Abstract
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.
Highlights
Regulation of the abundance of proteins expressed in living cells is mediated by multiple types of control, exerted over the rates of transcription, post-transcriptional mRNA processing, mRNA decay, translation, and protein degradation
For example the simultaneous measurement of mRNA and protein abundance for 5000 genes in mouse fibroblasts revealed that about 55% of the correlation between mRNA and protein level can be explained by variation in translation rate [7]
This work draws attention to the role played by translation rate fluctuation in determining the shape of steady state protein concentration distributions
Summary
Regulation of the abundance of proteins expressed in living cells is mediated by multiple types of control, exerted over the rates of transcription, post-transcriptional mRNA processing, mRNA decay, translation, and protein degradation. Detailed experimental measurements carried out in S. cerevisiae have shown that the contribution of extrinsic noise to protein abundance increases with level of expression [1, 34] Factors such as ribosome number fluctuations and variations in kinetic parameters like elongation rates, have been categorized as extrinsic noise [1, 9]. For any particular mRNA in a collection of cells, the rate constant at any arbitrary location along the mRNA is a stochastic variable and can be described most appropriately by a distribution With this consideration, the stochastic movements of a set (ensemble) of ribosomes along the mRNA during elongation under the collective influence of various noise sources can be modeled as a unidirectional random walk on a chain with circular boundary conditions (see Fig 1), with each incorporation of a residue taken to follow first order kinetics, with rate constant i for the ith residue. The transition matrix (see Fig 1) describing movement of codon along the length of the mRNA which produces a polypeptide of length d, is given by
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