Novel Mannich Bases of Benzimidazole Derivatives: An Antibacterial Study of Environmental Bacterial Strains
Evrard Ablo1,2, Ouehi Dosso1, Bakary Coulibaly3, Kouassi Franscesco Adingra1, Penayori Marie-Aimée Coulibaly1, Armand Patrick Achi1,2, Tchambaga Etienne Camara1, Souleymane Coulibaly1*orcid, Siomenan Coulibali1
1Laboratoire de Constitution et Réaction de la Matière, UFR Sciences des Structures de la Matière et Technologie, Université Félix Houphouët-Boigny de Cocody, Abidjan, Côte d’Ivoire.
2Laboratoire des Procédés Industriels de Synthèse, de l’Environnement et des énergies Nouvelles (LAPISEN), Institut National Polytechnique Félix Houphouët-Boigny, Yamoussoukro, Côte d’Ivoire.
3Laboratoire d’Agrovalorisation, Département de Biochimie-Microbiologie, UFR Agroforesterie, Université Jean Lorougnon Guédé, Daloa, Côte d’Ivoire.
DOI: 10.4236/abc.2023.135013   PDF    HTML   XML   62 Downloads   263 Views  

Abstract

A previous study was conducted on the synthesis and antibacterial evaluation of Mannich bases of 2-(thioalkyl)-1H-methylbenzimidazole derivatives. The results of this study showed that certain 2-(thioalkyl)-1H-methylbenzimidazole and 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl)benzimidazole derivatives possess antibacterial activities against clinical strains, such as Escherichia coli, Klebsiella pneumonia (Gram-negative bacteria), Staphylococcus aureus and Pseudomonas aeruginosa (Gram-positive bacteria). Following these favorable results, we extended the antibacterial evaluation of this series of molecules to environmental strains. The aim of this study was to assess the impact of the methyl-piperidine group fixed at position-1 of this new series of benzimidazoles on the antibacterial activity of environmental strains. In addition, we first evaluated the antibacterial activity of four 2-(thioalkyl)methylbenzimidazole derivatives and then that of five 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) benzimidazole derivatives. This study allowed us to show that compounds 1d and 1e could inhibit bacterial growth in vitro of the Enterobacteria P1 strain with inhibition diameters of 17.3 ± 0.6 mm and 10 ± 0.0 mm, respectively. However, addition of methyl-piperidinyl in this series showed that five (5) of 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) benzimidazole derivatives had an inhibitory effect on the in vitro growth of bacterial strains used except on Enterobacteria P2 with inhibition diameters between 10.0 ± 0.8 mm and 27.9 ± 1.4 mm. The introduction of the methyl-piperidinyl group at the 1-position of 2-(thioalkyl)-1H-methylbenzimidazole derivatives greatly improved the antibacterial activity against environmental bacteria such as Escherichia coli A1, A2, A3, and A4 and two Enterobacteria P1.

Share and Cite:

Ablo, E. , Dosso, O. , Coulibaly, B. , Adingra, K. , Coulibaly, P. , Achi, A. , Camara, T. , Coulibaly, S. and Coulibali, S. (2023) Novel Mannich Bases of Benzimidazole Derivatives: An Antibacterial Study of Environmental Bacterial Strains. Advances in Biological Chemistry, 13, 182-191. doi: 10.4236/abc.2023.135013.

