Article of scientific and technological research
Facing bioprocess modeling: a review of the methodologies of modeling
Published 2017-06-30
Keywords
- bioprocess,
- phenomenology,
- empirical,
- explicative,
- descriptive
- modeling ...More
How to Cite
Ortega Quintana, F. A., Álvarez, H., & Botero castro, H. A. (2017). Facing bioprocess modeling: a review of the methodologies of modeling. Revista ION, 30(1). https://doi.org/10.18273/revion.v30n1-2017006
Abstract
This article presents a detailed review of different approaches for process modeling, indicating their deficiencies and limitations when applied to bioprocesses modeling. As a result of the analysis it is concluded that these methodologies fail in bioprocesses modeling because they do not explicitly take into account the interaction between environment and cellular material, at least descriptively. It is noted that so far the way to bring these two worlds has been through purely predictive functions. Finally, the trends in bioprocess model are described; concluding that the approach is oriented to phenomenological based mathematical models with descriptive or explanatory features, to represent the relationship between the cell and its environment.Downloads
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References
[1] Zaid A, Hughes H, Porceddu E, Nicholas F. Glossary of Biotechnology and Genetic Engineering. Italia: Editorial Food and Agriculture’s Organization of the United Nations (FAO); 2001.
[2] Doran P. Bioprocess Engineering Principles.2 ed. Reino Unido: Editorial Academic Press; 2012.
[3] Dutta R. Fundamentals of Biochemical Engineering. India: Editorial Springer-Ane Books; 2008.
[4] Almquist J, Cvijovic M, Hatzimanikatis V, Nielsen J, Jirstrand M. Minireview: Kinetic models in industrial biotechnology-Improving cell factory performance. Metab. Eng. 2014;24:38-60.
[5] Gao J, Wang L, Feng E, Xiu Z. Modeling and identification of microbial batch fermentation using fuzzy expert system. Appl. Math. Model. 2013;37(16-17):8079-90.
[6] López-Rosales L, Gallardo-Rodríguez J, Sánchez-Mirón A, Contreras-Gómez A, García-Camacho F, Molina-Grima E. Modelling of multi-nutrient interactions in growth of the dinoflagellate microalga Protoceratium reticulatum using artificial neural networks. Bioresource Technol. 2013;146:682-8.
[7] Díaz JM. Ingeniería de bioprocesos. España: Editorial Paraninfo S.A.; 2012.
[8] Dodic’ J, Vucurovic D, Dodic’ S, Grahovac J, Popov S, Nedeljkovic N. Kinetic modelling of batch ethanol production from sugar beet raw juice. Appl. Energ. 2012;99:192-7.
[9] Setoodeh P, Jahanmiri A, Eslamloueyan R. Hybrid neural modeling framework for simulation and optimization of diauxie-involved fed-batch fermentative succinate production. Chem. Eng. Sci. 2012;81:57-76.
[10] Gueguim E, Oloke J, Lateef A, Adesiyan M. Modeling and optimization of biogas production on saw dust and other co-substrates using Artificial Neural network and Genetic Algorithm. Renew. Energ. 2012;46:276-81.
[11] Peres J, Oliveira R, Feyo de Azevedo S. Bioprocess hybrid parametric/nonparametric modeling based on the concept of mixture of experts. Biochem. Eng. J. 2008;39(1):190-206.
[12] Ccopa E, Mantovaneli I, Da Costa A, Filho R. Hybrid modeling for continuous production of bioethanol. Comput. Aided Chem. Eng. 2006;21:613-8.
[13] Chang J, Lee J, Chang A. Neural-network rate-function modeling of submerged cultivation of Monascus anka. Biochem. Eng. J. 2006;32(2):119-26.
[14] Dutta J, Dutta P, Banerjee R. Modeling and optimization of protease production by a newly isolated Pseudomonas sp. using a genetic algorithm. Process Biochem. 2005;40(2):879-84.
[15] Chen B, Woodley J. Wavelet shrinkage data processing for neural networks in bioprocess modeling. Comput. Chem. Eng. 2002;26(11):1611-20.
[16] Horiuchi J. Fuzzy modeling and control of biological processes. J. Biosci. Bioeng. 2002;94(6):574-8.
[17] Schügerl H, Bellgardt K. Bioreaction Engineering. Modeling and control. Alemania: Editorial Springer; 2000.
[18] Varner J, Ramkrishna D. The non-linear analysis of cybernetic models. Guidelines for model formulation. J. Biotechnol. 1999;71(1-3):67-104.
[19] Peskov K, Mogilevskaya E, Demin O. Kinetic modeling of central carbon metabolism in Escherichia coli. FEBS J. 2012;279:3374-85.
[20] Luo Y, Zhang T, Wu H. The transport and mediation mechanism of the common sugars in Escherichia coli. Biotechnol. Adv. 2014;32(5):905-19.
[21] Smolke C. The metabolic pathway engineering handbook. USA: Editorial CRC Press Taylor and Francis group LLC; 2009.
[22] Bequette BW. Process Control. Modeling, design and simulation. USA: Editorial Prentice Hall; 2003.
[23] Williams D, Yousefpour P, Swanick B. On-line adaptative control of a fermentation process. Contr. Theor. Appl. (IEEE Proceedings D). 1984;131(4):117-24.
[24] Takamatsu T, Shioya S, Kurome H. Dynamics and control of a mixed culture in activated sludge process. En: Modelling and Control of Biotechnical Processes. Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983.p. 103-10.
[25] Rodrigues A, Minceva M. Modelling and simulation in chemical engineering: Tools for process innovation. Comput. Chem. Eng.. 2005;29(6):1167-83.
[26] Ljung L. System identification: Theory for the user. USA: Editorial Prentice-Hall; 1987.
[27] Alvarez H. Introducción al diseño simultáneo de proceso y control. La controlabilidad de estado como restricción. España: Editorial académica española; 2012.
[28] Ribas M, Hurtado R, Garrido N, Domenech F, Sabadi R. Metodología para la modelación matemática de procesos. Caso de estudio, la fermentación alcohólica. ICIDCA. 2011;45(1):37-47.
[29] Alvarez H, Lamanna R, Vega P, Revollar S. Metodología para la obtención de modelos semifísicos de base fenomenológica aplicada a una sulfitadora de jugo de caña de azúcar. Rev. Iberoam. Automática e Informática Ind. 2009;6(3):10-20.
[30] Gómez L, Amicarelli A, Alvarez H, di Sciascio F. El rol de los modelos en el diseño de equipos de procesos y sistemas de control. En: Universidad del Tolima, editor. VI Congreso Nacional de la Asociación Colombiana de Automática, ACA’2004; 2004 nov 1-3; Ibagué, Colombia. Ibagué: Universidad del Tolima; 2004. p. 1-6.
