KCN 1 μM, which acts synergistically favoring the opening of MPT-pore. However only carboxylated-CNT (5) and hydroxylated-CNT (2, 3, 6) were able to reverse the pro-oxidant effects generated by iron overload combined with ascorbic acid 300 μM, a strong reducing agent. Also according to the walls number, it was observed higher values of mitoprotection in the order MW-motifs > SW + DW-motif > SW-motifs, these evidences are coherent with studies performed using K562 and HeLa cells cultured in the presence of SWCNT, SWNTs-OH, MWCNT-COOH at concentrations ranging from 1 to 100 μg ml⁻¹ based in inhibition of telomerase activity.⁵⁹

Finally, assessments were performed to analyze the potential of CNT family to reverse the MPT induced in pro-oxidant conditions of high mitochondrial H₂O₂ levels as shown in Table 5. It was performed mitochondrial swelling assays in the presence of H₂O₂ 300 μM and using a known antioxidant, quercetin 50 μM as negative MPT-control as [H₂O₂ 300 μM + quercetin 50 μM] (assay P₁).⁷⁰ The same protocol was run taking CsA 1 μM as [H₂O₂ 300 μM + CsA 1 μM] a negative additional MPT-control (assay P₂). Also it was performed a mitochondrial swelling assay induced by H₂O₂ 300 μM using Fe²⁺ 20 μM to produce MPT-synergism conditions, for this instance the combination [H₂O₂ 300 μM + Fe²⁺ 20 μM + CNTs, 5 μg ml⁻¹] (assay P₃) was employed, to intensify the pro-oxidant conditions. In this case it was also used quercetin 50 μM as negative MPT-control of references to find similarities or significant differences in the MPT-modulation based in pro-oxidant induced by H₂O₂ 300 μM of CNT family.

Table 5 Experimental values of mitochondrial swelling induced by H₂O₂ for CNT family

CNT^a						Experimental mitoprotective activity vs. H2O2^b
ni	Type	Function	Wi	Di	cij	P1	Nj	P2	Nj	P3	Nj
a MWCNT = Multiple-Walled, SWCNT = Single-Walled, SW/WTCNT = MWCNT + SWCNT mixture.b Mitoprotective activity, P(%) = 100[εij(CNT + TC + S)obs − εij(TC + S)obs]/[εij(IC + TC + S)obs − εij(TC + S)obs] and N is the number of replicates of the assay. CNT = carbon nanotube, TC = toxic control (MPT-inductor), IC = inhibitor control (MPT-inhibitor), S = solvent. The details of the assays are the following: assay P1 (a = 1) TC1 = H2O2, IC = Q and solvent = DMSO; assay P2 (a = 2), TC1 = H2O2, IC = CsA, and solvent = DMSO; assay P3 (a = 2), TC1 = H2O2, TC2 = Fe^2+, IC = Q, and solvent = DMSO.
1	MWCNT	—	3.03^b	8	0.5	0	0	0	0	0	0
					1	0	7	0	7	0	7
					3	0	7	0	7	0	7
					5	0	7	100	7	0	7
2	SW/DWCNT	OH	3.96	1	0.5	0	0	0	0	0	0
					1	0	21	65	21	0	21
					3	100	21	80	21	0	21
					5	100	21	81.0	21	72.7	21
3	MWCNT	OH	3.86	1	0.5	0	0	0	0	0	0
					1	100	21	95	21	0	21
					3	100	21	97	21	0	21
					5	100	21	97.5	21	98.0	21
4	MWCNT	OH	4	10	0.5	0	0	0	0	0	0
					1	100	21	51	21	0	21
					3	100	21	97.5	21	0	21
					5	100	21	95.5	21	100	21
5	MWCNT	OH	1.06	30	0.5	0	0	0	0	0	0
					1	100	21	95	21	0	21
					3	100	21	97	21	0	21
					5	100	21	97.5	21	100	21
6	MWCNT	COOH	0.73	30	0.5	0	0	0	0	0	0
					1	100	21	51	21	0	21
					3	100	21	97	21	0	21
					5	100	21	97.5	21	91.0	21
7	MWCNT	COOH	4	10	0.5	0	0	0	0	0	0
					1	100	21	80	21	0	21
					3	100	21	81	21	0	21
					5	100	21	91	21	100	21
8	SWCNT	COOH	2.73	1	0.5	0	0	0	0	0	0
					1	100	21	80	21	0	21
					3	100	21	81	21	0	21
					5	100	21	91	21	90.2	21
9	MWCNT	COOH	3.86	1	0.5	0	0	0	0	0	0
					1	100	21	86	21	0	21
					3	100	21	97	21	0	21
					5	100	21	95.5	21	100	21
	Groups		〈Wi〉	〈Di〉	〈cij〉	〈eij〉	Nj	〈eij〉	Nj	〈eij〉	Nj
	IC + S	Average	2.435	10.25	2.5	0.366	175	0.404	175	0.241	105
		± SD				0.000		0.000		0.000
	TC + IC + S	Average				0.375	525	0.375	525	0.375	525
		± SD				0.0015		0.0068			0.00