1. Introduction

In recent decades, scientists have prioritized the fight against antimicrobial resistance because it affects most countries with varying levels of infection. These levels of variation are believed to be due to multiple reasons, including different rates of antibiotic use, hospital practices, income, and hygiene levels [1] . Indeed, the WHO states that more than 700,000 people die each year from these resistant infections and countless numbers of sick animals do not respond to the treatments administered. At the economic level, the same institution says that in just 10 years, more than 24 million people could fall into extreme poverty because of antimicrobial resistance [2] . Among resistant or multi-resistant bacteria, multidrug-resistant enterobacteria, such as Escherichia coli (E. coli) and Klebsiella pneumoniae (K. Pneumoniae), which are digestive tract bacteria responsible for a large number of infections, such as urinary tract infections [3] , mild diarrhea, and other more severe forms such as hemorrhagic diarrhea. There is also methicillin-resistant staphylococcus aureus (MRSA), multiresistant tuberculous pyocyaneus bacilli, and Acinetobacter baumannii, which are bacteria that infect the lungs of people with cystic fibrosis [1] . Among the heterocyclic compounds with strong biological potential, benzimidazoles may be suitable. Indeed, this scaffold is present in a large number of drugs such as Thiabendazole, Mebendazole, Triclabendazole, Albendazole, and Oxibendazole and has a range of biological activities [4] including antibacterial [5] , antimicrobial [6] , anti-inflammatory [7] , antiviral [8] , anticancer [9] , and anti-tuberculosis [10] activities. However, some studies have shown that Mannich bases associated with various heterocyclic compounds may be biologically effective [11] [12] [13] . They are found in the scaffolds of many commercial drugs, such as fluoxetine, an antidepressant, and trihexyphenidyl hydrochloride, which is used as an antispasmodic. Additionally, some benzimidazole compounds associated with Mannich bases have shown good biological activities [14] [15] [16] .

Indeed, M. P. Vatsal et al. [17] synthesized benzimidazole N-Mannich bases with pyridine-3-amine and 5-methyl-pyridine-2-amine and evaluated them in vitro for their antibacterial, antimycotic, and antiprotozoal activities. These compounds were potent against Leishamania mexicana (L. mexicana), and Trypanosoma cruzi (T. cruzi) respectively with Inhibition Concentration 50 (IC50) values of 0.25 and 1.02 mg/mL. Also, V. K. Sekar et al. [15] synthesized a series of Mannich bases of 2-substituted benzimidazole derivatives. The results of in vitro studies of these benzimidazole derivatives revealed that 3-(1-[(dimethylamino)methyl]-1H-benzimidazol-2-yl)-4-hydroxybenzene sulfonic acid and 3-(1-[(diethylamino)methyl]-1H-benzimidazol-2-yl)-4-hydroxybenzene sulfonic acid showed broad-spectrum antibacterial and antifungal activities. After a toxicity test on Artemia salina, these compounds were found to be non-toxic and completely cut the genomic DNA of the E. coli strain. They assumed that with appropriate molecular modifications, these compounds could be potent antimicrobial agents in the future. Our contribution to this research is to evaluate the antibacterial activity of a new series of base derivatives of Mannich benzimidazolés on environmental bacterial strains. We also demonstrated the impact of the 1-position methyl-piperidinyl group of the benzimidazole ring of 2-(thioalkyl)-methylbenzimidazole on antibacterial activity.

2. Material and Methods

2.1. Material

2.1.1. Microbial Strains

The microbial support consists of clinical strains of Escherichia coli (Gram-negative bacteria), called E. coli A1, E. coli A2, E. coli A3, and E. coli A4 and two Enterobacteria (P1 and P2). These strains were provided by the Unit of Antibiotics, Natural Substances, and Surveillance of Microorganisms in the Anti-infectious (ASSURMI) of the Bacteriology and Virology Department of the Pasteur Institute Côte d’Ivoire.

2.1.2. Chemicals

The synthetic compounds used were composed of four derivatives of 2-(thioalkyl)-methylbenzimidazole, namely 2-((methylthio)methyl)-1H-benzimidazole, 2-((isobutylthio)methyl)-1H-benzimidazole, 2-((butylthiomethyl)-1H-benzimidazole, 3-((1H-benzimidazol-2-yl)methyl) thio)ethyl propionate and five 2-mercapto benzimidazole-bearing Mannich bases such as 2-(methylthio)-1-(piperidine-1-yl)methyl)-1H-benzimidazole, 2-(isobutylthio)methyl)-1-(piperidine-1-yl)methyl)-1H-benzimidazole, 2-(ethylthio)-1-(piperidine-1-yl)methyl)-1H-benzimidazole, 2-(1-(piperidin-1-yl)methyl)-1H-benzimidazol-2-yl)methylthio) ethyl propionate, 3-((1-(piperidin-1-yl)methyl)-1H-benzimidazol-2-yl)methylthio)ethyl propionate [18] .

