  Large-scale simultaneous mRNA translation and the resulting competition for
the available ribosomes has important implications to the cell's functioning
and evolution. Developing a better understanding of the intricate correlations
between these simultaneous processes, rather than focusing on the translation
of a single isolated transcript, should help in gaining a better understanding
of mRNA translation regulation and the way elongation rates affect organismal
fitness. A model of simultaneous translation is specifically important when
dealing with highly expressed genes, as these consume more resources. In
addition, such a model can lead to more accurate predictions that are needed in
the interconnection of translational modules in synthetic biology. We develop
and analyze a general model for large-scale simultaneous mRNA translation and
competition for ribosomes. This is based on combining several ribosome flow
models (RFMs) interconnected via a pool of free ribosomes. We prove that the
compound system always converges to a steady-state and that it always entrains
or phase locks to periodically time-varying transition rates in any of the mRNA
molecules. We use this model to explore the interactions between the various
mRNA molecules and ribosomes at steady-state. We show that increasing the
length of an mRNA molecule decreases the production rate of all the mRNAs.
Increasing any of the codon translation rates in a specific mRNA molecule
yields a local effect: an increase in the translation rate of this mRNA, and
also a global effect: the translation rates in the other mRNA molecules all
increase or all decrease. These results suggest that the effect of codon
decoding rates of endogenous and heterologous mRNAs on protein production is
more complicated than previously thought.
