  Efficient protein synthesis depends on the availability of charged tRNA
molecules. With 61 different codons, shifting the balance among the tRNA
abundances can lead to large changes in the protein synthesis rate. Previous
theoretical work has asked about the optimization of these abundances, and
there is some evidence that regulatory mechanisms bring cells close to this
optimum, on average. We formulate the tradeoff between the precision of control
and the efficiency of synthesis, asking for the maximum entropy distribution of
tRNA abundances consistent with a desired mean rate of protein synthesis. Our
analysis, using data from E. coli, indicates that reasonable synthesis rates
are consistent only with rather low entropies, so that the cell's regulatory
mechanisms must encode a large amount of information about the "correct" tRNA
abundances.
