Mechanism and Kinetics of the Degradation of Nitazoxanide and Hydroxychloroquine Drugs by Hydroxyl Radicals: Theoretical Approach to Ecotoxicity

The efforts of contrasting the effects caused by the COVID-19 (coronavirus disease 2019) pandemic increased the disposal of active pharmaceutical ingredients. This paper reports the mechanisms and kinetics of the degradation in aqueous environments induced by •OH of two drugs, among those most widely probed at the outbreak of coronavirus, nitazoxanide and hydroxychloroquine. The investigation exploits quantum chemistry techniques and a reaction rate theory combined with diffusion-controlled processes and quantum mechanical tunneling. The reaction rate constants are obtained in an environmentally relevant temperature range. The results show that (i) the deacetylation of nitazoxanide with formation of tizoxanide is kinetically the most favorable channel, in agreement with experimental work; (ii) for hydroxychloroquine, the present theoretical calculations show that the most favorable channel is the addition of •OH at the aromatic ring. The half-life time degradation products are for both cases in the range between 12 to 138 days. Both drugs presented toxicities between harmful and toxic as obtained by computational toxicology calculations. The toxicity is also calculated for the degradation products: (i) in the nitazoxanide degradation process, tizoxanide was characterized as more toxic, while (ii) in the case of hydroxychloroquine, the major degradation product showed a decrease in the toxicity.