---

P% values mitoprotection of CNT family were remarkably high in the swelling assays P₁ and P₂ except for pristine-CNT. The result showed %P very similar between CNT-COOH and CNT-OH in the conditions listed above to mitochondrial swelling assays induced by Ca²⁺ and Fe²⁺ at 20 μM. This suggests that OH and COOH functionalization are important to reverse the mitochondrial swelling associated to pro-oxidant conditions.⁷¹ The high %P values of functionalized-CNT exhibited a similar pattern of inhibition, when compared with the two controls used quercetin 50 μM (non-specific MPT-inhibitors) and CsA 1 μM (specific MPT-inhibitors), pointing that the inhibition of functionalized-CNT could be associated with the ability to attenuate the loss of redox balance induced by H₂O₂ overload.^51,53

The mitochondria has an efficient antioxidant defense system, including superoxide dismutase, glutathione peroxidase, glutathione reductase, reduced glutathione, NAD(P)⁺ and other cofactors. In physiological conditions the mitochondrial superoxide dismutase transforms the superoxide radical (O₂˙) to the less reactive H₂O₂, which is reduced to H₂O by the action of GSH and glutathione peroxidase.⁵¹

However, several mito-pathological conditions as peroxide overload (300 μM) reduced the antioxidant defenses and increases oxidative stress by H₂O₂ accumulation, in our study. The presence of Fe²⁺ induces formation of hydroxyl radical (˙OH) through Fenton–Haber–Weiss reaction involved in the oxidation of thiol groups constituents of MPTP. In the case of assay P₃, only the highest concentration, 5 μg ml⁻¹ was able to reverse the mitochondrial swelling induced by pro-oxidant condition⁵¹ similar to quercetin 50 μM.^70–72 The obtained results should contribute for the rational design of novels carbon nanomaterial and point the way to new areas of research as Mitochondrial Nanomedicine,^73,74 based in the effects of carboxylated and hydroxylate carbon nanotubes on mitochondrial permeability transition.

