A population balance model unveils the intracellular protein accumulation dynamics of recombinant E. coli in cascaded continuous fermentation systems

Abstract

Cascaded continuous fermentation systems are a promising pathway to the realization of the Integrated Contin- uous Biomanufacturing strategy. While advances in molecular biology and bioprocess engineering have enabled robust and long-term production-stable strains suitable for continuous operation, a fundamental gap remains in the mathematical understanding of cascaded reactor systems, compromising the development and implemen- tation of predictive digital twins. In this contribution, we introduce a novel mechanistic model to describe the intracellular protein accumulation dynamics in cascaded continuous stirred tank reactor (CCSTR) systems. From the transient behavior observed in chemostats of recombinant β-casein producing E. coli strains upon induction, we formulate a novel cell-aging process that parametrizes the activation and exhaustion of protein synthesis. This aging state is then incorporated as an extra coordinate in a population balance framework to describe the age-distributed biomass and intracellular protein balances in cascaded continuous systems. The model parame- ters and confidence intervals were estimated from a combination of transient chemostat datasets and steady-state observations in cascaded mode. Finally, the new model was validated against a transient CCSTR culture from the moment of induction. Our model provides a mathematical explanation for the commonly observed adapta- tion and constant production phases and unveils the missing link between the operating conditions in cascaded rectors and its behavior in the steady state. This novel formulation can help the development of digital-twins for biomass-specific cell-age distributed systems in Bioprocess Engineering.