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Modeling and parameters identification of 2-keto-l-gulonic acid fed-batch fermentation

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Abstract

This article presents a modeling approach for industrial 2-keto-l-gulonic acid (2-KGA) fed-batch fermentation by the mixed culture of Ketogulonicigenium vulgare (K. vulgare) and Bacillus megaterium (B. megaterium). A macrokinetic model of K. vulgare is constructed based on the simplified metabolic pathways. The reaction rates obtained from the macrokinetic model are then coupled into a bioreactor model such that the relationship between substrate feeding rates and the main state variables, e.g., the concentrations of the biomass, substrate and product, is constructed. A differential evolution algorithm using the Lozi map as the random number generator is utilized to perform the model parameters identification, with the industrial data of 2-KGA fed-batch fermentation. Validation results demonstrate that the model simulations of substrate and product concentrations are well in coincidence with the measurements. Furthermore, the model simulations of biomass concentrations reflect principally the growth kinetics of the two microbes in the mixed culture.

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Abbreviations

a, b :

Parameters of the Lozi map

CR:

Crossover constant of DE

DE:

Differential evolution algorithm

D :

Dimension of parameter vector in DE

e :

Simulation error

f :

Cost function

F O :

Withdrawal rate by sampling (L/h)

F B :

Base solution feeding rate (L/h)

F S :

Substrate feeding rate (L/h)

F :

Mutation factor of DE

GA:

Genetic algorithm

m ATP :

Maintenance coefficient for ATP (mol/g/h)

m 1, m 2 :

Mutualism coefficients

M S :

Molecular weight of substrate

NP:

Number of parameter vectors in a population

N i :

Number of sampling points of the ith batch

P(T k ):

Measurement of 2-KGA concentration at T k (g/L)

P m(T k ):

Model simulation of 2-KGA concentration at T k (g/L)

P/O :

Effectiveness coefficient of oxidative phosphorylation

P :

Product concentration (g/L)

r ATP :

Specific ATP uptake rate (mol/g/h)

r B1, r B2 :

Specific bio-synthesis rate of biomass (mol/g/h)

r G6P :

Specific Gluconate-6-phosphate uptake rate in glycolysis (mol/g/h)

\(r_{{{\text{O}}_{2} }}\) :

Specific oxygen uptake rate (mol/g/h)

r gr :

Specific Ribulose-5- phosphate production rate (mol/g/h)

r S :

Specific substrate uptake rate of K. vulgare (mol/g/h)

r S max :

The maximum specific substrate uptake rate in Monod model (mol/g/h)

r S min :

The initial input value of r S in the regulator model (mol/g/h)

r TCC :

Specific acetyl CoA uptake rate (mol/g/h)

r AC :

Specific acetyl CoA production rate (mol/g/h)

r SM :

Specific l-sorbose uptake rate obtained from Monod model (mol/g/h)

r SR :

Specific l-sorbose uptake rate obtained from the regulator model (mol/g/h)

r NAD :

Specific NADH uptake rate in the respiratory chain (mol/g/h)

r 1, r 2 :

Random indexes

RMSE:

Root mean square error

S :

Substrate concentration in the medium (g/L)

S R :

Substrate concentration in the feed (g/L)

T k :

The kth sampling point of 2-KGA fermentation (h)

u i,G+1 :

The ith trial vector for generation G + 1 of DE

V :

Culture volume (L)

v i,G+1 :

The ith mutant vector for generation G + 1 of DE

X B :

B. megaterium concentration (g/L)

X K :

K. vulgare concentration (g/L)

X B max :

Maximum concentration of B. megaterium (g/L)

X K max :

Maximum concentration of K. vulgare (g/L)

X n+1 :

Random number generated by the Lozi map

x i,G :

The ith parameter vector for generation G of DE

x Best,G :

Best performed parameter vector in generation G

Y ATP :

Yield coefficient of ATP (g/mol)

Y n+1 :

Random number generated by the Lozi map

Y P/S :

Product yield coefficient (g/g)

μ 1 :

Specific growth rate of B. megaterium (/h)

μ 2 :

Specific growth rate of K. vulgare (/h)

μ b1 :

Specific B. megaterium substance uptake rate by K. vulgare (mol/g/h)

γ :

Coefficient of evaporation (/h)

K 21, K 22, α, β, K B1, K B2, K S2 :

Model parameters

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Acknowledgments

This study is supported by the Key Laboratory of Systems Microbial Biotechnology, Tianjin Institute of Industrial Biotechnology/Chinese Academy of Sciences,the Doctoral Program of Higher Education of China (Grant No. 20110073110018) and the National Science Foundation of China (Grant No. 61233004). J.Q.Yuan acknowledges the financial support of Alexander von Humboldt-Stiftung/Germany during the early stage of the study.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, and the Key Laboratory of System Control and Information Processing, Ministry of Education of China, 800 Dongchuan Road, Shanghai, 200240, China

    Tao Wang & Jingqi Yuan

  2. Key Laboratory of Systems Microbial Biotechnology, Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin, 300308, China

    Jibin Sun

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  1. Tao Wang
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Correspondence to Jingqi Yuan.

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Wang, T., Sun, J. & Yuan, J. Modeling and parameters identification of 2-keto-l-gulonic acid fed-batch fermentation. Bioprocess Biosyst Eng 38, 605–614 (2015). https://doi.org/10.1007/s00449-014-1300-8

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