PT-NQSPR model in multiple boundary conditions

In classic response-concentration models, we can use alternative forms of the hill-shaped curve to seek a dose–response equation in order to calculate IC₅₀ values.⁵⁰ For instance, the software MasterPlex (http://psg.hitachi-solutions.com/masterplex) allows to choose different algorithms such as: 4 parameters logistic (4PL), 5 parameters logistic (5PL), quadratic log–log it, log–log or linear model. The reader can see examples of the use of this software and these algorithms in previous works.^51–55 However, the 4PL and 5PL forms have some drawbacks. Some authors have reported studies towards the search of alternatives models to these curves. For instance, Liao et al. (2009) reported a re-parameterization of 5PL dose–response curve.⁷⁵ In any case, almost all of these alternatives fail when we need to account for multiple experimental boundary conditions (b_j). It means that the model fails when we want to predict the response ε_i for the ith compound not only for different concentrations of the compound (c_i) in a single assay. This points to the need of a model able to predict multiple responses ε_ij for the same ith compound when we change multiple boundary conditions like b₀ = multiple experimental conditions of j-th MPT-assays, b₂ = different values of concentration c_ij for the compound on the different j-th MPT-assays, different exposure time (0–600 s) to the compound b₁ = t_ij. We can talk here also of different structural or physicochemical properties of the compound under study. For instance, in the case of CNT we consider the CNT type, b₃ = Single-Walled (SW), Multiple-Walled (MW), or mixtures of SW + DW. In these cases, 4PL/5PL and similar models are unable to fit all the data at the same time and we need to seek a different equation for each sub-set of changing boundary conditions b_kj. In this work, we propose by the first time a PT-NQSPR model able to account for changes in multiple experimental boundary conditions (b_j). The general formula of this models the following:

′f(ε_ij)_new = e₀ + a₀·〈ε_ij〉_new + a₁·¹f(Δt_ij) + a₂·²f(Δc_ij) + a₃·³f(ΔW_ij) + a₄·⁴f(ΔD_ij) (4)

′f(ε_ij)_new = e₀ + a₀·〈ε_ij〉_new + a₁·¹f(t_i − 〈t_ij〉) + a₂·²f(c_i − 〈c_ij〉) + a₃·³f(W_i − 〈W_ij〉) + a₄·⁴f(D_i − 〈D_ij〉) (5)

We can compare the equation above with the compact notation presented in the Materials and methods section. In this PT-NQSPR model we can also use (like in 4PL/5PL models) optional weighting schemes for the response variable (output function): ′f(ε_ij) = ε_ij, 1/ε_ij, (1/ε_ij)², or −log(ε_ij). We can incorporate different functions ⁰f = 〈ε_ij〉 of the expected value of ε_ij for a sub-set of conditions (e.g., different MPT-assays). We can also use different functions for the input variable; such as: ¹f = Δt_ij, 1/Δt_ij or exp(−Δt_i) for exposure time, or ²f = Δc_i, 1/Δc_i or 1/(Δc_i)² for CNT concentration. A particular case is when the concentration function takes the classic form of PL4/PL5 models.⁷⁶ This equation is represented through a sigmoid curve. The formula below illustrates two examples of alternative models following the eqn (6):

The parameters of 4PL/5PL models are: A, B, C, D, and E. A is the value for the minimum asymptote. B is the hill slope. C is the concentration at the inflection point. D is the ε_ij for the maximum asymptote. The last parameter E, is present only on 5PL model (E = 1 in 4PL model), is the asymmetry factor (E ≠ 1 for a non-symmetric curve).⁷⁶

PT-NQSTR model for mitoprotective activity of CNTs. The ε_i values are obtained after exposure of the mitochondrial suspension to one volume of 100 μl of CNT at different c_i values. We used physic-chemical parameters of CNTs (V_kj) and the values of the Box–Jenkins operators (ΔV_kj) of these parameters as inputs of the model in statistical analysis. The best PT-QSPR model found using MLR algorithm and linear operators (functions) of ΔV_k,j was the following:

^newε_ij = 1.001191·ε_ijnew − 0.000066·Δt_ij(s) + 0.002344·Δc_ij (μg ml⁻¹) − 0.001191·ΔW_ij()_max − 0.000688·ΔD_ij (nm)_min + 0.000086, N = 6045,  R² = 0.75, F = 2482.1, p < 0.005 (7)

As we mentioned above, in the simplest case the output function ′f(ε_ij)_new = ^newε_ij is the value of absorbance predicted by the linear model under the set of boundary conditions of test of reference. N = number of cases used to train the model, R² the determination coefficient, and F the Fisher ratio with the corresponding p-value are the statistical elements used to describe the statistical significance and goodness-of-fit of the model. We can expand the input terms and substitute each symbol V_k(b_j) by the classic symbol of the respective property in order to understand better this equation. The model predicts values of absorbance ^newε_ij when assaying the ith CNT in a new experimental situation (jth set of conditions) given the expected values of reference calculated from the data set. The correlation between the inputs and the answer is statistically significant according to p-error values (p < 0.005). The values R² are high (75% of variance explained) but, unfortunately, we can observe an important dispersion of data points from the straight line in Fig. 6(A).