Introduction
In recent years, the occurrence of micropollutants, such as those originated from waste of pharmaceuticals and pesticides, has turned into a global environmental concern. 1,2The COVID-19 (coronavirus disease 2019) pandemic worsened this scenario, since the effort to control the adverse health effects caused by the disease increased the variety and the quantities of pharmaceuticals in surface waters and sewage. 3,4Persistent and excessive use makes the metabolization of these drugs incomplete within the human body and a significant fraction are excreted by the organism of patients through their feces and urines, which will end up in sewage. 5hen active pharmaceutical ingredients (APIs) are dispersed in the environment, they become threats to aquatic wildlife, being often associated with several negative effects, e.g., disruption of cellular processes, intracellular ion concentrations, antibiotic resistance of microorganisms and the bio-accumulation of pharmaceuticals. 6Furthermore, these pharmaceuticals represent a potential danger to human health since a lot of reports have been confirmed their persistence in water bodies, oceans, groundwater, and even in the drinking water of several countries around the world. 5,7onventional widely used urban wastewater treatment plants, either primary (physical and physicochemical) or secondary (biological), are inefficient to remove APIs. 8Over the past decades, many efforts have been allocated in the development of new technologies as an alternative to wastewater treatment plants that can eliminate pharmaceuticals from wastewater, such as granular activated carbon, 9 membrane filtration, 10 and AOP, advanced oxidation processes. 11,12Researchers have been pointing out the AOP as one of the most effective and versatile advanced water treatments.
This method is based on the generations of a powerful oxidizing agent, such as the hydroxyl radical ( • OH) in solution, which is then able to degrade recalcitrant organic pollutants up less harmful compounds or even completely mineralize to CO 2 and H 2 O. 13 This method has gained increasing attention in studies of the removal of pharmaceuticals involving fast reaction rates and strong oxidation capability. 12,14,15][31][32] The reactive elementary steps for mitigation of micropollutants by • OH radicals evolve primarily along three paths: [32][33][34][35] addition of • OH to an aromatic ring or to other unsaturated bonds, hydrogen-atom transfer (HAT), and single electron transfer (SET).][39][40] As soon as the SARS-COV-2 pandemic emerged, there has been a huge number of reports from all over the world proposing options for treatments of the disease and also for preventive therapy.Today we have some drugs indicated for use in specific conditions of COVID-19, such as monoclonal and antiviral antibodies, 41,42 in parallel keep going investigations for the development of effective vaccines.However, large quantities of drugs such as chloroquine/ hydroxychloroquine, lopinavir/ritonavir, azithromycin, nitazoxanide, and colchicine have been produced for testing, and also prescribed by doctors to patients worldwide, even with several studies indicating ineffectiveness against COVID-19. 1,43,44Their fate and removal represent a relevant environmental worldwide concern.In this study, we focus from a theoretical point of view on the degradation mediated by • OH radicals of two of those drugs, nitazoxanide and hydroxychloroquine, that have been widely produced and distributed, especially in Brazil.
Nitazoxanide (NTZ) belongs to the class of drugs known as thiazolides, which has broad-spectrum antiparasitic and antiviral properties. 45Very recently, a multicenter, randomized, double-blind, placebo-controlled study involving COVID-19 patients, 46 showed that five days of NTZ treatment did not accelerate symptom resolution but reduced the viral load compared to the placebo group with no serious adverse events. 46Specifically, this study has some methodological flaws that will not be discussed in this work.Stress degradation study 47 of raw material and NTZ showed that the major degradation product is tizoxanide (2-hydroxy-N-(5-nitro-2-thiazolyl)benzamide) originated from its deacetylation for all tested stress conditions (thermal, acid, alkaline and oxidative).
2][53] The nitrogenous heterocyclic quinolone increases hydrophilicity which rising the persistence of HCQ that bioaccumulate in the environment.Investigations of fate and degradation of HCQ in aqueous environment are rare and concentrate specifically on the photochemical degradation of HCQ in water solution. 54,55Bensalah et al. 56 recently presented a study of the degradation of HCQ in water solution by elaborated electrochemical involving oxidation treatment including boron doped diamond combined with sonication and UV irradiation.It was demonstrated that release of chloride ions at the first stages of degradation of HCQ, followed by conversion of organic nitrogen compounds into NO 3 -and NH 4 + , confirming the formation of 7-chloro-4-quinolinamine, oxamic and oxalic acids as final products of HCQ degradation by electrochemical oxidation.
Thus, the focus of this work is to provide a detailed understanding of the mechanism and kinetics of nitazoxanide and hydroxychloroquine degradation mediated by  OH radicals using a combination of quantum chemistry calculations and reaction rate theory.In addition, we provide the toxicity of nitazoxanide and hydroxychloroquine and of their main degradation products from Ecological Structure-Activity Relationships predictive model.As far as we are aware, of the two most common mechanisms, radical adduct formation to the carbon (RAF) and hydrogen atom transfer (HAT) reactions involving • OH are the major steps for mitigation of contaminants because the energetic barrier involved in SET reactions are much higher, 38,39,57 and consequently it is of no concern here.
To identify the most reactive sites of the APIs (NTZ and HCQ) with the  OH radical, appropriate local reactivity descriptors, such as the Fukui function (f) 58,59 were calculated according to equations , , and .It was used Multiwfn package program, 60 where the contributions of the atomic orbitals of the frontier molecular orbital are weighted by the c i coefficients of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) orbitals.
All the quantum chemical calculations were carried out using the Gaussian 16 package. 61The electronic structure properties of the reactants, products, and the transition states of the degradation channels of the pharmaceutical compounds (NTZ and HCQ) by • OH radicals were calculated at the MP2/6-31+G//M06HF/6-31G(d) level of calculation, including the SMD version of the Continuum Solvation Model 62 to simulate the aqueous environment.The stationary points were characterized by analytical harmonic frequency analysis of the optimized structures, no imaginary frequency individuating local minima, one imaginary frequency individuating transition states.The zero-point vibrational energy contributions have been considered in the calculation of the energy barrier.

Reaction rate theory
The reaction rate constants of the degradation of the pharmaceuticals compounds (HCQ and NTZ) by •OH radicals were calculated using a combination of formulations derived from the Transition State Theory.To account for the tunneling effect, the deformed Transition State Theory (d-TST) 63 was adopted (equation 1): (1)   where h is the Planck's constant, k B is the Boltzmann constant, R is the universal gas constant, d is the deformation parameter, while Q Reac and are the partition functions of the reactants and transition state, respectively.To include the contribution of molecular diffusion in solution, the calculated rate constant k d -TST is combined with the Smoluchowski rate constant, k D , following the steady-state suggestion by Collins and Kimball, 64 yielding the overall rate constant k OBS , according to equation 2: (2) Additional details about the parameter d and the calculation of k D can be found elsewhere 65 and the references therein.The overall reaction rate constant for the Ri channel were used to calculate the total reaction rate constant .The Aquilanti-Mundim formula 66 (equation 3) was used to represent the temperature dependence our results for k Total (T) for comparison with other works and for use in kinetic models. ( where A and are the pre-exponential factor and the deformation parameter, respectively.Note a change in the notation here, needed in order to avoid ambiguities: in general, the parameters and from the fitting equation 3 can differ from the d and E 0 parameter in equation 1. Equation 3 permits to evaluate prototypical systems where the temperature dependence of the rate constant according to this equation is described by > 0 and > 0 or < 0, corresponding to convex (Super-Arrhenius) and concave (sub-Arrhenius).In the limit ⟶ 0, the term can be identified with the Arrhenius exponential law.Other case for < 0 will also be documented and indicated as anti-Arrhenius.
All kinetic and associated parameters have been calculated with the Transitivity Code version 1.0.4. 67Details of the computational program can be found on the literature. 68

