A unifying autocatalytic network-based framework for bacterial growth laws

Abstract

Significance Bacterial cells contain various autocatalytic cycles, e.g., the ribosome cycle, where ribosomes translate ribosomal proteins that subsequently self-assemble to form new ribosomes. Here, we show that the transcription–translation machinery couples all cellular autocatalytic cycles, resulting in balanced exponential growth. Each autocatalytic cycle generates two types of growth laws. We derive the RNA polymerase (RNAP) growth law based on the RNAP autocatalytic cycle, where RNAPs transcribe messenger RNAs (mRNAs) of its constituent Rpo protein subunits. Before degrading, these mRNAs catalyze Rpo proteins employing ribosomes. The Rpo proteins subsequently self-assemble, forming new RNAPs, thus completing the cycle. Contrary to ribosome growth law, a reduction in growth rate due to shortage in RNAPs occurs without affecting the ribosomal protein mass fraction. 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.