Figure 12

Illustrative use of Bayes’s Theorem to estimate the enhancement of posterior probability under the RO hypothesis given by the catalytic activities of the 46-residue ATP binding sites expressed from a designed, sense/antisense gene. All probability distribution functions are bivariate normal probability distributions. A. Prior probabilities centered at a mean rate acceleration of 1000 (green), and for the null hypothesis (brown) that the peptides are catalytically inactive. The likelihood function derived from experimental results obtained for Class I and II ATP binding sites (blue) is centered at a rate acceleration of 400-fold. Standard deviations of all three distributions in A are 0.4 log₁₀ units, corresponding to a 40% uncertainty. X and Y axes are logarithmic in the rate enhancement, and 1000-fold is drawn from the ratio of the uncatalyzed rates of activated amino acid assembly to form peptides to that for amino acid activation by ATP. B. Posterior probabilities obtained for the null prior (purple) and for the two active peptides (turquoise). The integrated experimental posterior probability under the RO hypothesis is larger than that under the Null hypothesis by ~10¹⁴. The latter posterior probability (brown) has been multiplied by a factor of 10¹⁴ to be visible.