Coupled ribosome allocation and nutrient sensing lead to incoherent feedback and oscillatory response in bacterial growth

Current theories describing bacterial growth physiology across environments have demonstrated an impressive predictive power, but they are typically phenomenological. Incorporating mechanistic details into these frameworks remains an open challenge that would greatly improve our ability to predict and control bacterial growth in varying environmental conditions. For example, the “Flux Controlled Regulation” (FCR) model is a reference out-of-equilibrium framework that links ribosome allocation to translation efficiency by means of a steady-state assumption. By making use of this assumption, this model does not account for ppGpp-mediated nutrient sensing and transcriptional regulation of ribosomal operons. In this study, we propose a simple model that integrates the FCR framework with a mechanistic description of three key components: (i) the amino-acid pool, (ii) ppGpp sensing of translation elongation rate, and (iii) transcriptional programming of protein allocation strategy by ppGpp-sensitive promoters. Our framework is fully coherent with observed steady-state growth laws and makes testable predictions for unobserved quantities. Furthermore, our theory predicts that under environmental changes the incoherent feedback between sensing and regulation leads to oscillatory relaxation towards new equilibria, a feature observed experimentally but not captured by previous phenomenological models. SIGNIFICANCE STATEMENT Existing theories that explain cellular growth by considering resource allocation do not provide mechanistic details connecting the nutrient precursors pools, the sensing process responsible for allocation and the allocation process itself. Instead, these theories view growth as an outcome of either flux balance or resource optimization, neglecting finer mechanistic aspects. An outstanding challenge is to describe mechanistically how resource allocation at the proteome level is implemented by regulatory circuits that can sense the environment and regulate protein synthesis accordingly. This study focuses on E. coli bacteria and proposes a theoretical frame-work based on contemporary formalisms that includes the description of the sensing and the regulation of protein synthesis at the mRNA level. Intriguingly, the interplay between sensing and regulatory architecture gives rise to oscillatory adaptation to environmental changes, which emerges in experiments but remains not well characterized. ### Competing Interest Statement The authors have declared no competing interest.