Thermal Stability Kinetics and Shelf Life Estimation of the Redox-Active Therapeutic and Mimic of Superoxide Dismutase Enzyme, Mn(III) meso-Tetrakis(N-ethylpyridinium-2-yl)porphyrin Chloride (MnTE-2-PyPCl5, BMX-010)

Mn(III) meso-tetrakis(N-ethylpyridinium-2-yl)porphyrin chloride (MnTE-2-PyPCl5, BMX-010, and AEOL10113) is among the most studied superoxide dismutase (SOD) mimics and redox-active therapeutics, being currently tested as a drug candidate in a phase II clinical trial on atopic dermatitis and itch. The thermal stability of active pharmaceutical ingredients (API) is useful for estimating the expiration date and shelf life of pharmaceutical products under various storage and handling conditions. The thermal decomposition and kinetic parameters of MnTE-2-PyPCl5 were determined by thermogravimetry (TG) under nonisothermal and isothermal conditions. The first thermal degradation pathway affecting Mn-porphyrin structural integrity and, thus, activity and bioavailability was associated with loss of ethyl chloride via N-dealkylation reaction. The thermal stability kinetics of the N-dealkylation process leading to MnTE-2-PyPCl5 decomposition was investigated by using isoconversional models and artificial neural network. The new multilayer perceptron (MLP) artificial neural network approach allowed the simultaneous study of ten solid-state kinetic models and showed that MnTE-2-PyPCl5 degradation is better explained by a combination of various mechanisms, with major contributions from the contraction models R1 and R2. The calculated activation energy values from isothermal and nonisothermal data were about 90 kJ mol–1 on average and agreed with one another. According to the R1 modelling of the isothermal decomposition data, the estimated shelf life value for 10% decomposition (t90%) of MnTE-2-PyPCl5 at 25°C was approximately 17 years, which is consistent with the high solid-state stability of the compound. These results represent the first study on the solid-state decomposition kinetics of Mn(III) 2-N-alkylpyridylporphyrins, contributing to the development of this class of redox-active therapeutics and SOD mimics and providing supporting data to protocols on purification, handling, storage, formulation, expiration date, and general use of these compounds.

Thermogravimetric (TG) analyses are important for the evaluation and/or comparison of thermal stabilities of pharmaceutical materials, the study of drug-excipient compatibility in drug products, and the determination of kinetic parameters associated with thermal processes (such as activation energies, frequency factor, and reaction order) [31-34, 39, 40]. Overall, this information is useful for the development of pharmaceutical products and quality control [32,34,39,41]. Studies on the kinetics of thermal degradation are recommended to evaluate the thermal stability of active pharmaceutical ingredients (API) and/or their solid-state pharmaceutic formulations [31-34, 39, 41, 42]. These kinetic studies are often carried out in the pharmaceutic field by nonisothermal (dynamic) or isothermal thermogravimetric analyses [43][44][45][46][47][48][49]. Kinetic studies under isothermal TG conditions are particularly relevant as they are amenable to Arrhenius equation treatment and make possible the estimation of room temperature degradation rate from extrapolation of accelerated, experimental, hightemperature degradation rates [34,42]. These kinetic studies are particularly useful to provide reliable estimates of the shelf life of pharmaceutical products under various storage and handling conditions [31,34].
We describe herein the first study on the kinetics of thermal degradation of MnP-based redox-active therapeutics under isothermal and nonisothermal conditions. Additionally, it is worth noting that thermal decomposition kinetic models were evaluated using a state-of-the-art approach, based on the multilayer perceptron (MLP) artificial neural network [48][49][50][51][52]. MnTE-2-PyPCl 5 was chosen as a representative API of the class of Mn(III) 2-N-alkylpyridylporphyrins, currently developed as SOD mimics, biomimetic models, catalytic antioxidants, and redoxactive therapeutics.

