Efficient estimation of the maximum metabolic productivity of batch systems

BACKGROUND 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. Previous studies have therefore typically focused on simpler strategies that are more feasible to implement in practice, such as the time-dependent control of a single flux or control variable. RESULTS This work presents an efficient method for the calculation of a maximum theoretical productivity of a batch culture system using a dynamic optimization framework. The proposed method follows traditional assumptions of dynamic flux balance analysis: first, that internal metabolite fluxes are governed by a pseudo-steady state, and secondly 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 calculate the complete Pareto surface of productivity as a function of yield. We apply this method to succinate production in two engineered microbial hosts, Escherichia coli and Actinobacillus succinogenes, and demonstrate that maximum productivities can be more than doubled under dynamic control regimes. CONCLUSIONS The maximum theoretical yield is a measure that is well established in the metabolic engineering literature and whose use helps guide strain and pathway selection. We present a robust, efficient method to calculate the maximum theoretical productivity: a metric that will similarly help guide and evaluate the development of dynamic microbial bioconversions. Our results demonstrate that nearly optimal yields and productivities can be achieved with only two discrete flux stages, indicating that near-theoretical productivities might be achievable in practice.