Hybrid physics-informed metabolic cybergenetics: process rates augmented with machine-learning surrogates informed by flux balance analysis

Metabolic cybergenetics is a promising concept that interfaces gene expression and cellular metabolism with computers for real-time dynamic metabolic control. The focus is on control at the transcriptional level, serving as a means to modulate intracellular metabolic fluxes. Recent strategies in this field have employed constraint-based dynamic models for process optimization, control, and estimation. However, this results in bilevel dynamic optimization problems, which pose considerable numerical and conceptual challenges. In this study, we present an alternative hybrid physics-informed dynamic modeling framework for metabolic cybergenetics, aimed at simplifying optimization, control, and estimation tasks. By utilizing machine-learning surrogates, our approach effectively embeds the physics of metabolic networks into the process rates of structurally simpler macro-kinetic models coupled with gene expression. These surrogates, informed by flux balance analysis, link the domains of manipulatable intracellular enzymes to metabolic exchange fluxes. This ensures that critical knowledge captured by the system's metabolic network is preserved. The resulting models can be integrated into metabolic cybergenetic schemes involving single-level optimizations. Additionally, the hybrid modeling approach maintains the number of system states at a necessary minimum, easing the burden of process monitoring and estimation. Our hybrid physics-informed metabolic cybergenetic framework is demonstrated using a computational case study on the optogenetically-assisted production of itaconate by $\textit{Escherichia coli}$.