Optimal control and dynamic modulation of the ATPase gene expression for enforced ATP wasting in batch fermentations

Competitive biotechnological processes need to operate over various conditions and adapt to changing economic contexts. Dynamic ATP turnover allows trading off declines in biomass formation and volumetric productivity for enhancements of product yields in fermentations where the product pathway is linked to ATP synthesis. To facilitate its practical implementation, we propose to dynamically manipulate the cellular ATP turnover by putting the ATPase enzyme, which hydrolyzes ATP into ADP, under the control of an optogenetic gene expression system. This allows achieving dynamic control of the ATP wasting online via a tunable external input. While light as control input is promising because it is easily tunable, generally non-invasive/non-toxic, and more affordable than classical chemical inducers, it makes the overall control task challenging. Thus, we derive an expanded version of dynamic enzyme-cost flux balance analysis that takes into account the dynamics of the optogenetic actuator. We then formulate a suitable optimal control problem to find optimal inputs for achieving the desired process performance. We test our approach in simulations using the batch anaerobic lactate fermentation of glucose by Escherichia colias a case study.