Conditions for Exponential Growth in a Ribosome Biosynthesis Model Across Multiple Scales

Ribosome biosynthesis is essential for cell growth because it provides the molecular machinery necessary for protein production. Proteins constitute about 50% of total dry biomass, and ribosomes (comprising 60% RNA and 40% proteins) can make up as much as 30% of dry biomass. Since ribosome biogenesis requires significant energy, cells must carefully regulate their production based on growth conditions. Starting from a simplified model of ribosome biosynthesis that explicitly accounts for the dynamics of ribosomal subunits and their shared precursor, we identify specific parameter conditions that ensure exponential growth and derive a closed-form expression for the growth rate. These findings extend previous results obtained according to simplifying constraints, offering a more detailed understanding of ribosome biosynthesis dynamics without approximations. By integrating the ribosome biosynthesis module into a multi-scale population model of Saccharomyces cerevisiae metabolism, growth, and cell cycle, we assess the biological relevance of our analysis, demonstrating consistency between intracellular ribosome production constraints and population-level growth behavior.