Mathematical Modeling of Molybdenum Reduction to Molybdenum Blue by Burkholderia sp. Strain Dr.Y27 and Model Selection Using the MOORA Method
DOI:
https://doi.org/10.54987/jebat.v7i2.1033Keywords:
Mo-reducing bacterium, Molybdenum blue, Burkholderia sp., Growth models, MOORAAbstract
The microbial detoxification process of molybdenum reduction to molybdenum blue directly correlates with bacterial development during Mo-blue production. The reduction process can be modeled mathematically to determine essential kinetic parameters, which include the specific Mo-blue production rate and theoretical maximum Mo-blue generation, as well as the possible effects of high molybdenum concentrations on the lag phase of reduction. Applying linearization techniques including natural logarithmic transformations remains common, but these methods deliver imprecise results that produce only approximate values for specific parameters such as the specific growth rate or specific Mo-blue production rate. This research introduced a complete range of nonlinear growth and models to study Mo-blue production from Burkholderia sp. strain Dr.Y27. The research incorporated nine growth models, including the modified Gompertz and modified Logistic. The modified logistic model demonstrated the highest fit to the Mo-blue production curve of Burkholderia sp. strain Dr.Y27 based on multiple statistical performance criteria which included root-mean-square error (RMSE), Marquardt percent standard deviation (MPSD), adjusted coefficient of determination (adjR²), bias factor (BF), accuracy factor (AF), Bayesian information criterion (BIC), Hannan-Quinn criterion (HQC), and the corrected Akaike information criterion (AICc). The Multi-Objective Optimization by Ratio Analysis or MOORA approach based on Ratio Analysis was applied to enhance model selection and is the first method used to find the best model for primary modeling of bacterial growth or Mo-blue production rate. The fitted model generated essential parameters to serve as a solid foundation for developing additional models that describe how environmental variables and substrate concentrations affect Mo-blue production.
References
King RB, Long K, Sheldon JK. Practical Environmental Bioremediation. The Field Guide. Lewis Publisher, Florida; 1992.
Neunhäuserer C, Berreck M, Insam H. Remediation of soils contaminated with molybdenum using soil amendments and phytoremediation. Water Air Soil Pollut. 2001;128(1-2):85-96.
Underwood EJ. Environmental sources of heavy metals and their toxicity to man and animals. 1979;11(4-5):33-45.
Kincaid RL. Toxicity of ammonium molybdate added to drinking water of calves. J Dairy Sci. 1980;63(4):608-10.
Abo-Shakeer LKA, Ahmad SA, Shukor MY, Shamaan NA, Syed MA. Isolation and characterization of a molybdenum-reducing Bacillus pumilus strain lbna. J Environ Microbiol Toxicol. 2013;1(1):9-14.
Lim HK, Syed MA, Shukor MY. Reduction of molybdate to molybdenum blue by Klebsiella sp. strain hkeem. J Basic Microbiol. 2012;52(3):296-305.
Othman AR, Bakar NA, Halmi MIE, Johari WLW, Ahmad SA, Jirangon H, et al. Kinetics of molybdenum reduction to molybdenum blue by Bacillus sp. strain A.rzi. BioMed Res Int. 2013;2013.
Shukor MY, Ahmad SA, Nadzir MMM, Abdullah MP, Shamaan NA, Syed MA. Molybdate reduction by Pseudomonas sp. strain DRY2. J Appl Microbiol. 2010;108(6):2050-8.
Shukor MY, Habib SHM, Rahman MFA, Jirangon H, Abdullah MPA, Shamaan NA, et al. Hexavalent molybdenum reduction to molybdenum blue by S. marcescens strain Dr. Y6. Appl Biochem Biotechnol. 2008;149(1):33-43.
Shukor MY, Rahman MF, Shamaan NA, Syed MS. Reduction of molybdate to molybdenum blue by Enterobacter sp. strain Dr.Y13. J Basic Microbiol. 2009;49(SUPPL. 1):S43-54.
Shukor MY, Rahman MF, Suhaili Z, Shamaan NA, Syed MA. Hexavalent molybdenum reduction to Mo-blue by Acinetobacter calcoaceticus. Folia Microbiol (Praha). 2010;55(2):137-43.
