The genetic information in DNA is transcribed to mRNA and then translated to proteins, which form the building blocks of life. Translation, or protein synthesis, is hence a central cellular process that is well conserved among all living organisms. Translation is essentially a polymerization process facilitated by the ribosome on an mRNA template consisting of initiation, elongation, and termination phases, and the term polysome refers to the structure consisting of several ribosomes simultaneously translating the same mRNA. A better understanding of protein synthesis is of great importance in many areas of medicine and biotechnology. For instance, many antibiotics function by inhibiting bacterial translational machinery, and translational malfunction has been implicated in cancer cell proliferation. Decades of experimentation have elucidated a wealth of molecular information about the discrete elementary mechanistic steps of translation. However, the sheer complexity of the translation mechanism necessitates that these results be integrated in a systematic framework to better understand system properties of protein synthesis and make quantitative predictions. We have developed a gene sequence specific mechanistic model for the translation machinery which accounts for all the elementary steps of the translation mechanism. Specifically, our model includes all the elementary steps involved in the elongation cycle at every codon along the length of the mRNA. We performed a sensitivity analysis in order to determine the effects of kinetic parameters and concentrations of the translational components on protein synthesis rate. Utilizing our mathematical framework and sensitivity analysis, we investigated the translation kinetic properties of a single mRNA species in E. coli. We propose that translation rate at a given polysome size depends on the complex interplay between ribosomal occupancy of elongation phase intermediate states and ribosome distributions with respect to codon position along the length of the mRNA, and this interplay leads to polysome self-organization that drives translation rate to maximum levels. Our results have implications in design of rational protein production systems, wherein quantitative knowledge of responses of protein expression to genetic or environmental perturbations can be used to optimize a cellular system towards the production of a protein of interest.