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Biotechnol. Appl. Biochem. (2007) Immediate Publication, doi:10.1042/BA20070001 
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| A semi-empirical mathematical model useful for describing the relationship between carbon dioxide, pH, lactate, and base in a bicarbonate-buffered cell culture process |
| Michael J Gramer and Tad Ogorzalek |
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| Process Development, PDL BioPharma, Inc., BROOKLYN PARK, MN 55445, U.S.A..
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The purpose of this 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 = BT - s * dCO2 * 10(pH-pK), where L is the lactate concentration (mM), BT is the total amount of base added (mM), s is the solubility of CO2 (mM/%), dCO2 is the dissolved CO2 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 = BT - 0.88 * dCO20.79 * 10(pH-6.38). This equation was tested against actual cell culture data, from inoculum preparation in a T-flask through a 10,000-L fed-batch bioreactor, by comparing the lactate concentration calculated from base, pH and dCO2 data to that actually measured in the bioreactor using a YSI instrument. 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-L, 600-L, and 10,000-L scale bioreactors. This procedure enables a new approach for quantitatively evaluating and understanding factors associated with bioreactor pH control.
doi:10.1042/BA20070001
Received 2 January 2007/13 February 2007; Accepted 15 March 2007
Published as Immediate Publication 15 March 2007
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