Materials and Methods
MnTE-2-PyPCl 5 and the nonalkylated analogue MnT-2-PyPCl (see Figure 1) were prepared and purified as previously reported [2,53] and showed characterization features consistent with published data [28,[53][54][55]. Although these compounds are usually labeled as anhydrous species (i.e., MnTE-2-PyPCl 5 ), the isolated solids often contain variable amounts of water molecules, depending on sample workup, 2 Oxidative Medicine and Cellular Longevity handling, and storage [28]. In this work, the cationic MnP, MnTE-2-PyPCl 5 , contained 8 molecules of water, whereas the neutral MnP, MnT-2-PyPCl, was analyzed as an anhydrous species, according to thermogravimetric data (see below). All samples were investigated by simultaneous thermogravimetric and differential thermal analyses (TG/DTA) under isothermal and nonisothermal conditions. The experimental kinetic designs described below for these two conditions of analyses agree with the International Confederation for Thermal Analysis and Calorimetry (ICTAC) recommendations [45][46][47].
2.1. Thermal Analysis. TG curves were obtained on a Shimadzu DTG60 thermal analyzer using 2-3 mg samples, accurately weighed in alumina crucibles directly in the thermobalance, under a dynamic atmosphere of synthetic air with a flow rate of 50 mL min -1 .
For the kinetic studies, various TG curves were registered independently using heating rates of 5, 7.5, 10, and 12.5°C min -1 in the temperature range from 30 to 600°C for nonisothermal experiments. Isothermal experiments were carried out at 158, 160, 162, and 164°C for a period of 60 minutes; in these experiments, the samples were heated from room temperature to the target isothermal temperature with a heating rate of 10°C min -1 .

Kinetic Study Using the Vyazovkin Isoconversional
Method in Nonisothermal TG Data. The solid-state decomposition process follows the general first-order kinetic equation: with kðTÞ as the rate constant following the Arrhenius equation and f ðαÞ as the reaction model, with α as the conversion  (1) can be rewritten as The isoconversional Vyazovkin [44] method assumes that the reaction model is independent of the heating rate; for this, we have for a given conversion The frequency factor, A α , is considered constant for the processes submitted to small variation of the heating rate, so this equation can be treated considering the following optimization: The temperature integral can be solved assuming the following approximation [56]: with x = E/RT and pðxÞ calculated using the Senum-Yang approximation [56] of the third degree: The percentage error of the pðxÞ function for the 3 rd rational approximation is about 10 -5 percent [56].

Kinetic Study Using the MLP Neural Network in
Isothermal TG Data. The MLP neural network applied in this study was proposed initially by Sebastião et al. [48][49][50]. The architecture of this MLP has only one artificial neuron in the input and output layers. The intermediate layer, however, has ten artificial neurons, according to the number of kinetic models considered in the process of the  Table 1 presents the kinetic models studied.
The states of neurons o k are defined as with x k being the state of the artificial neuron in the previous layer and w kj being the weights between the neurons k and j.
In this particular type of network, there are also weights called bias, w i0 , defined as unity parameters to amplify or reduce the linear correlation of the network [48,49].
In this proposed architecture of MLP, the weights w i1 and the bias w i0 were predetermined from the fit of experimental data by each kinetic model in each studied temperature, where the weights are the rate constants and linear coefficient of the kinetic models. These weights do not change in the learning process of the network and can be represented assuming a weight matrix w 1 as Assuming x to be the experimental time data for each studied temperature, In this case, the w 1 x matrix calculates the state of the artificial neurons in the intermediate layer W 1 x: The neurons in the intermediate layer must be activated by an activation function, f , to send out information to the output layer. From this, their states are defined by The activation functions should assume a predetermined value; generally, f ðxÞ = 0 before calculating the state of neurons; activate the neurons assuming values near to the unity and making sure this is a increasing function df ðxÞ/dx ≥ 0, to warranty the energy function optimization [49]. If we chose a linear activation function in the output layer, the network response, given by the state of the neuron in the output layer, is with W 2 being the interconnection weight vector of the output layer. The MLP learning process consists of an energy function optimization, from which only the w 2 vector has to be Oxidative Medicine and Cellular Longevity determined [49]. Considering α exp as the experimental data, this energy function is To solve this equation, the w 2 contribution of each kinetic model to describe the experimental data can be calculated by the well-known pseudo-inverse algorithm [49] with B = f ðw 1 xÞ.

