Fast uncertainty quantification for dynamic flux balance analysis using non-smooth polynomial chaos expansions

Area of Science:

• Systems Biology
• Computational Biology
• Biotechnology

Background:

• Dynamic flux balance analysis (DFBA) models are crucial for understanding cellular metabolism but are computationally intensive.
• Uncertainty quantification (UQ) in nonlinear, non-smooth biological models presents significant computational challenges.
• Existing methods struggle with the discrete events and singularities inherent in DFBA models.

Purpose of the Study:

• To introduce a novel surrogate modeling method, non-smooth polynomial chaos expansion (nsPCE), for accelerating UQ in complex biological models.
• To address the computational expense and unique challenges of UQ in DFBA models, particularly those with discrete events.
• To demonstrate the effectiveness and scalability of nsPCE for UQ tasks in metabolic network modeling.

Main Methods:

• Developed nsPCE, an extension of traditional PCE, to handle singularities in DFBA model responses by partitioning the parameter space.
• Employed a basis-adaptive sparse regression approach for fitting PCE models within partitioned parameter spaces.
• Applied nsPCE to a large-scale DFBA model of E. coli and a synthetic metabolic network.

Main Results:

• Traditional PCE failed to handle the complexity of the DFBA model, while nsPCE effectively captured singularities.
• Achieved over 800-fold computational cost savings for uncertainty propagation and parameter estimation using nsPCE surrogates.
• Demonstrated the scalability of nsPCE for global sensitivity analysis and Bayesian estimation in larger metabolic models.

Conclusions:

• nsPCE offers a computationally efficient and accurate solution for UQ in complex, non-smooth biological models like DFBA.
• The method significantly reduces the computational burden of analyzing metabolic networks, enabling more extensive investigations.
• nsPCE is a scalable approach suitable for advanced UQ tasks, including sensitivity analysis and parameter estimation in large biological systems.