Enzyme Multicollinearity in Genome-Scale Metabolic Models Revealed By an Efficient Coupling Algorithm

Numerous reactions control bacterial behavior and homeostasis. Dimensionality reduction is often necessary to analyze COBRA models, especially non-convex models that require intensive computations. One method to reduce networks is to identify reactions with colinear, or fully coupled, fluxes. In a COBRA model, coupled reactions can be identified using the Flux-Coupling Finder (FCF) algorithm. However, identification of coupled reaction sets is not as useful as identification of coupled enzyme sets, since enzymes are targets of metabolic engineering and drug discovery efforts. To calculate coupling between enzymes, we developed a mathematical transformation linking reaction fluxes and enzyme activity while preserving the nonlinear mapping between genes, proteins, and reactions. This framework, called Flux and Activity Linked Constraints (FALCON) expands the original linear program to a larger mixed-integer linear program (MILP). Although solving MILPs requires significantly more computational power, we developed an efficient variant of FCF (cached-FCF) that drastically reduces the runtime required to identify couplings in both COBRA and FALCON models.

We tested cached-FCF on the FALCON model for the bacterium Pseudomonas aeruginosa. We discovered that the enzymes in coupled sets showed significantly higher correlation of expression and fitness than sets of enzymes created from sets of coupled reactions. The coupled enzyme sets form the functional units of the organism’s metabolic network. We further tested the effects of perturbing the metabolic network with single-gene knockouts. We observed that gene deletions force additional couplings among enzyme sets. These additional couplings link enzyme sets with similar expression or fitness patterns.