A cell growth model accounting for both ribosomal sub-units synthesis: conditions for the exponential growth

Ribosomes play a pivotal role in cell growth, since they are deputed to build amino acids for proteins assembly. Ribosomes consist of a small and a large sub-unit, whose binding occurs on mRNA strands. Both small and large sub-units origin from a common precursor of rRNA. In this note we propose a novel model of cell growth explicitly dealing with small and large ribosomal sub-units, as well as with their common precursor. Proteins are also included, since it is known they exert a control feedback on ribosome biogenesis: the modeling assumption is that the precursor synthesis is switched off when the ribosome-over-protein ratio exceeds a given threshold. The qualitative analysis of the proposed model is carried out with the aim of showing that there exist conditions on the model parameters according to which the exponential growth is ensured, that means all the state variables have an exponential time law, all sharing the same (positive) exponential growth rate. The model parameters have been assessed in order to provide meaningful time evolution of all the molecular players involved, and to result consistent with an existing, less complex model of cellular growth accounting for only ribosomes and proteins, recently exploited as a growth module inside a scaffold whole-cell model connecting metabolism, growth and cycle for the budding yeast Saccharomyces cerevisiae, the experimental model usually exploited for eukaryotic cells.