A coarse-grain model for cellular growth accounting for ribosome synthesis

Protein synthesis in eukaryotes is carried out by ribosomes, large RNA-protein complexes consisting of a small and a large subunit. In this work we present a mathematical model for cellular growth comprising both protein production and ribosome synthesis, properly accounting for both small and large subunits dynamics. The qualitative analysis of the model is carried out according to a simplifying assumption on the proportion of the two ribosomal subunits in stationary growth conditions; such hypothesis is based on a reasonable biological ground. Conditions are given on the model parameters in order to ensure exponential growth and the corresponding growth rate is straightforwardly computed from the model parameters. These results are validated by numerical simulations carried out according to a set of biologically meaningful model parameters. The modified model is better suited to host molecular blow-up of ribosomal synthesis and cell growth within a modular whole-cell model able to act as a scaffold connecting metabolism, growth and cycle.