  In $\textit{Escherichia coli}$ bacterium, the molecular compounds involved in
protein synthesis, messenger RNAs (mRNAs) and ribosomes, show marked
intracellular localization patterns. Yet a quantitative understanding of the
physical principles which would allow one to control protein synthesis by
designing, bioengineering, and optimizing these localization patterns is still
lacking. In this study, we consider a scenario where a synthetic modification
of mRNA reaction-diffusion properties allows for controlling the localization
and stoichiometry of mRNAs and polysomes$\mathrm{-}$complexes of multiple
ribosomes bound to mRNAs. Our analysis demonstrates that protein synthesis can
be controlled, e.g., optimally enhanced or inhibited, by leveraging mRNA
spatial localization and stoichiometry only, without resorting to alterations
of mRNA expression levels. We identify the physical mechanisms that control the
protein-synthesis rate, highlighting the importance of colocalization between
mRNAs and freely diffusing ribosomes, and the interplay between polysome
stoichiometry and excluded-volume effects due to the DNA nucleoid. The
genome-wide, quantitative predictions of our work may allow for a direct
verification and implementation in cell-biology experiments, where localization
patterns and protein-synthesis rates may be monitored by fluorescence
microscopy in single cells and populations.
