Abstract
The mathematical modelling of the behaviour of microbial growth is widely desired in order to control, predict and design food and bioproduct processing, stability and safety. This work develops and proposes a new semi-empirical mathematical model, based on an autocatalytic kinetic, to describe the microbial growth through its biomass concentration. The proposed model was successfully validated using 15 microbial growth patterns, covering the three most important types of microorganisms in food and biotechnological processing (bacteria, yeasts and moulds). Its main advantages and limitations are discussed, as well as the interpretation of its parameters. It is shown that the new model can be used to describe the behaviour of microbial growth.
Abbreviations
- a, b :
-
Parameters of model fit evaluation (Eq. 27) [different units]
- A, B :
-
Parameters for the partial fractions integration (Eq. 8) [different units]
- k :
-
Kinetic parameter of the reaction (Eq. 1) [g L−1 h−1]
- K 1 , K 2 , K 3 :
-
Parameters of the new model (Eq. 20) [g L−1, h−1, dimensionless, respectively]
- M :
-
Microorganism biomass concentration [g L−1]
- M 0 :
-
Initial microorganism biomass concentration [g L−1]
- M ∞ :
-
Maximum microorganism biomass concentration [g L−1]
- MRSS :
-
Residual sum-of-squares values (Eq. 26) [(g L−1)2]
- Q :
- S :
-
Substrate concentration [g L−1]
- S 0 :
-
Initial substrate concentration [g L−1]
- t :
-
Time [h]
References
Bokhari SAI, Latif F, Rajoka MI (2008) Kinetics of high-level of β-glucosidase production by a 2-deoxyglucose resistant mutant of Humicola lanuginosa in submerged fermentation. Braz J Microbiol 39:724–733
Borzani, W. (1975). Cinética de processos fermentativos [Fermentation process kinetic]. In: Borzani, W.; Lima, U. A. L.; Aquarone, E. Biotecnologia: Engenharia Bioquímica [Biotechnology: Biochemical Engineering]. São Paulo: Ed. Edgard Blücher
Chmielewska J (2003) Selected biotechnological features of hybrids of Saccharomyces cerevisiae and Yamadazyma stipites. Electron J Polish Agric Univ 6:1
Hughes DB, Tudroszen NJ, Moye CJ (1984) The effect of temperature on the kinetic of ethanol production by a thermotolerant strain of Kluveromyces marxianus. Biotechnol Lett 6(1):1–6
Lee JH, Williamson D, Rogers PL (1980) The effect of temperature on the kinetics of ethanol production by Saccharomyces uvarum. Biotechnol Lett 2(4):80–88
Levenspiel, O. (1986). El Omnilibro de los Reactores Químicos [The Chemical Reactor Omnibook]. Barcelona: Ed. Reverté
Martínez, A.; Rodrigo, M.; Rodrigo, D.; Ruiz, P.; Martínez, A.; Ocio, M. J. (2005). Predictive Microbiology and Role in Food Safety Systems. In: Barbosa-Cánovas, G. V.; Tapia, M. S.; Cano, M. P. (Ed).. Martín-Belloso, O.; Martínez, A. (As.Ed.). Novel Food Processing Technologies. Boca Raton: CRC Press
Ottoni CA, Cuervo-Fernández R, Piccoli RM, Moreira R, Guilarte-Maresma B, Silva ES, Rodrigues MFA, Maiorano AE (2012) Media optimization for β-fructofuranosidase production by Aspergillus oryzae. Braz J Chem Eng 29(1):49–59
Parente E, Ricciardi A, Addario G (1994) Influence of pH on growth and bacteriocin production by Lactococcus lactis subsp, lactis 140NWC during batch fermentation. Appl Microbiol Biotechnol 41:388–394
Parrondo J, García LA, Díaz M (2009) Nutrient balance and metabolic analysis in a Kluyveromyces marxianus fermentation with lactose-added whey. Braz J Chem Eng 26(3):445–456
Peleg M, Corradini MG (2011) Microbial growth curves: what the models tell us and what they cannot. Crit Rev Food Sci Nutr 51(10):917–945
Rogers PL, Lee KJ, Tribe DE (1979) Kinetics of alcohol production by Zymomonas mobilis at high sugar concentrations. Biotechnol Lett 1(4):165–170
Tian Y, Yue T, Yuan Y, Soma PK, Williams PD, Machado PA, Lo YM (2010) Tobacco biomass hydrolysate enhances coenzyme Q10 production using photosynthetic Rhodospirillum rubrum. Bioresour Technol 101(20):7877–7881
Vuyst L, Callewaert R, Crabbé K (1996) Primary metabolite kinetics of bacteriocin biosynthesis by Lactobacillus amylovorus and evidence for stimulation of bacteriocin production under unfavourable growth conditions. Microbiology 142(4):817–827
Zwietering MH, Jongenburger I, Rombouts FM, van’t Riet K (1990) Modeling the bacterial growth curve. Appl Environ Microbiol 56(6):1875–1881
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Ibarz, A., Augusto, P.E.D. An autocatalytic kinetic model for describing microbial growth during fermentation. Bioprocess Biosyst Eng 38, 199–205 (2015). https://doi.org/10.1007/s00449-014-1256-8
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DOI: https://doi.org/10.1007/s00449-014-1256-8