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.

On the Types of Bacterial Growth Laws

Volume, mass and envelope surface area of a bacterium are significant parameters of cell development during one bacterial cell cycle. In our previous studies it was shown that during one division cycle cells can encounter the problem of unlimited size growth. Two fundamental types of bacterial growth laws, which were called “exponential” and “linear”, have been identified. Under certain conditions exponentially growing cells encounter the problem of unlimited growth, whereas lineally growing cells don’t. In this study the laws of bacterial size growth were shown to belong exclusively to the linear type. It was demonstrated that this phenomenon is a consequence of the universal principle of storage and transmission of genetic information essential to all living organisms. The bacterial growth laws of exponential type could exist only at the very early stages of cell evolution, when the genetic machinery had not evolved yet into its modern form.