[31] Concari S. Las teorías y modelos en la explicación científica: Implicadas para la enseñanza de las ciencias. Cienc. Educ. 2001;7:85-94.
[32] Murthy DN, Rodin EY. A comparative evaluation of books on mathematical modeling. Math. Model. 1987;9(1):17-28.
[33] Bastin G, Dochain D. On-line estimation and adaptative control of bioreactors. Holanda: Editorial Elsevier; 1990.
[34] Marlin T. Process control: designing process and control systems for dynamic performance. USA: Editorial McGraw-Hill; 1995.
[35] Haefner J. Modeling biological system. USA: Editorial Springer; 1996.
[36] Woods R, Lawrence K. Modeling and simulation of dynamic systems. USA: Editorial Prentice Hall, Inc.; 1997.
[37] Luyben W. Process modeling, simulation, and control for chemical engineering. USA: Editorial McGraw-Hill; 1999.
[38] Basmadjian D. The art of modeling in science and engineering. USA: Editorial Chapman & Hall/CRC; 1999.
[39] Hangos K, Cameron I. Process modeling and model analysis.Reino Unido: Editorial Academic Press; 2001.
[40] Tijskens L, Hertog L, Nicolaï B. Food Process Modeling. Inglaterra: Editorial CRC Press LLC; 2001.
[41] McKellar R, Lu X. Modeling Microbial Responses in Food. USA: CRC Press LLC; 2004.
[42] Heinzle E, Biwer A, Cooney C. Development of Sustainable Bioprocess modeling and Assessment. Inglaterra: Editorial Wiley; 2006.
[43] Sablani S, Datta A, Shafiur M, Mujumdar A. Handbook of food and bioprocess modeling techniques. USA: Editorial CRC Press; 2006.
[44] Ҫengel Y. Transferencia de Calor y Masa. México: Editorial McGraw-Hill; 2007.
[45] Ingham J, Dunn E, Heinzle J, Prenosil J, Snape B. Chemical Engineering Dynamics. Alemania: Editorial WILEY-VCH; 2007.
[46] Dobre T, Sánchez J. Chemical Engineering. Modelling, simulation and similitude. Alemania: Editorial Wiley-VCH; 2007.
[47] Gómez C, Calderón Y, Alvarez H. Construcción de modelos semifísicos de base fenomenológica. Caso proceso de fermentación. Rev. Bio. Agro. 2008;6(2):28-39.
[48] Alvarez H, Gómez L, Botero H. Abstracciones Macroscópicas de la Fenomenología para el Modelado de Procesos. En: Martínez C, Bello L, Martínez R, Rosero D, editores. XXVII Congreso Interamericano y colombiano de Ingeniería Química; 2014 oct 6-8; Cartagena, Colombia. Cartagena: CIIQ editor; 2014. p. 23.
[49] Epstein JM. Why model? (sitio en Internet). Department of Sociology, University of Surrey. Disponible en: http://jasss.soc.surrey ac.uk/11/4/12.html. Acceso el 19 de junio 2015.
[50] Atkinson B. Reactores bioquímicos. España: Editorial Reverté S.A.; 2002.
[51] Trujillo M, Valdez N. El estrés hidrodinámico: Muerte y daño celular en cultivos agitados. Rev. Latinoam. Microbiol. 2006;48(3-4):269-80.
[52] Sundar R, Liji T, Rajila C, Suganyadevi P. Amylase production by Aspergillus nigerunder submerged fermentation using Ipomoea batatas. Int. J. Appl. Biol. Pharmaceut. Technol. 2012;3(2):175-82.
[53] Lok M, Krycer J, Burchfield J, James D, Kuncic Z. A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems. FEBS Open Bio.. 2015;5:226-39.
[54] Hoppe G, Hansford G. Ethanol inhibition of continuous anaerobic yeast growth. Biotechnol. Lett. 1982;4(1):39-44.
[55] Arroyo-López F, Orlić S, Querol A, Barrio E. Effects of temperature, pH and sugar concentration on the growth parameters of Saccharomyces cerevisiae, S. kudriavzeviiand their interspecific hybrid. Int. J. Food Microbiol. 2009;131(2-3):120-27.
[56] Bajpai R, Reuẞ M. A mechanistic model for penicillin production. J. Chem. Technol. Biotechnol. 1980;30(1):332-44.
[57] Jørgensen H, Nielsen J, Villadsen J, Møllgardt H. Analysis of the penicillin V biosynthesis during fed-batch cultivations with a high yielding strain of Penicillium chrysogenum. Appl. Microbiol. Biotechnol. 1995;43(1):123-30.
[58] Kosaric N, Vardar-Sukan F. Microbiology and Biochemistry of Ethanol Formation. En:The Biotechnology of ethanol: Classical and future applications.Roehr M, Editor. Alemania: Editorial WILEY-VCH; 2001. p. 89-106.
[59] Teusink B, Passarge J, Reijenga C, Esgalhado E, Van der Weijden C, Schepper M, et al. Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. Eur. J. Biochem. 2000;267(17):5313-29.
[60] Blackman F. Optima and limiting factors. Ann. Bot. 1905;19(2):281-95.
[61] Michaelis L, Menten M. Die kinetic invertinwirkung. Biochem. Zeitsch. 1913;49:333-69.
[62] Monod J. Recherches sur la croissance des Cultures Bactériennes. Francia: Editorial Hermann & Cie.; 1942.
[63] Teissier G. Croissance des populations bacteriennes et quantite d’aliment disponible. Rev. Sci. Extrait. 1942;320(8):209-31.
[64] Bailey J, Ollis D. Biochemical Engineering Fundamentals. USA: Editorial McGraw-Hill; 1986.
[65] Tiana Y, Kasperski A, Sund K, Chen L. Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect. Biosystems. 2011;104:77-86.
[66] Sun K, Tian Y, Chen L, Kasperski A. Universal modelling and qualitative analysis of an impulsive bioprocess. Comput. Chem. Eng. 2011;35(3):492-501.
[67] Sun K, Kasperski A, Tian Y, Chen L. Modelling of the Corynebacterium glutamicum biosynthesis under aerobic fermentation conditions. Chem. Eng. Sci. 2011;66(18):4101-10.
[68] Roman M, Selistenau D, Bobasu E, Sedrescu D. Bond Graph modeling of a Baker’s yeast bioprocess. En: Zhou M, editor. The 2010 International Conference on Modelling, Identification and Control (ICMIC); 2010 jul 17-19; Okayama, Japón. Okayama: IEEE Digital Lybrary; 2010. p. 82-7.
