On the optimality of the enzyme–substrate relationship in bacteria

Abstract

Much recent progress has been made to understand the impact of proteome allocation on bacterial growth; much less is known about the relationship between the abundances of the enzymes and their substrates, which jointly determine metabolic fluxes. Here, we report a correlation between the concentrations of enzymes and their substrates in Escherichia coli. We suggest this relationship to be a consequence of optimal resource allocation, subject to an overall constraint on the biomass density: For a cellular reaction network composed of effectively irreversible reactions, maximal reaction flux is achieved when the dry mass allocated to each substrate is equal to the dry mass of the unsaturated (or “free”) enzymes waiting to consume it. Calculations based on this optimality principle successfully predict the quantitative relationship between the observed enzyme and metabolite abundances, parameterized only by molecular masses and enzyme–substrate dissociation constants (Km). The corresponding organizing principle provides a fundamental rationale for cellular investment into different types of molecules, which may aid in the design of more efficient synthetic cellular systems.

An optimal growth law for RNA composition and its partial implementation through ribosomal and tRNA gene locations in bacterial genomes

“…Cellular dry mass density appears to be approximately constant across conditions [ 42 , 43 ]. Dry mass may thus be considered a limiting resource [ 9 , 39 ] if the dry mass density is occupied by one particular molecule, less will be available for all other molecules. In terms of dry mass allocation, translation is the most expensive process in fast-growing bacteria [ 2 , 44 ].…”

“…Here, we consider a much simpler representation of the elongation step of protein translation, which can be modeled as an enzymatic reaction following Michaelis-Menten kinetics [5]. In this case, the minimization of the combined mass concentration of ribosome and TC can be performed analytically, as demonstrated by Dourado et al [9]; following this work, we here briefly summarized the derivation of the optimal TC/ribosome expression ratio.…”

“…These laws have been successfully applied to the prediction of a range of phenotypic observations [3,[5][6][7][8]. Recently, it has been argued that they arise from an optimal balance between the cellular investment into catalytic proteins and their substrates [9].…”

“…rRNA forms the central part of the catalyst of peptide elongation, while tRNA forms the core of the substrate; together, they account for the bulk of cellular RNA [2]. Their cytosolic concentrations at different growth rates in E. coli are well described by an optimality assumption [9,38,39]. Moreover, chromosomal gene positions in E. coli are known to affect the expression of both tRNA and rRNA genes [40,41]; both types of genes are located closer to oriC in fast-compared to slow-growing bacteria, with rRNA genes positioned closer to oriC than tRNA genes in most examined fast-growing bacteria [29].…”

“…Their cytosolic concentrations at different growth rates in E . coli are well described by an optimality assumption [ 9 , 38 , 39 ]. Moreover, chromosomal gene positions in E .…”