Fig. 6 Observed vs. predicted values for models with ⁰f(ε_ij) = ε_ij (A), and (B) ⁰f(ε_ij) = −log(ε_ij).

We carry out some transformations of output ⁰f(ε_ij) and/or input functions in order to increase the R² and decrease the dispersion. The transformation of the output function ε_ij were: ′f(ε_ij) = 1/ε_ij, (1/ε_ij)², or −log(ε_ij). Some of the transformations of the input functions ^kf(ΔV_kj) were ¹f(Δt_ij) = 1/(Δt_ij), exp(−Δt_ij) and ²f(Δc_ij) = 1/Δc_ij or 1/(1 + Δc_ij), between others (see details on Materials and method section). In Table 6 we depict the results obtained after some of these transformations. The transformation of the output function into a logarithmic function have lead to an outstanding increase in the determination coefficient from R² = 0.75 to R² = 0.994 (Model 2) with respect to the linear model (Model 1). This result also supposed a notably reduction on the dispersion of data, see Fig. 6(B).

Table 6 Statistical analysis for alternative PT-NQSPR models developed in this work^a

Model parameters^b					Model
Vk	ak	s.e.	t	p	Specifications
a ^0f(εij)ref = 〈εij〉 is the average of εij (expected value of absorbance) for a given assay carried out under the conditions bj.b Symbols of input variables used. The parameters ΔVkj = (^kVi − 〈Vkj〉) are PT operators in form of moving averages, for more details see Materials and methods.
a0	−0.000780	0.003041	−0.26	0.79	Model 1
〈εij〉^a	1.002419	0.008302	120.75	0.00	′f(εij)	^0f(εij)	^1f(tij)	^2f(cij)
Δtij	−0.000066	0.000002	−42.77	0.00	εij	〈εij〉	Δtij	Δcij
Δcij	0.002395	0.000199	12.02	0.00	R^2	F	p	q^2
ΔWmax	−0.001175	0.000237	−4.97	0.00	0.73	3308.1	<0.05	0.70
ΔDmin	−0.000735	0.000174	−4.21	0.00
a0	0.92771	0.000488	−1900.43	0.00	Model 2
〈εij〉	−1.33764	0.001332	1003.91	0.00	′f(εij)	^0f(εij)	^1f(tij)	^2f(cij)
Δtij	0.00001	0.000000	−2.02	0.04	−log(εij)	〈εij〉	Δtij	Δcij
Δcij	−0.00038	0.000032	11.92	0.00	R^2	F	p	q^2
ΔWmax	−0.00042	0.000038	11.11	0.00	0.994	203 384.0	<0.05	0.994
ΔDmin	−0.00044	0.000028	15.79	0.00
a0	32.5709	0.190990	170.53	0.00	Model 3
〈εij〉	−67.6535	0.521307	−129.78	0.00	′f(εij)	^0f(εij)	^1f(tij)	^2f(cij)
Δtij	0.0035	0.000096	36.33	0.00	1/(εij)^2	〈εij〉	Δtij	Δcij
Δcij	−0.1744	0.012517	−13.93	0.00	R^2	F	p	q^2
ΔWmax	−0.0111	0.014857	−0.75	0.45	0.75	3647.4	<0.005	—
ΔDmin	−0.0295	0.010953	−2.69	0.01
a0	6.5064	0.028482	228.44	0.00	Model 4
〈εij〉	−10.2097	0.077742	−131.33	0.00	′f(εij)	^0f(εij)	^1f(tij)	^2f(cij)
Δtij	0.0006	0.000014	39.71	0.00	1/εij	〈εij〉	Δtij	Δcij
Δcij	−0.0259	0.001867	−13.86	0.00	R^2	F	p	q^2
ΔWmax	0.0027	0.002216	1.20	0.23	0.76	3780.1	<0.05	—
ΔDmin	−0.0003	0.001633	−0.20	0.84
a0	0.002922	0.003037	0.96	0.33	Model 5
〈εij〉	0.998287	0.008275	120.63	0.00	′f(εij)	^0f(εij)	^1f(tij)	^2f(cij)
Δtij	−0.000060	0.000002	−39.37	0.00	εij	〈εij〉	Δtij	1/(1 + Δcij)
Δcij	−0.000467	0.000207	−2.25	0.02	R^2	F	p	q^2
ΔWmax	−0.000420	0.000166	−2.53	0.01	0.734	3331.7	<0.05	—
ΔDmin	−0.006490	0.000488	−13.29	0.00
a0	−0.927407	0.000494	−1877.49	0.00	Model 6
〈εij〉	1.337072	0.001346	993.49	0.00	′f(εij)	^0f(εij)	^1f(tij)	^2f(cij)
Δtij	0	0	0.47	0.64	log(εij)	〈εij〉	Δtij	1/(1 + Δcij)
Δcij	0.000634	0.000034	18.80	0.00	R^2	F	p	q^2
ΔWmax	0.000539	0.000027	19.96	0.00	0.993	199 112.8	<0.05	—
ΔDmin	−0.000286	0.000079	−3.60	0.00