2.2. Methods

2.2.1. Chemical Method

We recently published the synthesis and physicochemical characteristics of this new series of derivatives of 2-(thioalkyl)-1-methyl-(piperidin-1-ylmethyl) benzimidazole and their antibacterial activities on clinical resistant strains such as P. aeruginosa, K. pneumoniae, E. coli, and S. aureus [18] . The chemical structures of these molecules are listed in Table 1 and Table 2, respectively.

Table 1. 2-(thioalkyl)methylbenzimidazole derivatives.

Table 2. Chemical structure of 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) benzimidazole derivatives.

2.2.2. Biological Method

1) Preparation of inoculum for solid medium testing

The inoculum was prepared from a young colony and incubated for 24 h. It was emulsified in 2 mL NaCl solution. Then, the optical density was adjusted to 0.5 MC Farland using a densimat. The sample volumes were 100 µL for E. coli, 1000 µL for S. aureus, and 10 µL for P. aeruginosa. This suspension was mixed with 10 mL of physiological water (NaCl 0.9%), and the bacterial inoculum was estimated to be 106 bacteria/mL.

The striae method was used to transplant the different preserved bacterial strains onto Muller-Hinton agar. They were then incubated in an oven at 37˚C for 18 - 24 h to obtain young and isolated colonies. These colonies were used to prepare bacterial inocula.

2) Preparation of the stock solution of chemicals

The substances were weighed and placed in test tubes to which a quantity of ethanol (70˚) was added. Different concentrations were tested.

3) Sensitivity test

a) Determination of areas of inhibition

The gel diffusion technique in cupules (wells) and the liquid macrodilution method were used to perform the tests [19] [20] . A 500 µg/mL concentration solution of the chemical was prepared. Petri dishes containing Muller-Hinton agar were seeded with the prepared inoculum using swabs. The cups were then dug by inserting the large tip of a Pasteur pipette into the agar and filled with 50 µL of the prepared chemical solution. The units were incubated at 37˚C for 24 h. The inhibition diameter around each cup was measured using a caliper. The effectiveness of the extracts was assessed according to the criteria described by Poncé et al. [21] . Thus, a substance is said to be ineffective if the inhibition diameter is less than 8 mm, whereas it is said to be effective if the diameter is between 9 and 14 mm. However, it is considered very effective when the diameter is between 15 and 19 mm and extremely effective if the diameter is greater than 20 mm. This test allowed for the selection of the most active extracts for the determination of antibacterial parameters.

b) Preparation of the inoculum for liquid tests

A 24-hour bacterial colony was collected using a Pasteur pipette and emulsified in a test tube containing 10 mL of sterile Muller-Hinton broth. The mixture was incubated at 37˚C for 3 h. After incubation, a suspension of 0.3 mL of this pre-culture was taken and diluted in 10 mL of sterile Muller-Hinton broth and then homogenized.

Preparation of the concentration range

The concentration range was determined using the double-dilution method. To this end, a solution of retained chemicals (µg/mL) was prepared. A series of reason 2 dilutions were performed on this solution to obtain the concentration ranges.

c) Determination of antibacterial parameters

The determination of antibacterial parameters was carried out by dilution in a liquid medium according to the method used by Kouadio et al. [22] . Thus, in 10 experimental hemolysis tubes, 1 mL of each concentration range of chemical substances was brought into contact with 1 mL of the bacterial inoculum. The growth control tube received 1 mL of sterile distilled water in addition to the inoculum, whereas the sterility control group received only 2 mL of sterile Muller-Hinton broth (BMH). The tubes were then incubated for 24 h at 37˚C. After this incubation time, observations were made with the naked eye and the lowest concentration at which no bacterial growth was observed corresponded to the Minimum Inhibitory Concentration (MIC). The Minimum Bactericidal Concentration (MBC), it makes it possible to obtain 0.01% viable bacteria after 24 h of incubation at 37˚C. His determination begins with a number. This consisted of diluting the starting inoculum from 10−1 to 10−4 and seeding these different dilutions using a calibrated loop of 2 µL in 5 cm long striations, on a Muller-Hinton agar and then incubating for 24 h. These petri dishes were named A. After reading the MIC, the contents of tubes in which there was no visible growth were used to plant GMH on 5 cm streaks. This series of Petri dishes was named B. MBC was determined by comparing the bacterial growth of boxes A and B. Thus, the smallest tube concentration that had less than 0.01% viable bacteria compared with the initial inoculum was MBC. The MBC/MIC report clarified the modality of action of the substance [23] . As reported by Kamanzi et al. [24] , extract is bactericidal when MBC is equal to MIC, it is bacteriostatic when its MBC is greater than its MIC or if the MBC/MIC ratio is higher than 4. When this ratio was equal to 32, the strain was considered tolerant.

