Bacterial growth laws and their applications

Abstract

Quantitative empirical relationships between cell composition and growth rate played an important role in the early days of microbiology. Gradually, the focus of the field began to shift from growth physiology to the ever more elaborate molecular mechanisms of regulation employed by the organisms. Advances in systems biology and biotechnology have renewed interest in the physiology of the cell as a whole. Furthermore, gene expression is known to be intimately coupled to the growth state of the cell. Here, we review recent efforts in characterizing such couplings, particularly the quantitative phenomenological approaches exploiting bacterial 'growth laws.' These approaches point toward underlying design principles that can guide the predictive manipulation of cell behavior in the absence of molecular details.

Figure 1

Bacterial growth laws: A. When growth is modulated by changes in nutrient quality, the RNA mass fraction r (proportional to the ribosomal content) of E. coli increases linearly with growth rate γ (solid line): r = r₀ +γ/κ_t, where the parameter κ_t is related to the translation rate [8^••], and r₀ is the offset. When growth is modulated by changes in translational efficiency, a conjugate relation is observed. The RNA mass fraction is inversely related to growth rate (dashed lines): r = r_max −γ/κ_n, where the parameter κ_n describes the nutrient quality of the growth medium, and r_max is the maximum allocation to ribosomal synthesis in the limit of complete translational inhibition. B. Symmetric linear relations are observed in the mass fraction of a constitutively expressed protein, implying a linear constraint between ribosome-affiliated and constitutive proteins. C. The simplest constraint is a three-component partition of the proteome: a fixed fraction that is invariant to growth-rate change (blue), ribosome and ribosome-affiliated proteins (green) and the remainder (pink), including constitutive proteins. For E. coli K-12 MG1655, the fixed fraction appears to occupy roughly half of the protein fraction [8^••].

Figure 2

Analogy with Kirchoff's law: The Monod-like relation for growth, Eq. (2), is mathematically identical to the description of electric current flow through a pair of resistors connected in series to a battery with voltage (1−ϕ_fixed). In this analogy, the growth rate γ is the current through the resistors. The translation- and nutrient- modes of growth limitation correspond to changing the conductance of one of the resistors, while the expression of unnecessary protein corresponds to changing the applied voltage by increasingϕ_fixed (see Fig. 3A).

Figure 3

Some applications of the growth laws: A. The burden of protein overexpression. Expression of an unnecessary protein (orange) effectively decreases the fraction allocable to the protein sectors responsible for protein synthesis (green) and nutrient uptake/processing (pink), leading to a decrease in the growth rate [8^••]. B. Growth-mediated feedback. Constitutive expression of a toxin affecting nutrient influx (R) could lead to bistability through positive feedback generated by the interdependence of gene expression levels and growth rate (dotted line). A decrease in growth rate under conditions of nutrient limitation results in an increase in the constitutively expressed toxin R, reinforcing further growth rate reduction [7^•].