A mathematical model for fed-batch culture of hybridoma cells [24] has been employed for generating simulation data in this study. The model is a seventh-order nonlinear model where both glucose and glutamine concentrations are used to describe the specific growth rate, /. The cell death rate, kd, is governed by lactate, ammonia and glutamine concentrations. The specific MAb production rate, qMAb, is estimated using a variable yield coefficient model related to the physiological state of the culture through the specific growth rate. The mass balance equations for the system in fed-batch mode are:

dX. dt dGlc dt dGln dt dLac dt dAmm dMAb dt dV dt

with the following kinetic expressions:

kd qgln qglc qlac qamm

Glc |
Gln | |

K... +Glc |
K... +Gln |

kdmax(Mmax kdlacLac) (Mmax kdammAmm) — M

Ylac/glc qglc Yamm/gln qgln qMAb = a.' m + ß where

where Xv, Glc, Gln, Lac, Amm and MAb are respectively the concentrations in viable cells, glucose, glutamine, lactate, ammonia and monoclonal antibodies; V is the fermentor volume and F the volumetric feed rate; Glcin and Glnin are the concentrations of glucose and glutamine in the feed stream,

L. Z. Chen et al.: Modelling and Optimization of Biotechnological Processes, Studies in Computational Intelligence (SCI) 15, 111-112 (2006)

www.springerlink.com © Springer-Verlag Berlin Heidelberg 2006

112 A A Model of Fed-batch Culture of Hybridoma Cells respectively; qgic, qgn, qiac, qamm and qMAb are the specific rates; Yxv/gin, Yxv/glc and Ylac/glc are yield coefficients. The parameter values are tabulated in Table A.1.

Parameters |
Values |

l^max |
1.09d-1 |

^dmax |
0.69d-1 |

Yxv/glc |
1.09 x 108cells/mmol |

Yxv/gin |
3.8 x 108cells/mmol |

mglc |
0.17mmol ■ 10-8cells ■ d-1 |

kmglc |
19.0mM |

Kglc |
1.0mM |

Kgln |
0.3mM |

ao |
2.57mg ■ 10-8cells ■ d-1 |

0.02d-1 | |

ft |
0.35mg ■ 10-8cells ■ d-1 |

kdlac |
0.01d-1mM-1 |

k, damm |
0.06d-1mM-1 |

kdgln |
0.02mM |

Ylac/glc |
1.8mmol/mmol |

Yamm/gln |
0.85mmol/mmol |

The multi-feed case, which involves two separate feeds F\ and F2 for glucose and glutamine respectively, is reformulated as follows:

X _ (i - kd)Xv - ^Xv d<dlc _ (Glcin - Glc) Fl+F2 — qglcXv dGn =(Glnin - Gln) - qginXv dLac _ qiacXv - Lac (A.3)

dAmm _ q X — V Amm dt — hamm^v v -rilli'iii dMdA _ qMAbXv - ^ MAb dd _ F1 + F2

The following initial culture conditions and feed concentrations are used in the work:

Xv (0) _ 2.0 x 108cells/L Glc(0) _ 25mM Gln(0) _ 4mM

The above mathematical models and initial conditions have been used to generate a 'reality' for testing the schemes proposed in the work.

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