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Modeling of Fermentation Process of Bacillus Thuringiensis as a Sporulating Bacterium

Soroush Soleymani, Mohammad-Hossein Sarrafzadeh and Navid Mostoufi


This paper intended to develop a model for predicting the progress in sporulation of Bacillus thuringiensis as an industrially important sporulating bacterium. Three distinct forms of B. thuringiensis can be observed during the fermentation process: vegetative cells, sporangia and mature spores. A mathematical model was developed for estimating the population of these three cell forms of this bacterium. A cell population balance was derived to represent the dynamic behavior of the fermentation process in a fed-batch culture. An unstructured and segregated model was used for this purpose. Experimental data at various oxygen saturation levels (0, 50 and 100 %) were used for validating the model. The model consists of a partial differential equation that describes the distribution of the cell population based on the cell age. This equation was solved by the method of lines in MATLAB. The proposed model can properly describe the cell populations and sporulation development in the mentioned conditions.



dilution rate (h−1)


feed rate (h−1)


step size


natural numbers


time (h)


time that the vegetative cells have the highest amount (h)


broth volume (mL)


maximum vegetative cell density (cells/mL)


sporangium age density function (cells/h/mL)


vegetative cell density (cells/mL)

Greek letters


specific death rate (h−1)


net specific growth rate (h−1)


specific growth rate of vegetative cell (h−1)


sporulation rate (h−1)


spore mature age (h)


age of sporangium (h)


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Received: 2018-02-06
Revised: 2018-08-10
Accepted: 2018-10-01
Published Online: 2018-10-12

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