A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic
Steffen Klamt1, Stefan Müller2, Georg Regensburger3
1Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.
Metabolic Engineering
|February 11, 2018
Summary
This study introduces a new mathematical framework for optimizing metabolic yields in cellular models. This approach enables accurate prediction of yield-optimal flux distributions, crucial for metabolic engineering and biotechnology.
Area of Science:
- Metabolic Engineering
- Systems Biology
- Computational Biology
Background:
- Flux-balance analysis (FBA) is standard for genome-scale metabolic models, optimizing metabolic rates as linear objectives.
- Metabolic yields, crucial for biotechnology, are ratios of rates and cannot be optimized using current FBA techniques due to nonlinear objective functions.
- A comprehensive mathematical framework for yield optimization in constraint-based modeling is currently lacking.
Purpose of the Study:
- To develop a systematic mathematical theory for computing and analyzing yield-optimal solutions in metabolic models.
- To address the limitations of current FBA techniques in optimizing nonlinear yield objectives.
- To provide a framework for understanding and predicting yield-optimal flux distributions.
Main Methods:
- Formulated yield optimization as a linear-fractional program.
- Transformed the linear-fractional problem into a higher-dimensional linear problem for practical computation.
- Analyzed the linear-fractional problem directly for theoretical insights.
- Investigated yield-optimal elementary flux vectors and their relation to rate-optimal solutions.
Main Results:
- Presented a novel mathematical theory enabling systematic computation and analysis of yield-optimal solutions.
- Demonstrated that yield-optimal solutions are determined by yield-optimal elementary flux vectors.
- Showed that yield- and rate-optimal solutions can differ, meaning optimal yields are not always achieved at optimal rates.
- Proved yield spaces are convex and provided algorithms for their computation, illustrated with E. coli models.
Conclusions:
- Developed a comprehensive mathematical framework for yield optimization in metabolic models.
- The framework is valuable for studying and rationally modifying cell factories based on yield and/or rate requirements.
- This work advances constraint-based modeling for biotechnological applications and metabolic engineering.
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