Optimal dilution strategy for  a microbial continuous culture  based  on the biological robustness

Jingang Zhai; Guangmao Jiang; Jianxiong Ye

doi:10.3934/naco.2015.5.59

Article Contents

2015, Volume 5, Issue 1: 59-69. Doi: 10.3934/naco.2015.5.59

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Optimal dilution strategy for a microbial continuous culture based on the biological robustness

1.
School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025
2.
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350108

Received: January 2015

Revised: March 2015

Published: February 2015

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Abstract

A robust optimal parameter selection model is proposed to formulate the microbial continuous culture process of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD), in which the dilution rate and the glycerol concentration in feed medium are taken as the optimization variables. In consideration of the uncertain factors that some system parameters may be changed with the change of the optimization variables, we establish a novelty mathematical model which is represented by an eight-dimensional nonlinear dynamical system with the unknown parameters. On the basis of biological robustness, we give a quantitative definition of robustness index. The concentration of 1,3-PD at the approximately steady-state time together with the robustness index are taken as the cost functional in consideration of uncertain metabolic mechanisms. A parallel particle swarm optimization -- optimal parameter selection algorithm (PPSO-OPSA) is constructed to find the optimal dilution rate and the feeding glycerol concentration. Numerical results show that, by employing the obtained optimal input strategy, not only the concentration of 1,3-PD at the approximately steady-state time can be increased considerably compared with the previous experimental results, but also the obtained optimal parameters are robust for the dynamical system.

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Mathematics Subject Classification: Primary: 35Q92, 35Q93; Secondary: 65Y05.

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