---

We can note that other transformations of inputs variables like Δc_ij and Δt_ij do not improved the results of the regression (Models 3 and 4). In particular, the transformation of the Δc_ij function into hill-shaped curves of common use in dose-effect studies was not effective (Model 5). In addition, the transformation of both output and input functions at the same time increased the correlation but as a result we obtained a more complex model with loss of statistical significance (p > 0.05) for some input variables (Model 6). In closing, the best PT-NQSPR model found here was the one using the negative logarithmic transformation for the output. The model have also a very high validation regression coefficient q² = 0.994, obtained in Leave-One-Out (LOO) cross-validation. The model equation is the following:

^newlog(ε_ij) = 1.33764ε_ijnew − 0.000001·Δt_ij(s) + 0.00381·Δc_ij (μg ml⁻¹) + 0.000422·ΔW_ij (%)_max + 0.000442·ΔD_ij (nm)_min − 0.927714, N = 6045, R² = 0.994, F = 203 384.0, p < 0.005, q² = 0.994 (8)

We presented the previous equation in a compacted form for the sake of simplicity. However, we want to give also the expanded form of the equation to make easier the understanding of the method. In the following equation, we expanded each moving average term. It can be noted that each term quantifies the deviation (perturbation) of the original variable (t_ij, c_ij, W_ij, or D_ij) from its average value (〈t_ij〉, 〈c_ij〉, 〈W_ij〉, or 〈D_ij〉). In this sense, each moving average term account for the deviation of the original variable from its expected value (the average value).^33–39

^newlog(ε_ij) = 1.33764·ε_ijnew − 0.000001·(t_ij − 〈t_ij〉) + 0.00381·(c_ij − 〈c_ij〉) + 0.000422·(W_ij − 〈W_ij〉)_max + 0.000442·(D_ij − 〈D_ij〉)_min − 0.927714, N = 6045, R² = 0.994, F = 203 384.0, p < 0.005, q² = 0.994 (9)

Prediction of mitoprotective activity of CNT in other conditions. We can use the previous PT-QSPR model to carry out a computational simulation of mitoprotection by CNT in other conditions (not measured experimentally). In so doing, we need to substitute three different types of values in the equation. The first is the expected value of absorbance 〈ε_ij〉_ref for a given sub-set of experimental conditions or assay (b_ij). We also need to substitute the average values of the physic-chemical properties of the CNTs 〈V_k〉 in these sub-sets of different experimental conditions 〈V_kj〉, see Table 7 (right).

