  Bacterial growth depends crucially on metabolic fluxes, which are limited by
the cell's capacity to maintain metabolic enzymes. The necessary enzyme amount
per unit flux is a major determinant of metabolic strategies both in evolution
and bioengineering. It depends on enzyme parameters (such as kcat and KM
constants), but also on metabolite concentrations. Moreover, similar amounts of
different enzymes might incur different costs for the cell, depending on
enzyme-specific properties such as protein size and half-life. Here, we
developed enzyme cost minimization (ECM), a scalable method for computing
enzyme amounts that support a given metabolic flux at a minimal protein cost.
The complex interplay of enzyme and metabolite concentrations, e.g. through
thermodynamic driving forces and enzyme saturation, would make it hard to solve
this optimization problem directly. By treating enzyme cost as a function of
metabolite levels, we formulated ECM as a numerically tractable, convex
optimization problem. Its tiered approach allows for building models at
different levels of detail, depending on the amount of available data.
Validating our method with measured metabolite and protein levels in E. coli
central metabolism, we found typical prediction fold errors of 3.8 and 2.7,
respectively, for the two kinds of data. ECM can be used to predict enzyme
levels and protein cost in natural and engineered pathways, establishes a
direct connection between protein cost and thermodynamics, and provides a
physically plausible and computationally tractable way to include enzyme
kinetics into constraint-based metabolic models, where kinetics have usually
been ignored or oversimplified.