[69] Roman M, Selisteanu D, Bobasu E, Petre E. Application of Bond Graph modeling on a fed-batch alcoholic fermentation bioprocess. En: Miclea L, Stoian I, editors. IEEE International Conference on Automation Quality and Testing Robotics (AQTR); 2010 may 28-30; Cluj-Napoca, Rumania. Cluj-Napoca: IEEE Digital Lybrary; 2010. p. 1-6.
[70] Roman M, Selisteanu D, Petre E, Ionete C, Popescu D. Modeling and estimation strategies for a Fed-batch prototype Bioprocess. En: Meng M, editor. IEEE International Conference on Automation and Logistics (ICAL); 2010 ago 16-20; Hong Kong y Macau, China. Hong Kong y Macau: IEEE Digital Lybrary; 2010. p. 103-8.
[71] Dochain D. Automatic control of bioprocesses. USA: Editorial John Wiley & Sons, Inc.; 2008.
[72] Moser H. The dynamics of bacterial populations in the chemostat. USA: Editorial Carnegie Institution Publication; 1958.
[73] Powell EO. (1967). The growth rate of microorganisms as a function of substrate concentration. En: Microbial Physiology and Continuous Culture Proceedings of the Third International Symposium. Powell O, Evans C, Strange R, Tempest D, Editores. Inglaterra: Her Majesty’s Stationary Office; 1967. p. 34-55.
[74] Shehata T, Marr A. Effect of nutrient concentration on the growth of Escherichia coli. J. Bacteriol. 1971;107(1):210-6.
[75] Jost J, Drake J, Frederickson A, Tsuchiya H. Interactions of Tetrahymena pyroformis, Escherichia coli, Azobacter vinelandii and glucose in a minimal medium. J. Bacteriol. 1973;113(2):834-40.
[76] Konak A. Derivation of a Generalized Monod equation and its application. J. Appl. Chem. Biotechnol. 1974;24(8):453-5.
[77] Wayman M, Tseng M. Inhibition-threshold substrate concentrations. Biotechnol. Bioeng. 1976;18(3):383-7.
[78] Aborhey S, Williamson D. Modelling of lactic acid production by Streptococcus cremoris HP. J. Gen. Appl. Microbiol. 1977;23(1):7-21.
[79] Chen YR, Hashimoto AG. Kinetics of methane fermentation. En: USDOE, editor. Symposium on biotechnology in energy production and Conservation; 1978 may 10-12; Gatlinburg, USA. Gatlinburg: Science and Education Administration, Clay Center editor; 1978. p. 1-27.
[80] Kargi F, Schuler M. Generalized differential specific rate equation for microbial growth. Biotechnol. Bioeng. 1979;21(10):1871-5.
[81] Sokol W, Howell J. Kinetics of phenol oxidation by washed cells. Biotechnol. Bioeng. 1981;23(9), 2039-49.
[82] Mattiason B, Mandenius CF, Axelsson J, Hagander P. Control of baker’s yeast production based on ethanol measurements. En: N.N editor. Proc. 3rd European Congress on Biotechnology. 1984 ene 15; Munich, Alemania. Munich: Verlag Chemie editor; 1984. p. 629-36.
[83] Ming F, Howell J, Canovas-Diaz M. Mathematical simulation of anaerobic stratified biofilm processes. En: Computer Applications in Fermentation Technology: Modelling and Control of Biotechnological Processes. Fish NM, Fox R, Thornhill N, Editores. Holanda: Editorial Springer; 1988. p. 69-77.
[84] Andrews JF. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substance. Biotechnol. Bioeng. 1968;10(6):707-23.
[85] Hinshelwood C. Chemical Kinetics of the Bacterial cell. Inglaterra: Oxford, Univ. Press.; 1946.
[86] Kono T, Asai T. Kinetics of fermentation processes. Biotechnol. Bioeng. 1969;11(3):293-321.
[87] Contois D. Kinetics of bacterial growth relationship between population density and specific growth rate of continuos cultures. J. Gen. Microbiol. 1959;21:40-50.
[88] Nihtilä M, Virkkunnen J. Practical identifiability of growth and substrate consumption models. Biotechnol. Bioeng. 1977;19(12):1831-50.
[89] Kishimoto M, Sawano T, Yoshida T, Taguchi T. (1983). Optimization of a fed-batch culture by statistical data analysis. En: Modelling and Control of Biotechnical Processes.Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983. p. 161-8.
[90] Staniskis J, Levisaukas D. An adaptative control algorithm for fed-batch culture. Biotechnol. Bioeng. 1984;26(5):419-25.
[91] Holzberg I, Finn R, Steinkraus K. A kinetic study of the alcoholic fermentation of grape juice. Biotechnol. Bioeng. 1967;9(3):413-27.
[92] Aiba S, Shoda M, Nagatani M. Kinetics of product inhibition in alcohol fermentation. Biotechnol. Bioeng. 1968;10(6):845-64.
[93] Jerusalimski N, Engambervediev N. Continuous cultivation of Microorganisms. USA: Editorial Academic Press; 1969.
[94] La Motta E. Kinetics of continuous growth cultures using the logistic growth curve.Biotechnol. Bioeng. 1976;18(7):1029-32.
[95] Ghose T, Tyagi R. Rapid ethanol fermentation of cellulose hydrolysate: II. Product and substrate inhibition and optimization of fermentor design. Biotechnol. Bioeng. 1979;21(8):1387-1400.
[96] Levenspiel O. The Monod equation: a revisit and a generalization to product inhibition situations. Biotechnol. Bioeng. 1980;22(8):1671-87.
[97] Hägglund T. Incubation time prediction in yoghurt manufacturing. En: Modelling and Control of Biotechnical Processes. Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983. p. 307-11.
[98] Bazua C, Wilke C. Ethanol effects on the kinetics of a continuous fermentation with Saccharomyces cerevisiae. Biotechnol. Bioeng. 1977;7:105-18.
[99] Moulin G, Boze H, Galzy P. Inhibition of alcoholic fermentation by substrate and ethanol. Biotechnol. Bioeng. 1980;22(11):2375-81.
[100] Jin C, Chiang H, Wang S. Steady-state analysis of the enhancement in ethanol productivity of a continuous fermentation process employing a protein-phospholipid complex as a protecting agent. Enzyme Microb. Tech. 1981;3(3):249-57.
[101] Sevely Y, Pourciel J, Rauzy G, Bovée J. Modelling, identification and control of the alcohol fermentation in a cascade reactor. En: Akashi H, Editor. Proc. 8th IFAC World Congress; 1981; Kyoto, Japón. Reino Unido: Pergamon Press editor; 1982. p 177-84.
[102] Dourado A, Calvet J. Static optimization of the ethanol production in a cascade reactor. En: Modelling and Control of Biotechnical Processes. Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983. p. 177-85.
