MOTIVATION: Expanding on constraint-based metabolic models, protein allocation models (PAMs) enhance flux predictions by accounting for protein resource allocation in cellular metabolism. Yet, to this date, there are no dedicated methods for analyzing and understanding the growth-limiting factors in simulated phenotypes in PAMs. RESULTS: Here, we introduce a systematic framework for identifying the most sensitive enzyme concentrations (sEnz) in PAMs. The framework exploits the primal and dual formulations of these models to derive sensitivity coefficients based on relations between variables, constraints, and the objective function. This approach enhances our understanding of the growth-limiting factors of metabolic phenotypes under specific environmental or genetic conditions. Compared to other traditional methods for calculating sensitivities, sEnz requires substantially less computation time and facilitates more intuitive comparison and analysis of sensitivities. The sensitivities calculated by sEnz cover enzymes, reactions and protein sectors, enabling a holistic overview of the factors influencing metabolism. When applied to an Escherichia coli PAM, sEnz revealed major pathways and enzymes driving overflow metabolism. Overall, sEnz offers a computational efficient framework for understanding PAM predictions and unraveling the factors governing a particular metabolic phenotype. AVAILABILITY AND IMPLEMENTATION: sEnz is implemented in the modular toolbox for the generation and analysis of PAMs in Python (PAModelpy; v.0.0.3.3), available on Pypi (https://pypi.org/project/PAModelpy/). The source code together with all other python scripts and notebooks are available on GitHub (https://github.com/iAMB-RWTH-Aachen/PAModelpy).

BACKGROUND: Metabolic coupling of product synthesis and microbial growth is a prominent approach for maximizing production performance. Growth-coupling (GC) also helps stabilizing target production and allows the selection of superior production strains by adaptive laboratory evolution. To support the implementation of growth-coupling strain designs, we seek to identify biologically relevant, metabolic principles that enforce strong growth-coupling on the basis of reaction knockouts. RESULTS: We adapted an established bilevel programming framework to maximize the minimally guaranteed production rate at a fixed, medium growth rate. Using this revised formulation, we identified various GC intervention strategies for metabolites of the central carbon metabolism, which were examined for GC generating principles under diverse conditions. Curtailing the metabolism to render product formation an essential carbon drain was identified as one major strategy generating strong coupling of metabolic activity and target synthesis. Impeding the balancing of cofactors and protons in the absence of target production was the underlying principle of all other strategies and further increased the GC strength of the aforementioned strategies. CONCLUSION: Maximizing the minimally guaranteed production rate at a medium growth rate is an attractive principle for the identification of strain designs that couple growth to target metabolite production. Moreover, it allows for controlling the inevitable compromise between growth coupling strength and the retaining of microbial viability. With regard to the corresponding metabolic principles, generating a dependency between the supply of global metabolic cofactors and product synthesis appears to be advantageous in enforcing strong GC for any metabolite. Deriving such strategies manually, is a hard task, due to which we suggest incorporating computational metabolic network analyses in metabolic engineering projects seeking to determine GC strain designs.