d) Statistical analysis

The results were analyzed using Excel 2013 software for descriptive analyses. The results of the antibacterial tests are expressed as the mean standard deviation.

3. Results and Discussion

We first evaluated the antibacterial activity of four 2-(thioalkyl)methylbenzimidazole derivatives by determining their inhibition diameters.

The results for these diameters are presented in Table 3.

The result of this antibacterial test performed on environmental strains indicates that among the derivatives derived from the synthesized benzimidazole S-alkylation (1a, 1d, 1c, and 1e), compounds 1d and 1e inhibited the in vitro growth of the Enterobacteria P1 strain with inhibition diameters of 17.3 ± 0.6 mm and 10 ± 0.0 mm, respectively. Compounds 1a and 1c showed no inhibitory activity against any bacterial strains. Compounds with inhibitory activity against the in vitro growth of bacterial strains were selected to determine the antibacterial parameters (MBC and MIC), as shown in Table 4. Thus, the determination of the Minimum Inhibitory Concentration and the Minimum Bactericidal Concentration of these different compounds allowed us to calculate the MBC/MIC ratio of each compound. This allowed us to determine the modality of action of each compound. For this purpose, we can affirm that compounds 1d and 1e have bactericidal effects on the Enterobacteria strain P1.

To determine the influence of the 1-position methylpiperidinyl group of the 2-(thioalkyl)methylbenzimidazole derivatives, new antibacterial tests were performed on five derivatives of 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) benzimidazole by determining their inhibition diameters on environmental strains. Table 5 presents the results.

The five compounds tested had an inhibitory effect on the in vitro growth of the bacterial strains used except on enterobacteria P2 with inhibition diameters between 10.0 ± 0.8 mm and 27.9 ± 1.4 mm. The inhibitory effect (bacterial resistance) varied depending on the strain (Table 5). The absence of a zone of inhibition of the different compounds in the Enterobacteria P2 strain reflects the resistance of this strain to these compounds. The same was also observed for compound 2e in E. coli A1. Based on the results obtained, we can therefore affirm that the addition of a methylpiperidine group in position-1 of the derivatives 2-(thioalkyl)methylbenzimidazole is favorable for antibacterial activity against environmentally resistant strains such as E. coli A2, E. coli A3, and Enterobacteria P1. However, this addition had no advantage over the Enterobacterial P2 strain. For this series of molecules, if we closely observe the antibacterial

Table 3. Diameters of inhibition zones of compounds derived from S-alkylation benzimidazole on environmental strains.

Table 4. Mean values (mean ± SD of three tests) of antibacterial parameters of chemicals derived from S-alkylation benzimidazole on environmental strains.

Table 5. Mean diameter values of inhibition zones of benzimidazole 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) derivatives on environmental strains (averages ± SD).

activity of the strain E. coli A1, we can claim that the length (carbon chain) substitutes linked to the sulfur atom could have an influence on the improvement of antibacterial activity both in the alkyl series and ester. Therefore, when the carbon chain was increased, the antibacterial activity of the molecule decreased. The sulfur atom was substituted for ethyl propionate, the methylpiperidyl group was added, and there was no improvement in the activity of the E. coli A1 strain.

4. Conclusion

Studies on this new series of benzimidazole molecules showed that compounds 1d and 1e had antibacterial activity against the Enterobacteria P1 strain. However, the addition of the methylpiperidin-1 group of the benzimidazole nucleus of this molecule series allowed us to confirm the excellent antibacterial activity of the 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) benzimidazole derivatives against all strains tested, except Enterobacteria P2. In addition, the substitution of the sulfur atom by ethyl propionate and the benzimidazole-1-ring position by the methylpiperidine group were not considered in the search for antibacterial compounds against these environmental strains. Based on the antibacterial activity of these strains, compounds 2a, 2b, 2d, and 2g could be used as antibacterial controls against environmental strains such as E. coli A1, E. coli A2, E. coli A3, and Enterobacteria P2. It would be interesting to conduct in vivo tests to study the toxicity of these compounds.