[103] Peringer P, Blachere H, Corrieu G, Lane A. A generalized mathematical model for the growth kinetics of Saccharomyces cerevisiae. Biotechnol. Bioeng. 1974;16(4):431-54.
[104] Olsson G. State of the art in sewage treatment plant control. AIChe Symp. 1976;72:52-76.
[105] Andreyeva L, Biryukov V. Analysis of mathematical models of the effect of pH on fermentation processes and their use for calculating optimal fermentation conditions. Biotechnol. Bioeng. Symp. 1973;0(4-1):61-76.
[106] Cheruy A, Durand A. Optimization of erythromycin biosynthesis by controlling pH and temperature: theoretical aspects and practical applications. Biotechnol. Bioeng. Symp. 1979;9:303-20.
[107] Jackson J, Edwards V. Kinetics of substrate inhibition of exponential yeast growth. Biotechnol. Bioeng.. 1975;17(7):943-64.
[108] Topiwala H, Sinclair C. Temperature relationship in continuous culture. Biotechnol. Bioeng. 1971;13(6):795-813.
[109] Hashimoto A. Methane from cattle waste: effects of temperature, hydraulic retention time and influent substrate concentration on kinetic parameter (K). Biotechnol. Bioeng. 1982;24(9):2039-52.
[110] Constantinides A, Spencer J, Gaden E. Optimization of batch fermentation processes. I. Development of mathematical models for batch penicillin fermentations. Biotechnol. Bioeng. 1970;12(5):803-30.
[111] Tamiya H, Hase E, Shibata K, Mituya A, Sasa T. Kinetics of growth of Chorella, with special reference to its dependence on quantity of available light and on temperature. En: Algae Culture: From Laboratory to Pilot Plant, Growth of algae in mass culture. Burlew JS, Editor. USA: Carnegie Inst. Washington DC; 1953. p. 205-32.
[112] Luedeking R, Piret E. A kinetic study of the lactic acid fermentation. Batch process at controlled pH. J. Biochem. Microbiol. Tech. Eng. 1959;1(4):393-412.
[113] Moser A. Bioprocess Technology, Kinetics and Reactors. USA: Editorial Springer Verlag; 1988.
[114] Grady C, Daigger G, Lim H. Biological Wastewater Treatment. USA: Editorial Marcel Dekker; 1999.
[115] Button D. Nutrient uptake by microorganism according to kinetic parameters from theory as related to cytoarchitecture. Microbiol. Mol. Biol. Rev. 1998;62(3):636-45.
[116] Merchuk J, Asenjo J. The Monod equation and mass transfer. Biotechnol. Bioeng. 1994;45(1):91-4.
[117] Schwartzemberg H, Chao R. Solute diffusivities in leaching processes. Food Technol. 1982;36(2):73-86.
[118] Liu Y. A simple thermodynamic approach for derivation of a general Monod equation for microbial growth. Biochem. Eng. J. 2006;31(1):102-5.
[119] Gofferjé G, Stäbler A, Herfellner T, Schweiggert-Weisz U, Flöter E. Kinetics of enzymatic esterification of glycerol and free fatty acids incrude Jatropha oil by immobilized lipase from Rhizomu cormiehei. J. Mol. Catal. B Enzym. 2014;107:1-7.
[120] Vega R, Zuniga M. A new mechanism and kinetic model for the enzymatic synthesis of short-chain fructo oligosaccharides from sucrose. Biochem. Eng. J. 2014;82:158-65.
[121] Mulholland A. Modelling enzyme reaction mechanism, specificity and catalysis. Drug Discov. Today. 2005;10(20):1393-1402.
[122] Ortega F, Pérez O, López E. Modelo Semifísico de Base Fenomenológica del Proceso de Fermentación Alcohólica. Inf. Tecnol. 2016:27(1):21-32.
[123] Melgarejo R, Castillo C, Dutta A, Bény G, Torres D, Gutiérrez M, et al. Mathematical model of a three phase partitioning bioreactor for conversion of ketones using whole cells. Chem. Eng. J. 2015;260:765-75.
[124] Geng X, Boufadel M, Personna Y, Lee K, Tsao D, Demicco E. BIOB: A mathematical model for the biodegradation of low solubility hydrocarbons. Mar. Pollut. Bull. 2014;83(1):138-47.
[125] Kythreotou N, Florides G, Tassou S. A review of simple to scientific models for anaerobic digestion. Renew. Energ. 2014;71:701-14.
[126] Akpa J. Modeling of a bioreactor for the fermentation of palmwine by Saccaharomyces cerevisiae (yeast) and lactobacillus (bacteria). Am. J. Sci. Ind. Res. 2012;3(4):231-40.
[127] Roeva O, Pencheva T, Tzonkoc S, Arndt M, Hitzmann B, Kleist S, et al. Multiple model approach to modelling of Escherichia colifed-bacth cultivation extracelular production of bacterial phytase. Electr. J. Biotechnol. 2007;10(4):592-603.
[128] Atehortúa P, Alvarez H, Orduz S. Modeling of growth and sporulation of Bacillus thuringiensis in an intermittent fed batch culture with total cell retention. Bioprocess Biosyst. Eng. 2007;30(6):447-56.
[129] Lokshina L, Vavilin V, Kettunen R, Rintala J, Holliger C, Nozhevnikova A. Evaluation of kinetic coefficients using integrated Monod and Haldane models for low-temperature acetoclastic methanogenesis. Water Res. 2001;35(12):2913-22.
[130] Lagowski J. Viewpoints: Chemist on Chemistry. Chemical Education: Past, Present, and Future. J. Chem. Edu. 1998;75:425-36.
[131] Machado D, Rodrigues L, Rocha I. A kinetic model for curcumin production in Escherichia coli. Biosystems. 2014;125:16-21.
[132] Chassagnole C, Noisommit N, Schmid J, Mauch K, Reuss M. Dynamic modeling of the central carbon metabolism of Escherichia coli. Biotechnol. Bioeng. 2002;79(1):53-73.
[133] Usuda Y, Nishio Y, Iwatani S, Van Dien S, Imaizumi A, Shimbo K, et al. Dynamic modeling of Escherichia coli metabolic and regulatory systems for amino-acid production. J. Biotechnol. 2010;147(1):17-30.
[134] Roche R, Lamanna R, Delgado M, Rocaries F, Hamam Y, Pecker F. Simulation of a cardiac cell. Part I: An electro-chemical model. Rev. Fac. Ing. UCV. 2009;24(1):71-87.
[135] Umulis D, Gürmen N, Singh P, Fogler H. A physiologically based model for ethanol and acetaldehyde metabolism in human beings. Alcohol. 2005;35(1):3-12.