Results and Discussion
3.1. Thermal Decomposition of MnTE-2-PyPCl 5 . In our previous studies on the thermal stability of MnTE-2-PyPCl 5 [28], we established that the thermogravimetric events of this Mn-porphyrin under dynamic air were associated with three major processes: (i) dehydration, (ii) Ndealkylation, and (iii) organic matter degradation to yield Mn oxide as the final residue at 900 or 950°C. The N-dealkylation reaction of MnTE-2-PyPCl 5 during the thermogravimetric analyses under air at a heating rate of 10°C min -1 takes place between 134 and 279°C (see Figure 2). The loss of ethyl chloride (EtCl) was characterized by gas chromatography-mass spectrometry (GC-MS) of the evolved gas (EtCl) and by characterization of the residue at 279°C, which was consistent with MnT-2-PyPCl (see Figure 1) by spectroscopic and chromatographic analyses [28]. Additionally, thermogravimetric analysis of an analytical sample of MnT-2-PyPCl with no N-alkyl moieties (prepared independently [53]) showed no major events in the temperature range associated with EtCl loss in MnTE-2-PyPCl 5 (see Figure 2; see also Figures S1 and S2 and Tables S1 and S2 in Supplementary Materials for complementary data by derivative thermogravimetry (DTG) and differential thermal analysis (DTA)). Whereas dehydration is a reversible process, the N-dealkylation of MnTE-2-PyPCl 5 to yield MnT-2-PyPCl (see Figure 1) represents the first irreversible thermal event that compromises the MnP structural integrity, affecting permanently its catalytic efficiency, lipophilicity, bioavailability, and expected therapeutic outcome [17,28,38,54]. Thus, understanding the kinetics of the MnTE-2-PyPCl 5 thermal N-dealkylation process may prove useful to provide researchers and the pharmaceutic industry with information on handling/storage of MnTE-2-PyPCl 5 , shelf life, and usage. Commercially impure samples of Mn(III) 2-N-alkylpyridylporphyrins, containing a mixture of partially N-dealkylated compounds most likely derived from inadequate thermal workup procedures [38,54], have already clouded some biological conclusions on the in vivo SOD activity of these Mn-porphyrins [54,57]. The kinetic studies on the thermal N-dealkylation of MnTE-2-PyPCl 5 were carried out by nonisothermal and isothermal protocols as presented below, observing the recommendations of the International Confederation for Thermal Analysis and Calorimetry (ICTAC) [45,47]. The specific temperature ranges for the kinetic studies were chosen based on the interval in which only the N-dealkylation process of MnTE-2-PyPCl 5 is prevalent (see Figure 2) [54]. Although thermal kinetic data are usually collected at high temperature under accelerated thermal degradation conditions, the isothermal results may be extrapolated to lower temperatures using the Arrhenius equation, to provide estimates of drug thermal stability under different target temperatures of interest to handling and storage associated with good manufacturing practices [34,42,58].

Nonisothermal Kinetic Analysis.
The decomposition process associated with MnTE-2-PyPCl 5 thermal N-dealkylation under nonisothermal conditions was investigated. From this methodology, the kinetic parameters of activation energy (E a ) and frequency factor (A) were determined according to the conversion degree (α). The nonlinear isoconversional method proposed by Vyazovkin et al. [45] was used. This method allows an indirect analysis of multistep processes, considering the activation energy as a function of the conversion degree. Figure 3 shows the nonisothermal experimental data obtained from the four heating rates chosen to follow the MnTE-2-PyPCl 5 N-dealkylation process: 5.0, 7.5, 10.0, and 12.5°C min -1 . The curves are not overlapped, and observe the ICTAC recommendations for kinetic studies [45][46][47]. These curves were treated by the nonlinear Vyazovkin method, and Figure 4 shows the activation energy   Figure 4 reveals that the activation energy increases as the conversion proceeds, starting from 75 kJ mol -1 at the beginning of the process, reaching 100 kJ mol -1 at α = 0:5, and finishing with values of 125 kJ mol -1 . These high activation energies not only indicate but also are consistent with the observed high thermal stability of the compound [28]. The standard deviations for the Vyazovkin adjustments are presented in Table 2, and their small values warranty that the Vyazovkin method was used properly to treat the MnTE-2-PyPCl 5 thermal Ndealkylation data. It is worth noting that the activation energy represents the energy necessary to initiate the MnTE-2-PyPCl 5 decomposition.

