Ribosome Composition Maximizes Cellular Growth Rates in E. coli

Bacterial ribosomes are composed of one-third protein and two-thirds RNA by mass. The predominance of RNA is often attributed to a primordial RNA world, but why exactly two-thirds remains a long-standing mystery. Here we present a quantitative analysis, based on the kinetics of ribosome self-replication, demonstrating that the $1:2$ protein-to-RNA mass ratio uniquely maximizes cellular growth rates in E. coli. A previously unrecognized growth law, and an invariant of bacterial growth, also follow from our analysis. The growth law reveals that the ratio between the number of ribosomes and the number of polymerases making ribosomal RNA is proportional to the cellular doubling time. The invariant is conserved across growth conditions and specifies how key microscopic parameters in the cell, such as transcription and translation rates, are coupled to cellular physiology. Quantitative predictions from the growth law and invariant are shown to be in excellent agreement with E. coli data despite having no fitting parameters. Our analysis can be readily extended to other bacteria once data become available.

Figure 1

Autocatalytic production of the ribosome. Bacterial ribosomes are composed of two-thirds RNA (gray) and one-third protein (blue) by mass. r-protein is synthesized directly by ribosomes, as illustrated by the blue autocatalytic loop on the right. rRNA is synthesized by RNA polymerases, symbolized by the top left gray arrow. RNA polymerases, in turn, are made of protein that is synthesized by ribosomes (bottom left blue arrow). These autocatalytic processes impose counteracting bounds on cellular growth. In E. coli they are mutually satisfied when protein constitutes one-third the ribosome mass, thereby maximizing growth rates in various conditions.

Figure 2

Upper bounds imposed on cellular growth rate by r-protein and rRNA production for two hypothetical cases (blue and orange). The bounds from Eq. (5) monotonically increase with ribosome protein mass fraction, while the bounds from Eq. (2) monotonically decrease. Accessible cellular growth rates lie in the shaded regions below the bounds. The intersection of similarly colored curves corresponds to the joint optimization of r-protein and rRNA production and gives the maximal accessible growth rate. The ribosome composition corresponding to this maximal growth rate can, in principle, be either RNA-rich (blue) or protein-rich (orange).

Figure 3

rRNA processing in E. coli. Ribosomes in E. coli have 4566 nucleotides from three rRNA molecules: the 23S (2904 nts), 16S (1542 nts), and 5S (120 nts). To produce them, an RNA polymerase transcribes the DNA rrn operon into a precursor rRNA of approximately 5400 nts [22]. This pre-rRNA encodes for three rRNA molecules (totaling 4566 nts) and at least one tRNA molecule (82 nts), along with $\sim 700$ flanking nucleotides [12]. The flanking nucleotides are cleaved and trimmed by various ribonucleases in the cell, yielding the 23S, 16S, and 5S rRNAs which go into mature ribosomes.

Figure 4

Ribosome composition maximizes cellular growth rates in E. coli. (a) The r-protein and rRNA bounds from Eqs. (2) and (5) are plotted as a function of the protein mass fraction of the ribosome, for E. coli in six different growth media. Data are publicly available [6, 20] (Table S1 [12]). (b) The envelopes of allowed growth rates as obtained from the minimum of the two bounds in (a). The maximal growth rate allowed occurs at the cusp, i.e., where bounds intersect. It can be seen that this always happens at a protein mass fraction of about one-third which closely resembles that of the bacterial ribosome (dashed black line). (c) The theoretical prediction of Eq. (6) (solid line) is in excellent agreement with several E. coli datasets [5, 6, 7] (symbols, Tables S1–S3 [12]). (d) The theoretical prediction of Eq. (7) (solid line), is in excellent agreement with data for E. coli grown in six different media (blacked-rimmed circles) [6]. (e) Agreement between the left-hand side (solid black line) and right-hand side (black-rimmed circles) of Eq. (8) is shown for E. coli data. As expected, invariance with respect to growth conditions is observed.