[136] Huang M, Fan S, Xing W, Liu C. Microfluidic cell culture system studies and computational fluid dynamics. Math. Comput. Model. 2010;52(11-12):2036-42.
[137] Shah P, Vedarethinam I, Kwasny S, Andresen L, Dimaki M, Skov S, et al. Microfluidic bioreactors for culture of non-adherent cells. Sensor. Actuat. B-Chem. 2011;156(2):1002-8.
[138] Leclerc K, Kirat E, Griscom L. In situ micropatterning technique by cell crushing for co-cultures inside microfluidic biochips. Biomed. Microdev. 2008;10(2):169-77.
[2] Doran P. Bioprocess Engineering Principles.2 ed. Reino Unido: Editorial Academic Press; 2012.
[3] Dutta R. Fundamentals of Biochemical Engineering. India: Editorial Springer-Ane Books; 2008.
[4] Almquist J, Cvijovic M, Hatzimanikatis V, Nielsen J, Jirstrand M. Minireview: Kinetic models in industrial biotechnology-Improving cell factory performance. Metab. Eng. 2014;24:38-60.
[5] Gao J, Wang L, Feng E, Xiu Z. Modeling and identification of microbial batch fermentation using fuzzy expert system. Appl. Math. Model. 2013;37(16-17):8079-90.
[6] López-Rosales L, Gallardo-Rodríguez J, Sánchez-Mirón A, Contreras-Gómez A, García-Camacho F, Molina-Grima E. Modelling of multi-nutrient interactions in growth of the dinoflagellate microalga Protoceratium reticulatum using artificial neural networks. Bioresource Technol. 2013;146:682-8.
[7] Díaz JM. Ingeniería de bioprocesos. España: Editorial Paraninfo S.A.; 2012.
[8] Dodic’ J, Vucurovic D, Dodic’ S, Grahovac J, Popov S, Nedeljkovic N. Kinetic modelling of batch ethanol production from sugar beet raw juice. Appl. Energ. 2012;99:192-7.
[9] Setoodeh P, Jahanmiri A, Eslamloueyan R. Hybrid neural modeling framework for simulation and optimization of diauxie-involved fed-batch fermentative succinate production. Chem. Eng. Sci. 2012;81:57-76.
[10] Gueguim E, Oloke J, Lateef A, Adesiyan M. Modeling and optimization of biogas production on saw dust and other co-substrates using Artificial Neural network and Genetic Algorithm. Renew. Energ. 2012;46:276-81.
[11] Peres J, Oliveira R, Feyo de Azevedo S. Bioprocess hybrid parametric/nonparametric modeling based on the concept of mixture of experts. Biochem. Eng. J. 2008;39(1):190-206.
[12] Ccopa E, Mantovaneli I, Da Costa A, Filho R. Hybrid modeling for continuous production of bioethanol. Comput. Aided Chem. Eng. 2006;21:613-8.
[13] Chang J, Lee J, Chang A. Neural-network rate-function modeling of submerged cultivation of Monascus anka. Biochem. Eng. J. 2006;32(2):119-26.
[14] Dutta J, Dutta P, Banerjee R. Modeling and optimization of protease production by a newly isolated Pseudomonas sp. using a genetic algorithm. Process Biochem. 2005;40(2):879-84.
[15] Chen B, Woodley J. Wavelet shrinkage data processing for neural networks in bioprocess modeling. Comput. Chem. Eng. 2002;26(11):1611-20.
[16] Horiuchi J. Fuzzy modeling and control of biological processes. J. Biosci. Bioeng. 2002;94(6):574-8.
[17] Schügerl H, Bellgardt K. Bioreaction Engineering. Modeling and control. Alemania: Editorial Springer; 2000.
[18] Varner J, Ramkrishna D. The non-linear analysis of cybernetic models. Guidelines for model formulation. J. Biotechnol. 1999;71(1-3):67-104.
[19] Peskov K, Mogilevskaya E, Demin O. Kinetic modeling of central carbon metabolism in Escherichia coli. FEBS J. 2012;279:3374-85.
[20] Luo Y, Zhang T, Wu H. The transport and mediation mechanism of the common sugars in Escherichia coli. Biotechnol. Adv. 2014;32(5):905-19.
[21] Smolke C. The metabolic pathway engineering handbook. USA: Editorial CRC Press Taylor and Francis group LLC; 2009.
[22] Bequette BW. Process Control. Modeling, design and simulation. USA: Editorial Prentice Hall; 2003.
[23] Williams D, Yousefpour P, Swanick B. On-line adaptative control of a fermentation process. Contr. Theor. Appl. (IEEE Proceedings D). 1984;131(4):117-24.
[24] Takamatsu T, Shioya S, Kurome H. Dynamics and control of a mixed culture in activated sludge process. En: Modelling and Control of Biotechnical Processes. Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983.p. 103-10.
[25] Rodrigues A, Minceva M. Modelling and simulation in chemical engineering: Tools for process innovation. Comput. Chem. Eng.. 2005;29(6):1167-83.
[26] Ljung L. System identification: Theory for the user. USA: Editorial Prentice-Hall; 1987.
[27] Alvarez H. Introducción al diseño simultáneo de proceso y control. La controlabilidad de estado como restricción. España: Editorial académica española; 2012.
[28] Ribas M, Hurtado R, Garrido N, Domenech F, Sabadi R. Metodología para la modelación matemática de procesos. Caso de estudio, la fermentación alcohólica. ICIDCA. 2011;45(1):37-47.
[29] Alvarez H, Lamanna R, Vega P, Revollar S. Metodología para la obtención de modelos semifísicos de base fenomenológica aplicada a una sulfitadora de jugo de caña de azúcar. Rev. Iberoam. Automática e Informática Ind. 2009;6(3):10-20.
[30] Gómez L, Amicarelli A, Alvarez H, di Sciascio F. El rol de los modelos en el diseño de equipos de procesos y sistemas de control. En: Universidad del Tolima, editor. VI Congreso Nacional de la Asociación Colombiana de Automática, ACA’2004; 2004 nov 1-3; Ibagué, Colombia. Ibagué: Universidad del Tolima; 2004. p. 1-6.
[31] Concari S. Las teorías y modelos en la explicación científica: Implicadas para la enseñanza de las ciencias. Cienc. Educ. 2001;7:85-94.
[32] Murthy DN, Rodin EY. A comparative evaluation of books on mathematical modeling. Math. Model. 1987;9(1):17-28.
[33] Bastin G, Dochain D. On-line estimation and adaptative control of bioreactors. Holanda: Editorial Elsevier; 1990.
[34] Marlin T. Process control: designing process and control systems for dynamic performance. USA: Editorial McGraw-Hill; 1995.
[35] Haefner J. Modeling biological system. USA: Editorial Springer; 1996.
