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

TL;DR

The paper addresses the bottleneck of bilevel optimization in constraint-based metabolic control by introducing a hybrid physics-informed dynamic framework. It couples gene-expression dynamics to metabolic fluxes through neural surrogates trained on flux balance analysis, producing a physics-informed, single-level model with a reduced state count. The approach enables model predictive control and state estimation for metabolic cybergenetics and is validated in a computational case study of optogenetically driven itaconate production in E. coli, showing improved titers and resource utilization under uncertainty. This framework offers a tractable, physics-aware pathway to real-time, feedback-driven metabolic engineering with practical implications for bioprocess optimization and design.

Abstract

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 $\textit{Escherichia coli}$.

Figures (9)

• Figure 1: Scheme of a metabolic cybergenetic control system. Optimal system inputs are obtained through computational methods such as dynamic optimization. These external input signals modulate the expression of metabolic enzymes and thereby metabolic fluxes. Closed-loop control is implemented by incorporating state feedback and re-optimizing the system. Optionally, if not all the state information can be measured, soft sensors in the form of state estimators can be employed to reconstruct the system state. The dynamic model can contain prior knowledge such as physics (e.g., metabolic networks) and phenomenological relations (e.g., kinetic functions), which can either be modeled explicitly or indirectly via machine-learning surrogates. Process data can also be used to capture certain parts of the model using machine learning.
• Figure 2: Flow diagram showing the interdependence of the external inputs and the dynamic states of the proposed hybrid physics-informed cybergenetic model for (a) prokaryotic and (b) eukaryotic cells. Refer to the text for details on the notation.
• Figure 3: Flow diagram of our integrated hybrid physics-informed dynamic modeling and control strategy for metabolic cybergenetics. Details on steps 1 and 2 are provided in Section \ref{['sec:hyb_pi_mod']}, while details on steps 3 and 4 are provided in Section \ref{['sec:contol_est']}.
• Figure 4: Scheme of E. coli vOpt for itaconate biosynthesis. We represent gene deletions with red crosses. We indicate in italics genes encoding relevant enzymes. Orange dotted arrows denote metabolic exchange reactions. The green arrow with a resistor shape represents the reaction associated with the light-inducible cis-aconitate decarboxylase. $v_i \in \mathbb{R}$ denotes the metabolic exchange flux of the external species $i$.
• Figure 5: (a) Changes of metabolic exchange fluxes with varying intracellular cis-aconitate decarboxylase concentration predicted by the FBA model. (b) Solution space of the yield trade-off between itaconate and biomass synthesis from the exploration with FBA. glc: glucose, ita: itaconate, bio: biomass, ace: acetate, cadA: cis-aconitate decarboxylase.