A semi‐empirical mathematical model useful for describing the relationship between carbon dioxide, pH, lactate and base in a bicarbonate‐buffered cell‐culture process

The purpose of the present study was to develop a quantitative relationship between the primary factors of state affecting pH control in a bicarbonate-buffered medium. Starting with the Henderson-Hasselbach equation, several assumptions led to the following equation: L = B(T)-s x dCO2 x 10(pH-pK) where L is the lactate concentration (mM), B(T) is the total amount of base added (mM), s is the solubility of CO(2) (mM/%), dCO(2) is the dissolved CO(2) concentration (%) and pK is the acid ionization constant for bicarbonate. This equation appropriately described the relationship of these factors when using bicarbonate, carbonate and HCl (as a lactic acid surrogate) in water. However, the equation required modification to describe the relationship in cell culture medium, due presumably to the presence of other buffers and components; the final form of the equation from an empirical fit in the absence of cells was: L = B(T)-0.88 x dCO2(0.79) x 10(pH-6038) This equation was tested against actual cell culture data, from inoculum preparation in a T-flask through a 10000-litre fed-batch bioreactor, by comparing the lactate concentration calculated from base, pH and dCO(2) data with that actually measured in the bioreactor using a YSI 8500 SELECT Biochemistry Analyzer (YSI Inc., Yellow Springs, OH, U.S.A.). In every case, the calculated and actual lactate concentrations were in good agreement. The equation was useful for isolating the mechanisms leading to varied base addition across 2-, 600- and 10 000-litre-scale bioreactors. This procedure enables a new approach for quantitatively evaluating and understanding factors associated with bioreactor pH control.