Efficient estimation of the maximum metabolic productivity of batch systems

Abstract

Production of chemicals from engineered organisms in a batch culture involves an inherent trade-off between productivity, yield, and titer. Existing strategies for strain design typically focus on designing mutations that achieve the highest yield possible while maintaining growth viability. While these methods are computationally tractable, an optimum productivity could be achieved by a dynamic strategy in which the intracellular division of resources is permitted to change with time. New methods for the design and implementation of dynamic microbial processes, both computational and experimental, have therefore been explored to maximize productivity. However, solving for the optimal metabolic behavior under the assumption that all fluxes in the cell are free to vary is a challenging numerical task. This work presents an efficient method for the calculation of a maximum theoretical productivity of a batch culture system using a dynamic optimization framework. This metric is analogous to the maximum theoretical yield, a measure that is well established in the metabolic engineering literature and whose use helps guide strain and pathway selection. The proposed method follows traditional assumptions of dynamic flux balance analysis: (1) that internal metabolite fluxes are governed by a pseudo-steady state, and (2) that external metabolite fluxes are dynamically bounded. The optimization is achieved via collocation on finite elements, and accounts explicitly for an arbitrary number of flux changes. The method can be further extended to explicitly solve for the trade-off curve between maximum productivity and yield. We demonstrate the method on succinate production in two common microbial hosts, Escherichia coli and Actinobacillus succinogenes, revealing that nearly optimal yields and productivities can be achieved with only two discrete flux stages.