Before revision:  Our results show that if all the rates are modeled as i. i.d. random variables bounded from below by a value B then as the length of the mRNA increases the total protein production converges, with probability one, to a value that depends only on B. This reveals a principle of universality: total protein production is insensitive to many of the details underlying the distribution of the random variables .
After revision:  Our results show that if all the rates are modeled as i. i.d. random variables bounded from below by a value B then as the length of the mRNA increases the total protein production converges, with probability one, to a value that depends only on the of the set of possible values that the random variable may attain. This explains how total protein production is insensitive to many of the details underlying the distribution of the random variables .