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Multi-objective optimization in Aspergillus niger fermentation for selective product enhancement

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A multi-objective optimization formulation that reflects the multi-substrate optimization in a multi-product fermentation is proposed in this work. This formulation includes the application of ε-constraint to generate the trade-off solution for the enhancement of one selective product in a multi-product fermentation, with simultaneous minimization of the other product within a threshold limit. The formulation has been applied to the fed-batch fermentation of Aspergillus niger that produces a number of enzymes during the course of fermentation, and of these, catalase and protease enzyme expression have been chosen as the enzymes of interest. Also, this proposed formulation has been applied in the environment of three control variables, i.e. the feed rates of sucrose, nitrogen source and oxygen and a set of trade-off solutions have been generated to develop the pareto-optimal curve. We have developed and experimentally evaluated the optimal control profiles for multiple substrate feed additions in the fed-batch fermentation of A. niger to maximize catalase expression along with protease expression within a threshold limit and vice versa. An increase of about 70% final catalase and 31% final protease compared to conventional fed-batch cultivation were obtained. Novel methods of oxygen supply through liquid-phase H2O2 addition have been used with a view to overcome limitations of aeration due to high gas–liquid transport resistance. The multi-objective optimization problem involved linearly appearing control variables and the decision space is constrained by state and end point constraints. The proposed multi-objective optimization is solved by differential evolution algorithm, a relatively superior population-based stochastic optimization strategy.

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a P :

protease yield with respect to cell (unit protease (kg cell mass)−1)

b P :

protease yield with respect to maintenance (unit protease (kg cell mass)−1 s−1)

C :

concentration of sucrose (kg m−3)

C feed :

sucrose concentration in feed (kg m−3)

C R :

crossover factor

d :

hyphal diameter (m)

E i :

intracellular enzyme (catalase) (kmol (kg-cell)−1)

F :

feed rate (m3 s−1)

F C :

sucrose feed rate (m3 s−1)

F H :

hydrogen peroxide feed rate (m3 s−1)

F N :

nitrogen source feed rate (m3 s−1)

H :

hydrogen peroxide concentration in the medium (kmol m−3)

H feed :

hydrogen peroxide concentration in feed (kmol m−3)

H i :

hydrogen peroxide concentration in the cell (kmol m−3)

K :

rate constant for enzymatic reaction inside the cell (kmol m−3)−1 s−1)

K C :

monod type constant for sucrose (kg m−3)

K d :

rate constant for enzymatic reaction in the medium (kmol m−3)−1 s−1)

K H :

hydrogen peroxide permeability across the cell envelope (m s−1)

\( K_{{H_{i} }} \) :

monod type constant for intracellular hydrogen peroxide (kmol m−3)

K i :

inhibition constant for hydrogen peroxide in the medium (kmol m−3)

K N :

monod type constant for nitrogen source (kg m−3)

N :

nitrogen source concentration (kg m−3)

N d :

number of discretizations in fermentation time

N feed :

nitrogen source concentration in feed (kg m−3)

N P :

population size

P cat :

catalase concentration (kmol m−3)

P prot :

protease concentration (U m−3)

q P :

catalase yield with respect to cell (kmol catalase (kg cell mass)−1)

V :

reactor volume (m3)

V f :

maximum working volume of the reactor (m3)

X :

cell concentration (kg m−3)

Y C/X :

inverse of cell yield with respect to sucrose

Y C/peat :

inverse of catalase yield with respect to sucrose

Y C/Ppeat :

inverse of protease yield with respect to sucrose

Y N/X :

inverse of cell yield with respect to nitrogen source


penalty factor

μm :

maximum specific growth rate (s−1)


density of the cell (kg m−3)

f :

final time


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Correspondence to Ravindra D. Gudi.

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Mandal, C., Gudi, R.D. & Suraishkumar, G.K. Multi-objective optimization in Aspergillus niger fermentation for selective product enhancement. Bioprocess Biosyst Eng 28, 149–164 (2005). https://doi.org/10.1007/s00449-005-0021-4

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  • Fermentation
  • Catalase
  • Differential Evolution
  • H2O2 Concentration
  • Protease Production