Acknowledgements

We wish to thank the Unit of Antibiotics, Natural Substances, and Surveillance of Microorganisms in the Anti-infectious of the Bacteriology and Virology Department of the Pasteur Institute Côte d’Ivoire.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

References

[1] MOOC de l’Institut Pasteur (2021) Resistance to Antibacterial Agents.
https://www.pasteur.fr/fr/centre-medical/fiches-maladies/resistance-aux-antibiotiques
[2] ONU Info (2020) La résistance aux antimicrobiens est une réalité.
https://news.un.org/fr/story/2020/11/1082572
[3] Hamza, O. and Omran, R. (2022) Multidrug Drug Resistance of Escherichia coli and Klebsiella Isolated from Iraqi Patients and Microbiota. Journal of Biosciences and Medicines, 10, 240-252.
https://doi.org/10.4236/jbm.2022.1011019
[4] Shah, K., Chhabra, S., Shrivastava, S.K. and Mishra, P. (2013) Benzimidazole: A Promising Pharmacophore. Medicinal Chemistry Research, 22, 5077-5104.
https://doi.org/10.1007/s00044-013-0476-9
[5] Evrard, A., Siomenan, C., Etienne, C.T., Daouda, T., Souleymane, C., Drissa, S. and Ané, A. (2021) Design, Synthesis and in Vitro Antibacterial Activity of 2-Thiomethyl-benzimidazole Derivatives. Advances in Biological Chemistry, 11, 165-177.
https://doi.org/10.4236/abc.2021.114012
[6] Noolvi, M., Agrawal, S., Patel, H., Badiger, A., Gaba, M. and Zambre, A. (2014) Synthesis, Antimicrobial and Cytotoxic Activity of Novel Azetidine-2-One Derivatives of 1H-Benzimidazole. Arabian Journal of Chemistry, 7, 219-226.
https://doi.org/10.1016/j.arabjc.2011.02.011
[7] Luo, Y., Yao, J.P., Yang, L., Feng, C.L., Tang, W., Wang, G.F., Zuo, J.P. and Lu, W. (2010) Design and Synthesis of Novel Benzimidazole Derivatives as Inhibitors of Hepatitis B Virus. Bioorganic & Medicinal Chemistry, 18, 5048-5055.
https://doi.org/10.1016/j.bmc.2010.05.076
[8] Tonelli, M., Simone, M., Tasso, B., Novelli, F., Boido, V., Sparatore, F., et al. (2010) Antiviral Activity of Benzimidazole Derivatives. II. Antiviral Activity of 2-Phenylbenzimidazole Derivatives. Bioorganic & Medicinal Chemistry, 18, 2937-2953.
https://doi.org/10.1016/j.bmc.2010.02.037
[9] El Rashedy, A.A. and Aboul-Enein, H.Y. (2013) Benzimidazole Derivatives as Potential Anticancer Agents. Mini-Reviews in Medicinal Chemistry, 13, 399-407.
https://doi.org/10.2174/1389557511313030008
[10] Ramprasad, U., Nayak, N., Dalimba, U., Yogeeswari, P., Sriram, D., Peethambar, S.K., Achur, R. and Kumar, H.S.S. (2015) Synthesis and Biological Evaluation of New Imidazo[2,1-b][1,3,4]thiadiazole-benzimidazole Derivatives. European Journal of Medicinal Chemistry, 95, 49-63.
https://doi.org/10.1016/j.ejmech.2015.03.024
[11] Wenzel, I.N., Wong, P.E., Maes, L., Muller, T.J.J., Siegel, R.L.K., Barrett, M.P. and Charvet, E.D. (2009) Unsaturated Mannich Bases Active against Multidrug-Resistant Trypanosoma brucei brucei Strains. ChemMedChem, 4, 339-351.
https://doi.org/10.1002/cmdc.200800360
[12] Patel, V.M., Patel, N.B., Chan-Bacab, M.J. and Rivera, G. (2018) Synthesis, Biological Evaluation and Molecular Dynamics Studies of 1,2,4-Triazole Clubbed Mannich Bases. Computational Biology and Chemistry, 76, 264-274.
