Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models

Area of Science:

• Computational Biology
• Systems Biology
• Biochemical Engineering

Background:

• Metabolic models often have numerous parameters, making sensitivity analysis challenging.
• Traditional metabolic control analysis is not directly applicable to constraint-based models due to their optimization formulation.
• A need exists for efficient methods to analyze parameter sensitivity in constraint-based metabolic models.

Purpose of the Study:

• To develop and apply a method for efficiently differentiating optimal solutions of constraint-based metabolic models.
• To calculate sensitivities of reaction fluxes and enzyme concentrations to kinetic parameters in Escherichia coli.
• To demonstrate the utility of this method for parameter estimation and understanding metabolic regulation.

Main Methods:

• Utilizing constrained optimization duality and implicit differentiation to efficiently differentiate optimal solutions.
• Applying the method to an enzyme-constrained metabolic model of Escherichia coli.
• Generalizing the technique to models incorporating thermodynamic and kinetic rate equations.

Main Results:

• Accurate calculation of sensitivities for reaction fluxes and enzyme concentrations, identifying rate-limiting enzymes.
• Significant improvement of genome-wide turnover number estimates for E. coli.
• Demonstrated alignment between predicted metabolite sensitivities and experimental in vivo metabolome changes from gene knockdown studies.

Conclusions:

• Efficient differentiation of constraint-based models provides mathematically precise sensitivity analysis, surpassing traditional methods.
• This technique facilitates gradient-based parameter estimation, enhancing the accuracy of metabolic models.
• The developed method offers a powerful, generalizable approach to analyze metabolic systems and connect computational predictions with experimental data.