The protein cost of metabolic fluxes: prediction from enzymatic rate laws and cost minimization

TL;DR

This paper introduces enzyme cost minimization (ECM), a scalable convex optimization method that predicts enzyme amounts and costs supporting metabolic fluxes, integrating enzyme kinetics and thermodynamics for better metabolic modeling.

Contribution

The paper presents ECM, a novel convex optimization framework that accurately predicts enzyme levels and costs, incorporating thermodynamics and enzyme kinetics into metabolic models.

Findings

ECM predicts enzyme levels with a fold error of 3.8.

ECM predicts protein costs with a fold error of 2.7.

Validated with E. coli data, demonstrating accuracy and applicability.

Abstract

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.