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Application of a mathematical model and Differential Evolution algorithm approach to optimization of bacteriocin production by Lactococcus lactis C7

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Abstract

The effect of pH and temperature on cell growth and bacteriocin production in Lactococcus lactis C7 was investigated in order to optimize the production of bacteriocin. The study showed that the bacteriocin production was growth-associated, but declined after reaching the maximum titer. The decrease of bacteriocin was caused by a cell-bound protease. Maximum bacteriocin titer was obtained at pH 5.5 and at 22°C. In order to obtain a global optimized solution for production of bacteriocin, the optimal temperature for bacteriocin production was further studied. Mathematical models were developed for cell growth, substrate consumption, lactic acid production and bacteriocin production. A Differential Evolution algorithm was used both to estimate the model parameters from the experimental data and to compute a temperature profile for maximizing the final bacteriocin titer and bacteriocin productivity. This simulation showed that maximum bacteriocin production was obtained at the optimal temperature profile, starting at 30°C and terminating at 22°C, which was validated by experiment. This temperature profile yielded 20% higher maximum bacteriocin productivity than that obtained at a constant temperature of 22°C, although the total amount of bacteriocin obtained was slightly decreased.

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Abbreviations

J :

Objective function of optimal control problem

ϕ:

Linear or nonlinear function

f :

Dynamic function vector

u :

Control variable

x :

State vector

t :

Time in hours (h)

\(\tilde {\mathbf{u}}\) :

Expression defined by Eq. 6

m :

Number of time intervals

t f :

Final time

LB:

Lower bound on control variable

UB:

Upper bound on control variable

F :

Differential variation constant

CR:

Crossover constant

N P :

Population size

N G :

Maximum number of generations

ɛ:

Tolerance for convergence

ɛ1 :

Desired tolerance

ɛ2 :

Assigned tolerance for gene diversity

ρ:

Degree of population diversity

X :

Cell concentration (OD660)

μ:

Specific growth rate (h−1)

μmax :

Maximum specific growth rate (h−1)

S :

Residual glucose (g l−1)

L :

Lactic acid concentration (g l−1)

K S :

The saturation constant of Monod equation (g l−1)

K P :

Lactic acid inhibition constant (g l−1)

α:

Growth-associated constant for lactic acid production (g l−1)

β:

Non-growth associated constant for lactic acid production (g l−1 h−1)

γ:

Expression defined by Eq. 16

ξ:

Expression defined by Eq. 16

Y X :

Cell-yield coefficient (l/g)

Y P :

Yield coefficient of lactic acid

δ:

Cell maintenance coefficient (g l−1 h−1)

K :

Expression defined by Eq. 17

B :

Bacteriocin titer (AU ml−1)

K B :

Specific bacteriocin production rate (AU ml−1)

K D :

Specific bacteriocin degradation rate (h−1)

L :

Expression defined by Eq. 21

V:

Vector of parameters

T :

Temperature (°C)

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, 10400, Thailand

    Sompop Moonchai

  2. Department of Biotechnology, Faculty of Science, Mahidol University, Bangkok, 10400, Thailand

    Weeranuch Madlhoo, Kanidtha Jariyachavalit & Somchai Chauvatcharin

  3. Department of Bioinformatic Engineering, Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, 565-0871, Osaka, Japan

    Hiroshi Shimizu

  4. Department of Biotechnology, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, 565-0871, Osaka, Japan

    Suteaki Shioya

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  1. Sompop Moonchai
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Correspondence to Sompop Moonchai.

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Moonchai, S., Madlhoo, W., Jariyachavalit, K. et al. Application of a mathematical model and Differential Evolution algorithm approach to optimization of bacteriocin production by Lactococcus lactis C7. Bioprocess Biosyst Eng 28, 15–26 (2005). https://doi.org/10.1007/s00449-005-0004-5

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