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The interplay between turnover or degradation and ribosome loading of messenger RNA (mRNA) is studied theoretically using a stochastic model that is motivated by recent experimental results. Random mRNA degradation affects the statistics of polysomes, i.e., the statistics of the number of ribosomes per mRNA as extracted from cells. Since ribosome loading of newly created mRNA chains requires some time to reach steady state, a fraction of the extracted mRNA/ ribosome complexes does not represent steady state conditions. As a consequence, the mean ribosome density obtained from the extracted complexes is found to be inversely proportional to the mRNA length. On the other hand, the ribosome density profile shows an exponential decrease along the mRNA for prokaryotes and becomes uniform in eukaryotic cells. Copyright (C) EPLA, 2010
A simple measure for the efficiency of protein synthesis by ribosomes is provided by the steady state amount of protein per messenger RNA (mRNA), the so-called translational ratio, which is proportional to the translation rate. Taking the degradation of mRNA into account, we show theoretically that both the translation rate and the translational ratio decrease with increasing mRNA length, in agreement with available experimental data for the prokaryote Escherichia coli. We also show that, compared to prokaryotes, mRNA degradation in eukaryotes leads to a less rapid decrease of the translational ratio. This finding is consistent with the fact that, compared to prokaryotes, eukaryotes tend to have longer proteins.