https://doi.org/10.1016/j.compbiolchem.2018.07.020
[13] Al Nasr, I., et al. (2019) Antiparasitic Activities of New Lawsone Mannich Bases. Archiv der Pharmazie (Weinheim), 352, Article ID: 1900128.
https://doi.org/10.1002/ardp.201900128
[14] Taher, A.T., Khalil, N.A. and Ahmed, E.M. (2011) Synthesis of Novel Isatin-Thiazoline and Isatin-Benzimidazole Conjugates as Anti-Breast Cancer Agents. Archives of Pharmacal Research, 34, 1615-1621.
https://doi.org/10.1007/s12272-011-1005-3
[15] Vinoth Kumar, S., Subramanian, M.R. and Chinnaiyan, S.K. (2013) Synthesis, Characterisation and Evaluation of N-Mannich Bases of 2-Substituted Benzimidazole Derivatives. Journal of Young Pharmacists, 5, 154-159.
https://doi.org/10.1016/j.jyp.2013.11.004
[16] Jesudason, E.P., Sridhar, S.K., Malar, E.J.P., Shanmugapandiyan, P., Inayathullah, M., Arul, V., Selvaraj, D. and Jayakumar, R. (2009) Synthesis, Pharmacological Screening, Quantum Chemical and in Vitro Permeability Studies of N-Mannich Bases of Benzimidazoles through Bovine Cornea. European Journal of Medicinal Chemistry, 44, 2307-2312.
https://doi.org/10.1016/j.ejmech.2008.03.043
[17] Patel, V.M., Patel, N.B., Chan-Bacab, M.J. and Rivera, G. (2020) N-Mannich Bases of Benzimidazole as a Potent Antitubercular and Antiprotozoal Agents: Their Synthesis and Computational Studies. Synthetic Communications, 50, 858-878.
https://doi.org/10.1080/00397911.2020.1725057
[18] Coulibaly, S., Coulibali, S., Ablo, E., Coulibaly, B., Camara, T.E. and Adjou, A. (2022) Influence of N-methyl Piperidine on Antibacterial Activity of 2-(thioalkyl)-1H-methylbenzimidazole Derivatives. ChemXpress, 14, 1-11.
[19] Dosso, M. and Aye-Kette, H. (2000) Contrôle de qualité de l’antibiogramme en pratique courante: Expérience du laboratoire de bactériologie de l’Institut Pasteur de Côte d’Ivoire. Bactériolo int, n spécial.
[20] Koné, M. (2005) Potentiel des plantes médicinales de Côte-d’Ivoire dans le contrôle des haemonchoses chez les ovins. Thèse de Doctorat Unique en Biologie végétale, Spécialité: Phytochimie, Université de Cocody Abidjan, UFR Biosciences, Abidjan.
[21] Ponce, A.G., Fritz, R., Del Valle, C. and Roura, S.I. (2003) Antimicrobial Activity of Essential Oils on the Native Microflora of Organic Swiss Chard. LWT—Food Science and Technology, 36, 679-684.
https://doi.org/10.1016/S0023-6438(03)00088-4
[22] Kouadio, N.J., Guessennd, N.K., Kone, M.W., Moussa, B., Koffi, Y.M., Guede, K.B., Yao, K., et al. (2015) Evaluation de l’activité des feuilles de Mallotus oppositifolius (Geisel.) Müll.-Arg (Euphorbiaceae) sur des bactéries multirésistantes et criblage phytochimique. International Journal of Biological and Chemical Sciences, 9, 1252-1262.
https://doi.org/10.4314/ijbcs.v9i3.10
[23] Fauchère, J. and Avril, J. (2002) Bactériologie générale et médicale. Ellipses.
[24] Kamanzi, A. (2002) Plantes médicinales de Côte d’Ivoire: Investigations phytochimiques guidées par des essais biologiques. Doctorat d’Etat ès-Sciences en biologie végétale, UFR Biosciences, Université de Cocody, Abidjan.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.