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Suggested Citation:"APPLICATION TO RNA EVOLUTION." National Research Council. 1995. Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology. Washington, DC: The National Academies Press. doi: 10.17226/2121.
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Page 106
Suggested Citation:"APPLICATION TO RNA EVOLUTION." National Research Council. 1995. Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology. Washington, DC: The National Academies Press. doi: 10.17226/2121.
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Page 107

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HEARING DISTANT ECHOES: USING EXTREMAL STATISTICS TO PROBE EVOLUTIONARY ORIGINS 106 l−exp(−λ) = 0.135. A bound on the error may be calculated in a way similar to that for coin tossing. We note that again b2 = 0, and by breaking the sum for b1 into two sums, one of which is made up of all terms that involve the boundary, we find b1 < λ2 (2t + 1) / ((n − t + l)(m − t + 1)) + 2λpt. Hence, the probability above is correct to within 8.5 × 10−7. APPLICATION TO RNA EVOLUTION Now we bring these ideas to bear on our RNA evolution problem. We have a set of 33 tRNA molecules and one 16S rRNA molecule from E. coli. In Bloch et al. (1983), matchings between 16S and each of the tRNAs were intensely studied. tRNA evolution is a complex topic and tRNA/tRNA comparisons were not made in this study. Table 4.1 shows the length of the longest exact match Hn between these sequences, along with estimates of significance or p-values (1−e−λn) from our ChenStein method. There are no exceptionally good matchings in this list, and so this analysis discounts any deep relationship between the sequences. In fact the p-values seem unusually large. In the 33 comparisons the minimum p-value is 0.26. Still we should not give up the search. One estimate puts the origin of these sequences at 3 billion years ago. We should not expect large segments of sequence to be preserved in every position over such vast amounts of time. Instead, mutations such as substitutions, insertions, and deletions will accumulate, greatly complicating our task. It is possible that the hypothesis of common origin is correct and that so much evolutionary change has taken place that no significant similarity remains. The next section, "Two Behaviors Suffice," examines the results of this search for unusual similarity using more subtle sequence comparison algorithms.

HEARING DISTANT ECHOES: USING EXTREMAL STATISTICS TO PROBE EVOLUTIONARY ORIGINS 107 Table 4.1 Exact Match P-Values tRNA GenBank Locus Length (n) Hn 1 − e−λn b1 ala-la ECOTRA1A 76 9 0.26 1.87 × 10−5 ala-lb ECOTRA1B 76 9 0.26 1.87 × 10−5 cys ECOTRC 74 8 0.69 2.67 × 10−4 asp-l ECOTRD1 77 8 0.71 2.79 × 10−4 glu-1 ECOTRE1 76 10 0.71 1.25 × 10−6 glu-2 ECOTRE2 76 10 0.71 1.25 × 10−6 phe ECOTRF 76 9 0.26 1.87 × 10−5 gly-l ECOTRG1 74 7 0.99 3.90 × 10−3 gly-2 ECOTRG2 75 6 1.00 5.70 × 10−2 gly-3 ECOTRG3 76 9 0.26 1.87 × 10−5 his-1 ECOTRH1 77 9 0.26 1.89 × 10−5 ile-1 ECOTRI1 77 9 0.26 1.89 × 10−5 ile-2 ECOTRI2 76 10 0.71 1.25 × 10−6 lys ECOTRK 76 6 1.00 5.78 × 10−2 leu-1 ECOTRL1 87 8 0.76 3.19 × 10−4 leu-2 ECOTRL2 87 8 0.76 3.19 × 10−4 leu-5 ECOTRL5 87 9 0.29 2.16 × 10−5 met-f ECOTRMF 77 9 0.26 1.89 × 10−5 met-m ECOTRMM 77 8 0.71 2.79 × 10−4 asn ECOTRN 76 7 0.99 4.01 × 10−3 gln-1 ECOTRQ1 75 8 0.70 2.71 × 10−4 gln-2 ECOTRQ2 75 8 0.70 2.71 × 10−4 arg-1 ECOTRR1 76 7 0.99 4.01 × 10−3 arg-2 ECOTRR2 77 7 0.99 4.07 × 10−3 ser-1 ECOTRS1 88 8 0.76 3.23 × 10−4 ser-3 ECOTRS3 93 9 0.31 2.33 × 10−5 thr-ggt ECOTRTACU 76 7 0.99 4.01 × 10−3 val-1 ECOTRV1 76 8 0.70 2.75 × 10−4 val-2a ECOTRV2A 77 8 0.71 2.79 × 10−4 val-2b ECOTRV2B 77 9 0.26 1.89 × 10−5 trp ECOTRW 76 7 0.99 4.01 × 10−3 tyr-1 ECOTRYI 85 8 0.75 3.11 × 10−4 tyr-2 ECOTRY2 85 8 0.75 3.11 × 10−4 Hn, the length of the longest exact match between the listed tRNA molecule and a 16S rRNA molecule; 1 − e−λn, the p-value (estimate of significance) for nth tRNA molecule; b1, column entry is the calculated bound on b1.

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