Optimal density of bacterial cells

Abstract

A substantial fraction of the bacterial cytosol is occupied by catalysts and their substrates. While a higher volume density of catalysts and substrates might boost biochemical fluxes, the resulting molecular crowding can slow down diffusion, perturb the reactions’ Gibbs free energies, and reduce the catalytic efficiency of proteins. Due to these tradeoffs, dry mass density likely possesses an optimum that facilitates maximal cellular growth and that is interdependent on the cytosolic molecule size distribution. Here, we analyse the balanced growth of a model cell with metabolic and ribosomal reactions, accounting systematically for crowding effects on reaction kinetics. We find that changes in cytosolic density affect biochemical efficiency more strongly for ribosomal reactions than for metabolic reactions, which involve much smaller catalysts and reactants. Accordingly, optimal cytosolic density depends on cellular resource allocation into ribosomal vs. metabolic reactions. A shift in the relative contributions of these sectors to the cellular economy explains the 10% difference in the cytosolic density between E. coli bacteria growing in nutrient-rich and -poor environments. We conclude that cytosolic density variation in E. coli is consistent with an optimality principle of cellular efficiency.Significance statementThe cellular cytosol harbours diverse molecules, whose crowding slows down diffusion and perturbs the chemical equilibrium of biochemical reactions. Reaction rates thus depend not only on the reactants themselves, but also on the background density of other molecules; consequently, maximal cell growth requires an optimal density. Here, we simulate a model cell with crowding-adjusted metabolic reaction kinetics. Its cytosol accommodates two types of reactions: metabolic reactions involving small molecules, and protein production reactions involving much larger molecules. These two cellular subsystems have distinct optimal densities, and a shift in their relative contribution to the cellular biomass explains the 10% difference in the cytosolic density between E. coli bacteria growing in nutrient-rich and -poor environments.

On the optimality of the enzyme–substrate relationship in bacteria

“…Previous studies have independently focused on 2 different types of concentration bounds: (ii) a limit on the volume concentrations of large molecules such as proteins, DNA, and RNA, termed “macromolecular crowding” [ 3 , 20 ]; and (iii) a limit on the molar concentration of small molecules, ensuring the maintenance of internal osmolarity [ 37 , 38 ]. While the exact mechanisms connecting these 3 different types of concentration bounds are not currently understood and still require further investigation, a recent theoretical study indicates that large and small molecules jointly interfere with intracellular diffusion and the Gibbs free energies of reactions, resulting in an optimal combined mass density: At lower concentrations, enzymes are not sufficiently saturated with their substrates, while at higher concentrations, the slow down of diffusion limits the substrate supply [ 39 ]. The study’s estimate of the optimal dry mass density was highly consistent with observed values in E .…”

Resource allocation in biochemically structured metabolic networks

“…However, literature estimates of the cellular protein mass density vary, and we can not exclude that the composition of the cell varies under nutrient limitation which may lead to a modified biosynthetic protein density at constant dry mass density, or exclude that cellular dry mass density changes within the margins of experimental accuracy. A recent study has proposed potential underlying mechanisms to a constant intracellular protein density based on a model of cellular self-replication similar to the one we present here (67). Simultaneous optimization of protein density and proteome allocation under a nutrient limitation may be feasible but lies beyond the scope of this paper.…”

Growth Mechanics: General principles of optimal cellular resource allocation in balanced growth

“…In the following discussion, we assume that the kinetic rate laws do not depend on the total protein concentration c a , meaning for all reactions l . That would be different if, for example, one accounts for the macromolecular crowding effects via kinetic rate laws (30). The indirect elasticities E and direct elasticities ε share some resemblance with the Jacobian and elasticity matrices defined in Metabolic Value Theory and MCA, although we do not intend to explore the exact relationships in this work.…”

“…A higher dry mass density increases the “crowding effect” within cells (25), which entails a lower diffusion rate and by consequence a longer time for reactants to find their catalysts; this effect can be modeled directly by including a corresponding dependence in the Michaelis constants K m . A study on the crowding effects of all cellular concentrations – including those of small molecules – found that the observed E. coli dry mass density is in the range expected if evolution had optimized the cellular density for maximal growth rate (30). In this sense, a fixed density constraint on all molecules, as considered here, may be seen as a simplifying approximation, justified by the observed constancy of cellular buoyant and dry mass densities across different growth conditions (24, 48), with the exception only of large changes in environmental osmolarities (25).…”