  The sequence of amino acid monomers in the primary structure of a protein is
decided by the corresponding sequence of codons (triplets of nucleic acid
monomers) on the template messenger RNA (mRNA). The polymerization of a
protein, by incorporation of the successive amino acid monomers, is carried out
by a molecular machine called ribosome. We develop a stochastic kinetic model
that captures the possibilities of mis-reading of mRNA codon and prior
mis-charging of a tRNA. By a combination of analytical and numerical methods we
obtain the distribution of the times taken for incorporation of the successive
amino acids in the growing protein in this mathematical model. The
corresponding exact analytical expression for the average rate of elongation of
a nascent protein is a `biologically motivated' generalization of the {\it
Michaelis-Menten formula} for the average rate of enzymatic reactions. This
generalized Michaelis-Menten-like formula (and the exact analytical expressions
for a few other quantities) that we report here display the interplay of four
different branched pathways corresponding to selection of four different types
of tRNA.
