Influence of multiplicative stochastic variation on translational elongation rates

Experimental data indicate that stochastic effects exerted at the level of translation contribute substantially to the variation in abundance of proteins expressed at moderate to high levels. This study analyzes the theoretical consequences of fluctuations in residue-specific elongation rates during translation. A simple analytical framework shows that rate variation during elongation gives rise to protein production rates that consist of sums of products of random variables. Simulations show that because the contribution to total variation of products of random variables greatly exceeds that of sums of random variables, the overall distribution exhibits approximately log-normal behavior. Empirical fits of the data can be satisfied by either sums of log-normal distributions, or sums of log-normal and log-logistic distributions. Elongation rate stochastic variation offers an accounting for a major component of biological variation. The analysis provided here highlights a probability distribution that is a natural extension of the Poisson and has broad applicability to many types of multiplicative noise processes.