Table 7 Expected values of variables in different conditions^a

Experimental conditions					Expected values
Type	Function	CT1	CT2	IC	〈εij〉	〈V1〉	〈V2〉	〈V3〉	〈V4〉
a 〈V1〉 = 〈tij〉 (seg), 〈V2〉 = 〈cij〉 (μg ml^−1), 〈V3〉 = 〈^maxWij〉, 〈V4〉 = 〈^minDij〉 (nm).
MWCNT	NO	Ca^2+	NO	NO	0.3528	300	2.38	0	8
SW/DWCNT	OH	Ca^2+	NO	NO	0.3528	300	2.38	3.96	1
MWCNT	OH	Ca^2+	NO	NO	0.3528	300	2.38	2.97	13.67
MWCNT	COOH	Ca^2+	NO	NO	0.3528	300	2.38	2.86	13.67
SWCNT	COOH	Ca^2+	NO	NO	0.3528	300	2.38	2.73	1
MWCNT	NO	Fe^2+	NO	NO	0.3741	94.14	2.4	0	8
SW/DWCNT	OH	Fe^2+	NO	NO	0.3741	94.14	2.4	3.96	1
SW/DWCNT	OH	Fe^2+	VitC	NO	0.3361	90	5	3.96	1
MWCNT	OH	Fe^2+	NO	NO	0.3741	93.83	2.22	2.83	14.88
MWCNT	OH	Fe^2+	VitC	NO	0.3361	90	5	2.97	13.67
MWCNT	COOH	Fe^2+	NO	NO	0.3741	94.14	2.4	2.86	13.67
MWCNT	COOH	Fe^2+	VitC	NO	0.3361	90	5	2.37	20
SWCNT	COOH	Fe^2+	NO	NO	0.3741	94.14	2.4	2.73	1
SWCNT	COOH	Fe^2+	VitC	NO	0.3361	90	5	2.73	1
MWCNT	COOH	Fe^2+	VitC	NO	0.3479	90	5	3.86	1
SW/DWCNT	OH	H2O2	NO	NO	0.3751	300	3	3.96	1
MWCNT	OH	H2O2	NO	NO	0.3751	300	3	2.97	13.67
MWCNT	COOH	H2O2	NO	NO	0.3751	300	3	2.86	13.67
SWCNT	COOH	H2O2	NO	NO	0.3751	300	3	2.73	1
MWCNT	OH	Ca^2+	NO	NO	0.3528	300	2.38	2.46	15.5
NO	NO	Fe^2+	NO	NO	0.3741	247.5	0	0	0
MWCNT	NO	Fe^2+	VitC	NO	0.3361	90	5	0	8
SW/DWCNT	OH	Fe^2+	NO	NO	0.3741	94.14	2.4	3.96	1
SW/DWCNT	OH	Fe^2+	VitC	NO	0.3361	90	5	3.96	1
MWCNT	OH	Fe^2+	NO	NO	0.3741	94.14	2.4	2.97	13.67
MWCNT	COOH	Fe^2+	VitC	NO	0.3361	90	5	2.86	13.67

