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.