Growth laws and invariants from ribosome biogenesis in lower Eukarya

Eukarya and Bacteria are evolutionarily distant domains of life, which is reflected by differences in their cellular structure and physiology. For example, Eukarya feature membrane-bound organelles such as nuclei and mitochondria, whereas Bacteria have none. The greater complexity of Eukarya renders them difficult to study from both an experimental and theoretical perspective. However, encouraged by a recent experimental result showing that budding yeast (a unicellular eukaryote) obeys the same proportionality between ribosomal proteome fractions and cellular growth rates as Bacteria, we derive a set of relations describing eukaryotic growth from first principles of ribosome biogenesis. We recover the observed ribosomal protein proportionality, and assuming that rRNA synthesis is tightly coupled to ribosomal protein synthesis as in Bacteria, we continue to obtain two growth laws for the number of RNA polymerases synthesizing ribosomal RNA per ribosome in the cell. These growth laws, in turn, reveal two invariants of eukaryotic growth, i.e., quantities predicted to be conserved by Eukarya across growth conditions. The invariants clarify the coordination of transcription and translation kinetics as required by ribosome biogenesis, and link these kinetic parameters to cellular physiology. We demonstrate the application of the relations to the yeast S. cerevisiae and find several predictions from the growth laws to be in good agreement with currently available data. The remaining relations will require additional data for verification. We outline methods to quantitatively deduce several unknown kinetic and physiological parameters based on the invariants. The analysis is not specific to S. cerevisiae and can be extended to other lower (unicellular) Eukarya when data become available. The relations may also have relevance to certain cancer cells which, like bacteria and yeast, exhibit rapid cell proliferation and ribosome biogenesis.