---

Last, we need to substitute the values V_k for CNTs with different physic-chemical properties not assayed before. In this way, we can obtain new values of absorbance predicted for new CNT with changes in the original physic-chemical properties. Thus we can predict the values of mitoprotection P(%) using the values of ε_ij predicted and the values observed with MPT-inductor or toxic control (TC+) and solvent blank. The equation used was the following P(%)_pred = 100[ε_ij(CNT + TC + S)_pred − ε_ij(TC + S)_obs]/[ε_ij(IC + TC + S)_obs − ε_ij(TC + S)_obs].^77,78 In Table 8, we show the prediction of P(%)_pred if we increase at the same time the maximal molecular weight to functionalization ratio ^maxW and the minimal ^minD of the CNT in x(%) at t(s) = 600 seg and c_ij = 2.5 μg ml⁻¹. The effect of dose or concentration (1–5 μg ml⁻¹) influenced poorly the model and, for this reason, an intermediate value (2.5 μg ml⁻¹) was established for the theoretical analysis of CNT-nanodescriptors. This was considered reasonable because it allows the study of the nanostructure–activity relationship and at the same time considers non-agglomeration conditions for simulation of CNT-nanodescriptors in mitochondrial exposure.¹⁸ In this sense the predictions show that ^minD_i and ^maxW_i are relevant nanodescriptors strongly implicated in the inhibition of mitochondrial permeability transition induced by Ca²⁺, Fe²⁺, H₂O₂ for carbon nanotubes. Small increments of ^minD_i including SWCNT and MWCNT may affect the function of certain proteins and enzymes and induce serious cytotoxic effects at the biochemical and/or sub-cellular level as we assayed in the isolated mitochondria experimental model. Theoretical predictions model the variations of carbon nanotubes diameter (0% < ^minD_i < 10%) associated with mitochondrial dysfunction (swelling). The results suggest that larger diameters also could act blocking or interfering with the function of carriers and mitochondrial proteins which forms MPTP (like VDAC and ANT) and in this way inhibit apoptosis through deficient MPTP assembly in swelling experimental conditions.

Table 8 Simulation of P(%)_pred if ^maxW_i and ^minD_i increase in x(%) at t(s) = 600 and c(μg ml⁻¹) = 2.5

CNT and assay^a						x(%) increase of ^maxWi and ^minDi^b
Assay	CNT	CNT structural parameters				0	1	5	10
		^maxWi	^minDi	Type	Function	P0 (%)	P1 (%)	P5 (%)	P10 (%)
a MWCNT = Multiple-Walled, SWCNT = Single-Walled, SW/WTCNT = MWCNT + SWCNT mixture.b P(%)pred = 100[εij(CNT + TC + S)pred − εij(TC + S)obs]/[εij(IC + TC + S)obs − εij(TC + S)obs] is mitoprotective protective activity, CNT = carbon nanotube, TC = toxic control, IC = inhibitor control, S = solvent. Assay details are the following. For toxicity assay 1 (a = 1), TC = Ca^2+, IC = CsA, and solvent = DMSO. For assay 2 (a = 2), TC = Fe^2+, IC = EGTA and S = DMSO. For toxicity assay 3 (a = 3), TC = H2O2, IC = Q, and solvent = DMSO. N is the number of replicas of this assay.
Ca^2+	1	0	8	MWCNT	H	9.77	10.45	13.14	16.53
	2	3.96	1	SW/DWCNT	OH	7.89	8.51	11.03	14.18
	3	3.86	1	MWCNT	OH	7.82	8.45	10.96	14.12
	4	4	10	MWCNT	OH	13.52	14.21	16.97	20.44
	5	1.06	30	MWCNT	OH	24.28	25.11	28.43	32.60
	6	0.73	30	MWCNT	COOH	24.07	24.90	28.21	32.39
	7	4	10	MWCNT	COOH	13.52	14.21	16.97	20.44
	8	2.73	1	SWCNT	COOH	7.12	7.75	10.26	13.41
	9	3.86	1	MWCNT	COOH	7.82	8.45	10.96	14.12
Fe^2+	1	1	8.08	MWCNT	H	37.66	38.63	42.54	47.44
	2	4.96	1.01	SW/DWCNT	OH	34.92	35.83	39.47	44.04
	3	4.86	1.01	MWCNT	OH	34.83	35.74	39.38	43.95
	4	5	10.1	MWCNT	OH	43.08	44.08	48.08	53.10
	5	2.06	30.3	MWCNT	OH	58.67	59.87	64.68	70.72
	6	1.73	30.3	MWCNT	COOH	58.37	59.56	64.37	70.42
	7	5	10.1	MWCNT	COOH	43.08	44.08	48.08	53.10
	8	3.73	1.01	SWCNT	COOH	33.82	34.72	38.36	42.93
	9	4.86	1.01	MWCNT	COOH	34.83	35.74	39.38	43.95
H2O2	1	5	8.4	MWCNT	H	0	0.97	5.72	11.68
	2	8.96	1.05	SW/DWCNT	OH	0	0	1.99	7.55
	3	8.86	1.05	MWCNT	OH	0	0	1.88	7.44
	4	9	10.5	MWCNT	OH	6.38	7.59	12.46	18.57
	5	6.06	31.5	MWCNT	OH	25.34	26.80	32.65	40.01
	6	5.73	31.5	MWCNT	COOH	24.97	26.43	32.28	39.63
	7	9	10.5	MWCNT	COOH	6.38	7.59	12.46	18.57
	8	7.73	1.05	SWCNT	COOH	0	0	0.64	6.19
	9	8.86	1.05	MWCNT	COOH	0	0	1.88	7.44

