We present robust methods for online estimation of cell specific oxygen uptake and carbon dioxide production rates (q(O2) and q(CO2), respectively) during perfusion cultivation of mammalian cells. Perfusion system gas and liquid phase mass balance expressions for oxygen and carbon dioxide were used to estimate q(O2), q(CO2) and the respiratory quotient (RQ) for Chinese hamster ovary (CHO) cells in perfusion culture over 12 steady states with varying dissolved oxygen (DO), pH, and temperature set points. Under standard conditions (DO = 50%, pH = 6.8, T = 36.5°C), q(O2) and q(CO2) ranges were 5.14-5.77 and 5.31-6.36 pmol/cell day, respectively, resulting in RQ values of 0.98-1.14. Changes to DO had a slight reducing effect on respiration rates with q(O2) and q(CO2) values of 4.64 and 5.47, respectively, at DO = 20% and 4.57 and 5.12 at DO = 100%. Respiration rates were lower at low pH with q(O2) and q(CO2) values of 4.07 and 4.15 pmol/cell day at pH = 6.6 and 4.98 and 5.36 pmol/cell day at pH = 7. Temperature also impacted respiration rates with respective q(O2) and q(CO2) values of 3.97 and 4.02 pmol/cell day at 30.5°C and 5.53 and 6.25 pmol/cell day at 37.5°C. Despite these changes in q(O2) and q(CO2) values, the RQ values in this study ranged from 0.98 to 1.23 suggesting that RQ was close to unity. Real-time q(O2) and q(CO2) estimates obtained using the approach presented in this study provide additional quantitative information on cell physiology both during bioprocess development and commercial biotherapeutic manufacturing.

Methods for robust logistic modeling of batch and fed-batch mammalian cell cultures are presented in this study. Linearized forms of the logistic growth, logistic decline, and generalized logistic equation were derived to obtain initial estimates of the parameters by linear least squares. These initial estimates facilitated subsequent determination of refined values by nonlinear optimization using three different algorithms. Data from BHK, CHO, and hybridoma cells in batch or fed-batch cultures at volumes ranging from 100 mL-300 L were tested with the above approach and solution convergence was obtained for all three nonlinear optimization approaches for all data sets. This result, despite the sensitivity of logistic equations to parameter variation because of their exponential nature, demonstrated that robust estimation of logistic parameters was possible by this combination of linearization followed by nonlinear optimization. The approach is relatively simple and can be implemented in a spreadsheet to robustly model mammalian cell culture batch or fed-batch data.