[36] Woods R, Lawrence K. Modeling and simulation of dynamic systems. USA: Editorial Prentice Hall, Inc.; 1997.
[37] Luyben W. Process modeling, simulation, and control for chemical engineering. USA: Editorial McGraw-Hill; 1999.
[38] Basmadjian D. The art of modeling in science and engineering. USA: Editorial Chapman & Hall/CRC; 1999.
[39] Hangos K, Cameron I. Process modeling and model analysis.Reino Unido: Editorial Academic Press; 2001.
[40] Tijskens L, Hertog L, Nicolaï B. Food Process Modeling. Inglaterra: Editorial CRC Press LLC; 2001.
[41] McKellar R, Lu X. Modeling Microbial Responses in Food. USA: CRC Press LLC; 2004.
[42] Heinzle E, Biwer A, Cooney C. Development of Sustainable Bioprocess modeling and Assessment. Inglaterra: Editorial Wiley; 2006.
[43] Sablani S, Datta A, Shafiur M, Mujumdar A. Handbook of food and bioprocess modeling techniques. USA: Editorial CRC Press; 2006.
[44] Ҫengel Y. Transferencia de Calor y Masa. México: Editorial McGraw-Hill; 2007.
[45] Ingham J, Dunn E, Heinzle J, Prenosil J, Snape B. Chemical Engineering Dynamics. Alemania: Editorial WILEY-VCH; 2007.
[46] Dobre T, Sánchez J. Chemical Engineering. Modelling, simulation and similitude. Alemania: Editorial Wiley-VCH; 2007.
[47] Gómez C, Calderón Y, Alvarez H. Construcción de modelos semifísicos de base fenomenológica. Caso proceso de fermentación. Rev. Bio. Agro. 2008;6(2):28-39.
[48] Alvarez H, Gómez L, Botero H. Abstracciones Macroscópicas de la Fenomenología para el Modelado de Procesos. En: Martínez C, Bello L, Martínez R, Rosero D, editores. XXVII Congreso Interamericano y colombiano de Ingeniería Química; 2014 oct 6-8; Cartagena, Colombia. Cartagena: CIIQ editor; 2014. p. 23.
[49] Epstein JM. Why model? (sitio en Internet). Department of Sociology, University of Surrey. Disponible en: http://jasss.soc.surrey ac.uk/11/4/12.html. Acceso el 19 de junio 2015.
[50] Atkinson B. Reactores bioquímicos. España: Editorial Reverté S.A.; 2002.
[51] Trujillo M, Valdez N. El estrés hidrodinámico: Muerte y daño celular en cultivos agitados. Rev. Latinoam. Microbiol. 2006;48(3-4):269-80.
[52] Sundar R, Liji T, Rajila C, Suganyadevi P. Amylase production by Aspergillus nigerunder submerged fermentation using Ipomoea batatas. Int. J. Appl. Biol. Pharmaceut. Technol. 2012;3(2):175-82.
[53] Lok M, Krycer J, Burchfield J, James D, Kuncic Z. A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems. FEBS Open Bio.. 2015;5:226-39.
[54] Hoppe G, Hansford G. Ethanol inhibition of continuous anaerobic yeast growth. Biotechnol. Lett. 1982;4(1):39-44.
[55] Arroyo-López F, Orlić S, Querol A, Barrio E. Effects of temperature, pH and sugar concentration on the growth parameters of Saccharomyces cerevisiae, S. kudriavzeviiand their interspecific hybrid. Int. J. Food Microbiol. 2009;131(2-3):120-27.
[56] Bajpai R, Reuẞ M. A mechanistic model for penicillin production. J. Chem. Technol. Biotechnol. 1980;30(1):332-44.
[57] Jørgensen H, Nielsen J, Villadsen J, Møllgardt H. Analysis of the penicillin V biosynthesis during fed-batch cultivations with a high yielding strain of Penicillium chrysogenum. Appl. Microbiol. Biotechnol. 1995;43(1):123-30.
[58] Kosaric N, Vardar-Sukan F. Microbiology and Biochemistry of Ethanol Formation. En:The Biotechnology of ethanol: Classical and future applications.Roehr M, Editor. Alemania: Editorial WILEY-VCH; 2001. p. 89-106.
[59] Teusink B, Passarge J, Reijenga C, Esgalhado E, Van der Weijden C, Schepper M, et al. Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. Eur. J. Biochem. 2000;267(17):5313-29.
[60] Blackman F. Optima and limiting factors. Ann. Bot. 1905;19(2):281-95.
[61] Michaelis L, Menten M. Die kinetic invertinwirkung. Biochem. Zeitsch. 1913;49:333-69.
[62] Monod J. Recherches sur la croissance des Cultures Bactériennes. Francia: Editorial Hermann & Cie.; 1942.
[63] Teissier G. Croissance des populations bacteriennes et quantite d’aliment disponible. Rev. Sci. Extrait. 1942;320(8):209-31.
[64] Bailey J, Ollis D. Biochemical Engineering Fundamentals. USA: Editorial McGraw-Hill; 1986.
[65] Tiana Y, Kasperski A, Sund K, Chen L. Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect. Biosystems. 2011;104:77-86.
[66] Sun K, Tian Y, Chen L, Kasperski A. Universal modelling and qualitative analysis of an impulsive bioprocess. Comput. Chem. Eng. 2011;35(3):492-501.
[67] Sun K, Kasperski A, Tian Y, Chen L. Modelling of the Corynebacterium glutamicum biosynthesis under aerobic fermentation conditions. Chem. Eng. Sci. 2011;66(18):4101-10.
[68] Roman M, Selistenau D, Bobasu E, Sedrescu D. Bond Graph modeling of a Baker’s yeast bioprocess. En: Zhou M, editor. The 2010 International Conference on Modelling, Identification and Control (ICMIC); 2010 jul 17-19; Okayama, Japón. Okayama: IEEE Digital Lybrary; 2010. p. 82-7.
[69] Roman M, Selisteanu D, Bobasu E, Petre E. Application of Bond Graph modeling on a fed-batch alcoholic fermentation bioprocess. En: Miclea L, Stoian I, editors. IEEE International Conference on Automation Quality and Testing Robotics (AQTR); 2010 may 28-30; Cluj-Napoca, Rumania. Cluj-Napoca: IEEE Digital Lybrary; 2010. p. 1-6.
[70] Roman M, Selisteanu D, Petre E, Ionete C, Popescu D. Modeling and estimation strategies for a Fed-batch prototype Bioprocess. En: Meng M, editor. IEEE International Conference on Automation and Logistics (ICAL); 2010 ago 16-20; Hong Kong y Macau, China. Hong Kong y Macau: IEEE Digital Lybrary; 2010. p. 103-8.
