Table 1.
Calculated activation energies (ΔETS1‡), relative reactivities [log(kcat/kcat(g))], and NMR chemical shifts (δEI1) for seven model systems (a–g) of KSI
| Residues (mutants) | ΔETS1‡, kcal/mol B3LYP [MP2] | log(kcat/kcat(g))
|
δEI1, ppm HF | |
|---|---|---|---|---|
| Calc. B3LYP [MP2] | Exp. (PI;TI) | |||
| (a) Parent | 14.2 [17.0] | −6.9 [−8.2] | ||
| (b) L103+F16 (D103L+Y16F) | 11.7 [13.9] | −5.1 [−6.0] | ||
| (c) D103 (Y16F) | 8.7 [10.9] | −2.9 [−3.7] | (−3.3; −4.7) | 15.1 |
| (d) Y16 | 8.2 [10.7] | −2.6 [−3.6] | 13.9 | |
| (e) Y16/57 (D103A, D103N) | 7.1 [8.8] | −1.7 [−2.2] | (−2.1, −2.0; −3.5, −1.4) | 15.1 |
| (f) D103+Y16 (Y57F) | 5.5 [6.8] | −0.6 [−0.8] | (−0.9; −0.6) | 17.1 |
| (g) D103+Y16/57 (WT) | 4.7 [5.8] | 0.0 [0.0] | (0.0; 0.0) | 16.0 |
Calculated relative reactivities were compared with the PI and TI experimental values (26, 31–35). The experimental activation barrier at TS1 of WT is estimated to be 10≈11 kcal/mol by Pollack and coworkers (46). The B3LYP/6-31+G* [or MP2/6-31+G*//B3LYP/6-31+G*] predicted barriers seem to be underestimated. However, the SCRF(B3LYP/6-31+G*) correction of the dielectric medium effect (ɛ = 18) (31) is 2.4 kcal/mol. Thus, the dielectric medium effect-corrected MP2 barrier is 8.2 kcal/mol, which is close to the experimental value. Since the dielectric medium effects are similar for all mutated residues because of the similar environments, the relative reactivities are very consistent without large change in values (due to the cancellation effects), regardless of the calculation levels employed. Thus, the results are considered reliable. Furthermore, these relative reactivities are in good agreement with experimental PI and TI values. To obtain relative reactivities, kcat was approximated by the reaction constant for the transition from ES to TS1, since this rate constant is the rate-determining step (see the text and Fig. 2A). However, in case a, the reaction constant was obtained from the activation barrier of TS2 relative to ES, because their barrier is responsible for the rate. The chemical shift δ at EI1 (δEI1) was calculated at the Hartree—Fock (HF)/6-31+G*//B3LYP/6-31+G* level.