---

On the other hand the theoretical predictions to increase the functionalization (0% < ^maxW_i < 10%) reveals interesting aspects about the relationship nanostructure–mitoprotective activity (MPT-inhibitors) of oxidized carbon nanotubes family particularly related to motif structure in order (carboxylated-motif) > (hydroxylated-motif) and considering the walls number of CNT (MW-motif) > (SW-motif) in pro-oxidant conditions against mitochondrial swelling in order (swelling assays induced by Fe²⁺; P₂) > (swelling assay induced by H₂O₂; P₃), suggesting mechanisms based on the inhibition of Fenton–Haber–Weiss reaction.

Conclusions

The prediction of relationships between carbon nanomaterials physic-chemical properties and biological responses, has gained a significant importance to reduce their toxic effects and extend their nanotechnology applications. The structural determinants for mitochondrial mechanisms of functionalized CNTs (oxidized) are remaining poorly understood actually. We found that the CNTs-COOH and CNT-OH were more biocompatibility compared with the p-MWCNTs to prevent the mitochondrial dysfunction.

We can use mixed experimental-theoretic methodology to study the effects of different CNT in the modulation of mitochondrial permeability transition pore under the influence of multiple factors. In this context the modulation of mitochondrial physiology through MPTP in experimental swelling condition (Ca²⁺, Fe²⁺, H₂O₂ overload) using oxidized CNT can represent a qualitative advance in the treatment of several chronic diseases (hepatotoxicity, Alzheimer, Parkinson, cardiac ischemia) where MPTP has been directly involved.

Particularly NQSPR perturbation approach used here can contribute to predict nanotoxicological data allowing to infer the effects of new nanomaterials in a short time. Indeed, the derived nano-QSTR perturbation model to mitochondrial swelling provided new insights regarding the typical CNT-nanodescriptors (length, diameter, shape, partition coefficient, chemical functionalization, solubility and Young's modulus) related to mitochondrial responses as therapeutic target at the sub-cellular level, as well as the influence of different experimental conditions under which these physico-chemical properties were evaluated. Finally this in silico method allows the prediction of the potential mitoprotective effects of several nanoparticles under conditions not tested in our original database, which could be used to make regulatory decisions, rational design of CNT more selective and less mitotoxic.

Acknowledgements

M. González-Durruthy acknowledges Doctoral fellowship (Post-graduate Students Program PEC-PG No.062/2013) from Brazilian Agencies CAPES-CNPq. J. M. Monserrat is a productivity fellow from CNPq (PQ 307880/2013-3). This study was supported with funds from Brazilian CNPq (Project numbers 552131/2011-3, 479053/2012-0 and 452088/2015-1) given to J. M. Monserrat.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra14435c

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