[71] Dochain D. Automatic control of bioprocesses. USA: Editorial John Wiley & Sons, Inc.; 2008.
[72] Moser H. The dynamics of bacterial populations in the chemostat. USA: Editorial Carnegie Institution Publication; 1958.
[73] Powell EO. (1967). The growth rate of microorganisms as a function of substrate concentration. En: Microbial Physiology and Continuous Culture Proceedings of the Third International Symposium. Powell O, Evans C, Strange R, Tempest D, Editores. Inglaterra: Her Majesty’s Stationary Office; 1967. p. 34-55.
[74] Shehata T, Marr A. Effect of nutrient concentration on the growth of Escherichia coli. J. Bacteriol. 1971;107(1):210-6.
[75] Jost J, Drake J, Frederickson A, Tsuchiya H. Interactions of Tetrahymena pyroformis, Escherichia coli, Azobacter vinelandii and glucose in a minimal medium. J. Bacteriol. 1973;113(2):834-40.
[76] Konak A. Derivation of a Generalized Monod equation and its application. J. Appl. Chem. Biotechnol. 1974;24(8):453-5.
[77] Wayman M, Tseng M. Inhibition-threshold substrate concentrations. Biotechnol. Bioeng. 1976;18(3):383-7.
[78] Aborhey S, Williamson D. Modelling of lactic acid production by Streptococcus cremoris HP. J. Gen. Appl. Microbiol. 1977;23(1):7-21.
[79] Chen YR, Hashimoto AG. Kinetics of methane fermentation. En: USDOE, editor. Symposium on biotechnology in energy production and Conservation; 1978 may 10-12; Gatlinburg, USA. Gatlinburg: Science and Education Administration, Clay Center editor; 1978. p. 1-27.
[80] Kargi F, Schuler M. Generalized differential specific rate equation for microbial growth. Biotechnol. Bioeng. 1979;21(10):1871-5.
[81] Sokol W, Howell J. Kinetics of phenol oxidation by washed cells. Biotechnol. Bioeng. 1981;23(9), 2039-49.
[82] Mattiason B, Mandenius CF, Axelsson J, Hagander P. Control of baker’s yeast production based on ethanol measurements. En: N.N editor. Proc. 3rd European Congress on Biotechnology. 1984 ene 15; Munich, Alemania. Munich: Verlag Chemie editor; 1984. p. 629-36.
[83] Ming F, Howell J, Canovas-Diaz M. Mathematical simulation of anaerobic stratified biofilm processes. En: Computer Applications in Fermentation Technology: Modelling and Control of Biotechnological Processes. Fish NM, Fox R, Thornhill N, Editores. Holanda: Editorial Springer; 1988. p. 69-77.
[84] Andrews JF. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substance. Biotechnol. Bioeng. 1968;10(6):707-23.
[85] Hinshelwood C. Chemical Kinetics of the Bacterial cell. Inglaterra: Oxford, Univ. Press.; 1946.
[86] Kono T, Asai T. Kinetics of fermentation processes. Biotechnol. Bioeng. 1969;11(3):293-321.
[87] Contois D. Kinetics of bacterial growth relationship between population density and specific growth rate of continuos cultures. J. Gen. Microbiol. 1959;21:40-50.
[88] Nihtilä M, Virkkunnen J. Practical identifiability of growth and substrate consumption models. Biotechnol. Bioeng. 1977;19(12):1831-50.
[89] Kishimoto M, Sawano T, Yoshida T, Taguchi T. (1983). Optimization of a fed-batch culture by statistical data analysis. En: Modelling and Control of Biotechnical Processes.Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983. p. 161-8.
[90] Staniskis J, Levisaukas D. An adaptative control algorithm for fed-batch culture. Biotechnol. Bioeng. 1984;26(5):419-25.
[91] Holzberg I, Finn R, Steinkraus K. A kinetic study of the alcoholic fermentation of grape juice. Biotechnol. Bioeng. 1967;9(3):413-27.
[92] Aiba S, Shoda M, Nagatani M. Kinetics of product inhibition in alcohol fermentation. Biotechnol. Bioeng. 1968;10(6):845-64.
[93] Jerusalimski N, Engambervediev N. Continuous cultivation of Microorganisms. USA: Editorial Academic Press; 1969.
[94] La Motta E. Kinetics of continuous growth cultures using the logistic growth curve.Biotechnol. Bioeng. 1976;18(7):1029-32.
[95] Ghose T, Tyagi R. Rapid ethanol fermentation of cellulose hydrolysate: II. Product and substrate inhibition and optimization of fermentor design. Biotechnol. Bioeng. 1979;21(8):1387-1400.
[96] Levenspiel O. The Monod equation: a revisit and a generalization to product inhibition situations. Biotechnol. Bioeng. 1980;22(8):1671-87.
[97] Hägglund T. Incubation time prediction in yoghurt manufacturing. En: Modelling and Control of Biotechnical Processes. Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983. p. 307-11.
[98] Bazua C, Wilke C. Ethanol effects on the kinetics of a continuous fermentation with Saccharomyces cerevisiae. Biotechnol. Bioeng. 1977;7:105-18.
[99] Moulin G, Boze H, Galzy P. Inhibition of alcoholic fermentation by substrate and ethanol. Biotechnol. Bioeng. 1980;22(11):2375-81.
[100] Jin C, Chiang H, Wang S. Steady-state analysis of the enhancement in ethanol productivity of a continuous fermentation process employing a protein-phospholipid complex as a protecting agent. Enzyme Microb. Tech. 1981;3(3):249-57.
[101] Sevely Y, Pourciel J, Rauzy G, Bovée J. Modelling, identification and control of the alcohol fermentation in a cascade reactor. En: Akashi H, Editor. Proc. 8th IFAC World Congress; 1981; Kyoto, Japón. Reino Unido: Pergamon Press editor; 1982. p 177-84.
[102] Dourado A, Calvet J. Static optimization of the ethanol production in a cascade reactor. En: Modelling and Control of Biotechnical Processes. Halme A, Editor. Finlandia: Editorial Pergamon Press; 1983. p. 177-85.
[103] Peringer P, Blachere H, Corrieu G, Lane A. A generalized mathematical model for the growth kinetics of Saccharomyces cerevisiae. Biotechnol. Bioeng. 1974;16(4):431-54.
[104] Olsson G. State of the art in sewage treatment plant control. AIChe Symp. 1976;72:52-76.
[105] Andreyeva L, Biryukov V. Analysis of mathematical models of the effect of pH on fermentation processes and their use for calculating optimal fermentation conditions. Biotechnol. Bioeng. Symp. 1973;0(4-1):61-76.