Assessment of toxicity
The ecotoxicity of NTZ and HCQ and its main degradation products were determined using the Ecological Structure-Activity Relationship Model (ECOSAR V2.0). 69COSAR is an effective predictive program and has been successfully applied to the ecotoxicity assessment of organic contaminants. 70,71Three aquatic organisms (green algae, daphnia, and fish) were chosen as targets.Acute toxicity (feature characterized by LC 50 and EC 50 values) and chronic toxicity (defined by ChV) of the compounds studied were obtained from ECOSAR platform.LC 50 means the concentration of a chemical compound (in mgL −1 ) that causes the death of half of the fish and daphnia population after exposures of 96 and 48 h, respectively.In addition, EC 50 represents the concentration that permits 50% of green algae to grow normally after 96 h of exposure (in mg L -1 ).

Results and Discussion
The results of the present study can help understanding the mechanism and kinetic of reactions of nitazoxanide and hydroxychloroquine with •OH, also providing relevant clues on risk assessment in aqueous environments.Fukui functions are descriptors that allow the identification of the most reactive sites on a molecule, both for electrophilic as for nucleophilic and radical reactions. 72Here, f 0 parameters identify the most important reactive sites on NTZ and HCQ under  OH attack. 36,58,59,73The relevant values of the Fukui function are shown in Figures S1 and S2 in Supplementary Information (SI) section for the selected atoms.

Nitazoxanide
The nomenclature and main mechanism of hydrogen atom abstraction and addition reaction of NTZ and •OH radicals are shown in Figure 1: (i) hydrogen atom transfer (HAT) from carbon (R1, R2, and R4) or nitrogen (R3) of NTZ to the •OH radical and (ii) •OH addition (RAF) to the carbon of the NTZ (R5 and R6).
Figure 1 shows the energetic kinetic and thermodynamic parameters of the reaction of NTZ with  OH radicals showing that R1, R5 and R6 channels are thermodynamically favorable (free energy ∆G° < 0) (while R5 channel shows the lowest barrier heights (reaction barrier energies (E 0 ) = -3.55kcal mol -1 ), indicating that R5 is the most kinetically favorable channel and tizoxanide (2-hydroxy-N-(5-nitro-2-thiazolyl)benzamide) is the majority degradation product: this agrees with previous experimental results. 51ere, it is worth noting that the rate of some process increase as temperature decreases accordingly to an apparently negative activation energy.These processes are classified as anti-Arrhenius.][81] The simulations confirmed the suggestion obtained experimentally: the stereodynamical effect arises at low temperature permitting, the reactants reorient to find the propitious alignment leading to reaction; however, this adjustment is progressively less effective for higher temperatures, where the wandering paths evidence the roaming effect.
The Cartesian coordinates of the transition states and NTZ calculated in this work are listed in Table S1 (SI section).Geometric parameters and imaginary frequencies of the transition states involved in the reaction of • OH radicals with NTZ are listed in Table S2 (SI section).For the transition state of the R5 channel, we found the values 97.76° for C 5 -O 7 -H 8 angle, the imaginary frequency of 525 cm -1 , energy barrier E 0 = -3.55kcal mol -1 and deformation parameter d = -0.0149.

