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

The distribution of cellular resources across bacterial proteins has been quantified through phenomenological growth laws. Here, we describe a complementary bacterial growth law for RNA composition, emerging from optimal cellular resource allocation into ribosomes and ternary complexes. The predicted decline of the tRNA/rRNA ratio with growth rate agrees quantitatively with experimental data. Its regulation appears to be implemented in part through chromosomal localization, as rRNA genes are typically closer to the origin of replication than tRNA genes and thus have increasingly higher gene dosage at faster growth. At the highest growth rates in E. coli, the tRNA/rRNA gene dosage ratio based on chromosomal positions is almost identical to the observed and theoretically optimal tRNA/rRNA expression ratio, indicating that the chromosomal arrangement has evolved to favor maximal transcription of both types of genes at this condition.

Scaling between DNA and cell size governs bacterial growth homeostasis and resource allocation

Bacteria maintain a stable cell size and a certain DNA content through proliferation as described by classic growth laws. How cells behave when this inherent scaling is broken, however, has rarely been interrogated. Here we engineered Escherichia coli cells with extremely low DNA contents using a tunable synthetic tool CRISPRori that temporarily inhibited chromosome replication initiation. A detailed mechanistic model coupling DNA replication, cell growth, and division revealed a fundamental DNA-centric growth law, which was validated by two observations. First, lineage dynamics were robust to large CRISPRori perturbations with division cycles rapidly restoring through a timer mechanism rather than the adder rule. Second, cellular growth transitioned into a linear regime at low DNA-cytoplasm ratios. Experiments and theory showed that in this regime, cellular resource was redirected to plasmid-borne gene expression. Together with the ability of CRISPRori to bi-directionally modulate plasmid copy numbers, these findings suggest a novel strategy for bio-production enhancement.

Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource

The dynamics of a specific consumer-resource model for Daphnia magna is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the model are compared as different parameters involved in the model change. In the case of Gompertz growth law, a new complex dynamic is found as the carrying capacity for the resource population increases. The numerical study is carried out with a second-order scheme that approximates the size-dependent density function for individuals in the consumer population. The numerical method is well adapted to the situation in which the growth rate for the consumer individuals is allowed to change the sign and, therefore, individuals in the consumer population can shrink in size as time evolves. The numerical simulations confirm that the shortage of the resource has, as a biological consequence, the effective shrink in size of individuals of the consumer population. Moreover, the choice of the growth law for the resource population can be selected by how the dynamics of the populations match with the qualitative behaviour of the data.

Cellular perception of growth rate and the mechanistic origin of bacterial growth laws

Cells organize many of their activities in accordance to how fast they grow. Yet it is not clear how they perceive their rate of growth, which involves thousands of reactions. Through quantitative studies of E. coli under exponential growth and during growth transitions, here we show that the alarmone ppGpp senses the rate of translational elongation by ribosomes, and together with its roles in controlling ribosome biogenesis and activity, closes a key regulatory circuit that enables the cell to perceive the rate of its own growth for a broad class of growth-limiting conditions. This perception provides the molecular basis for the emergence of simple relations among the cellular ribosome content, translational elongation rate, and the growth rate, as manifested by bacterial growth laws. The findings here provide a rare view of how cells manage to collapse the complex, high-dimensional dynamics of the underlying molecular processes to perceive and regulate emergent cellular behaviors, an example of dimension reduction performed by the cells themselves.

A unifying autocatalytic network-based framework for bacterial growth laws

Recently discovered simple quantitative relations, known as bacterial growth laws, hint at the existence of simple underlying principles at the heart of bacterial growth. In this work, we provide a unifying picture of how these known relations, as well as relations that we derive, stem from a universal autocatalytic network common to all bacteria, facilitating balanced exponential growth of individual cells. We show that the core of the cellular autocatalytic network is the transcription–translation machinery—in itself an autocatalytic network comprising several coupled autocatalytic cycles, including the ribosome, RNA polymerase, and transfer RNA (tRNA) charging cycles. We derive two types of growth laws per autocatalytic cycle, one relating growth rate to the relative fraction of the catalyst and its catalysis rate and the other relating growth rate to all the time scales in the cycle. The structure of the autocatalytic network generates numerous regimes in state space, determined by the limiting components, while the number of growth laws can be much smaller. We also derive a growth law that accounts for the RNA polymerase autocatalytic cycle, which we use to explain how growth rate depends on the inducible expression of the rpoB and rpoC genes, which code for the RpoB and C protein subunits of RNA polymerase, and how the concentration of rifampicin, which targets RNA polymerase, affects growth rate without changing the RNA-to-protein ratio. We derive growth laws for tRNA synthesis and charging and predict how growth rate depends on temperature, perturbation to ribosome assembly, and membrane synthesis.

Role of protein degradation in growth laws

Growing cells adopt common basic strategies to achieve optimal resource allocation under limited resource availability. Our current understanding of such “growth laws” neglects degradation, assuming that it occurs slowly compared to the cell cycle duration. Here we argue that this assumption cannot hold at slow growth, leading to strong qualitative consequences. We propose a simple framework showing that at slow growth protein degradation is balanced by a fraction of “maintenance” ribosomes. Through a detailed analysis of compiled data, we show how this model is predictive with E. coli data and agrees with S. cerevisiae measurements. Intriguingly, model and data show an increased protein degradation at slow growth, which we interpret as a consequence of active waste management and/or recycling. Our results highlight protein turnover as an underrated factor for our understanding of growth laws across kingdoms.