Sensitivities in protein allocation models reveal distribution of metabolic capacity and flux control.

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).