Reaction rate constants
Reaction rate constants are key quantities for evaluating the efficiency of the kinetics for degradation of drugs 80 permitting to quantify the relevance of the alternative reactive paths for the global conversion of each compound.Inclusion of molecular diffusion in solution is performed by the combination of the rate constant k d -TST and the steady-state Smoluchowski rate constant k D , according to the Collins-Kimball theory at 250-310 K (see equation 2 and results in Table 1).Our calculations provided values of the total reaction rate constant around 5.82 × 10 12 cm 3 mol -1 s -1 at 298.15 K, however, the comparison with experimental data is impeditive since there is no known data.The reaction rate constant are much larger than the overall reaction rate constants (see Table S3, SI section), reporting diffusion-controlled processes.
Web applications recently developed by our group used machine learning and a molecular fingerprint algorithm to evaluate the reaction rate constants for the degradation of contaminants in aqueous and atmospheric environments (the pySiRC platform). 81,82The reaction rate constant calculated by the Random Forest Machine Learning model in pySiRC platform demonstrated an excellent agreement with high-level reaction rate constant calculated with a value of 5.04 × 10 12 cm 3 mol -1 s -1 .The CAS-numbers used for NTZ and HCQ are 55981-09-4 and 118-42-3, respectively.
To evaluate the total reaction rate constant of NTZ with  OH radicals, we fitted the temperature dependence using the Aquilanti-Mundim (AM) formula (equation 3), which has been used successfully to describe the temperature dependence k of chemical processes under condition from Non-Arrhenius behavior. 78The equation obtained from fit for the overall rate constant is expressed as: The phenomenological parameters obtained from the fit by the AM formula were = 3.764 kcal mol -1 and = 0.0344.Positive values of these parameters are characteristic of the super-Arrhenius behavior of the viscosity of the solvent involved in the reaction.
From the data of the total reaction rate constant of NTZ with the • OH radical, it is possible to calculate the half-life time using t 1/2 = ln2/(k Total × [•OH]), where [•OH] is the concentration of • OH radicals in the specific aqueous medium.The half-life of the reaction was studied by us in the temperature range 273.15-310K, using [•OH] = 10 -15 -10 -18 mol L -1 , which usually represents values typical of surface waters.The calculated half-lives are shown in Figure 2 and they vary from 14 to 138 days at 298.15 K, considering a concentration of • OH radicals in the restricted range 10 -16 -10 -17 mol L -1 .

Hydroxychloroquine
Based on Fukui functions, we proposed seven degradation channels by  OH attack in the neutral form of HCQ.The nomenclature is shown in Figure 3 being: (i) •OH addition to the carbon (RAF) of the HCQ (R1-R4); (ii) hydrogen transfer from carbon (HAT) of HCQ to the • OH radical (R5-R7).
The calculated energy parameters of the reaction of HCQ with •OH radicals show that, with the exception of R6, all other channels are thermodynamically favorable (∆G° < 0), wherein R2 is the most favorable one (∆G° = -19.01kcal mol -1 ), while the R6 channel shows the lowest barrier height (E 0 = -18.86kacl mol -1 ).The Cartesian coordinates and imaginary frequencies of the transition states and HCQ calculated in this work are listed in Tables S4 and S5 (SI section).

Reaction rate constant
The reaction rate constants for all seven channels were combined with the Collins-Kimball formulation in the relevant temperature range 250.0-310.0K to elucidate the most important products of degradation.The results are presented in Table 2.The R2 channel was found to have the fastest reaction rate constant, and its product is most kinetically favorable by • OH attack in HCQ.The value of the total reaction rate constant at 298.15 K is 6.64 × 10 12 cm 3 mol -1 s -1 , however, there are no experimental reaction rate constants in the same theoretical conditions simulated and consequently, these results and the mechanism proposed here can be confronted with future experimental results.For R2 channel, we found the values E 0 = -4.21kcal mol -1 for energy barrier and d = -0.1642for deformed parameter.
As observed for NTZ, the reaction rate constant for HCQ showed a diffusion-controlled process (see Table S6, SI section).The reaction rate constant estimated by the random forest machine learning (ML) model in pySiRC showed a value of 6.09 × 10 12 cm 3 mol -1 s -1 , which showed a good agreement with high-level reaction rate constant calculation.The fitting of temperature dependence of the rate constant using AM formula is expressed as: (5) The phenomenological parameters obtained from the fit by the AM formula were Ē = 3.517 kcal mol -1 and = 0.0376.Similarly to kinetic behavior observed for the NTZ drug, here the parameters also presented positive values, which are related with super-Arrhenius behavior.
In an advanced oxidative experimental study, Lu and Chen 60 evidenced the formation of the CQLA (7-chloro-4-quinolinamine) as one of the most important intermediate degradant products, however, in their experimental conditions, two of the functional groups exist in protonated forms, which may facilitate the rupture of C-N bonds by  OH radical attack.
The half-life of the reaction was studied by us in the temperature range 273.15-3104][85] The calculated half-lives are shown in Figure 4, and they vary from 12 to 121 days at 298.15 K, considering a concentration of  OH radicals in the restricted range 10 -16 -10 -17 mol L -1 .acute toxicity (LC 50 or EC 50 ) and chronic toxicity (ChV), respectively (see technical details in "Assessment of toxicity" sub-section).