Shukor MY, Rahman MF, Suhaili Z, Shamaan NA, Syed MA. Bacterial reduction of hexavalent molybdenum to molybdenum blue. World J Microbiol Biotechnol. 2009;25(7):1225-34.
Yunus SM, Hamim HM, Anas OM, Aripin SN, Arif SM. Mo (VI) reduction to molybdenum blue by Serratia marcescens strain Dr. Y9. Pol J Microbiol. 2009;58(2):141-7.
Campbell AM, Del Campillo-Campbell A, Villaret DB. Molybdate reduction by Escherichia coli K-12 and its chl mutants. Proc Natl Acad Sci U S A. 1985;82(1):227-31.
Capaldi A, Proskauer B. Beiträge zur Kenntniss der Säurebildung bei Typhus-bacillen und Bacterium coli - Eine differential-diagnostische Studie. Z Für Hyg Infect. 1896;23(3):452-74.
Khan A, Halmi MIE, Shukor MY. Isolation of Mo-reducing bacterium in soils from Pakistan. J Environ Microbiol Toxicol. 2014;2(1):38-41.
Levine VE. The reducing properties of microorganisms with special reference to selenium compounds. J Bacteriol. 1925;10(3):217-63.
Yamaguchi S, Miura C, Ito A, Agusa T, Iwata H, Tanabe S, et al. Effects of lead, molybdenum, rubidium, arsenic and organochlorines on spermatogenesis in fish: Monitoring at Mekong Delta area and in vitro experiment. Aquat Toxicol. 2007;83(1):43-51.
Zhang YL, Liu FJ, Chen XL, Zhang ZQ, Shu RZ, Yu XL, et al. Dual effects of molybdenum on mouse oocyte quality and ovarian oxidative stress. Syst Biol Reprod Med. 2013;59(6):312-8.
Ricker, F.J. 11 Growth Rates and Models. In: W.S. Hoar DJR and JRB, editor. Fish Physiology [Internet]. Academic Press; 1979 [cited 2014 Jun 27]. p. 677-743. (Bioenergetics and Growth; vol. Volume 8). Available from: http://www.sciencedirect.com/science/article/pii/S1546509808600345
Zwietering MH, Jongenburger I, Rombouts FM, Van't Riet K. Modeling of the bacterial growth curve. Appl Environ Microbiol. 1990;56(6):1875-81.
Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans R Soc London. 1825;115:513-85.
Richards, F.J. A flexible growth function for empirical use. J Exp Bot. 1959;10:290-300.
Baranyi J. Mathematics of predictive food microbiology. Int J Food Microbiol. 1995;26(2):199-218.
Babák L, Šupinová P, Burdychová R. Growth models of Thermus aquaticus and Thermus scotoductus. Acta Univ Agric Silvic Mendel Brun. 2012;60(5):19-26.
López S, Prieto M, Dijkstra J, Dhanoa MS, France J. Statistical evaluation of mathematical models for microbial growth. Int J Food Microbiol. 2004;96(3):289-300.
Buchanan RL. Predictive food microbiology. Trends Food Sci Technol. 1993;4(1):6-11.
Huang L. Optimization of a new mathematical model for bacterial growth. Food Control. 2013;32(1):283-8.
Halmi MIE, Abdullah SRS, Johari WLW, Ali MSM, Shaharuddin NA, Khalid A, et al. Modelling the kinetics of hexavalent molybdenum (Mo6+) reduction by the Serratia sp. strain MIE2 in batch culture. Rendiconti Lincei. 2016 Dec 1;27(4):653-63.
Othman AR, Bakar NA, Halmi MIE, Johari WLW, Ahmad SA, Jirangon H, et al. Kinetics of molybdenum reduction to molybdenum blue by Bacillus sp. strain A.rzi. BioMed Res Int. 2013;2013:Article number 371058.
Yakasai HM, Babandi A, Ibrahim S. Modelling the Inhibition Kinetics of Molybdenum Reduction by the Molybdate-reducing Enterobacter cloacae. Bull Environ Sci Sustain Manag. 2020 Dec 31;4(2):11-7.