[106] Cheruy A, Durand A. Optimization of erythromycin biosynthesis by controlling pH and temperature: theoretical aspects and practical applications. Biotechnol. Bioeng. Symp. 1979;9:303-20.
[107] Jackson J, Edwards V. Kinetics of substrate inhibition of exponential yeast growth. Biotechnol. Bioeng.. 1975;17(7):943-64.
[108] Topiwala H, Sinclair C. Temperature relationship in continuous culture. Biotechnol. Bioeng. 1971;13(6):795-813.
[109] Hashimoto A. Methane from cattle waste: effects of temperature, hydraulic retention time and influent substrate concentration on kinetic parameter (K). Biotechnol. Bioeng. 1982;24(9):2039-52.
[110] Constantinides A, Spencer J, Gaden E. Optimization of batch fermentation processes. I. Development of mathematical models for batch penicillin fermentations. Biotechnol. Bioeng. 1970;12(5):803-30.
[111] Tamiya H, Hase E, Shibata K, Mituya A, Sasa T. Kinetics of growth of Chorella, with special reference to its dependence on quantity of available light and on temperature. En: Algae Culture: From Laboratory to Pilot Plant, Growth of algae in mass culture. Burlew JS, Editor. USA: Carnegie Inst. Washington DC; 1953. p. 205-32.
[112] Luedeking R, Piret E. A kinetic study of the lactic acid fermentation. Batch process at controlled pH. J. Biochem. Microbiol. Tech. Eng. 1959;1(4):393-412.
[113] Moser A. Bioprocess Technology, Kinetics and Reactors. USA: Editorial Springer Verlag; 1988.
[114] Grady C, Daigger G, Lim H. Biological Wastewater Treatment. USA: Editorial Marcel Dekker; 1999.
[115] Button D. Nutrient uptake by microorganism according to kinetic parameters from theory as related to cytoarchitecture. Microbiol. Mol. Biol. Rev. 1998;62(3):636-45.
[116] Merchuk J, Asenjo J. The Monod equation and mass transfer. Biotechnol. Bioeng. 1994;45(1):91-4.
[117] Schwartzemberg H, Chao R. Solute diffusivities in leaching processes. Food Technol. 1982;36(2):73-86.
[118] Liu Y. A simple thermodynamic approach for derivation of a general Monod equation for microbial growth. Biochem. Eng. J. 2006;31(1):102-5.
[119] Gofferjé G, Stäbler A, Herfellner T, Schweiggert-Weisz U, Flöter E. Kinetics of enzymatic esterification of glycerol and free fatty acids incrude Jatropha oil by immobilized lipase from Rhizomu cormiehei. J. Mol. Catal. B Enzym. 2014;107:1-7.
[120] Vega R, Zuniga M. A new mechanism and kinetic model for the enzymatic synthesis of short-chain fructo oligosaccharides from sucrose. Biochem. Eng. J. 2014;82:158-65.
[121] Mulholland A. Modelling enzyme reaction mechanism, specificity and catalysis. Drug Discov. Today. 2005;10(20):1393-1402.
[122] Ortega F, Pérez O, López E. Modelo Semifísico de Base Fenomenológica del Proceso de Fermentación Alcohólica. Inf. Tecnol. 2016:27(1):21-32.
[123] Melgarejo R, Castillo C, Dutta A, Bény G, Torres D, Gutiérrez M, et al. Mathematical model of a three phase partitioning bioreactor for conversion of ketones using whole cells. Chem. Eng. J. 2015;260:765-75.
[124] Geng X, Boufadel M, Personna Y, Lee K, Tsao D, Demicco E. BIOB: A mathematical model for the biodegradation of low solubility hydrocarbons. Mar. Pollut. Bull. 2014;83(1):138-47.
[125] Kythreotou N, Florides G, Tassou S. A review of simple to scientific models for anaerobic digestion. Renew. Energ. 2014;71:701-14.
[126] Akpa J. Modeling of a bioreactor for the fermentation of palmwine by Saccaharomyces cerevisiae (yeast) and lactobacillus (bacteria). Am. J. Sci. Ind. Res. 2012;3(4):231-40.
[127] Roeva O, Pencheva T, Tzonkoc S, Arndt M, Hitzmann B, Kleist S, et al. Multiple model approach to modelling of Escherichia colifed-bacth cultivation extracelular production of bacterial phytase. Electr. J. Biotechnol. 2007;10(4):592-603.
[128] Atehortúa P, Alvarez H, Orduz S. Modeling of growth and sporulation of Bacillus thuringiensis in an intermittent fed batch culture with total cell retention. Bioprocess Biosyst. Eng. 2007;30(6):447-56.
[129] Lokshina L, Vavilin V, Kettunen R, Rintala J, Holliger C, Nozhevnikova A. Evaluation of kinetic coefficients using integrated Monod and Haldane models for low-temperature acetoclastic methanogenesis. Water Res. 2001;35(12):2913-22.
[130] Lagowski J. Viewpoints: Chemist on Chemistry. Chemical Education: Past, Present, and Future. J. Chem. Edu. 1998;75:425-36.
[131] Machado D, Rodrigues L, Rocha I. A kinetic model for curcumin production in Escherichia coli. Biosystems. 2014;125:16-21.
[132] Chassagnole C, Noisommit N, Schmid J, Mauch K, Reuss M. Dynamic modeling of the central carbon metabolism of Escherichia coli. Biotechnol. Bioeng. 2002;79(1):53-73.
[133] Usuda Y, Nishio Y, Iwatani S, Van Dien S, Imaizumi A, Shimbo K, et al. Dynamic modeling of Escherichia coli metabolic and regulatory systems for amino-acid production. J. Biotechnol. 2010;147(1):17-30.
[134] Roche R, Lamanna R, Delgado M, Rocaries F, Hamam Y, Pecker F. Simulation of a cardiac cell. Part I: An electro-chemical model. Rev. Fac. Ing. UCV. 2009;24(1):71-87.
[135] Umulis D, Gürmen N, Singh P, Fogler H. A physiologically based model for ethanol and acetaldehyde metabolism in human beings. Alcohol. 2005;35(1):3-12.
[136] Huang M, Fan S, Xing W, Liu C. Microfluidic cell culture system studies and computational fluid dynamics. Math. Comput. Model. 2010;52(11-12):2036-42.
[137] Shah P, Vedarethinam I, Kwasny S, Andresen L, Dimaki M, Skov S, et al. Microfluidic bioreactors for culture of non-adherent cells. Sensor. Actuat. B-Chem. 2011;156(2):1002-8.
[138] Leclerc K, Kirat E, Griscom L. In situ micropatterning technique by cell crushing for co-cultures inside microfluidic biochips. Biomed. Microdev. 2008;10(2):169-77.