([S]) and Km of the substrate for stromelysin, we can convert the IC50 values to Ki values, which can in turn be used to calculate ΔGobind of the tethered fragments.
The original stromelysin report gives [S] as 200 µM. Km is not provided, but a very similar enzyme has a Km of 4,000 µM for stromelysin. Using these values, we can determine Ki and ΔGobind for the best hit formed by tethering fragments. The most potent hit is compound 4.
An interesting thing about fragment binding is that Ki and ΔGobind of hit can be determined based on the fragments that were combined. Specifically, if fragments 1 and 2 are correctly combined to form a new hit, then Ki of the hit should be equal to the product of the Ki values of the two fragments. Ki (hit) = Ki (fragment 1) × Ki (fragment 2) Similarly, ΔGobind of the hit should be equal to the sum of the ΔGobind of the two fragments. ΔGobind (hit) = ΔGobind (fragment 1) + ΔGobind (fragment 2) Under this logic, Ki of compound 4 should be 4.8×10−6 M (17×10−3 × 0.28×10−3 = the product of the two fragment Ki values). Instead, the actual value is 0.30×10−6 M. ΔGobind of compound 4 should be −7.2 kcal/mol (−2.4 + −4.8). Instead, the actual value is −8.9 kcal/mol. Compound 4 (the hit) binds more strongly than we would predict based on its fragments. Why do the predictions (which are theoretically sound) differ from the experimental value? The discrepancy is the tether. Compound 4 has two more CH2 groups than the individual fragments. These CH2 groups lie within a channel in the protein and generate binding energy through the hydrophobic effect. In Chapter 9, the binding energy of a CH2 group through the hydrophobic effect was listed as 0.8 kcal/mol. The energy difference between 4 and the fragments