Yakasai HM, Babandi A, Manogaran M. Modelling the Kinetics Molybdenum Reduction Rate by Morganella sp. J Environ Microbiol Toxicol. 2020 Dec 31;8(2):18-23.
Dey S, Mukherjee S. Performance and kinetic evaluation of phenol biodegradation by mixed microbial culture in a batch reactor. Int J Water Resour Environ Eng. 2010;2(3):40-9.
Ibrahim S, Mansur A, Ahmad SA. Mathematical Modelling of the Growth of Caulobacter crescentus on Caffeine. J Environ Microbiol Toxicol. 2018 Dec 31;6(2):13-7.
Ingram HR, Martin RJ, Winterburn JB. Optimized cell growth and poly(3-hydroxybutyrate) synthesis from saponified spent coffee grounds oil. Appl Microbiol Biotechnol. 2022 Sep 1;106(18):6033-45.
Schröder M, Müller C, Posten C, Deckwer WD, Hecht V. Inhibition kinetics of phenol degradation from unstable steady-state data. Biotechnol Bioeng. 1997 Jun 20;54(6):567-76.
Szilveszter S, Fikó DR, Máthé I, Felföldi T, Ráduly B. Kinetic characterization of a new phenol degrading Acinetobacter towneri strain isolated from landfill leachate treating bioreactor. World J Microbiol Biotechnol. 2023 Jan 17;39(3):79.
Ezekiel M. The Sampling Variability of Linear and Curvilinear Regressions: A First Approximation to the Reliability of the Results Secured by the Graphic "Successive Approximation" Method. Ann Math Stat. 1930;1(4):275-333.
Akaike H. A New Look at the Statistical Model Identification. IEEE Trans Autom Control. 1974;19(6):716-23.
Burnham KP, Anderson DR. Multimodel inference: Understanding AIC and BIC in model selection. Sociol Methods Res. 2004;33(2):261-304.
Schwarz G. Estimating the Dimension of a Model. Ann Stat. 1978;6(2):461-4.
Hannan EJ, Quinn BG. The Determination of the Order of an Autoregression. J R Stat Soc Ser B Methodol. 1979;41(2):190-5.
Saaty TL. The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. New York: McGraw-Hill; 1980. 287 p.
Hwang CL, Yoon K. Multiple Attribute Decision Making: Methods and Applications A State-of-the-Art Survey. 1st edition. Berlin Heidelberg: Springer; 1981. 280 p.
Brans JP. L'ingénierie de la décision; elaboration d'instruments d'aide à la décision. La méthode PROMETHEE [Decision engineering; development of decision support tools. The PROMETHEE method]. In: Nadeau R, Landry M, editors. L'aide à la décision: nature, instruments et perspectives d'avenir. Québec, Canada: Presses de l'Université Laval; 1982. p. 183-213.
Fishburn PC. Additive Utilities with Incomplete Product Sets: Application to Priorities and Assignments. Oper Res. 1967 May 1;15:537.
Triantaphyllou E. Multi-criteria Decision Making Methods: A Comparative Study. 2000th edition. Dordrecht: Springer; 2000. 320 p.
Hamurcu M, Eren T. Applications of the MOORA and TOPSIS methods for decision of electric vehicles in public transportation technology. Transport. 2022 Nov 18;37:251-63.
Homayounfar M, Fadaei M, Gheibdoust H, Rezaee Kelidbari H. A Systematic Literature Review on MOORA Methodologies and Applications. Iran J Oper Res. 2022 Jan 1;13:164-83.
Halmi MIE, Gusmanizar N, Syed MA, Shamaan NA. Characterization of a Molybdenum-reducing Burkholderia sp. Dr.Y27 with Phenol and Acrylamide-degrading Capability. Bull Environ Sci Sustain Manag E-ISSN 2716-5353. 2023 Dec 31;7(2):58-67.
Shukor MS, Shukor MY. A microplate format for characterizing the growth of molybdenum-reducing bacteria. J Environ Microbiol Toxicol. 2015;2(2).
