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Precision and functional specificity in mRNA decay
Yulei Wang, Chih Long Liu, John D. Storey, Robert J. Tibshirani, Daniel Herschlag, and Patrick O. Brown
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Statistics: Materials and Methods

To evaluate the generality of the observation that transcripts encoding subunits of a stoichiometric complex decay coordinately, we identified a set of 95 hetero-multimeric protein complexes based on the following criteria: (1) They are documented as protein complexes by both the MIPS database and the YPD database (in either case, physical interactions detected solely by yeast two-hybrid analysis were not considered); (2) Good measurements of mRNA decay rates for at least 2 of the subunits were obtained for any given complex. To test the significance of the apparent coordination, we used a permutation method to model the distribution of subunit decay rates under the null hypothesis: For a protein complex containing N different subunits, the null distribution of the mRNA decay rates was modeled by randomly sampling sets of N mRNA decay rates from our set of 4482 unique measurements. We could then ask whether the decay rates of transcripts encoding members of a bonafide protein complex of size N were more closely matched than would be expected for a random set of N transcripts. Specifically, the concordance of the decay rate constants of transcripts encoding components of stoichiometric protein complexes was assessed by comparison to size-matched sets of decay rate constants for randomly selected transcripts. Because the standard deviations of sets of decay rate constants were not independent of the means, a normalized standard deviation (sd*) was calculated by a non-parameteric statistical method so that they were functionally independent from the means of the decay rates. This is accomplished by first plotting the standard deviations of decay rate constants for random groups of genes as a function of their means. Then a natural cubic spline was fit to the scatter plot. The standard deviations were then divided by the fitted value of the spline at their corresponding means. It can be shown mathematically that this method transforms the standard deviations so that they are functionally uncorrelated with the means. To measure the concordance of the decay rates for a complex of size N, we calculated the normalized standard deviation sdn of its decay rates. We also calculated the normalized standard deviations sdn* of 104 randomly selected groups of N mRNAs. The p-value of the test was calculated as the proportion of sdn* less than or equal to sdn. An additional statistic was used to evaluate the concordance of subunit decay rates for the 33 heterodimeric complexes. Let ki, 1 and ki, 2 be the two decay rate constants for the ith heterodimeric complex. The statistic we used was S(ki, 1 - ki, 2)2. This statistic was compared to 104 sets of random pairings of the 66 mRNAs.

References:

  1. Hastie, T., and R. Tibshirani 1990. Generalized Additive Models.

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