Simulation and optimization of dynamic flux balance analysis models using an interior point method reformulation

Abstract

This work presents a novel, differentiable, way of solving dynamic Flux Balance Analysis (dFBA) problems by embedding flux balance analysis of metabolic network models within lumped bulk kinetics for biochemical processes. The proposed methodology utilizes transformation of the bounds of the embedded linear programming problem of flux balance analysis via a logarithmic barrier (interior point) approach. By exploiting the first-order optimality conditions of the interior-point problem, and with further transformations, the approach results in a system of implicit ordinary differential equations. Results from four case studies, show that the CPU and wall-times obtained using the proposed method are competitive with existing state-of-the art approaches for solving dFBA simulations, for problem sizes up to genome-scale. The differentiability of the proposed approach allows, using existing commercial packages, its application to the optimal control of dFBA problems at a genome-scale size, thus outperforming existing formulations as shown by two dynamic optimization case studies.

Multi-omics Study of Planobispora rosea, Producer of the Thiopeptide Antibiotic GE2270A

“…This method assumes that bacterial metabolism reaches an internal steady state almost immediately after a change in the extracellular environment. This allows the update of the extracellular concentrations based on the exchanges predicted by the model, which in turn update the uptake rates of the substrates needed for growth ( 49 , 50 ). In this experiment, we considered a minimal medium where glucose is the only source of carbon (initial concentration, 222.2 mmol/liter), the initial concentration of inorganic phosphate is relatively low (4.6 mmol/liter), and the initial biomass concentration is 0.5 gDW/liter where gDW stands for grams in dry weight.…”

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

“…No ethanol production is observed under aerobic conditions (i.e., this phase is mainly used to increase the biomass), such that the concentration of ethanol can be omitted from the dynamics. This case study is commonly used as a benchmark for comparing DFBA solvers (see, e.g., [16, 27, 31]), as it exhibits stiff dynamics and multiple singularities.…”

“…However, the most commonly used UQ methods are intractable for expensive-to-evaluate computational models [15], which has severely limited their application to DFBA models. An overview of the various challenges in DFBA simulations can be found in [16].…”

Combining Kinetic and Constraint-Based Modelling to Better Understand Metabolism Dynamics

“…This method is also less computationally demanding compared to the DOA approach as the optimisation is done locally. However, new approaches are still presented to include more constraints such as nonlinear objective function [45] or linear kinetic constraints [46] or to improve the computation of the simulations [47,48].…”