Shukor MY, Lee CH, Omar I, Karim MIA, Syed MA, Shamaan NA. Isolation and characterization of a molybdenum-reducing enzyme in Enterobacter cloacae strain 48. Pertanika J Sci Technol. 2003;11(2):261-72.
Ross T. Indices for performance evaluation of predictive models in food microbiology. J Appl Bacteriol. 1996;81(5):501-8.
Marquardt DW. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J Soc Ind Appl Math. 1963;11(2):431-41.
Seidel A, Gelbin D. On applying the ideal adsorbed solution theory to multicomponent adsorption equilibria of dissolved organic components on activated carbon. Chem Eng Sci. 1988 Jan 1;43(1):79-88.
Porter JF, McKay G, Choy KH. The prediction of sorption from a binary mixture of acidic dyes using single- and mixed-isotherm variants of the ideal adsorbed solute theory. Chem Eng Sci. 1999;54(24):5863-85.
Motulsky HJ, Ransnas LA. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J. 1987;1(5):365-74.
Karel W, Brauers W, Zavadskas E. The MOORA method and its application to privatization in a transition economy. Control Cybern. 2006 Jan 1;35.
Brauers W. Multi-objective seaport planning by MOORA decision making. Ann Oper Res. 2013 Jul 1;206.
Johnsen AR, Binning PJ, Aamand J, Badawi N, Rosenbom AE. The Gompertz function can coherently describe microbial mineralization of growth-sustaining pesticides. Environ Sci Technol. 2013;47(15):8508-14.
Agarry SE, Audu TOK, Solomon BO. Substrate inhibition kinetics of phenol degradation by Pseudomonas fluorescence from steady state and wash-out data. Int J Environ Sci Technol. 2009;6(3):443-50.
Brauers WK. Multiobjective optimization (moo) in privatization. J Bus Econ Manag. 2004 Jan 1;5(2):59-65.
Rahim R, Siahaan APU, Farta Wijaya R, Hantono H, Aswan N, Thamrin S, et al. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method for decision support system in top management. Int J Eng Technol. 2018 Jan 1;7:290-3.
Barik T, Parida S, Pal K. Optimizing Process Parameters in Drilling of CFRP Laminates: A Combined MOORA-TOPSIS-VIKOR Approach. Fibers Polym. 2024 May 1;25(5):1859-76.
Azari A, Nabizadeh R, Mahvi AH, Nasseri S. Integrated Fuzzy AHP-TOPSIS for selecting the best color removal process using carbon-based adsorbent materials: multi-criteria decision making vs. systematic review approaches and modeling of textile wastewater treatment in real conditions. Int J Environ Anal Chem. 2022 Dec 28;102(18):7329-44.
Gibson AM, Bratchell N, Roberts TA. The effect of sodium chloride and temperature on the rate and extent of growth of Clostridium botulinum type A in pasteurized pork slurry. J Appl Bacteriol. 1987;62(6):479-90.
Lu X, Withers MR, Seifkar N, Field RP, Barrett SRH, Herzog HJ. Biomass logistics analysis for large scale biofuel production: Case study of loblolly pine and switchgrass. Bioresour Technol. 2015;183:1-9.
Mondala A, Hernandez R, French T, Green M, McFarland L, Ingram L. Enhanced microbial oil production by activated sludge microorganisms from sugarcane bagasse hydrolyzate. Renew Energy. 2015;78:114-8.
Muralidharan R, Radha KV. A kinetic study of polyhydroxybutyrate production on nitrogen limited medium using Bacillus subtilis MTCC 9763 through a two stage cultivation strategy. J Environ Biol. 2015;36(3):537-42.
Musavi SF, Dhavale A, Balakrishnan RM. Optimization and kinetic modeling of cell-associated camptothecin production from an endophytic fusarium oxysporum NFX06. Prep Biochem Biotechnol. 2015;45(2):158-72.
Zerbini PE, Vanoli M, Rizzolo A, Grassi M, Pimentel RMDA, Spinelli L, et al. Optical properties, ethylene production and softening in mango fruit. Postharvest Biol Technol. 2015;101:58-65.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
