Fed-batch culture of hybridoma cells: comparison of optimal control approach and closed loop strategies

Control of fed-batch culture of hybridoma cells was investigated based on two approaches optimal control theory and feedback control. Experiments were conducted for both approaches-with a feed enriched in glutamine. The optimal feed trajectory, a decreasing one, yielded a final monoclonal antibody (MAb) concentration of 170 mg/l, a three-fold increase compared to a typical batch operation.The feedback strategy relied on the on-line estimation of the net specific growth rate of cells from the measurement of the CO₂ production rate with a mass-spectrometer. A PI controller was then used to maintain the growth rate at a desired value by adjusting the dilution rate to the reactor. For the chosen set-point (0.1 d^–1), the final MAb concentration achieved was about 100 mg/1. It was found that there was a delay in the assimilation of the glutamine that should be included in the model to explain the lower MAb production in feedback mode. A higher production can be expected also for a lower set-point in feedback operation.List of Symbols Amm mM ammonia concentration - CPR l/(ld) carbon dioxide production rate - D _t l/d dilution rate - e _t l/d control error - F L/d feed flow rate - Glc mM glucose concentration - Gln mM glutamine concentration - Lac mM lactate concentration - I mg performance index - k _d l/d specific death rate - K _damm l/(mM · d) kinetic parameter for death rate - K _dgln mM kinetic parameter for death rate - K _dlac l/(mM·d) kinetic parameter for death rate - K _c l controller gain - K _glc mM kinetic parameter for growth rate - K _gln mM kinetic parameter for growth rate - K _tr L/(cell·d) transport coefficient - K l/d kinetic parameter for Mab production - m _glc mM/(cell·d) maintenance coefficient - M _Ab mg/l monoclonal antibody concentration - P _t covariance matrix - q _glc l/(l·cell·d) specific CO₂ production rate - q _glc mM/(cell·d) specific glucose uptake rate - q _gln mM/(cell·d) specific glutamine uptake rate - q _Mab mg/(l·cell·d) specific monoclonal antibody production - t _f d final culture time - T d sampling rate - u control input - V l reactor volume - X cell/l total cells concentration - X _v cell/l viable cells concentration - Y yield coefficient Greek mg/cell variable yield coefficient - ₀ mg/(cell·d) growth-associated kinetic parameter - mg/(cell·d) non growth-associated kinetic parameter - _t+1 defined by Eq. (19) - forgetting factor - l/d specific growth rate - _max l/d specific growth rate - _i d controller integral time constant