Phenotypic Mutation Rates and the Abundance of Abnormal Proteins in Yeast

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Abstract
Phenotypic mutations are errors that occur during protein synthesis. These errors lead to amino acid substitutions that give rise to abnormal proteins. Experiments suggest that such errors are quite common. We present a model to study the effect of phenotypic mutation rates on the amount of abnormal proteins in a cell. In our model, genes are regulated to synthesize a certain number of functional proteins. During this process, depending on the phenotypic mutation rate, abnormal proteins are generated. We use data on protein length and abundance in Saccharomyces cerevisiae to parametrize our model. We calculate that for small phenotypic mutation rates most abnormal proteins originate from highly expressed genes that are on average nearly twice as large as the average yeast protein. For phenotypic mutation rates much above 5 × 10−4, the error-free synthesis of large proteins is nearly impossible and lowly expressed, very large proteins contribute more and more to the amount of abnormal proteins in a cell. This fact leads to a steep increase of the amount of abnormal proteins for phenotypic mutation rates above 5 × 10−4. Simulations show that this property leads to an upper limit for the phenotypic mutation rate of approximately 2 × 10−3 even if the costs for abnormal proteins are extremely low. We also consider the adaptation of individual proteins. Individual genes/proteins can decrease their phenotypic mutation rate by using preferred codons or by increasing their robustness against amino acid substitutions. We discuss the similarities and differences between the two mechanisms and show that they can only slow down but not prevent the rapid increase of the amount of abnormal proteins. Our work allows us to estimate the phenotypic mutation rate based on data on the fraction of abnormal proteins. For S. cerevisiae, we predict that the value for the phenotypic mutation rate is between 2 × 10−4 and 6 × 10−4. A functional protein machinery, built from genetic information, is central to every living organism. Surprisingly, the decoding of genes into amino acid sequences is fairly inaccurate. Errors in this process (phenotypic mutations) are several orders of magnitude more frequent than errors during DNA replication (genotypic mutations). Many researchers have explored the evolution of genotypic mutation rates, but there are as yet few investigations into the evolutionary dynamics of phenotypic mutation rates. Here we present a mathematical model that describes the effect of phenotypic mutation on the amount of abnormal proteins in cells. We parameterize our model using data from yeast (Saccharomyces cerevisiae). We show that for phenotypic mutation rates above 5 × 10−4 per amino acid, the error-free synthesis of large proteins becomes nearly impossible. We estimate the phenotypic mutation rate of S. cerevisiae to be between 2 × 10−4 and 6 × 10−4 per amino acid.