Isothermal Kinetic Analysis by the MLP Artificial Neural
Network. Isothermal decomposition of solids generally occurs at the product-reagent interface [44], being described by kinetic models well established in the literature [48][49][50].
These models correlate the decomposition fraction, αðtÞ, with time at chosen appropriate temperatures. An adapted multilayer perceptron (MLP) neural network algorithm was developed by our group [48,49] as a homemade algorithm using the MATLAB language [50,51]. The algorithm is different from traditional MLP approaches as it does not vary the interconnection weights between the input and intermediate layers. In this MLP approach, only the weights between the intermediate and output layers are optimized, which provides the contribution of each kinetic model in the experimental data description.
In the current study, a total of 12 kinetic models (see Table 1) were investigated simultaneously, out of which 10 models (i.e., D1, D2, D3, D4, R1, R2, R3, Am2, Am4, and Au) were found to describe in a combined manner the thermal decomposition kinetics associated with MnTE-2-PyPCl 5 thermal N-dealkylation reaction. The curves of decomposition fraction, αðtÞ, for MnTE-2-PyPCl 5 isothermal experiments at 158, 160, 162, and 164°C are presented in Figure 5 along with the MLP adjustment considering ten kinetic models for the decomposition process. As shown in Figure 5, the residual error of the MLP adjustment in all cases is about 10 -4 , attesting the robustness of the method.
The MLP neural network approach is exceptionally accurate compared to the adjustment of each individual kinetic model separately. Figure 6 presents the residual error of each kinetic model considered individually to fit the experimental data. It is worth noting that fitting of experimental data with various kinetic models resulted in comparable residual errors, many of which are of the same order of magnitude (see Figure 6). This result strongly suggests that the Ndealkylation of MnTE-2-PyPCl 5 via a thermal decomposition process is better understood as an overlapping contribution of many mechanisms combined [48,49]; for this case, the R1, R2, Am2, and Am4 mechanisms presented smaller residual error to fit the experimental data. Nonetheless, the contraction models R1 and R2 explain the experimental data with more accuracy. The R2 model assumes the nucleation occurring rapidly on the surface of the crystal, which presents a cylinder shape. In this kinetic model, that accounts for a contracting area; the radius contraction follows r = r 0 − kt, where r is the radius at time t, r 0 is the initial radius, and   Oxidative Medicine and Cellular Longevity k is the rate constant, as schematically represented in Figure 7. The generalized Rn models, which encompass R1 and R2, are mathematical functions that describe reactions taking place in the boundary phase, with diffusion processes being extremely fast, which prevents an adequate interaction of reactants in the interface [41,59]. These phase boundary-controlled reaction processes are, thus, controlled by the rearrangement of the reactants in the limitrophe phase. The Rn models are known as geometrical contraction models, but R1 is similar to the ones usually applied to describe the reaction order mechanisms in a homogeneous system, following a zero-order reaction rate.
In the MLP artificial neutral network approach, ten kinetic models (i.e., D1, D2, D3, D4, R1, R2, R3, Am2, Am4, and Au, see Table 1) were considered simultaneously in the intermediate layer, with the w 1 matrix (equation (8)) determined by the rate constant (k) and linear coefficient (k0) of kinetic models by the fitting experimental data of each isothermal curve. The contribution of the kinetic models to the MnTE-2-PyPCl 5 isothermal decomposition process is presented in Figure 8, which reveals that for all studied temperatures (158, 160, 162, and 164°C), the most significant contributions were those associated with the contraction models R1 and R2. Thus, the contraction models R1 and R2 showed both smaller error and greater contribution in describing the phenomenon of MnTE-2-PyPCl 5 thermal decomposition.
The rate constants determined by the experimental data adjustment into the kinetic models via the MLP neural network approach (w 1 matrix, equation (8)) were used to calculate the activation energy of MnTE-2-PyPCl 5 thermal decomposition. The MLP-derived values shown in Figure 9 are comparable to the activation energies calculated using the Vyazovkin method (see Figures 4 and 9). This agreement with the nonisothermal result indicates that the decomposition process is not affected by the experimental condition (i.e., isothermal or nonisothermal protocol) and, again, the MLP values of activation energy are consistent with the overall stability of MnTE-2-PyPCl 5 .
MnTE-2-PyPCl 5 is often stored as a nonformulated solid or as aqueous solution formulations [9], [10,17]. Nonformulated solid MnTE-2-PyPCl 5 has often been stored at room temperature, presumably between 15 and 35°C [9,10,28]. Thus, considering the activation energy values and rate constants determined at high temperature, the kinetic parameters at 25°C were estimated, using the Arrhenius equation. These kinetic data also allowed the estimation of the t 90% shelf life value for MnTE-2-PyPCl 5 (i.e., the time in which the initial MnP concentration decays by 10%) at 25 and 158°C (see Table 3). The t 90% value is an important parameter that is recommended for estimating the API shelf life [34,60]. As the model R1 showed smaller error and  7 Oxidative Medicine and Cellular Longevity greater contribution to the phenomenon of thermal decomposition of the material, the t 90% value found by this model is the most adequate to describe the behavior of MnTE-2-PyPCl 5 over time. Therefore, it is expected that it would take nearly 17 years for solid MnTE-2-PyPCl 5 to reach a 10% Ndealkylation at 25°C, which is consistent with the high stability empirically observed for this compound on daily routine handling and storage in the laboratory [54]. Of note, a solid sample of high-purity MnTE-2-PyPCl 5 stored in a closed vial at room temperature in the dark for 7 years in our laboratories showed no noticeable signs of N-dealkylation when analyzed by thin-layer chromatography (data not shown). As shelf life values may be significantly affected by storage and drug formulations (including the nature of excipients) [34,52,60], the calculated t 90% value for MnTE-2-PyPCl 5 is valid if the net solid material is kept in ideal conditions of humidity. As noted, MnTE-2-PyPCl 5 is a hydratable molecule. The presence of humidity can trigger hydrolytic processes. High humidity generates absorption of the excess moisture in the air, which can be just as destructive as environments with low humidity. A humidity excess can compromise potency and effectiveness, leading to degradation or even toxicity in some products. It may promote the    Oxidative Medicine and Cellular Longevity growth of microorganisms, compromising their biological integrity. The International Conference on Harmonization (ICH) in the topic Q1 A(R2) deals with the stability testing of new drugs and products, delimiting good practices of manipulation and storage concerning temperature and humidity parameters. Those variables take into account the country climate zone classification. MnTE-2-PyPCl 5 must be stored in a hermetically sealed flask and kept at a storage temperature of 30°C ± 2°C and relative humidity of 75% ± 5% whereas Brazil belongs to climate zone IV [61,62]. It is worth noting that these data drive further studies on MnTE-2-PyPCl 5 formulations and stability.

