Metabolic states with maximal specific rate carry flux through an elementary flux mode

Abstract

Specific product formation rates and cellular growth rates are important maximization targets in biotechnology and microbial evolution. Maximization of a specific rate (i.e. a rate expressed per unit biomass amount) requires the expression of particular metabolic pathways at optimal enzyme concentrations. In contrast to the prediction of maximal product yields, any prediction of optimal specific rates at the genome scale is currently computationally intractable, even if the kinetic properties of all enzymes are available. In the present study, we characterize maximal-specific-rate states of metabolic networks of arbitrary size and complexity, including genome-scale kinetic models. We report that optimal states are elementary flux modes, which are minimal metabolic networks operating at a thermodynamically-feasible steady state with one independent flux. Remarkably, elementary flux modes rely only on reaction stoichiometry, yet they function as the optimal states of mathematical models incorporating enzyme kinetics. Our results pave the way for the optimization of genome-scale kinetic models because they offer huge simplifications to overcome the concomitant computational problems. Database The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at

How fast‐growing bacteria robustly tune their ribosome concentration to approximate growth‐rate maximization

“…However, non-linear protein costs have also been reported [17], possibly as a result of effects related to protein activity rather than production [18]. Secondly, the concentration of each protein should be precisely tuned [16,19]. This has been found for several enzymes in E. coli, [20,21,17,22], Lactococcus lactis [23][24][25] and Saccharomyces cerevisiae [26].…”

Expanding Metabolic Capabilities Using Novel Pathway Designs: Computational Tools and Case Studies

“…If one considers a fixed flux through the metabolic pathway, then minimization of the enzyme mass allocated yields a biologically convenient solution. Particularly in the context of maximum growth rate prediction of microbial cells, there are theoretical results that support the existence of such optimal rates defined by a single EFM . More recently, enzyme‐flux cost minimization (EFCM) has been proposed to rationally explain the trade‐offs between growth rate and yield(s) based on the ECM framework …”

“…Particularly in the context of maximum growth rate prediction of microbial cells, there are theoretical results that support the existence of such optimal rates defined by a single EFM. [70,71] More recently, enzyme-flux cost minimization (EFCM) has been proposed to rationally explain the trade-offs between growth rate and yield(s) based on the ECM framework. [72] Application of ECM has been mostly focused on evaluating alternative metabolic pathways fulfilling known biological functions such as carbon assimilation [20] and efficient carbon conversions.…”

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“…It has recently been shown (Müller et al 2014, Wortel et al 2014) that maximal steady state specific flux is attained in special type of pathway, called an Elementary Flux Mode (EFM). An EFM is a pathway that has a minimal number of enzymes involved: it allows for a balanced flow of metabolism, but this possibility is void if any one of its enzymes is removed from the pathway.…”