  Eukarya and Bacteria are the most 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 then
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 regardless of growth conditions. The invariants, which
are the first of their kind for Eukarya, clarify the coordination of
transcription and translation kinetics as required by ribosome biogenesis, and
link these kinetic parameters to cellular physiology. We demonstrate
application of the relations to the yeast S. cerevisiae and find the
predictions to be in good agreement with currently available data. We then
outline methods to quantitatively deduce several unknown kinetic and
physiological parameters. 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.
