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An autocatalytic kinetic model for describing microbial growth during fermentation

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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.

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Fig. 1
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Fig. 3

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 :

Fractional yield (Eqs. 3, 4) [dimensionless]

S :

Substrate concentration [g L−1]

S 0 :

Initial substrate concentration [g L−1]

t :

Time [h]

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Correspondence to Pedro E. D. Augusto.

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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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