Evaluation of toxicity
The experimental cytotoxicity assay with mononuclear cell showed that the tizoxanide, the main degradation product (R5 channel), has a higher cytotoxicity when compared to NTZ with a reduction in cell viability of 75.25%, i.e., 27% higher than that obtained with NTZ in the concentration and tested conditions. 80As can be seen in Table 4, the estimated toxicities of the compounds to fish, daphnia, and green algae showed that tizoxanide is more toxic than NTZ, in agreement with experimental results: it is attributed the harmful classification according to the European Union and Chinese Regulations.
The degradation of HCQ occurs by successive steps that lead to the formation of organic intermediates that end to mineralize.Here, we identified that R2 product is the most degradant product of neutral form of HQC.As can be seen in Table 5, the estimated toxicities of the compounds to fish, daphnia, and green algae showed that the R2 product is less toxic than HCQ.

Conclusions
In the "Reaction rate theory" section, the parameters couple (E 0 , d) and ( , ) were differentiated to avoid confusion.The former is related to molecular parameters at potential energy channel of the elementary step evaluated.The late is related with several contributions to the overall reaction rate constant.In both drugs, the energetic barriers E 0 and deformation parameters d for the most probable degradation product show apparent negative activation energy 47,85 and propensity to quantum tunneling effect. 88,89hese molecular phenomena guide the kinetic behavior to anti-Arrhenius and sub-Arrhenius behavior. 90,91However, these reactions are diffusion-controlled processes which are typical cases of classical and cooperative effects mediated by the viscosity of the solvent in reactive molecular encounters. 91,92Equations 4 and 5 capture the majority contribution of the solvent effect in reactive processes providing positive phenomenological parameters ( , ) with kinetic behavior befitting with super-Arrhenius cases, where transport phenomena, e.g., diffusion and viscosity, decelerate as the temperature decreases.
A theoretical study was performed on the degradation of nitazoxanide and hydroxychloroquine via •OH radicals in aqueous media using a combination of quantum chemistry calculations and reaction rate theories.The degradation mechanism and reaction kinetics were reported, and the results showed that deacetylation of nitazoxanide with formation of tizoxanide was the most kinetic favorable channel agreeing with experimental work.For hydroxychloroquine, the theoretical calculations showed that the addition •OH at carbon of aromatic ring (R2) was the most kinetic favorable channel.The reaction rate constants were calculated by formulations derived both from the Transition State Theory modified for quantum tunneling and from the theory of diffusion-controlled processes.The halflives time for NTZ and HCQ degradation varied from 12 to 138 days.Both drugs presented toxicities between harmful and toxic.However, in the nitazoxanide degradation process, the R5 degradation compound was characterized as more toxic, while in the case of hydroxychloroquine the major degradation product, R2, showed a decrease in the toxicity.

Figure 2 .
Figure 2. Half-life time, in days, of nitazoxanide degradation as a function of  OH concentration, in mol L -1 , in the temperature range 273.15-310K of interest in natural waters.

Figure 4 .
Figure 4. Half-life time, in days, of hydroxychloroquine degradation as a function of  OH concentration, in mol L -1 , in the temperature range 273.15-310K of interest in natural waters.

Table 1 .
Reaction rate constants of NTZ degradation by  OH attack calculated at the MP2/6-31+G//M06HF/6-31G(d) level with the SMD continuous solvation model using d-TST formulation combined with the steady-state Smoluchowski rate constant

Table 3 exploit
discrimination criteria established by the European Union 86 and Chinese Regulations 87 for

Table 4 .
Toxicity of NTZ and its main by-product generated through •OH radical attack.The definition on Table3was used to classify the toxicity of compounds

Table 5 .
Toxicity of HCQ and of its main by-product generated through •OH radical attack.The definition on Table3was used to classify the toxicity of compounds 50: acute toxicity; ChV: chronic toxicity; HCQ: hydroxychloroquine; R2: the most kinetically favorable channel.