Conclusions
The first study on the thermal stability kinetics of Mn(III) 2-N-alkylpyridylprophyrin was carried out with the prototypical MnTE-2-PyPCl 5 compound using thermogravimetry (TG) under nonisothermal and isothermal conditions. The new multilayer perceptron (MLP) artificial neural network approach allowed the simultaneous study of ten solid-state kinetic models and showed that N-dealkylation associated with MnTE-2-PyPCl 5 degradation is better explained by a combination of various mechanisms, with major contributions from the contraction models R1 and R2. The calculated activation energy values from isothermal and nonisothermal data agreed with one another and were consistent with the observed high thermal stability of MnTE-2-PyPCl 5 in the solid state. The t 90% shelf life value at 25°C estimated from the isothermal decomposition data was approximately 17 years. These results contribute to the development of this class of redox-active therapeutics and SOD mimics and provide supporting data to protocols on purification, handling, storage, formulation, expiration date, and general use of these compounds. Additionally, these MnTE-2-PyPCl 5 results not only set the grounds for studying other Mn(III) porphyrin-based SOD mimics and redox-active therapeutics but also represent a first approximation to the thermal stability kinetic parameters of the chemically related Zn(II) porphyrin counterpart, ZnTE-2-PyPCl 4 , and its Zn(II) 2-N-alkylpyridylporphyrin analogues, which are being actively pursued as efficient and selective photosensitizers for antimicrobial photodynamic inhibition (aPDI) [63][64][65][66][67].

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.