Efficiency of Protein Production from mRNA

Adapting arguments from queuing theory, we investigate a mathematical model for protein production efficiency from mRNA. Our model involves six parameters: the mRNA length, the clearance distance a ribosome must travel from the initiation site before another ribosome can attach, the ribosomal attachment rate, the ribosomal traveling speed along the mRNA, the mRNA degradation rate, and the probability that a ribosome prematurely disengages from the mRNA. The model allows for different mechanisms of mRNA degradation; the more complicated mechanisms postulate a functional role for the mRNA poly A tail. We determine the probability generating function of the number N of fully formed proteins from a single mRNA. This function yields the moments of N exactly and the entire distribution of N numerically via the finite Fourier transform. Using biologically plausible estimates, we examine the sensitivity of protein production to the model parameters and degradation mechanisms. Model predictions are most sensitive to the degradation and attachment rates, two parameters which are poorly measured in vivo. AMS Subjection Classification: 60G55; 60K25; 92B05; 92C40